U.S.E.P.A.
GROUNDWATER MODELING WORKSHOP
Coordinated by
PEI Associates, Inc.
11499 Chester Rd.
Cincinnati, OH 45246
Contract No. 68-03-3413
Work Assignment No. 0-20E
PN 3741-20E
EPA Technical Project Monitor
Don Draper
U.S. ENVIRONMENTAL PROTECTION AGENCY
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
P.O. BOX 1198
ADA, OK 74820
-------
U.S. EPA
RSKERL
Ground Water Modeling Workshop
Evaluation Form
In order to make this series of workshops and upcoming technology
transfer events as useful as possible, we ask that you please
complete this evaluation form. Your comments will remain
confidential. Feel free to use the back of the page for
additional comments. Thank you for your honesty and cooperation.
Position
Division/Branch
1-3 3-5 5-10
Years experience; 0-1 1-3 3-5 5-10 10+
Background: Geology Engineering Other (specify)
Name (optional)
1. Please rate this workshop for its value to you and
the tasks you perform as an EPA employee.
1
(poor)
(excellent)
Was the subject matter adequately covered during each
workshop session?
Geochemical Modeling Yes
Unsaturated Zone Modeling Yes"
Saturated Zone Modeling Yes"
No
No"
No"
Were the sessions well paced within allotted time?
Geochemical Modeling Yes
Unsaturated Zone Modeling Yes"
Saturated Zone Modeling Yes"
No
No"
No"
Were the handouts relevant, and appropriate for the
workshop?
Geochemical Modeling Yes
Unsaturated Zone Modeling Yes"
Saturated Zone Modeling Yes
No
No"
No"
How would you rate this workshop in relation to other
training programs you have attended?
Excellent
Good
Average
Fair
Poor
Unsaturated Saturated
Geochemical Zone Zone
Modeling Modeling Modeling
-------
6. Please rate the speakers conducting this workshop.
Geochemical Modeling
Content Presentation
Excellent '
Good
Average
Fair
Poor
Unsaturated Zone Modeling
Content Presentation
Excellent
Good
Average
Fair
Poor •
Saturated Zone Modeling
Content Presentation
Excellent
Good •
Average •
Fair
Poor
7. To what extent will you make use of the content and
materials presented, either directly or indirectly?
Unsaturated Saturated
Geochemical Zone . Zone
Modeling Modeling Modeling
Will use frequently
May be useful
Of limited use ._
Don't see any application
Don't know
8. What was the most valuable part of the workshop?
9. What was the least valuable part of the workshop?
10. Do you have any suggestions to improve the content and
presentation of the workshop (please be as specific as
possible)?
-------
Background
The Superfund Amendments and Reauthorization Act of 1986
(SARA) directs the EPA, as part of the overall Superfund site
clean-up program, to conduct a program of research, evaluation
and demonstration of alternative or innovative technologies for
response actions that will achieve more permanent solutions. Due
to the magnitude of the problem and the potential economic and
environmental benefits of inplace reclamation, the Office of
Solid Waste and Emergency Response has identified the need to
have in operation a dedicated technical support program that can
provide a readily-available source of technology transfer
support, including up-to-date technical information plus
associated expert assistance and review services, to those
responsible for making remediation decisions at Superfund sites.
Four technical support centers have been established at the
following locations:
1. Robert S. Kerr Environmental Research Laboratory
(RSKERL)-Ada, Oklahoma, (Ground-Water/Soil Fate and
Transport Technology)
2. Hazardous Waste Environmental Research Laboratory-
Cincinnati, Ohio, (Engineering and Treatment
Technology)
3. Environmental Monitoring Systems Laboratory-Las Vegas,
Nevada, (Monitoring and Site Characterization
Technology)
4. Environmental Research Laboratory-Athens, Georgia and
Research Triangle Park, (Health Risk and Ecology)
The Subsurface Remediation Support Program has been
established at RSKERL. The components of this program include:
- Subsurface Remediation Technical Support Team — composed
of ten scientists and engineers to provide a readily available
source of technical assistance;
- Subsurface Remediation Information Clearinghouse —
designed to provide the user community highly specialized, fate,
transport, and remediation information;
- National Center for Ground Water Research — consortium of
Oklahoma, Oklahoma State and Rice Universities charged with
developing and conducting a long-range exploratory research
-------
program to help anticipate and solve the Nation's emerging
ground-water problems;
- International Ground Water Modeling Center (IGWMC) --
Holcomb Research Institute Indianapolis, Indiana, clearinghouse
for ground-water modeling software, providing research short
courses, seminars and educational activities;
- National Ground Water Information Center — National Water
Well Association, Dublin, Ohio, repository of ground water
quality information accessible to scientists, government
agencies, business and the public; and
- RSKERL Extramural Research Program — expertise of
subsurface processes and systems from more than thirty
universities and research institutions.
The EPA Ground Water Modeling Workshop results directly from
Superfund technology transfer efforts planned by RSKERL. This
series of introductory ground water modeling workshops is being
conducted to introduce EPA personnel to a selected group of
geochemical characterization models, and saturated and
unsaturated zone contaminant transport models. The overall
objectives of this workshop include:
1. Provide a general overview of the use of models and the
limitation of using model results. Emphasis will be placed on
both the identification of modeling parameters and on the
importance of understanding the assumptions and limitations of
specific models as applicable to Superfund sites;
2. Familiarization of selected models through hands-on
experience and with case studies. Workshop participants will be
provided with the software presented to keep for future use; and
3. Identification of data quality objectives during the
site characterization process to satisfy both modeling data input
and site characterization requirements.
RSKERL has made arrangements with IGWMC to: (1) provide EPA
Regional staff easy access to the groundwater modeling
information services available from IGWMC's Indianapolis office;
(2) demonstrate type and level of assistance available from IGWMC
in the selecting and use of groundwater modeling software by EPA
-------
Regional staff; (3) provide, on a limited basis, assistance to
EPA Regions in improving usability of Agency-sponsored public
domain software, by installing user-friendly interfaces, model
demonstration software, and computer-aided instruction software;
(4) advise EPA regions regarding development of groundwater
modeling policies and preparation of RFP's and workplans for
groundwater modeling projects in the Regions; and (5) provide EPA
Regions with IGWMC experts for limited review of proposals,
workplans, software, and reports related to groundwater modeling
insofar as these activities are initiated and managed by EPA
Regions.
For further IGWMC information, call AC317/283-9458. Specific
requests for assistance from IGWMC should be made through M.R.
Scalf at RSKERL, AC405/332-8800.
Although the Ground Water Modeling Workshop has been funded
by the United States Environmental Protection Agency, the models
presented herein may not necessarily reflect the view of the
Agency and no official endorsement should be inferred.
-------
U.S.E.PA
GROUNDWATER MODELING WORKSHOP
EPA-RSKERL, Ada, OK
August 16,17 and 18,1988
AGENDA
DAY 1 Topic: Geochemical Characterization Models
WATEVAL - Water analyses, rock/water
interactions, graphical methods
BALANCE - Mass balance calculations
Speaker: Dr. Arthur W. Hounslow
Oklahoma State University
DAY 2 Topic: Unsaturated Zone Modeling
RITZ - Regulatory and Investigative
Treatment Zone Model
CHEMRANK - Ranks which contaminants
might reach groundwater first
CHEMFLOW - Yields actual concentrations for
contaminants
Speaker: Dr. David L. Nofziger
Oklahoma State University
DAY 3 Topic: Saturated Zone Solute Transport Modeling
MOC - Method of Characteristics
Speaker: Dr. Randy Charbeneau
University of Texas
-------
U.S.E.P.A.
GROUNDWATER MODELING WORKSHOP
FALL/WINTER, 1988
Name/Address
LIST OF INSTRUCTORS
Work /Research Interests
Dr. Arthur W. Hounslow
Oklahoma State University
Department of Geology
Stillwater, OK 74078
Organic and environmental
Geochemistry; organic pollutants
in air/water/soil systems.
Dr. P. S. C. Rao
University of Florida
Science Department
2169 McCarty Hall
Gainesville, FL 32611
Environmental chemodynamics of
agrochemicals, nontoxic wastes, soil
and toxic/hazardous wastes.
Mr. Mark L. Brusseau
University of Florida
Soil Science Department
2169 McCarty Hall
Gainesville, FL 32611
Transport and fate of organic
contaminants in the subsurface;
experimental investigation of
sorption dynamics.
Dr. David L. Nofziger
Oklahoma State University
Agronomy Department
265 Ag Hall
Stillwater, OK 74078
Modeling of the fate and
transport of chemicals in soils;
modeling of water movement in
soils.
Mr. Joe Williams
Soil Scientist
U. S. EPA- RSKERL
P.O. Box1198
Ada, OK 74820
Modeling of organic contaminant
transport and fate in soils; variability
of physical properties of soils.
-------
U.S.E.P.A.
GROUNDWATER MODELING WORKSHOP
FALL/WINTER, 1988
LIST OF INSTRUCTORS (Continued)
Name/Address Work/Research Interests
Mr. Peter F. Anderson, P.E. Saturated zone solute transport
Vice President, Herndon Office modeling.
GeoTrans, Inc.
250 Exchange Place, Suite A
Herndon, VA 22070
Dr. Leonard F. Konikow Saturated zone solute transport
U.S. Geological Survey modeling.
Water Resources Division
431 National Center
Reston, VA 22092
Dr. Daniel J. Goode Saturated zone solute transport
U.S. Geological Survey modeling.
Water Resources Division
431 National Center
Reston, VA 22092
Dr. Randy Charbeneau Saturated zone solute transport
University of Texas modeling.
Ernest Cockrell Jr. Hall
Austin, TX 78712
-------
D
>
-<
DAY 1
GEOCHEMICAL
CHARACTERIZATION
MODELS
WATEVAL
BALANCE
-------
CONTEMPORARY INTERPRETATION OF WATER QUALITY DATA
A Practical Geochemical Approach Using Personal Computers
Arthur W. Hounslow
School of Geology
Oklahoma State University
Environmental Protection Agency
Regional Ground Water Modeling Workshop
Fall 1988
-------
CONTEMPORARY INTERPRETATION OF WATER-QUALITY DATA
Arthur W. Hounslow
I. WATER ANALYSES 1
A. SOURCE
1. RIVERS
2. WELLS
3. SPRINGS
B. SAMPLES
1. COLLECTION
2. CONTAINER
3. PRESERVATION
C. FIELD DETERMINATIONS
D. ANALYSES
1. SELF
2. SUBMIT TO LABS
3. PUBLISHED DATA
4. DATA BANKS
5. PARTIAL ANALYSES
E. INTERPRETATION
1. INDIVIDUAL ANALYSES
2. COLLECTIVELY
F. CALCULATIONS
FIGURE 1. GROUND WATER GEOCHEMISTRY 3
II. UNITS 4
A. MASS UNITS
i. g./i
2. FRACTION
3. PERCENT %
4. SALINITY °/OQ
5. PPM
B. MOLES
1. MOLES AND ATOMIC WEIGHTS
FIGURE 2. PERIODIC TABLE 5
2. MOLE FRACTION
3. UNITS AND CONVERSIONS
4. EQUIVALENTS
EXERCISES 1-7 9
III. COMMONLY DETERMINED CONSTITUENTS 11
A. SOURCE OF MAJOR IONS IN WATERS
1. SODIUM
2. CHLORIDE
3. POTASSIUM
4. CALCIUM
5. STRONTIUM
6. SULFATE
7. GYPSUM
8. BARIUM
9. MAGNESIUM
10. CARBONATE / BICARBONATE
11. CARBON DIOXIDE
11
-------
B. MISCELLANEOUS DETERMINATIONS
1. HARDNESS
2. DISSOLVED SOLID CONTENT
3. CONDUCTIVITY
4. CALCULATED DENSITY
FIGURE 3. IONIC VOLUMES 19
5. pH
6. ALKALINITY AND ACIDITY
FIGURE 4. CARBONATE SPECIES .22
EXERCISES 8-18 24
IV. ANALYSIS INTERPRETATION 27
A. SPOTTING QUESTIONABLE ANALYSES
1. ANION - CATION BALANCE
2. RELATIVE AMOUNTS OF IONS
3. MISCELLANEOUS CHECKS
B. COMPLETING PARTIAL ANALYSES
1. GIVEN HARDNESS, Ca OR Mg
2. TEMPORARY HARDNESS OR ALKALINITY
3. CARBONATE / BICARBONATE
4. MISSING VALUES
EXERCISE 19 30
V. ROCK - WATER INTERACTIONS 31
A. MINERALS
B. BALANCING EQUATIONS
EXERCISE 20 35
C. SOURCE ROCK DEDUCTION
TABLE OF WEATHERING PRODUCTS 38
FIGURE 5. WEATHERING FLOWCHART 39
EXERCISE 21 40
VI. GRAPHICAL METHODS 41
A. AREAL TRENDS
1. ONE COMPONENT PLOTS
2. MULTI-COMPONENT PLOTS
a. BAR GRAPHS
b. PIE DIAGRAMS
C. RADIAL DIAGRAMS
d. VECTOR DIAGRAMS
6. KITE DIAGRAMS
f. STIFF DIAGRAM
B. CHEMICAL TRENDS
1. PIPER DIAGRAMS
a. PRECIPITATION OR SOLUTION
FIGURE 6. TRIANGULAR DIAGRAMS 43
FIGURE 7. PIPER DIAGRAM 44
FIGURE 8. DUROV DIAGRAM 45
FIGURE 9. TRIANGULAR GRAPH PAPER 46
b. MIXING
C. ION EXCHANGE
d. WATER TYPES
2. DUROV GRAPHS
EXERCISES 22 48
111
-------
VII. GEOCHEMICAL ENVIRONMENTS 49
A. pH BARRIERS
1. STRONGLY ACID - pH < 4
2. MODERATELY ACID - pH 4-6.5
3. NEUTRAL pH 6.5-7.8
4. MODERATELY ALKALINE pH 7.8-9
5. STRONGLY ALKALINE - pH>ll
B. ADSORPTION BARRIERS
1. MONTMORILLONITE CLAYS
2. KAOLINITE CLAY
3. GOETHITE (FEOOH)
4. NATURAL ORGANIC MATTER
C. REDOX BARRIERS
THE FEW ELEMENTS IN NATURAL WATERS
IRON GEOCHEMISTRY
CARBON GEOCHEMISTRY - REDOX "BUFFER"
1. AEROBIC WATERS
2. ANAEROBIC WATERS (1)
3. ANAEROBIC WATERS (2)
FIGURE 10. REDOX ZONES 54
FIGURE 11. SEDIMENTARY GEOCHEMISTRY 55
FIGURE 12. FENCE DIAGRAMS 56
EXERCISE 23
VIII. MASS BALANCE MODELING 58
A. COMPOSITIONAL CHANGES
FIGURE 13. MASS BALANCE DIAGRAMS 59
B. MIXING
C. COMPUTER CALCULATION
EXERCISES 24 & 25
XI. WATER GEOCHEMISTRY - SELECTED BIBLIOGRAPHY 64
IV
-------
CONTEMPORARY INTERPRETATION OF WATER-QUALITY DATA
Arthur W. Hounslow
I. WATER ANALYSES
A. SOURCE
1. RIVERS
Ground water contribution greatest under low flow conditions.
2. WELLS
Most difficult samples to avoid contamination and the change in
parameters during collection of sample.
3. SPRINGS
Deposits around spring will indicate water conditions prior to
being exposed to atmospheric temperatures and pressures.
B. SAMPLES
1. COLLECTION
2. CONTAINER
3. PRESERVATION
Other determinations are done in the laboratory but in
order to reduce the effects of adsorption or biodegradation
they must be collected and transported in special containers,
preserved either in ice or by the addition of acid or some
other preservative depending on the constituent being
considered.
For each constituent in a water analysis the E.P.A has a
recommended preservation and analysis procedure which must be
followed.
C. FIELD DETERMINATIONS
Any determinations dependent on dissolved gases must be run as
soon as possible after collection. For some ground waters that
contain gases under pressure even this may be too late.
Determinations usually done in the field include:
temperature
pH
DO - dissolved oxygen
Eh - redox potential
alkalinity - dependent on C02
D. ANALYSES
1. SELF
2. SUBMIT TO LABS
3. PUBLISHED DATA
4. DATA BANKS
US E.P.A - STORET,
US Geol. Survey - WATSTORE
5. PARTIAL ANALYSES - ESTIMATING MISSING PARAMETERS
-------
E. INTERPRETATION
1. INDIVIDUAL ANALYSES
" a. accuracy checks
b. dissolved minerals
(1) mass balance
BALANCE
(2) thermodynamics
WATEQF
(a) speciation
(b) saturated or unsaturated with
respect to a mineral
(c) redox
2. COLLECTIVELY
a. Graphical representation
(1) areal plots
(2) trends - graphs
b. Statistical analysis
(1) anomalous samples or values
mixtures of 2 or more populations
cumulative frequency plots
(2) mixed sources -
factor analysis
F. CALCULATIONS
Tedious but must be understood
Computer imperative
-------
§
50
M
M
O
58
O
td
o
td
o
s
GROUND-WATER GEOCHEMISTRY
LITHOSPHERE
ATMOSPHERE
Sulfldes
Carbonates
HYDROSPHERE
Soluble salts
Ionic strength
; Water
movement
Porosity
Permeability
BIOSPHERE
SorptTon
Degradation
Bacteria
Soli organic
matter
Ground water
Hydroxides
Mlcroflora
Rocks and minerals
-------
II. UNITS
A. MASS UNITS
MASS/VOLUME
1. g./i
small concentrations mg./l
1 g. = 1,000 mg.
MASS/MASS
2. fraction - part of total which equals 1
g. per g.
mole fraction - mole/mole
3. percent % - parts/hundred
g. per 100 g.
4. salinity °/QO - parts/thousand
g. per 1,000 g.
5. ppm - parts/million
g. per 1,000,000 g.
or
mg. per 1,000,000 mg.
1,000,000 mg. = 1,000 g.
= 1 kg.
1 ppm = 1 mg./kg.
B. MOLES
1. MOLES AND ATOMIC WEIGHTS
One mole of an item is defined as 6.023 * 1023 of that item.
It applies to atoms, molecules, ions, golf balls etc. This
number is known as Avogadro's Number.
The atomic weight of an atom is the mass of that atom
compared to that of the carbon isotope Cc, which is defined
as exactly 12.00. One gram atomic weight of an element or one
gram formula weight of a compound contains 6.023E23
atoms(formulas) of that material. Thus one mole of a compound
equals the atomic or molecular weight of that compound in
grams.
4
-------
H
o
G
JO
w
to
•a
w
»
H
o
o
H
O
§
f
n
(-. PERIODIC TABLE OK THE ELEMENTS
V Group
X
PailodN
1
2
3
4
5
8
.7
1
•
II
*
.
"
• * •
.
1.14
5 t
' Na
22.11
•19
J K
31.10
}37
i Rb
15.47
•55
' 'Cs
132.11
a >*
is F'
1 (373)
B*
9.01
2
Mg
34.31
20
C.
40.08
36
Sr
17.62
56
Ba
137.34
86
R.
(326)
.
t
H
1.001
• •
. •
•
.
"
TRANSITION ELEMENTS .•-*••.
• 21
: se
44.16
•39
t yf
a •
61.11
57-71
•
tl-1C3
"
.
.
•ta'ntSanlde Series
•
22
Tl
47.10
40
Zr
• 1.32
72
HI
171.41
104
Ku
(361)
• .
• Ls
a
130.11
23
V
50.14
41
'Nb
12.11
73
TA
•
110.15
IDS
Hat
(3(1)
• .
56.
Ct
1W.11
**
Cr
51.00
42
Mo
15.14
74
w •
113.15
106 •
(It3)
,5S9
'•; Pr
i
140.11
•
t •"
• Mn
84.14
a ^
a Tc
(171
S 7*
' Rai
a •*•
116.2
•26
• F.
55.15
s44
• Ru
101.07
a "
i o,
110.2
.
a *• a
a Co '«
51.93
,:45 ,i
!; Rh "
102.91
I"
i; tr i
112.2
28 J
NI "
51.71
48 j
Pd ;
1C1.4
jm
tw
PI i
115.01
a
Cu
63.55
41
Afl
107.17
79
AU
116.17
30
Zn
65.37
,«
i Cd
112.40
•80
190.51
III
•
IV
v.
yi
VII
.
B
10.11
|J
Al
36.11
It
G,
61.72
«9
In
114.12
81-
!•
It Tl
!• §i
304.37
« J
c
13.01
'4
SI
31.09
32
Ge
72.59
50
Sn
111.69
• 82
a
i pk
a
207.19
* t
H
14.01
15
P
30.17
p3
As
74.13
it
Sb
121.7S
83
Bl
301.11
•
o
16.00
16
S
3104
34
S.
71.96
52
T.
127.60
64
PO
(210)
*
F
11.00
7
"
Cl
3S.4S
w
Br
71.10
a
1
134.10
as
At
(310)
0
H»
4.00
10
N*
30.11
18
Ar
3115
36
Kr
83.10
54
*9
131.30
86
Rn
(222)
: . AlemTc vat(Mt art fcaitd e» tatbon-12;
•
•60
'•• Nd
t
144.24
•j Pm
a
(147)
tatutt !n f aranlfciatt an fer M>t meal lUt't or !h« meat famlTtar tactop*.
• t Sjmfcot fa wr»oWiet*l
* « ' * "
«; Sm
a
150.35
•• Eu
111.11
i"
'.; Gd
i
137.25
\"n
151.11
» Dy
163.50
I"
« Ho
164.13
{68
117 J 4
'•; Tm
111.13
•70
« Yb
• 173.04
>• Lu
174.17
•Acltnli!* Scrtts
t
II
SI
II
*
f
89
Ac
1227)
t
31
II
•i
90
Th
332.04
J19I
ii p.
•1 (131)
a
92
U
331.03
it
i
t
93
Np
(217)
a
ia
li
54
Pu
(144)
i
95
Am
(213)
i
u
a
S6
Cm
(247)
t
1
•7
BJc
(2«7)
I
;a
Cf
(151)
a
at
ti
a
99
Es
(154)
i
i
100
Frn
(157)
a
SI
a
101
Md
(251)
•1102
13 No
•l (351)
a
ia
tt
at
1
103
Lr
(160)
-------
2. MOLE FRACTION
Ratio of the number of moles of the give constituent to the
total number of moles of all constituents.
nl
Nl =
n2
Mole fraction of NaCl in 1.0 molal solution
1
= = 0.0177
1 + 55.51
where 55.51 = # moles of water in 1000 g water
EXAMPLES
1. 55.85 g. Fe contains 6.023E23 atoms of Fe
and 55.85 g. Fe =1 mole of Fe
and 173 g. Fe contains 173/55.85 =3.10 mole Fe
2. 70.91 g. C12 contains 6.023E23 molecules of C12
and 70.91 g. C12 = 1 mole C12
and 50 g. C12 contains 50/70.91 = .71 mole C12
3. 18.015 g. H2O contains 6.023E23 molecules of H20
and 18.015 g. H20 = 1 mole H20
and 1 1. of H20 = 1,000 g. H2O contains
1,000/18.012 = 55.51 mole H20
4. 44.009 g. C02 contains 6.023E23 molecules of C02
and 44.009 g. C02 = 1 mole C02
and 84 g. CO2 contains 84/44.009 = 1.91 mole CO2
-------
3. UNITS AND CONVERSIONS
* D
ppm
(mg/Kg)
•> mg/1
/(M.Wt.*1000)
/ M.Wt.
* Z
mmole/1
/1000
moles/Kg solution
(formality - f)
* X
moles/kg solvent
(molality - m)
/
* Z
moles/1
(molarity - M)
meq/1
/1000
•> equiv/1
(normality - N)
D = Density
Z = Valence
wt. solution
(wt. solution - wt. solute)
1000
(1000 - TDSg)
EXAMPLE
A brine has a density of 1.018 and contains 12,000 ppm
dissolved solids of which 3700 ppm is sodium.
Sodium concentrations:
3700 ppm
mg/1 = ppm * D = 3700 * 1.018 = 3767 mg/1
formality = ppm/(1000*M.Wt.)
= .1609
= 3700/(1000*23)
mmoles/1 = mg/1 /M.Wt. = 3767/23 = 163.7826 mmoles/1
molarity = mmoles/1 / 1000 = .1638 moles/1
TDS(g) = 12,000/1000 = 12 g./kg.
molality = formality * 1000 / (1000 - TDS g)
= 0.1609 * 1000 / ( 1000 - 12)
= .1629
-------
4. EQUIVALENTS
Equivalents /I = normality N
Normality (N) = g/1 / Eq. Wt.
Equivalents/ million = epm
Milliequivalents/1 = meq/1
epm = meq/1 / D
Calculation of equivalent weights based on:
* a. charge of an ion
Eq. Wt. = M Wt. / charge
e.g. Pe""" + 3C1~ <==> FeCl3; Eq. Wt. Fe"*"1"1" = 55.85/3 = 18.62
b. # of electrons transferred in
an oxidation - reduction reaction
Eq Wt. = M Wt. / # electrons transferred
e.g. Fe++ <==> Fe + e~; Eq. Wt. Fe = 55.85/1 = 55.85
c. # of protons or hydroxyls transferred in
an acid base reaction
Eq Wt. = M Wt./# of protons or hydroxyls transferred
e.g. H+ + Cl~ <==> HC1; Eq. Wt. Cl" = 35.45/1 = 35.45
d. neutral salts
Eq Wt. = M.Wt./# of H atoms equivalent
to total cations
e.g. Eq. Wt. Ca(N03)2 = 164.088/2 =82.044
* Most common method of calculation.
8
-------
Exercises
1. How many moles of sulfur are needed to combine with 1 mole of
iron to form pyrite (FeS2)?
2. How many moles of iron are needed to combine with 1.44 mole S to
form pyrite?
3. How many mole of S are in 3 mole of pyrite?
4. How many moles of sulfur are in 1 mole of
5. How many moles of CO? would be liberated from 1 mole of limestone
(CaC03)?
Answers: 1. 2, 2. 0.72, 3. 6, 4. 3, 5. 1
6. For the following analysis calculate mg/l,molarity,
formality, molality and meq/1.
ppm mg/1 M f m meq/1
Na+ 51600
K+ 2650
Ca++ 1360
Mg++ 1720
HC03~
C03=
S04= 3680
Cl~ 86600
Density 1.11
-------
7. For each of the following reactions calculate the equivalent
weight for the ion specified.
a. Ca + C03= — > CaC03 C03
b. HC1 + NaOH --> NaCl + H20 HC1
C. C03= + H2O --> HC03~ + OH" C03
d. Oo + 4H"1" + 4e~ — > 2H0O 00
10
-------
TDS= 147,610 ; D= 1.11
X = 1,0007 (1.000 - 147)= 1.1732
Na
K
Ca
Mg
SO 4
Cl
ppm
51,600
2,650
1.360
1.720
3.680
S6.600
mg/1
ppm*D
57,276
2.942
1,510
1,909
4,085
96,126
M
mg/1
/1000
/MWt
2.49
0.08
0.04
0.08
0.04
2.71
f
ppm
/1000
/MWt
2.24
0.07
0.03
0.07
0.04
2.44
m
f*X
2.63
0.08
0.04
0.08
0.04
2.87
meq/1
mg/1
/MWt
*Z
2491.2
75.2
75.3
157.1
83.2
2711.0
-------
III. COMMONLY DETERMINED CONSTITUENTS
The parameters usually measured in the field include
temperature, pH, conductivity and alkalinity.
The ions commonly determined in a water sample include
l~, S04~, HC03~ and C03=.
Na+, K+, Ca++, Mg++,
Other determinations include Si02, TDS (total dissolved solids)
and hardness. Density should be measured on brines.
A. SOURCE OF MAJOR IONS IN WATERS
1. SODIUM - Na+
Sources Sinks
plagioclase (albite) NaAlSi3Og
halite NaCl
nahcolite NaHCOo
nepheline
NaAlSiO,
montmorillonite Na - clay
2 Na-clay + Ca"1"1" —> Ca-clay + Na+
sea spray
brines
hot springs
2. CHLORIDE Cl~
Sources
halite NaCl
sea spray
brines
hot springs
Sinks
11
-------
3. POTASSIUM - K+
Sources Sinks
potash feldspar KAlSi3O8 clays + K+ --> illite
plants
mica KAl2(AlSi3)010(OH)2
leucite KAlSi206
4. CALCIUM Ca++
Sources Sinks
plagioclase (anorthite) CaAl2Si2Og calcite
calcite CaCOo gypsum
aragonite CaCO3 montmorillonite
(natural softening)
dolomite
gypsum CaSO^.2H20
anhydrite CaSO^
fluorite CaF2
pyroxene (diopside) CaMgSi2O6
amphibole NaCa2(Mg,Fe,Al)Sig022(OH)2
5. STRONTIUM Sr++
Sources Sinks
strontianite SrC03 strontianite
celestite SrSO^ celestite
aragonite CaC03
(Sr"*"*" substitutes for Ca*+ in
aragonite but not in calcite.)
12
-------
6. SULFATE S04=
Sources Sinks
pyrite FeS2 pyrite
gypsum CaS04.21^0 gypsum
anhydrite CaS04 sulfate reduction
organic sulfur compounds
combustion of coal and
petroleum
smelting of sulfide ores
geothermal waters
7. GYPSUM CaS04.2H20
Saturated solution in water
636 mg./l Ca"1"1"
1600 mg./l S04=
Increases with NaCl concentration
8. BARIUM Ba++
Sources Sinks
barite BaS04 barite
oil-field brines
Solubility in water < 1 ppm.
Brines may contain 10|S to 100|S ppm
13
-------
9. MAGNESIUM - Mg++
Sources
olivine (Mg,Fe)2Si04
pyroxene (diopside) CaMgSi206
amphibole NaCa2(Mg,Fe/A
mica K(Mg,Fe)3(AlSi3)010(OH)2
dolomite CaMg( 003)2
10. CARBONATE / BICARBONATE C03 = / HC03~
Sources
atmosphere C02 ~
[H20 + C02 <==> H2CO3 <==> H+ + HC03~]
nahcolite NaHCO3
sulfate reduction
[S04= + 2CH20 ==> H2S + 2HC03~
11. CARBON DIOXIDE C02
Atmosphere 0.03%
PC02 = 0*0003 atmospheres
Sinks
montmorillonite
Sinks
calcite
C02 -x ° -x higher in soils because of decomposition
of organic matter.
14
-------
B. MISCELLANEOUS DETERMINATIONS
1. HARDNESS
Hardness is the sum of the Ca and Mg concentrations expressed
in terms of mg/1 of calcium carbonate.
Hardness = Ca(mg/l) * (M.Wt. CaC03j/(At. Wt. Ca)
+ Mg(mg/l) * (M. Wt. CaC03j/(At. Wt. Mg)
EXAMPLE :
Ca = 200 mg/1 Ca"1"*"; Mg = 30 mg/1 Mg++
Hardness = 200 * 100.088 / 40.08 + 30 * 100.088 / 24.312
• = 499.4 + 123.5
= 622.9 mg/1
Ca and Mg form an insoluble residue with soap; bath tub ring.
Detergents introduced to overcome this. It may be a major
problem in boilers as CaCOg is precipitated, resulting in poor
heat conduction. Hardness of streams may vary seasonally
because of variation of ground-water / surface-water run-off.
The ground water is more likely to be harder than the surface
water.
Temporary hardness - calcium and magnesium carbonates, removed
by boiling with precipitation of CaC03.
Permanent hardness - calcium and magnesium sul fates, not
removed by boiling.
15
-------
2. DISSOLVED SOLID CONTENT
(Often called TDS or Total Dissolved Solids.)
Calculated by adding the mass of ions plus Si02 and
subtracting losses due to C02 losses from carbonates. It is
determined by evaporating to dryness a known volume of water
at a specified temperature, usually 105 -180°C. During this
heating bicarbonates are converted to carbonates in the solid
phase:
2HC03~ —> C03= + C02 + H20
Amount of carbonate formed
= mg/1 HC03~ *M.Wt. C03=/(2*M.Wt. HC03)
Amount of H20 and C02 lost
= mg/1 HC03~ *M.Wt. H2C03/(2*M.Wt. HC03)
Thus estimated TDS
= sum of ions + Si02
- mg/1 HC03~ * M.Wt. H2C03/(2* M.Wt. HC03)
= sum ions + Si02 - mg/1 HC03~ * 62.02 / 122.032
= sum ions + Si02 - mg/1 HC03~ * 0.5082
In waters with high calcium and sulfate the residue at 180°C
may still be slightly hydrated, thus giving high results.
3. CONDUCTIVITY
Also called B.C. - electrical conductivity, specific
conductivity or conductance.
Conductivity is the reciprocal of the resistance in ohms
between the opposite faces of a 1 cm cube of an aqueous
solution at a specified temperature (usually 25°C). It is
temperature dependent. The units are mho's. As these are too
big the units generally used are micromho's, i.e. mho's * 10°
It is a good estimator of TDS.
TDS (mg/1) approximately equals A * conductivity (micromho's)
where A = 0.54 - 0.96 (usually 0.55 - 0.76)
16
-------
4. CALCULATED DENSITY
Partial ionic volumes of dissolved constituents in water are
used primarily to estimate the effects of pressure on
solutions. They may also be used to estimate the density of a
solution.
The volume of ions in solution is the sum of the product of
the number of moles/1 * the partial molar volume.
where
V = sum (n± * V±)
V is the molar volume
V^ is the partial molar volume at 25°C
n is the concentration in moles/1 of ion i
Thus:
Total volume of solution = 1000 cmc
Mass of water
Mass of solids
Mass of water + solids
Density
= volume of water
* density of water
= (1000 - V) * 1 g.
= TDS(mg/l) / 1000 g.
= (1000-V) + TDS/1000
= mass / volume
= [(1000-V) + TDS/1000] / 1000
17
-------
ion
K1
Ca
++
mg/1
S04=
HCOr
Total
Density =
mole/1
EXAMPLE
partial
molar volume
molar volume
ni*Vi
11,162
414
427
1339
20,059
2811
146
36,358
0.4855
0.0106
0.0107
0.0551
0.5658
0.0293
0.0024
[(1000cc-8.75cc)*1.0]
- 1.5
8.7
- 17.7
-20.9
18.1
14.5
24
g + [36358/1000]
0.7283
0.0922
0.1894
1.1516
10.2410
0.4249
0.0576
8.75 cc
g
i
lOOOcc
18
-------
§
M
i
§
f
M
V)
TABLE 3
Partial metal ionic volumes aruf compressibilities at infinite dilution in water at 25°C.
and 1 atmosphere
(Relative to H+)
C ATI OK
H*
Ii+
Na+
K+
Rb+....
Ca+
NH4+.... ......
•*.! • :
Ag+
Mg4^
Ca4"1-
Sr4"1- v....
Ba4*
Be4-1".:....
Cd4*. .*.....
Cu4*
ZQ-H-....
La44*
Ce44*. i..
«
0
-1.0
-1.5
4-8.7
+13.7
+21.1
+17.9
-1.0
-20.9
-17.7
-18.2
-12.3
-13
-38.3
10<£j
0
—34
-42
—37
-27
—11
—83
—71
—99
—23
—57
—62
—70
—152
AX10X
i '
OH-
F-
ci-
Br"
I-
CHiCOr
NOr
CNS-...
HCOa~
MnO4~
do,-
BrOa-
CrOr~
cor -. . . .
sor~
* •
F;
—5.3
-2.1
+18.1
+25 0
+36.6
+41.5
+29 3
+24
+43
+46
+44
+19.7
—3.7
+14.5
io«je5
—44
-8
+2
T"
+18
i ***
-10
+7
i •
+15
i ***
+2
i *•
•
—85
-70
-------
5. pH
pH is a measure of the hydrogen ion concentration [H+], or
"more correctly activity which will be discussed later.
PH = -log10[H+]
Note:
mmole/1 H+ approx. = mg/1 H+
At pH = 10;
[OH~] = 10~4 moles/1 = 10"1 meq/1 = 10"1 * 17 = 1.7 mg/1
pH may be raised by adding a base or by removing CC>2 from a
solution, e.g. by photosynthetic assimilation.
There are three main sources of hydrogen ions in natural
waters,
a. hydrolysis:
H20 --> H+ + OH~ ; In pure water [H+] = 10~7
b. dissociation:
H2CO3 —> H+ + HC03~
c. oxidation:
2FeS2 + 7.5O2 + 7H20 ~> 2Fe(OH)3 + 8H+ + 4S04=
The [H+] in an aqueous solution is controlled by chemical
reactions that produce or consume hydrogen ions. One of the
most important of these is that set of reactions initiated
when CO2 is dissolved in water, i.e.
C02(g) + H20(l) --> H2C03(aq)
H2C03(aq) ~> H+ + HC03~
HC03~ --> H* + C03=
BUFFERED SOLUTIONS
If, when acids and bases are added to a solution the pH
changes very little, these solutions are said to be buffered,
e.g. if we add hydrogen ions to a solution of carbonate, then
C03= + H+ --> HC03"
or another ion, namely bicarbonate is formed that uses up the
added hydrogen ions, such that the pH does not decrease as it
otherwise would.
(This is an important concept when dealing with acid rain or
acid mine drainage.)
20
-------
INTENSITY AND CAPACITY VALUES
Most quantities in chemical analyses are "intensity"
functions, i.e. actual concentrations of a constituent. Thus
pH measures the concentration of hydrogen ions in a solution.
There are certain properties of solutions that are
"capacity" functions, that measure the response of the
solution to change. For example the capacity of a solution to
neutralize acids or bases is called the buffering capacity of
the solution.
As an example, if we have two solutions A and B, both with
a pH of 8.2, but A has no carbonate whereas B has a high
concentration of carbonate. If we add acid to both solutions
the pH of A will be lowered after only a few drops of acid
whereas the pH of B will remain relatively constant until
sufficient acid has been added to change all the carbonate to
bicarbonate.
6. ALKALINITY AND ACIDITY
Alkalinity and acidity are quantitative measurements of the
capacity of a solution to react to acids and bases.
a. Alkalinity
The alkalinity of a solution is defined as the capacity
of a solution to react with strong acid. It is
determined by a titration to specific end-points,
namely pH = 4.5 - methyl orange and pH = 8.3 —
phenolphthalein. A measured volume V of the water is
titrated with a strong acid such as HC1 having a
normality N.
Several different solute species contribute to the
alkalinity of a natural water sample, and the titration
with acid does not specifically identify them.
Alkalinity may be reported in several ways, the most
common being in terms of an equivalent amount of CaCOg,
usually meq/1 CaCOg.
where meq/1 = mg/1 CaCOg/50 ... 50 is Eq. Wt. of CaCOg
In most natural waters alkalinity is produced by the
dissolved CC>2 species, bicarbonate and carbonate. Non-
carbonate contributors to alkalinity include hydroxide,
silicate, borate and the organic ligands, especially
acetate and propionate. The inclusion of these ions in
the alkalinity figure will only effect the analysis if
they are also included as separate ions.
Carbonate species are the most important participants
in reactions that control the pH of natural waters.
These relations are often illustrated by a graph
showing the % of each species present at a particular
pH.
21
-------
ro
to
M
8
50
PJ
00
O
1
M
CO
t)
w
o
H
w
w
12.0
13.0
19.—FeruoUga of (oUl ilssotT»d ewboo dloild* ipecles la solution u » fonetloo of pH^li*C; prcuui* 1 ttaoepber*.
-------
EXERCISE
Comment on the reasonableness of the following water analyses
using the carbonate/bicarbonate graph.
# | pH | mg/1 HC03" | mg/1 C03=
1
2
3
4
5
6
7
8
10.8
5.9
4.2
11.7
6.5
12.6
2
7
51
23
151
162
2
170
10
500
0
23
2
0
121
20
10
50
b. Acidity
Acidity is the capacity of a solution to neutralize a
strong base, that is, to react with hydroxyl ions, and
in doing so to convert all Carbonate species to
carbonate. Measured by titrating a measured volume of
water (V) with a strong base (such as NaOH) with
normality N.
Origin of acidity
volcanic gases
acid rain
oxidation of sulfide minerals
coal and metal mines
dissolved undissociated CO2 (I^COg) in water
e.g. 160 mg/1 I^COg in a water has a pH = 5.2
oilfield waters
often contain dissolved acetate
natural dissolved organic matter
large molecules with -COOH and -OH sites
originate in vegetation rich areas
usually strongly colored waters
Note:
A solution possessing caustic alkalinity (OH~) has no
acidity and a solution possessing mineral acidity has
no alkalinity
23
-------
EXERCISES
8. Calculate the concentrations of Na+ and Cl~ in mg./l resulting
from the solution of 1 g. NaCl in 1 liter of water.
9. Rain water percolates through gypsum beds to an unconfined
aquifer. The sulfate content of the aquifer water was found to be
760 mg./l SO^". What is the sodium content of this water after
passing through an ion exchange column?
10. Calculate the hardness in terms of CaCOq of a water containing
350 mg./l Ca++ and 125 mg./l Mg++.
11. Given that a water has a hardness of 560 mg./l CaCOg and a Mg++
content of 72 mg./l. Calculate the concentration of Ca++ in
mg./l.
12. A water has a TDS(180°C) of 570 mg./l. It contains 155 mg./l
HC03. What is the true TDS of the water?
13. A water contains 800 mg./l SO^3 and 500 mg./l Ca++. The measured
TDS(180°C) was found to be 1750 mg./l. An XDR examination of the
residue revealed the presence of CaS04.0.5H20 but not anhydrite
nor gypsum. What is the true TDS content of the water?
14. Estimate the TDS of a solution having a conductivity of 2730
umho's.
15. Calculate the H+ concentration in mg./l in waters having pH's of
2, and 7.
16. A ground water is reported to have a hardness of 1000 mg/1
expressed as calcium carbonate. The aquifer is known to be
composed primarily of dolomite. What would you expect the Ca and
Mg contents to be in mg/1?
17. Calculate the dissolved solid content of the following water
Concentrations in mg/1.
Na = 2.14; Ca = 48; Mg - 3.6, HCOo = 152; S04 = 3.2; Cl = 8.0;
Si02 =8.6
18. Calculate the density of the Red Sea Brine whose analysis is
given below (all values are in g/1):
Na = 105, K = 3.61, Mg = 0.95, Ca = 6.44, SO* = 1.14, Cl = 195
Measured density = 1.196. Comment on the difference.
24
-------
ANSWERS
8. Na=1000*23/58.45=393mg/l; 01=1000*35.45/58.45=607mg/l.
9. 760 mg/1 S04= = 7.912 nunole S04= = 7.912 mmole Ca++
= 15.82 mmole Na+ = 364 mg/1 Na+
10. 350/40.08*100.09 = 874 mg./l CaC03 +
125/24.31*100.09 = 515 mg./l CaC03 «
Hardness = 1389 mg./l CaC03
11. Hardness = 560 mg./l CaC03 = 5.595 nunole CaC03
= mmole(Ca++ + Mg++)
72 mg./l Mg++ = 2.962 mmole Mg++;
Ca++ = 5.595 - 2.962 = 2.663 mmole = 106 mg./l
12. TDS(180°C) = 570 mg/1; 155 mg./l HC03~ =2.54 mmole/1
2HC03" <==> C03= + H20 + C02
2 mole bicarbonate loses 1 mole water + 1 mole CC>2
2.54 mmole bicarbonate loses 1.27 nunole water + 1.27 mmole C02
22.9 mg. 55.9 mg.
Total loss = 78.8 mg./l
True TDS = 570 + 79 = 649 mg./l
OR
2HC03~ <==> C03= + H20 + C02
122.036 60.01 18.016 44.01
v
122.036 mg loses 62.026 mg.
Loss is 50.83 % HC03~; Loss = .5083* 155 = 79 mg.
13. TDS(180°C) = 1750 mg./l;
800 mg./l S04= = 8.33 mmole/1; 500 mg./l Ca++ = 12.48 mmole/1
Limited by sulfate; CaS04.0.5H20 = 8.33 mmole/1
2CaS04.0.5H20 <==> 2CaS04 + H20
2 mmole 1 mmole
8.33 mmole 4.165 mmole
= 75 mg./l H20
25
-------
True TDS = 1750 -75 = 1675 mg./l
14. TDS - A * cond. ; A = 0.55 - 0.76
cond. o 2730; TDS - 1502 - 2075
15. pH = 2; [H+] = 10~2 mole/1 = 10 mmole/1 = 10.1 mg./l H+
pH = 7; [H+] = 10~7 mole/1 = 10~4 mmole/1 = 1E-4 mg./l H+
26
-------
IV. ANALYSIS INTERPRETATION
A. SPOTTING QUESTIONABLE ANALYSES
1. ANION - CATION BALANCE
The accuracy of many water analyses may be readily checked
because the solution must be electrically neutral, and thus
the sum of cations in meq/1 should equal the sum of the anions
in meq/1.
(meq/1 = mg/1 * valency / formula wt.)
The result is usually expressed as a percentage,
i.e. Balance = (C-A) / (C + A) * 100
where C = sum of cation and A = sum of anions.
If the balance is < 5% the analysis is likely to be good.
If the balance is exactly 0% it is likely that the Na or Na+K
were determined by difference, especially in older
analyses, i.e. prior to 1960.
If the balance is much greater than 5% then
a. the analysis is poor (inaccurate)
b. other constituents are present that were not used to
calculate the balance.
c. the water is acid and the H* were not included
d. organic ions are present in significant quantities,
often indicated by colored waters.
2. RELATIVE AMOUNTS OF IONS REPORTED
(Units used are meq/1)
The following is only a guide and it must be emphasized that
many accurate analyses may reflect exceptions to these general
statements, however, the objective is not to throw out all
analyses that do not comply with these generalizations but
rather to ensure their accuracy, by bringing potential
inconsistencies to the attention of the investigator.
a. Na » K
b. Ca >= Mg unless Ca removed by precipitation
c. Ca >= S04 unless Ca removed by precipitation or ion
exchange
d. Na >= Cl unless Na by ion exchange (reverse
softening)
27
-------
3. MISCELLANEOUS CHECKS
a. Calculated hardness should equal reported hardness. A
discrepancy may indicate incorrect copying of reported
data.
b. Calculated TDS should equal reported TDS Incorrect
transcription is a frequent cause of non equivalence.
c. TDS / Measured conductivity should be between 0.55 and
0.76
d. If C03= is absent pH should be < 8
e. Conductivity /(sum of cation) approx. = 100
Usual range 90-110.
f . Temporary hardness usually equals bicarbonate
B. COMPLETING PARTIAL ANALYSES
1. GIVEN HARDNESS, Ca OR Mg
Given any two of the following — hardness, Ca or Mg — the
other may be calculated.
2. TEMPORARY HARDNESS OR ALKALINITY
Temporary hardness is equivalent to alkalinity
3. CARBONATE / BICARBONATE
If HCOg~ or COg12 a
reasonable values.
If HCOg~ or CO12 are unreasonable recombine to obtain more
4. MISSING VALUES
A single missing value may be obtained by subtracting the sum
of cations from the sum of anions or vice versa.
28
-------
EXAMPLE
permanent hardness = 75 mg/1 CaC03
temporary hardness = 345 mg/1 CaCOg
Mg = 6 mg/1; NaCl = 35 mg/1; pH = 7.1
Total hardness = 345+75 = 420 mg/1 CaC03 = 8.4 meq/1
Mg = 6/12 = 0.5 meq/1
thus Ca = 8.4-0.5 =7.9 meq/1 = 7.9*20 = 158 mg/1
Alkalinity = temporary hardness = 345 mg/1 CaC03
At pH =7.1 HCOg" is the only carbonate species present
thus alkalinity = [HC03~] = 345/50*61 = 421 mg/1
As log[CO3=] = log[HC03~] + log K2 + pH
= -2.16 - 10.5 + 7.1 = -5.56
then C03= =0.17 mg/1
Permanent hardness = 75 mg/1 CaC03 = 75/50 = 1.5 mmole CaCO3
This is considered to be CaSO^
thus S04= = 1.5 * 48 =72 mg/1 S04=
Given 35 mg/1 NaCl
= 35/(23+35.5) = 0.598 mmole/1 NaCl
= 0.598 * 23 = 13.8 mg/1 Na+
= 0.598 * 35.5 = 21.2 mg/1 Cl
29
-------
EXERCISE
19. You are studying a limestone aquifer and collected a sample that
was sent to a commercial lab. The results obtained from the lab
are listed below. At the same time that you took the sample you
obtained a pH of 6.9 and a total alkalinity of 1400 mg/1
bicarbonate using simple field equipment.
mg/1
Na+ 130
K+ 130
Ca++ 57
Mg++ 375
HC03"" 645
C03= 360
S04= 121
Cl~ 156
Hardness (€3003) 1171
TDS (180°C) 1529
pH 6.72
Your Job if you decide to accept it is to list the suspect
numbers with all your evidence against them, and replace them with
more reasonable substitutes with appropriate documentation. Should
you be caught juggling the figures without the appropriate evidence
the Department will disavow all knowledge of you.
[ Note: Analytical errors as such are much less common than those
involving arithmetic, transposing of figures or columns, or slipping
a decimal point such as recording 67.0 as 6.70. ]
30
-------
V. ROCK - WATER INTERACTIONS
A. MINERALS
CARBONATES
ARAGONITE
CLAYS
CALCITE
DOLOMITE
KAOLINITE
MONTMORILLONITE
ILLITE
FELDSPARS
PLAGIOCLASE
ALBITE
ANORTHITE
POTASH FELDSPAR
FERROMAGNESIAN SILICATES
AMPHIBOLES
TREMOLITE
HORNBLENDE
MICAS
BIOTITE
OLIVINE
PYROXENES
DIOPSIDE
AUGITE
HALIDES
FLUORITE
HALITE
OXIDES/HYDROXIDES
BAUXITE
HEMATITE
LIMONITE
QUARTZ
SULFATES
GYPSUM
ANHYDRITE
BARITE
SULFIDES
PYRITE
CaC03
CaCOg
CaMg(C03)2
Al2Si205(OH)4
Al2Si4010(OH)2
KAl2(AlSi3010)(OH)2
NaAlSi308
CaAl2Si2Og
KAlSi308
Ca2(Mg,Fe)4AlSi7A1022(OH)2 X
NaCa2(Mg,Fe,Al)5Si8022(OH)2 X
K(Mg,Fe)3AlSi3010(OH)2
(Mg,Fe)2Si04
Ca(Mg,Fe)Si206
Ca(Mg,Fe,Al)(Al,Si)206
CaF2
NaCl
AIO(OH)
FE203
FeO(OH)
Si02
CaS04.2H20
CaS04
BaS04
FeSo
[
X
X
X
X
X
X
X
X
X
X
X
X
X
Mm Sed
X
X
X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X X
31
-------
B. BALANCING EQUATIONS
Pertaining to surface mineral weathering reactions involving C02
and H20
1. Mineral + C02 + H20.
2. Decide clay type to be formed.
kaolinite or montmorillonite
3. Balance aluminum.
4. balance cations released.
5. Set bicarbonate to balance cations released.
6. Balance Si with H4SiO4.
7. Set # C02 molecules to balance HC03~.
8. Set # H20 molecules to balance # of H atoms in products.
9. Count oxygen atoms on both sides to check balance.
EXAMPLES
Albite: — > kaolinite
2NaAlSi308 + 2C02 + 11H20 --> Al2Si205(OH)4 + 2Na+ + 2HC03~ + 4H4Si04
Albite: — > montmorillonite
2NaAlSi308 + 2C02 + 6H20 — > Al2Si4010(OH)2 + 2Na+ + 2HC03~ + 2H4Si02
Biotite: — > kaolinite
2KMg3AlSi301Q(OH)2 + 14C02 + 15H20 -->
Al2Si205(OH)4 + 2K+ + 6Mg++ + 14HC03~ + 4H4Si04
Biotite: — > montmorillonite
+ 14C02 + 10H20 -->
Al2Si401Q(OH)2 + 2K+
14HC03~ + 2H4Si04
32
-------
WEATHERING OF ORTHOCLASE TO KAOLINITE
. KAlSi3Og + ? C02 + ? H20 <===>
2. CLAY TYPE
3. BALANCE Al
2KAlSi308 + ? C02
4. BALANCE CATIONS
2KAlSi308 + • ? C02
< = = = > KAOLINITE
<===> Al2Si205(OH)4
H20 <===> Al2Si205(OH)4
H20 <===> Al2Si205(OH)4
+ 2K*
5. BALANCE CATIONS WITH BICARBONATE
2KA1S1308 + ? C02 + ? H20 <===> Al2Si205(OH)4
+ 2K+ + 2HC0~
6. BALANCE Si
2KA1S1308 + ? C0
7. DETERMINE O>2
2KA1S1308 + 2C02
8. DETERMINE H20
2KA1S1308 + 2C02
? H20 <===> A12S1205(OH)4
+ 2K+ + 2HC03~ + 4H4SiO4
? H20 <===> Al2Si205(OH)4
+ 2K* + 2HC03~ •*• 4H4Si04
11H20 <===> Al2Si205(OH)4
+ 2K+ + 2HC03~ + 4H4Si04
9. CHECK OXYGEN
16 + 4 + 11
31
9+6+16
31
33
-------
WEATHERING OF BIOTITE TO MONTMORILLONITE
1. KMg3AlSi3010(OH)2 + 1 C02 + ? H2O <===>
2. CLAY TYPE
<===> MONTMORILLONITE
Al2Si4010(OH)2
3. BALANCE ALUMINA
2KMg3AlSi3010(OH)2 + ? C02 + ? H20 <===> Al2Si4010(OH)2
4. BALANCE CATIONS
2KMg3AlSi3O10(OH)2 + ? C02 + ? H20 <===> A12S14010(OH)2
+ 2K+ + 6Mg++
5. BALANCE CATIONS WITH BICARBONATE
2KMg3AlSi301Q(OH)2 + ? C02 + ? H20 <===> Al2Si4010(OH)2
+ 2K"1" + 6Mg++ + 14HC03~
6. BALANCE Si
2KMg3AlSi3Ol0(OH)2 + ? C02 + ? H2O <===> A12S±4O10(OH)2
+ 2K+ + SMg"*"1" + 14HCO3~ + 2H4Si04
7. DETERMINE CO2
2KMg3AlSi301Q(OH)2 + 14C02 + ? H20 <===> A12S±4010(OH)2
•f 2K+ + 6Mg++ + 14HC03~ + 2H4SiO4
8. DETERMINE H20
2KMg3AlSi301Q(OH)2 + 14C02 + 10H20 <===> A12S±4010(OH)2
+ 2K+ + 6Mg+-f + 14HC03" + 2H4Si04
9. CHECK OXYGEN
24 + 28 +10 =12+42+8
62 62
34
-------
EXERCISE
20. Balance the equations for the weathering of the following
minerals. Try each with both clay minerals, kaolinite and
montmorillonite.
a. anorthite
b. tremolite
c. diopside CaMgSi206
d. dolomite CaMg(C03)2
35
-------
C. SOURCE ROCK DEDUCTION
The purpose of this technique is to help the reader gain an
insight into the possible origin of a typical water analysis. The
approach used is not infallible but it can be very helpful. The
method is a somewhat simplistic mass balance approach to water
quality interpretation and is no way intended to replace the more
sophisticated models such as WATEQ, BALANCE etc. It is based on
the calculations and discussion in Garrels and MacKenzie, 1967. A
flow chart of the technique is given in Figure 1.
Step 1. If the pH of the water is less than about 6 abandon
the project. Acid waters cannot be interpreted this way
without modifying the procedure.
Step 2. The concentration of the various constituents,
usually expressed as mg/1. must be changed to meq/1. in order
to be able to combine the various ions in a chemically
meaningful way. Silica which exists as a neutral complex is
converted to millimoles/ liter. This is accomplished by
dividing the ion concentration by its equivalent weight, and
silica by its molecular weight.
Step 3. Sum the cations and the anions separately, omitting
Silica. Their totals should be within about 5% of each other;
if not proceed with caution or throw the analysis out.
Step 4. Compare the chloride and sodium contents. We assume
that the primary source of chloride in the water is from
sodium chloride, directly or indirectly from the ocean via
precipitation. Sodium on the other hand can be derived from
other sources, for example the solution of feldspars, ion
exchange etc. Thus, if chloride > sodium then there is either
an analytical error, or the water derived its composition
from the solution of evaporite minerals. In the latter case
one would expect the dissolved solid content of the water to
be high, at least over 500 mg/1.
Step 5. Compare the sulfate and calcium contents. The primary
assumption is that sulfate is generally the result of direct
dissolution of gypsum or the neutralization of acid waters by
limestone or dolomite. In the latter case magnesium may be
prominent. If sulfate > calcium then the inference is that
calcium has been removed from solution, most likely by the
precipitation of calcite. Calcium may also be removed from
solution by ion exchange reactions such as:
Ca"1"*" + 2Na-CLAY --> 2Na+ + Ca--CLAY
Step 6. Compare bicarbonate with silica. Bicarbonate is formed
when carbon dioxide and water react with various minerals in a
process called acid hydrolysis. Carbonates dissolve without
releasing silica whereas albite releases considerable silica,
and other silicates a much lower amount, Table 1. An arbitrary
36
-------
division of silica/bicarbonate of 0.1 is used to indicate
silicate versus carbonate weathering.
Step 7. Compare silica with Ma"1" (-Cl~) + K+. We assume that
after subtracting the chloride from the sodium, then the
remaining sodium is due to the weathering of plagioclase, and
the potassium from the weathering of biotite and to a lesser
extent potash feldspar. If other ferromagnesian minerals are
present, silica will be present in a considerably excess over
the sodium plus potassium. It is also assumed that the solid
weathering product formed is either kaolinite or
montmorillonite; the former releasing more silica to the water
than the latter. Thus we may conclude that if:
a. SiOo > 2 * (Ma* + K+ - Cl~) then the minerals
subjected to weathering contained a considerable quantity
of ferromagnesian minerals, such as olivine, pyroxene or
amphibole. Under these conditions the source of much of the
calcium is probably plagioclase.
b. SiC>2 < (Na+ + K+ -Cl~) then cation exchange is probably
the source of most of the excess sodium, in which case it
is probable that calcium is less than the sulfate.
c. (Na+ + K+ - Cl") < Si02 < 2 * (Na* + K+ - Cl~) then Na-
feldspar weathering is suspect, and the product is either
kaolinite or montmorillonite.
There are some occasions when the application of these
calculations will lead to misleading conclusions, but I
suspect that 90% of the time they will be meaningful and
will lead to ideas for further investigation. .PA
37
-------
TABLE 1
Weathering products of common minerals.
Cations and SiC>2 based on 100 meq HC03
Ratios
Mineral
j
albite
albite
diopside
tremolite
tremolite
forsterite
phlogopite
phlogopite
anorthite
calcite
dolomite
Clay Na+ K+ Ca++ Mg+
formed
(1)
K 100 -
M 100 - - -
25 25
K - 17 33
M - 17 33
50
K - 14 43
M 14 43
K - - 50 -
-. - 50
25 25
+ Si02
200
100
50
42
25
25
29
14
-
-
-
SiO2 I
HC03~
2
1
0.5
0.4
0.25
0.25
0.29
0.14
0
0
0
«a++K+
Si02
0.5
1
0
0
0
0
0.5
1
0
0
0
(1) K = kaolinite
M= montmorillonite
38
-------
FIGURE 5. WEATHERING FLOWCHART
Flow chart illustrating logic of water quality
interpretation using simplified mass balance technique,
Water analysis
Na+, K+, Ca++, Mg"1"1", HC03~, C03=, S04=, Cl~, Si02
+ ' — 4- ' -•»
rasa s pi Ma S04= Ca"*"1" < S04=
Ca"1"1" removal, by
calcite precipitation, or
Ion exchange
HCO3~ > 10*Si02 HC03~ < 10*Si02
Carbonate weathering
,-—•----
Si02 > (Na +K -Cl ) Si02
cation exchange
probable Ca++ < S04=
Si02 > 2*(Na++K+-Cl~)
Weathering of
ferromagnesian minerals
Calcium from feldspar
Si02 < 2*(Na++K+-Cl~)
Granitic weathering
Calcium from feldspar
39
-------
EXERCISE
21. Interpret the origin of the waters listed below, values in
ing./I.
Na+
K+
Ca++
HC03'
S04=
Cl"
SiO2
1
9.5
1.4
27.0
6.2
93.0
32.0
5.2
39.0
2
0.2
0.0
2.5
7.7
44.0
0.0
0.7
16.0
3
24.0
7.0
74.0
9.5
277. 0
19.0
24.0
11.0
4
2.0
0.6
34.0
14.0
160.0
3.7
2.5
9.2
5
76.0
3.5
178.0
86.0
285.0
707.0
11.0
14.0
40
-------
VI. GRAPHICAL METHODS
Graphical methods of illustrating water analyses have two main
objectives:
A. AREAL TRENDS
To enable analyses to be plotted as symbols on a map.
These are shown on maps using a variety of plots to represent the
analyses. They are of two general types.
1. One component is usually plotted, generally TDS or
conductivity although other elements of interest or even
ratios of ions or elements may be plotted. They are readily
contoured and in some cases easily interpreted.
2. Multi-component plots although commonly used are are extremely
difficult to interpret because an interpretation involves an
eyeball examination of various shapes and sizes on a map.
The main types of such plots in common use are:
a. Bar graphs; usually expressed in meg/1 as this enables the
sum of anions and the sum of cations to be drawn the same
length.
b. Pie diagrams or circular diagrams. These may be drawn such
that the diameters of the circles are proportional to the
dissolved solid content.
c. Radial diagrams. Concentrations usually in meq/1 or %
meq/1. The arms of the plots are usually 60° apart and the
ends connected to form a polygon.
d. Vectors where along predefined directions the length is
proportional to the concentration which is usually
expressed in meq/1. The ends of the plot are not usually
connected.
e. Kite diagrams. This configuration is limited to four
concentrations and the axes are Ca+Mg, Na+K, Cl+SO^,
in meq/1.
f . Stiff diagram. This uses four parallel horizontal axes
extending on each side of a vertical zero axis. Four anions
and four cations can thus be plotted on the left and right
of the vertical respectively. The concentrations are in
meq/1. The resulting points are connected to give an
irregular polygonal pattern. The size of the pattern is
approximately equal to the total ionic content.
41
-------
B. CHEMICAL TRENDS
The determination of any trends existing in a collection of
water analyses is usually accomplished using either an x-y plot
or some type of trilinear plot.
Usually when considering plotting techniques only major
components are plotted, specifically Na (+K), Ca, Mg, Cl, SO^ and
HCOo (+033). This approximation results in 6 major ions or
combination of ions to be plotted.
In contrast to the plotting of areal trends, where individual
analyses are each plotted in some way on a map, chemical trend
plots are usually done on one type of diagram on which all the
analyses are plotted.
The simplest type of such a plot is a simple x-y plot of two ions
or variables, such as Na versus Ca. These are by far the simplest
graphs to interpret and many computer statistical packages such
as SAS can be set up to do many such plots.
A more complex method of plotting is the use of trilinear or
triangular diagrams. These diagrams have a disadvantage that only
three variables can be plotted on a triangle. This is overcome to
some extent by plotting cations and anions on separate triangles
and arranging them is such a way that they can be related to one
another. One major problem with this type of plot is that the
analyses plotted are only ratios, and the effect of dilution is
not immediately apparent. The two main techniques for plotting
water data are as follows:
1. Piper diagrams where the sides of the anion and cation
triangles are set at 60° apart and a diamond shape is used to
replot them on one diagram.
a. PRECIPITATION OR SOLUTION
If a series of water analyses are plotted on a Piper diagram
and they lie on a straight line which when extrapolated passes
through the corner of one or both of the triangles then it
is possible that the trend is the result of the component at
the corner of the triangle either being added or removed from
solution.
Examples include calcite precipitation or solution (calcium
and bicarbonate) or gypsum precipitation or solution (calcium
and sulfate). Mass balance and solubility equilibrium may be
used to further confirm or disprove this hypothesis.
42
-------
FIGURE 14
Determination of point C by the two-line method. Two line* urc drawn through C
parallel to tiny iwu of the tide* at the iriuaiflc (here AY urul \'Z\. The
interaction of thciic two lino wiih the third tide Uf/l divide* ilui Me into
three pun* wltotc kntihi we proponional m the rclMive aniuunu
A', f. uiul 2 ki pttint r.
100% X
CO 60 50 S> 20 10
KXJ %/
showing mcihixl of determining or pbuinu compoiiiion C
wiiliiu UM iliree-cumpoucnl kytlcm X-Y-Z.
Tte poiAl C on irUnituliir graph paper. The pereeniuge» ofcomponcnu AT, Y. and
2 krc rod directly from the numbered coordinate uxc*.
FIGURE 6. TRIANGULAR DIAGRAMS
43
-------
H
8
50
M
•a
H
•0
w
Permanent
hardness
Temporary
hardness
Saline
Cl
Alkali
carbonate
-------
Ca5+ 50%
HC0750V.
Ca 25%
Mg2+25%
Ion exchange
Reverse
Ion exchange
Fig. 6.19. Expanded Durov diagram with subdivisions and processes
demonstrated.
FIGURE 8. DUROV DIAGRAM
45
-------
8
»
w
NO
H
o
G
f<
g
O
I
33
w
S3
VWmVAVAVAAA
VvYWi;\ °i.'/VYYWVi1. . -W\ /WVv"
777?77^TO^A^W?90TO)TO
\7vAA *v^A /vA/VAJ* A\A A/\ A A.K 'v/vA A ^A A/v K 'v J
Vf)^yxVAV)5ggo'
^\ww\^w\rv^w **
mx\\W)ftgS55g
WVWWW7OTS
fMxWxWW
yyvYYV^^TK>^rxVYxvi
A AT* 'V^v A '•. ^* 'VA '» A />> 'V A /\ ^\ '
x
vY/V)Vyr/v^>^yyy'i\YY) xVy^>^\Y/A\\ A\\^.V^\^vv^vy/^^^VA\\nA.V\\^a
-------
b. MIXING
If two waters mix then the composition of the mixture will
lie on a straight line joining the two end members, and the
relative amount of each end member in the mixture is
inversely proportional to the distance of the mixture from
that end member. If a water is strictly the result of
mixing, without the addition or removal of any phase, then
the mixture will exhibit exactly the same proportions
between the end members on both cation and anion triangles
as well as on the diamond.
C. ION EXCHANGE
The replacement of calcium and magnesium by sodium is a
special case of addition and removal from solution. The
line connecting water compositions changed by ion exchange
starts parallel to constant magnesium and then curves down
towards the sodium apex. This suggests that ore calcium is
being exchanged than magnesium.
d. WATER TYPES
Waters may be divided into four basic types according to
their placement near the four corners of the diamond. Water
plotting at the top of the diamond is high in both Ca+Mg
and 804 resulting in an area of permanent hardness. The
waters plotting near the left hand side corner are rich in
Ca+Mg and HC03 and lie in the region of temporary hardness.
Those waters plotting at the lower end of the diamond are
primarily composed of alkali carbonates (Na+K and
HCC^+COg). Those waters lying near the right hand side of
the diamond may be considered saline (Na+K and Cl).
, The Durov or expanded Durov graphs are similar in that the
analyses are plotted on separate anion and cation triangles,
but in this case the sides of these triangles are 90° apart.
Also in the expanded Durov the three corners of each triangle
are physically separated from one another. The net result is a
square plot divided into nine areas characteristic of nine
different water types.
47
-------
A
12.2
1.2
0.8
B
4.6
1.0
6.4
C
4.6
4.0
2.4
D
6.3
1.1
5.0
EXERCISES
Analyses in meg/1
Ca
Na
Mg
Problem a.
Plot analyses A, B, C & D.
Label triangle LHS=Ca; RHS=Na; Vertex=Mg
Problem b.
Remove 1/4 (E), 1/2 (F) & 3/4 (G) of Ca from analysis A,
and plot the results. This could result from calcite precipitation.
What is your conclusion? Can you explain analysis C?
Problem c.
Combine analyses A & B in proportions 1:1 A:B (H) and
3:1 A:B (I). Use meq/1 not percentages.
What is your conclusion? Can you explain analysis D?
48
-------
VII. GEOCHEMICAL ENVIRONMENTS
Th.e rocks comprising an aquifer, through which ground water
flows, usually contain substances that provide sinks or sources for
hydrogen ions, electrons or soluble salts which in turn determine
the pH, redox potential or ionic strength of the water passing
through it. Changes in these parameters in turn may change the
chemical composition of the water because of precipitation, solution
or change of valence. When such conditions exist, they have
generally been referred to as geochemical barriers. Some of the more
important barriers will be discussed below.
A. pH BARRIERS
pH measures the ability of the environment to supply or remove
hydrogen ions to(from) the solution.
1. STRONGLY ACID - pH < 4
Ore deposits; coal mines
oxidation of pyrite
FeS2 + 3.502 + H20 <«> Fe"*"1" + 2S04= + 2H+
2Fe++ + 0.502 + 2H20 <==> Fe203 + 4H+
Fe2O3 + H20 <==> 2FeOOH
OR
FeS2 + 3.7502 + 2.5H20 <==> FeOOH + 2S04 + 4H+
Clays destroyed; aluminum mobile
Many trace metals mobile (e.g. Cu, Zn)
Increase after rain, varies seasonally
Sulfate » chloride
2. MODERATELY ACID - pH 4-6.5
Carbonic acids
C02 + H20 <==> H2C03 - pH = 5.6
atmospheric C02
oxidation of organic material
more C02 therefore higher pH
Humic acids
Partial breakdown of organic material
Low chain organic acids
oil field waters
Replacement of cations by H+ ions
cations in ground water
Alteration of feldspars to clays
Podzolic soils (leached A-horizon)
49
-------
3. NEUTRAL pH 6.5-7.8
Bicarbonate dominant
cations mainly Ca and Mg
Humid climate
karst topography
solution cavities
Dry climate
caliche layer in soil
carbonate concretion
+ HoO
humid
>
H2C03 + CaC03 Ca++ + 2HC03
dry
Mn often mobile as bicarbonate —> black stains
Good buffer for acids
4. MODERATELY ALKALINE pH 7.8-9
Carbonates precipitated
Many trace metals co-precipitated
Measurable carbonate (C03=) in water
Silica often mobile
may replace carbon, e.g. fossil wood
5. STRONGLY ALKALINE - pH>ll
Ca and Mg hydroxides
Leaching of fresh cement; Ca(OH)2 in water
B. ADSORPTION BARRIERS
1. MONTMORILLONITE CLAYS
Ca/Na exchange - natural softening
Na2-clay + Ca++ <==> Ca++-clay + 2Na+
Reversed by saline solutions - regeneration
2. KAOLINITE CLAY
Anion exchange
Phosphate, sulfate
F~/OH~ exchange (acid)
reversed (neutral)
50
-------
3. GOETHITE (FEOOH)
Anion exchange
selenate, molybdate
May be reversed under reducing conditions
4. NATURAL ORGANIC MATTER
Bonding to humic/fulvic acids
U02 > Hg > Cu > Pb > Zn > Ni > Co
pH dependent
Pb more strongly adsorbed under alkaline conditions
than under acid conditions
C. REDOX BARRIERS
The ability of a natural environment to bring about an oxidation
or reduction process is defined by what is called its redox
potential. This measures the ability of the environment to supply
electrons to an oxidizing agent or remove electrons from a
reducing agent. Because many elements have more than one
oxidation state and the stability of a particular oxidation state
depends on the availability of electrons the ratio of two such
oxidation states of a particular element in a water will also
depend on the environment.
THE FEW ELEMENTS IN NATURAL WATERS
0 - O2/H20
N - N03~/N02~; N03~/N2; N03~/NH4'f
C - C02/CH4
Fe - Fe++/Fe+++; Fe++/FeOOH, Fe"l"l"/Fe(OH)3
Mn - Mn"l"f/Mn02
S - S04S/H2S
51
-------
IRON GEOCHEMISTRY
High natural abundance
Ubiquitous
Exists in two valence states
Fe"*"*" - ferrous (reduced)
Pe"1"1"1" - ferric (oxidized)
Low solubility oxides and hydroxides
Low solubility sulfides
At pH > 3 ferric iron insoluble
Iron colloids have high adsorption capacity
2Fe(OH)3 —> 2FeOOH + H20
Y
Fe203 + H20
CARBON GEOCHEMISTRY - REDOX "BUFFER"
organic carbon
DO becomes depleted if NOM present
DO may decrease from recharge to discharge in
aquifer
Water may become anaerobic
highly reducing
H2S present
CH4 present (C —> CH4 + C02)
1. AEROBIC WATERS
Measurable dissolved oxygen
H2S absent
Fe(OH)o solid and gelatinous
adsorbed trace metals e.g. As
C + 02 —> C02
Fe"1"*"1" --> FeOOH or Fe(OH)3
2. ANAEROBIC WATERS (1)
Mildly reducing (Gley waters)
Dissolved oxygen absent
H2S absent
Soluble Fe+-f
Soluble arsenite (very toxic)
52
-------
3. ANAEROBIC WATERS (2)
Strongly reducing
H2S present
Insoluble sulfides, e.g.
Many co-precipitated heavy metal sulfides
sulfate reduction
2C + S04= + 2H2O <==> H2S + 2HC03~
Fe"1"1" —> FeS2
fermentation
2C + 2H20 <==> CH4 + C02
Fe"1"1" + C02 — > FeC03
53
-------
I"
FIGURE 10. REDOX ZONES
54
-------
Table 5-V11
Classification and composition t>J sediments
ui
in
M
1
M
£
*
CA
m
O
M
3
m
1
«!
o
M
0
33
2
CO
»
*^
w
CLASS ' RESISTATES IIVDROLYSATEi
Elements SI . . A). Si, Fe
•
Minerals Quartz Clay minerals
Accessory minerals Al hydroxide*
Glauconite
Chamosite
. •
«<•*»
1.6
^
.** 1-6
'c •
^ 1.4
E
:0
^1.2
to*
•~ 0.8
V)
5
'•5 f.6
<
V
0 0.4
'c
o
o
'
._ • sofuble
•Cs
• ?b
_
•K »Ba
• 5r
• Nil' «Ca
Mn /
• /
•i; FcX
XA\g
„
•Be
*-— ^*"
OXIDATES
Fe, Mn
Hematite
Gocthite
Tyrolusite
Psilomelane
.
cations
•i
A
/
/
/
/
JbfTa.
kin • V ^— — *--" ~
^~~^~*~~'^
^ '
soluble
* P cornplcx
an lops
: •N »S
01234-56
ionic charge
Fig. 5-3 Ionic potential and the behavior of elements in sedimentary processes.
-------
CHEMICAL WEATHERING REACTIONS 211
Table I. Avenge Composition of Igneous and Some Types of Sedimentary Rocks [6J*
Element
Si
Al
Ft
Ca
Na
K
Mg
Ti
P
Mn
F
Ba
S
Sr
C
a
Cr
Rb
Zr
V
Ce
Cu
Ni
Zn
Nd
U
N
Y
Li
Co
Nb
Ca
Pr
Pb
Sm
Sc
Th
Cd
Dy
B
Yb
Cs
Hf
Be
Er
U
Sn
Ho
Br
Igneous
Rocks
285.000
79.500
42.200
36,200
28.100
25.700
17.600
4.830
1.100
937
715
595
410
368
320
305
198
166
160
149
130
97
94
80
56
48
46
41
32
23
20
18
17
16
16
IS
11
9.9
9.8
7J
4.8
4.3
3.9
3.6
3.6
2.8
23
2.4
2.4
Resistatet
(sandstone)
359,000
32.100
18,600
22.400
3.870
13,200
8,100
1.950
539
392
220
193
945
28
13,800
IS
120
197
204
20
ss
IS
2.6
16
24
19
-
16
IS
0.33
0.096
5.9
7.0
14
6.6
0.73
3.9
4.4
3.1
90
1.6
2.2
3.0
0.26
0.88
1.0
0.12
1.1
1.0
Sedimentary Rock*
Hydrotyzale*
(shale)
260.000
80.100
38.800
22.500
4.850
24.900
16.400
4.440
733
S75
560
250
1.850
290
15.300
170
423
243
142
101
45
45
29
130
18
28
600
20
46
8.1
20
23
5.S
80
5.0
10
13
4.1
4.2
194
1.6
6.2
3.1
2.1
1.8
4.5
4.1
0.82
4.3
Precipitates
(carbonates)
34
8.970
8.190
272,000
393
2,390
45.300
377
281
842
112
30
4,550
617
113400
305
7.1
46
18
13
11
4.4
13
16
8.0
9.4
_
15
5.2
0.12
0.44
2.7
1.3
16
1.1
0.68
0.20
0.77
0.53
16
0.20
0.77
0.23
0.18
0.45
2.2
0.17
0.18
6.6
212 CHEMISTRY OF NATURAL WATERS
Table I, continued
Element
Eu
Ta
Tb
As
W
Ce
Mo
Lu
Tl
Tm
Sb
I
Hg
Cd
In
Ag
Se
Au
Igneous
Rocks
2.3
2.0
.8
.8
.4 •
.4
.2
.1
.1
0.94
0.51
0.45
0.33
0.19
0.19
0.15
0.050
0.0036
Resistates
(sandstone)
0.94
0.10
0.74
1.0
1.6
0.88
0.50
0.30
1.5
0.30
0.014
4.4
0.057
0.020
0.13
0.12
0.52
0.0046
Sedimentary Rocks
Hydtolyzates
(shale)
1.1
3.S
0.54
9.0
1.9
1.3
4.2
0.28
1.6
0.29
0.81
3.8
0.27
0.18
0.22
0.27
0.60
0.0034
Precipitates
(carbonates)
0.19
0.10
0.14
1.8
0.56
0.036
0.7S
0.11
0.06S
0.07S
0.20
1.6
0.046
0.048
0.068
0.19
0.32
0.0018
'Concentration in ppm by weight.
-------
HI
I
to
i
o
o
H
>
o
en
+0.1
Hematite
Limonite
Mn oxides
Silica
Glsuconile
8.0
Cslcite
Hematite
Limonite
Mn oiides
fence
t
Ch
Peat
Cilcite
Organic
matter
Silica
Organic
matter
Stterite
Rhodochrosite
Phosphorite
Glauconite
Peat
Marcasite
-OJ
CatcKe
Organic
matter
Organic
matter
Phosphorite
Pyr«e
Silica
Calcite
Organic
. matter
+ 1.0
+03
+0.6
+0.4
+05
Eh 0
-0.4
-0.6
-03
-1.0
6 8
PH
10
12 14
Figure 6.9 Approximate position of some natural environ-
ments as characterized by Eh and pH. (From
Garrets and Christ, Solutions, Mineralst and
Equilibria. Courtesy Harper and Row)
Figure 6.71 Sedimentary associations in relation to environmental limita-
tions imposed by oxidation potential and pH. (After Krvmbcin
and Carrels. J. Ceol. £0,26.1952)
-------
EXERCISE 23
26. Arrange in order of decreasing pe (giving your reasons) the
following environments:
A. water from a small mountain stream
B. a swamp where bubbles of an odorless gas sporadically rise
to the surface
C. ground water containing 0.5 mg/1 Fe"1"1"
D. water from a swamp in Northern Canada
E. ground water smelling of hydrogen sulfide
F. pore water from a deep lake sediment
G. lake water above a thermocline
H. lake water below a thermocline
57
-------
VIII. MASS BALANCE MODELING
A mass balance is simply the sum of what was originally present
plus whatever entered the system
minus whatever left the system.
For example, the number of people in a room at any instant in
time equals the number present in the room initially plus those that
entered minus those that left.
Three major processes are considered:
1. mineral dissolution or precipitation.
+ve results indicate dissolution
-ve results indicate precipitation or loss
2. variable fluxes of C02 gas
3. the mixing of two end member waters
A. COMPOSITIONAL CHANGES
A common application in water chemistry is the determination of
the change in chemical composition of water samples between two
points along a flow path. The program calculates the amounts of
solid phases (minerals) entering (dissolving) or leaving
(precipitating) the aqueous phase. The minerals to be considered
as well as their chemical compositions must be specified by the
user on the basis of geology, hydrology or mineralogy of the
system. In addition to minerals, gases, ion exchangers and even
other solutions may also be considered. In order to solve the
equations the number of phases must equal the number of elements.
The objective in selecting phases is to provide a source or sink
for each element in the initial and final solution. Although the
calculated mass transfer for one or more phases might be zero,
indicating that the phase(s) did not participate in the reaction,
the phase(s) must still be included in order to perform the
calculations.
The inclusion of minerals whose composition can be derived by
linear combinations of other minerals in the set will produce an
error message.
Thus if calcite, magnesite and dolomite are all included, the
program will crash because CaCOg •*• MgCO3 —> CaMg(003)2
The mass balance approach can never prove that a reaction has
taken place, although it may indicate that a certain reaction
could not happen as stated.
EXAMPLE
In general terms:
Consider elements x, y and z
with concentrations in water of (x), (y) and (z)
Also consider 3 solid phases A, B and C
such that A = xz, B = xyz and C = z
58
-------
MASS BAI-ANCE
IN
>
OUT
WATER
DXSSOL.VE
COMROSITIOM
F-RECXF1.
MIXIMG
WATER
XlxlERAL-S
I SSOL.VE
<
: COMPOSITION < ——— > GASES
MATER 4*2
s >
*-M X NER Al_S
R-RECIR-.
FIGURE 13. MASS BALANCE DIAGRAMS
59
-------
The coefficients giving the number of atoms of each
element in each phase are
phases
A B C
water comp. | xz xyz2 z
(x)
(Y)
(z)
i
0
i
i
i
2
0
0
1
The mass balance for each element is then:
(x) = 1*A + 1*B + 0*C
(y) - 0*A + 1*B + 0*C
(z) = 1*A + 2*B + 1*C
or
(x) = A + B
(Y) = B
(z) = A + 2B + C
Solving for the amounts of A, B and C
B = y
A = (x) - B
C = (z) - A - 2B
B. MIXING
In addition to the determination of possible compositional
changes along a flow path the balance program may be used to
determine the composition of a water resulting from the mixing of
2 waters with or without the precipitation or solution of any
other phases. In the simplest case it may be used to calculate
the composition that could result from evaporation and
precipitation, although care must be taken to avoid the
production of a singular matrix.
C. COMPUTER CALCULATION
BALANCE is a USGS FORTRAN computer program designed to define and
quantify reactions between ground water and minerals.
To aid in producing the required formatted file used by BALANCE
another interactive program B-INPUT.EXE is used.
Note that the units used are either moles/1 or mmoles/1, it does
not matter which but they must be consistent.
The number of elements must equal the number of phases, and the
program will ask for the number of elements and then will expect
the same number of phases to be input.
60
-------
1.
There are 3 input options:
1. the difference between final and initial concentrations
or one analysis
2. the final and initial concentrations
3. a final concentration and two end members
Note: If the end member waters calculation ends up
with values <0 or >1 then an impossible mix is
indicated, and other phases must then be chosen,
e.g. if a± = 1.33 and a2 = -0.33 there is a problem!
EXAMPLES
What minerals could dissolve to give the following water
analysis and in what amounts?
mg/1
meq/1
mmole/1
Ca
32
1.6
0.8
Mg
5
0.4
0.2
S04
48
1.0
0.5
HC03
61
1.0
1.0
Consider the minerals calcite, dolomite and gypsum and CC>2 gas
(4 phases and 4 elements)
Once the analysis is converted to moles/1 or mmole/1 the next
step is to determine the coefficients for each phase. That is, the
number of input elements present in each phase. Thus, calcite has 1
Ca and 1 C; dolomite has 1 Ca, 1 Mg and 2 C; gypsum 1 Ca and IS;
CC>2-gas 1 C. Note that we are dealing with moles and that 1 mole
CO3= equals 1 mole C.
water composition
(mmole/1)
0.8 Ca
0.2 Mg
0.5 S
1.0 C
Phases
number of elements in each phase
calcite
1
dolomite
1
1
gypsum
1
CC>2 gas
Sulfur balance
gypsum = 0.5
Magnesium balance
dolomite = 0.2
Calcium balance
calcite = 0.8 - 0.2 (dolomite) - 0.5 (gypsum)
= 0.1
Carbon balance
C02 gas = 1.0 - 0.1 (calcite) - 2 * 0.2 (dolomite)
= 0.5
Thus the above water could be obtained by dissolving
0.5 mmole/1 gypsum
0.1 mmole/1 calcite
0.2 mmole/1 dolomite
61
-------
2.
0.5 mmole/1 C02
What proportions of the two end member waters are necessary and
what minerals would dissolve or precipitate to give the
following water composition. The analyses are given in
mmoles/1.
Fina:
7
9
32
1
L
Ca
Mg
C
Mix
Init 1
Wl
8
6
28
1
Init 2
W2
9
10
38
1
Calcite
C
1
0
1
0
Dolomite
D
1
1
2
0
Mass balance for Ca
7 = 8W1 + 9W2 + C + D (1)
Mass balance for Mg
9 = 6W1 + 10W2 + D (2)
Mass balance for C
32 = 28W1 + 38W2 + C + 2D (3)
Mass balance for end members
1 B HI •+ H2 (4)
Thus
from (4) W2 •
substitute in (2)
9 = 6W1 + 10 - 10W1 + D
or D B 4W1 - 1
Substitute (5) and (6) in (1) and (3)
(1) 7 = 8W1 + 9 - 9 Wl + 4W1 - 1 + C
-1 = 3W1 + C (7)
(3) 32 = 28W1 + 38 - 38W1 + 8W1 - 2 + C
-4 = -2W1 + C (8)
1 - Wl
(5)
(6)
Subtracting (8) - (7)
3 = 5W1
or Wl =
W2 =
D =
0.6
0.4
1.4
C = -2.8
Therefore final water could result from mixing 60% of water 1
and 40% of water 2, dissolving 1.4 mmole/1 dolomite and
precipitating 2.8 mmoles/1 calcite.
62
-------
EXERCISES 24 & 25
23. Calculate by hand the amounts of minerals which when dissolved
would give a water of the following composition.
Na K Ba Cl HCOo
mg/1 46 20 7 71 37
BaCC>3 is witherite, NaHCOg is nahcolite
24. Three water sample are thought to be related by mixing. Verify
or negate this hypothesis.
Na K Ca Mg HCOo S04 Cl
1. mg/1 5 .4 12 1 18 20 7
2. mg/1 30 8 61 61 20 4
3. mg/1 22 6 8 1 48 33 5
In this example two end-member waters mix in unknown proportions
and, in addition, phases dissolve and precipitate to produce a final
water. The two initial waters are treated exactly like other phases
and ai is the fraction of solution 1 and a2 is the fraction of
solution 2, which combine, along with mineral reactions, to produce
the final solution. An additional equation is automatically included
to ensure that the 2 fractions are equal to I.
i.e. a^ + &2 = 1*
As a result the number of phases that can be included in the
calculations (other than the solutions) is the number of elements
minus 1.
In this example you may want to consider ion exchange;
NaX + Ca++ — > 2Na+ + CaX
In this case the coefficients are, Na =2, Ca = -1
That is, two Na ions are added to the water for every Ca removed.
63
-------
XI. WATER GEOCHEMISTRY - SELECTED BIBLIOGRAPHY
Drever, J. I., 1988. The Geochemistry of Natural Waters. Second
edition. Prentice Hall. 438 p.
Eriksson, E., 1985. Principles and Applications of
Hydrogeochemistry. Chapman and Hall. 187 p.
Faust, S. D. & O. M. Aly, 1981. Chemistry of natural waters. Ann
Arbor Science. 400 p.
Garrels, R. M. & C. L. Christ, 1965. Solutions, Minerals &
Equilibria. Freeman, Cooper & Company. 450 p.
Garrels, R. M. & F. T. MacKenzie, 1967. Origin of the chemical
compositions of some springs and lakes. In: Equilibrium concepts in
natural water systems. Am. Chem. Soc. Ser. 67, p. 222-242.
Gibbs, R. J., 1970. Mechanisms controlling world water chemistry.
Science 170, p. 1088-1090.
Goldschmidt, V. M., 1954. Geochemistry. Clarendon Press. 730 p.
Hem, J. D. 1985. Study and Interpretation of the Chemical
Characteristics of Natural Water. Third edition. U. S. Geological
Survey Water-Supply Paper 2254. 264 p.
Krauskopf, K. B., 1979. Introduction to geochemistry. Second
Edition. McGraw-Hill Book Co. 617 p.
Krumbein, W. C. and R. M. Garrels, 1952. Origin and classification
of chemical sediments in terms of pH and oxidation-reduction
potentials. The Journal of Geology, v.60, p. 1-33.
Levinson, A. A., 1974. Introduction to exploration geochemistry.
Applied Publishing Ltd. 614 p.
LLoyd, J. W. & J. A. Heathcote, 1985. Natural Inorganic
Hydrochemistry in Relation to Groundwater: An introduction.
Clarendon Press. 297 p.
Mason, B. & C. B. Moore, 1982. Principles of Geochemistry. John
Wiley & Sons. 344 p.
Parkhurst, D. L., L. N. Plummer and D. C. Thorstenson, 1982. BALANCE
- A computer program for calculating mass transfer for geochemical
reactions in ground water. U.S. Geological Survey, Water-Resources
Investigations 82-14. p.
Perel'man, A. I., 1986. Geochemical barriers. Applied Geochemistry,
v. 1, p. 669-680.
iper, A. M., 1944. A graphical procedure in the geochemical
interpretation of water-analyses. Amer. Geophys. Union Trans., v.
25, p. 914-923.
64
-------
Plummer, L. N., B. F. Jones & A. H. Truesdell, 1976. WATEQF- a
FORTRAN IV version of WATEQ, a computer program for calculating
chemical equilibrium in natural waters. U. S. Geol. Survey Water
Resour. Invest. 76-13, 73 p.
Rankama, K. & T. G. Bahama, 1950. Geochemistry. University of
Chicago Press. 912 p.
Stumm, W. and J. J. Morgan, 1981. Aquatic Chemistry: An introduction
emphasizing Chemical Equilibria in Natural Waters. Second edition.
Wiley-Interscience. 780 p.
Thurman, E. M., 1985. Organic Geochemistry of Natural Waters.
Martinus Nijhoff/DR W. Junk Publishers. 497 p.
Truesdell, A. H. and B. F. Jones, 1974. WATEQ, a computer program
for calculating chemical equilibria of natural waters. Jour.
Research U. S. Geol. Survey v. 2, p. 233-248.
65
-------
IT!
MG/L .
SODIUM 5.0" 4.8 8.3 5.4
POTASSIUM 0.5 ..1.1 0.9 1.2
CALCIUM 0.6 19 33 1.5
MAGNESIUM 0.5 0.9 1.5 0.6
CHLORIDE 89 10 7
SULFATE 4544
ALKALINITY 2 47 85 7
SILICON . 1.8 3.3 3.4 2.4
TABLE IV
-------
mm O
O
lO
c/j
N>
MW-6
PW to OW-1 is
OW-1 to OW-2 is
PW to OW-2 is
35 feet
15 feet
50 feet
ESTIMATED EXTENT
OF GROUNWATER
CONTAMINATION PLUME
STREAM
PW to MW-4 is 190 feet
MW-4 to OW-3 is 60 feet
PW to OW-3 is 250 feet
PW to OW-4 is 15 feet
OW-4 to OW-5 is ^Wfee
OW-5 to OW-6 is 65 feet
PW to OW-6 is 100 feet
• MWM MONiTQRWG WELL
• PW , PUMRfNG WELL
A OW-M O0SERVAT
-------
29
28'
27'
EXPLANATION
•
Sampling point
75
tinei of «qoo/
above sea /ere/,
in mefers
0 10 20 30 40 50 Km
i i •_ L—i—•
83
-------
TABLE 1
Standard chemical analyses of water from the FloriJan aquifer. Wells are listed from north to south
Milligrams per liter
Well
location
Ocala 4
Wildwood 2
Grovel and
Polk City
Fort Meade
Wauchula
Arcadia
Cleveland
V}/VU
interval, Temperature
meters °C
30-115
39-82
40-180
6-172
127-291
1 14-245
100-151
39-152
24.5
23.8
23.7
23.8
26.6
25.4
26.3
26.7
Si02
10
10
11
0.2
16
18
31
18
c.«
96
51
42
34
56
66
106
114
-
15
2.6
4.1
5.6
17
29
60
82
-
7.8
4.7
3.6
3.2
6.1
8.3
21
283
K+
1.0
0.2
0.5
0.5
0.7
2.0
3.7
9.6
Field
HCO,
175
150
143
124
163
168
206
145
so;.
148
3.2
1.6
2.4
71
155
344
216
ci-
11
8.0
6.5
4.5
9.0
10
28
655
F-
0.3
0.2
—
0.1
0.4
0.7
2.2
0.9
Dissolved
solids,
residue
N0« at 180'C
1.6
3.8
0.1
O.I
0.1
—
—
0.1
420
158
148
138
272
392
762
1600
Field
PH,
±0.02
7.50
7.59
7.80
8.00
7.75
7.69
7.44
7.51
-------
nesses ot
e presence o
for the
i contrast,
of the
• jor in the
raulic
circulation
• within a
i, the respective
•scharge to
ited near the
ove river
NGS
that range
ew gal/min
s 30 and 34.5.
jure 2 and
;gs become
• high river
10 ft3/sec
of the
in the
1 and discharge
vere first
ange (1956,
springs
Structural
Control
in
ro
e
(O
IO
O
to
to
10
Sompled Spring
®—
River Mile
Rim of Canyon
U^
0
Fault
-M-
Syncline
v*
Dtp, Degrees
0
I
Miles
>
North
,*VX':
'rt*
&
^
\
y
Fence Fault
-------
Table 1. Location, Estimated Discharge, and Geologic Setting of Springs Sampled
August 8, 1979, in the Vicinity of Vasey's Spring, Arizona
Approx.
No* Name River Mile"
1
2
3
4
5
6
7
8
E. Fence No. 1
E. Fence No. 2
W. Fence No. 1
W. Fence No. 2
Diagonal
Vasey's
Hanging No. 1
Hanging No. 2
30.1
30.2
30.2
30.7
30.9
31.9
34.4
34.5
Side of
Colo. River
East
East
West
West
West
West
West
West
Estimated
Discharge
(gal /m in)
500
6500
20
30
900
2500
30
10
Producing
Unitc
Mrm
Mrm
Mrm
Mrm
Mrm
Mrm
Mrw
Mrw
Structural
Control
Fence Fault
Fence Fault
Fence Fault
Fence Fault
Joint-Fence Fault
Joint
Joint
Joint
a Numbers are identical to numbers used on Figure 2.
b Distance measured from Lee's Ferry, Arizona.
c Mrm = Mooney Falls Member, Redwall Limestone. Mrw = Whitmore Wash Member, Redwall Limestone.
Nomenclature from McKee and Gutschick (1969).
Table 2. Temperatures and Concentrations of the Major Cations and Anions in the Water from
Springs in the Vicinity of Vasey's Spring, Marble Canyon, Arizona1
Cations (meq/l)
Anions (meq/l)
No.1
Name
Temp.
Ca Mg
Na
Total
K Cations
Cl
Total
F SO4 CO3 HCO3 Anions
1
2
3
4
5
6
7
8
E. Fence #1
E. Fence #2
W. Fence #1
W. Fence #2
Diagonal
Vasey's
Hanging #1
Hanging #2
69
70
71
70
71
62
65
64
7.49
7.49
5.99
2.10
1.60
2.00
2.50
2.35
3.45
3.54
3.54
1.73
1.56
1.56
1.56
1.56
10.87
11.31
8.70
0.61
0.09
0.06
0.04
0.07
0.56
0.64
0.49
0.04
0.03
0.02
0.03
0.02
22.37
22.98
18.72
4.48
3.28
3.64
4.13
4.00
9.90
10.43
7.92
0.51
0.06
0.07
0.07
0.07
0.01
0.02
0.01
0.01
0.01
0.02
0.05
0.00
0.03
0.03
0.02
0.01
0.01
0.01
0.01
0.01
4.63
5.17
3.70
0.45
0.17
0.27
0.41
0.72
0
0
0
0
0
0.40
0
0
8.89
9.06
7.93
3.80
3.31
3.24
3.56
3.56
23.46
24.71
19.58
4.78
3.56
4.01
4.10
4.36
es collected August 8, 1979. Chemical analyses byJ-ision of Laboratories, Wyoming Department of Agricuhure,
amie, Wyoming.
-------
T
o
t
a
1
H
a
r
d
n
e
s
s
Na
Ca
+
Mg
Permanent
Hardness
Temporary
Hardness
Cl
S04
C03
HC03
Alkalinity
T
o
t
a
1
H
a
r
d
n
e
s
s
Na
Ca
MB
Temporary
Hardness
Cl
S04
C03
HC03
Alkalinity
-------
WATEVAL
DRIVE
MEMORY
^V \
\\1
' lUIMU
X/FILE
SCREEN
B:
C:
T ANALYSIS
KEYBOARD
WATEVAL
OUTPUT
RAM - MEMORY - DEFAULT
FILE
SELECT OPTION
CHOOSE DRIVE
NAME FILE
SAVE EACH ANALYSIS
WATEVAL
INPUT
KEYBOARD - DEFAULT
RAM
SELECT OPTION
CHOOSE SAMPLE
WATEVAL
INPUT
FILE
SELECT OPTION
CHOOSE DRIVE
SELECT FILE
CHOOSE SAMPLE
WATEVAL
OUTPUT
SAVE RAM TO FILE
SELECT OPTION
CHOOSE.DRIVE
NAME FILE
SAVE RAM
CLOSE FILE
RESET OPTION
-------
CHLORIDE
Cl
1
I
Na Na Na
halite sink source
reverse silicates
exchange
cation
exchange
s
SULFAT
[E
r
I
Ca Ca Ca
source sink
gypsum
silicates precip.
carbonates exchange
SODIUM
Na Si Si Si
Ab •> M Ab - K Or - K + M
CALCIUM
la
Bi
Cc
An
Si Si Si
Di tremolite
no clay .. K -» M
la
SODIUM
1
Si
source
Fe/Mg
silicates
l'
Si
Na
source
cation
exchange
BICARBONATE
1
1
Bi Ca Si Si
1
Si
calcite albite diopside olivine
k-spar
-------
DAY 2
UNSATURATED
ZONE
MODELING
RITZ
CHEMFLOW
CHEMRANK
-------
Unsaturated Zone Modeling
Introduction to Models
Water Movement in Unsaturated Soils
- Introduction
- Infiltration: Film of Physical Model from
Washington State Univ.
- Infiltration: Simulation Using CHEMFLO
- Redistribution: Simulation using CHEMFLO
- Evaporation: Simulation using CHEMFLO
Water and Chemical Movement in Unsaturated Soils
- Introduction
- Non-adsorbed Chemicals Using CHEMFLO
- Steady-state Water Flow
- Transiant Water Flow
- Adsorbed Chemicals Using CHEMFLO
- Non-Uniform Initial Conditions Using CHEMFLO
Management Models:
- CHEMRANK
- RITZ
Concerns in Field Scale Use
- Assessing Validity of Assumptions Within Models
- Natural Variability within Soil
- Uncertainty in Model Parameters
-------
Some Interesting Reading Material
Garden, W.H. 1977. Historical highlight of American soil physics. Soil
Science Society of American Journal, Vol. 41, pp. 221-229.
Baveye, P. and G. Sposito. 1984. The operational significance of the
continuum hypothesis in the theory of water movement through soils
and aquifers. Water Resources Research, Vol. 20, pp. 521-530.
Donigian, Jr., A.S. and P.S.C. Rao. 1986. Overview of terrestrial processes
and modeling. lr± "Vadose Zone Modeling of Organic Pollutants", S.C.
Hern and S.M. Melancon (Eds.), Lewis Publishers, Inc.
Wagenet, R.J. and P.S.C. Rao. 1985. Basic concepts of modeling pesticide
fate in the crop root zone. Weed Science, Vol. 33, Suppl. 2, pp. 25-32.
Rao, P.S.C. and R.J. Wagenet. 1985. Spatial variability of pesticides in
soils: Methods for data analysis and consequences. Weed Science,
Vol. 33, Suppl. 2, pp. 18-24.
Rao, P.S.C., R.E. Jessup, and A.G. Hornsby. 1982. Simulation of nitrogen in
agro-ecosystems: Criteria for model selection and use. Plant and
Soil, Vol. 67, pp. 35-43.
-------
How Water Moves in the Soil
by Walter H. Gardner
Time-la pie photograph y
condenses hours of water
movement in soil into a \cw
minutes. This time reduction
helps show important principles
of water movement in different
soils. It also reveals tchat
cjjecls layers such as claypans
or coarse sands have on water
movement. Farmers should
consider these principles in
fertilizer placement and
irrigation practices . . .
scs
Part l-The Basic Concept
HOW WATHR CONTINUALLY MOVJ-S in the soil
is one of the most basic -and important agricultural
concepts.
It is from an understanding of water movement that we
learn how to solve such problems as supplying crops with
adctjuate water and nutrients.
Water itself is an important part of plants. It makes up
almost 85 percent of the fresh weight of growing plants.
Thus, water is not only a plant constituent but is a carrier
for mineral nutrients anil gases entering the plant.
Water is nearly always moving in the soil, cither as a
liquid or a vapor. In addition to moving downward follow-
ing rain or irrigation, water moves upward to cvajwrate
from the soil surface, or into plant roots and eventually
into the atmosphere through transpiration. Under many
conditions some water is lost from the root zone through
deep drainage. Water and water vapor can move horizon-
The Author
Walter II. Gardner is professor of soils .it Washington Sl.-ite
University, Pullman. Wash., where he specialises in the field of
soil physics. The pictures incluilccl with this article are taken
from the time-lapse motion picture, "Water Movement in Soil."
This 26-minnte. lo-niillimcter color film, with sound, was pro-
duced at Washington Stale University hy Gardner and J. C.
Hsich. More than -10 copies of (his film have hccn sold in (his
country and abroad. It may he purchased from the Washington
State University Agronomy Club or rented through numerous
audio-visual centers, or. in (he West, through the NV'SU Audio-
Visual Center.
October 1962
tally, upward or downward, depending on conditions. Only
rarely is soil water completely stationary.
Water (lows through open pores between soil particles.
In an ordinary silt loam the pore space makes up about
one-half of the soil volume. For most crops, some air must
be present in the soil pores. It must be possible for fresh
air rrom the surface to exchange with carbon dioxide laden
air from the root zone.
Soils vary as to pore size and number. Silty and clayey
soils generally have more total pore space but smaller pores
than sandy soils. And, when all of the pores are filled with
water, silly and clayey soils contain more total water than
sandy soils, simply because the heavy soils have so many-
pores. Although much of the water in soils with fine pores
is unavailable to plants, the amount availtible is still greater
than that available to plants in soils with large pores.
When a soil is near saturation, the larger the pores the
greater the rate of flow per unit of applied force. How-,
ever, when a soil is not saturated, large pores contribute
little to flow. Water moves on particle surfaces and through
the liner pores under these conditions.
Two forces cause liquid water to move through these
soil pores: Gravity and adhesion. Gravity causes a down-
ward pressure on water. This force is most important in
saturated soil. The second force, adhesion, is due to the
attraction of soil particle surfaces for water and becomes
important in misaluntied soil. Adhesion—together with co-
hesion, which causes water molecules to hang together—is
responsible for water rise in capillary tubes and the ab-
-------
1 UNIFORM OR HOMOGENEOUS SOIL—Water
added to the center of this dry, homogeneous soil.
Note that water moves out almost equally in all directions.
Gravity has small effect as seen by the slightly greater
downward wetting. This illustrates wator mi>vctiu'iit under
iintnlurnlcd conditions where there is no free water in the
soil. Under inttiraleil conditions, or as .saturation is ap-
proached, gravity begins to play a much greater role in
water movement.
r-;,-, • , .- '•••••• -
*•'.!•-•.' ' • . • • •*" ~
J
O CI.AYI'AN I.AYKU—When water readies a claypan.
•^ this layer with very line pores resists water lln«
due to Ihc liny transmitting channels. Although clatpuns
(In wet up, they transmit water so slowly that »ali-r lahli-s
often build up above llu'in. Some plow pans would act
similarly, creating inlillraliun problems.
il
sorptive properties of blotting paper nnd other porous
materials.
When soil is very wet the gravitational force predomi-
nates. But in soil in which most crops grow, the major
force causing water to move is due to adhesion.
Water moves until these forces are balanced in the soil.
Water films on soil particles will be uniform throughout
any homogeneous soil, except for some vertical differences
that exist because of gravitation. If the soil is not uniform
or homogeneous, water is retained most strongly by those
portions of the soil having the smallest pores.
In stratified soil—that in which various "layers" exist—
water flow is greatly affected by the sizes of pores in strata
encountered by an advancing wetting-front. II fine mate-
rials are encountered, the rate of advance may be slowed
by resistance to Ilo\v in the extremely fine pores. Bui wau-r.
nevertheless, docs continue to move. 11 coarse materaU arc-
encountered, water movement stops until the soil becomes
nearly saturated. Any porosity change occurring in soil
alTects the rate of water (low.
Water retained in stratified soil for plant use is greatly
alTcctcd by the nature of the strata. Generally, then, strati-
fied soils hold more water for plant use than uniform soils
of similar nature because of the effect of porosity crum:es
on water (low.
The pictures accompanying this article show some basic
principles of water movement using artificial soil profiles.
These principles, though not always striking, may be ob-
served in your field if you take time to examine soil soon
after water has been applied.
8
Crops i Soils
-------
3 SAND LAYER—When water passes throuch a Tine
soil and reaches a layer of coarse sand it stops un-
til sufficient water accumulates to nearly saturate the
overlying fine Roil. Water will move readily through the
large pores in tlic sand only under near-saturation condi-
tions. The saturation of the overlying soil works mncli tlic
same as adding water to a piece of Moiling paper which
must become saturated before it will drip.
JUi
?> \-£f'-':; &-}'-'-\.;--. > .
4 COARSE SAND OR GRAVEL SUHS01I/—This is
the rflTi-cl mi water movement when a line soil over-
lies a coarse sand or gravel suhsoil. Note that G hours of
wetting are required before soil water moves down into
the gravel. The overlying soil must become very wet be-
fore water will move down through the large pores in the
gravel. Under these conditions, the overlying soil will hold
considerable water—up to 2 or 3 times as much as would
the same material if the coarse sand and gravel were mil
present.
U LAYER OK COARSE SOIL AGGREGATES IN KINK
vJ SOIL—Any change in soil porosity encountered by
a wetting-front affects water movement. In these three.
photographs, a layer of coarse soil aggregates acts much
the same as a layer of sand, hut with one important dif-
ference: Water can move through the interior of the soil
aggregates themselves. Hut the amount of water that
moves through the layer of soil aggregates is limited hy
the relatively small number of contacts between soil ag-
gregates. Water moves rapidly through the soil aggre-
gate layer only under saturated conditions. In this lest,
such saturated conditions were not reached.
Part II—See Next Month's Issue
Jr 1 ' *i '- ) '"^ ' :>
4. TM^»F* ~ <-._^6-»'U**£U.\*—
T~"TP*is
JL -. Jfeai
October 1962
-------
How Water Moves in the Soil
by Walter H. Gardner
The Author
Walter H. Gardner is professor ol soils
at Washington Stale University. Pullman.
Wash. The first part ol the article was pub-
lished in the October I9o: issue of CHOI'S
.v Sou., bejjinninc «n p.ij!i- 7. The author
extends credit to Robert II. Kunkvl, \VSU
hortictitturjlt.tl. win* developed the new
method lor pl.miin.c potatoes.
WAT12R IS NEARLY ALWAYS
moving in I he soil, as was pointed
out in Part J of this article. Through
time-lapse photography, .scientists art-
able to condense hours of soil-water
movement into a few minutes. Their
findings highlight important principles
that farmers can use during irrigation,
and in seed and fertilizer placement.
Part I pointed oul that when water
reaches a claypan. movement is slowed
because of small soil pores. Likewise.
when water moves through a line soil
snd reaches a coarse saTilf or gravel
layer, water movement is restricted by
the coarse layer. In fact, movement
stops until sufficient water accumulates
to nearly saturate ihc overlaying fine
soil.
Straw or organic matter layers, and
vertical mulched straw, act much the
same way as a layer of coarse sand or
soil aggregates when the mulch is no
longer exposed to the soil surface or
!o free water.
Practical applications of such re-
search can he observed. Radial, up-
ward, and downward movement of
soluble fertilizers may be followed by
VERTIC
L'SDA
Part ll-ln The Field
the use- of dye tracers. I'rom basic re-
search, loo. a new method lor planting
potatoes has been developed to take
lull advantage ol available soil mois-
ture and to insure complete welting ol
the pot.Uo hill by irrigation.
A press-wheel method places jxitato
seed pieces ju.st below the surface of an
inverted "V" shaped mound. The
usual way ol planting is to put the
seed piece in ihe center of a high,
wide ridge ol soil.
The press wheels firm the coarse
soil aggregates, reducing the size ol
the pores and allowing water to move
into the ridge. Without this compac-
tion, the coarse soil aggregates often
stop water movement into the ridge,
leaving new tubers in dry soil.
By knowing the principles of soil-
water movement, farmers often can
take advantage of new techniques that
lit their soil conditions and availability
of water.
6 VERTICAL MULCHING—Here, deep vertical chan-
nels arc cm in the soil and Tilled with chopped or-
ganic, matter. If channels remain o|icn (o the surface,
large pores in the organic nialorinl.s rc-flily lake the free
water from rain or irrigation and transmit it deeply into
I ho soil. Tin1 n. it is absorbed under nnsaturaled condi-
tions. Hut if channels arc not open to the soil surface.
vertical mulching docs little good. Organic mailer chan-
nels, therefore, should be exposed In Hie source of free
water—rain or irrigation.
Holes left in the soil by angleworms, rodents, or de-
caying crop residue behave exactly the. same as vertical
mulch channels: if they remain open to the surface and
exposed to free water, they carry water readily, lint these
holes cannot transmit water unless they arc directly con-
nected to Ihc surface or n source of free water. These
open channels or holes also serve a useful purpose under
conditions where aeration may be poor. They permit cx-
chnngc of gases between soil atmosphere and air above.
November
-------
WATUi AtVUCD TOO RAPIDLY
,-'•-•.:•;:;,£.#. Y.1
7STKAW OR ORGANIC MATTEU LAYER—A layer
or straw or other coarse organic matter acts much
the same as a layer of sand or coarse soil aggregate*.
Note how the straw plowed under and left in a layer
forms a barrier to the downward movement of water, lint
if straw is worked into the soil, this helps to promote
Rood soil aggregation and to maintain :i porous structure
in contact with applied water. Downward movement of
rain or irrigation water thus is aided. Large pores—nude
by the incorporated straw—speed downward transmission
of free water.
8 SOIL TEXTURE AND INr'ILTKATlON—Soil tex-
ture has a significant effect on water movement. In
the photo, water was applied :il a uniform rate and time
to three soils. Note that infiltration and advance of the
wetting front is more rapid in a sandy soil than in either
a loam or clav soil.
9 SOIL TEXTURE AND WATER-HOLDING CAPAC-
ITY—Clay soils will hold more lulnl water than
either loams or sands, however. In this case, the same
amount of water was applied to each soil. Note the rela-
tively smaller portion of the clayey soil re(|iiired to hold
the water compared with sand. Silt loam and clay loan:
soils arc likely to be better soils for dryland farming
than the coarser sandy soils. This is because of the larger
amount of water that can be retained in the silly and
clayey soils. Under irrigation, however, such soils are nut
as good as sandier soils because of poor water-transmit-
ting properties of heavier soils.
1 A UNEVEN SURFACE SOIL—Water penetration
J- \J into soil is a (Tec led by an uneven surface, such
as in rolling or hilly terrain. Where water is applied more
rapidly than it can infiltrate, it runs off of high spots and
accumulates in low places. Here, the greater amount or
water penetrates to greater depths. Where soils are level
or where the application rale does not exceed the infiltra-
tion rate, uniform wetting results.
10
Crops & Soil*
-------
1 *~\ CLODDY MOUNDS CUT WATER MOVEMENT—
JL L* Coarse soil thrown up into hills between irrigation
furrows is often dillicult to wet because of excessively
large pores in the soil. These pores move water slowly
under unsaturated conditions. Here, in a potato Held, soil
on tops of the hills remains dry even though water had
been present in the furrows for several days. Under these
conditions, tubers must grow in dry soil. An inverted "V"
shaped mound, compacted to reduce the pore si/.c, may help
to solve this water movement problem. •*-
n SOLUBLE FEKTILIZEKS MOVE WITH VVATf
—Direction of water movement near irrigati-
furrows is indicated by dye tracers. The movement
\vatcr and soluble fertilizers is almost radially away frr
the point of water application in the furrows. After t
wetting fronts join, direction of flow changes slightl
Above the water level in furrows, movement is upwa
toward the drier soil. Below the free water level, mo\
mcnt of soluble materials is downward. Also, water cvapc
aline from Ihc soil surface causes an upward movement
soluble materials in the soil solution.
Photo by Kun
Potassium-Supplying Power Linked to Clay in Soil
A better measure of potassium-sup-
plying power of soils now may be ob-
tained by considering total potassium
(K) of the clay fraction—in addition
to regular soil tests, according to
Michigan State University studies.
Although soils often contain 33,000
to 50,000 pounds of K per acre in the
plow layer, 90 to 98 percent is unavail-
able to plants. Most K occurs as part
of the primary soil minerals. The bal-
ance exists in two forms: Readily avail-
able and slowly available. Doth are
measured by availability to plants.
The readily-available portion, 1 to 2
percent of the total, is the immediate
source of K for plant nutrition. It is
made up of the soluble K in soil water
solution plus the K attached to. the
surface of clay and organic matter par-
ticles. This attached K often is called
exchangeable potassium, since calcium
or magnesium may replace it. Routine
soil tests measure readily-available K.
Slowly-available K, 1 to 10 percent
of the total, is an important reserve
supply of K for plants. But, soils men
November 1962
have long had great trouble in measur-
ing this form. It is thought to be
trapped in the crystal structure of clay
minerals, and is often called non-
exchangeable potassium.
As plants use readily-available K,
exchangeable K is released gradually
to the exchangeable or soluble form.
Some soils, however, release more of
it than others. And, this is an impor-
tant factor when potassium fertilizer
recommendations are made.
Rough estimates of noncxchange-
able K arc made by washing the soil
sample with a salt solution to remove
all exchangeable K. Then, the soil is
cropped for several months to deter-
mine K uptake by plants from the
noncxchangcable portion. The total of
readily-available and slowly-available
K is then estimated as the potassium-
supplying power of the soil.
In Michigan research aimed at find-
ing a more accurate measure of potas-
sium-supplying power, clay and silt
portions in samples of six soils were
separated. Samples were washed with
a magnesium chloride solution to re-
move exchangeable K and cropped
with wheat for 12 weeks.
Afterwards plants were analyzed for
K. All K found in the wheat was con-
sidered to have come from the non-
exchangeable portion—that previously
trapped in clay crystals. There was a
very close relationship between plant
uptake of K and total K of clay but
not of the silt. Silt may be an impor-
tant factor in some soils.
A better understanding of the potas-
sium-supplying power of soils now
may be obtained, when total K in the
clay fraction is known. This procedure
is much quicker and cheaper than the
long-time cropping method now used
to determine the potassium-supplying
power of soils.
Such knowledge greatly increases
the accuracy of fertilizer recommenda-
tions made from soil tests for ex-
changeable potassium.—E. C. DOLL,
M. M. MORTLAND, and K. LAVPTON,
Michigan State University, East Lan-
sing, Mich.
11
-------
-------
H =
— oo < h <
Y-C«
^'t 'Pe>4<,^-ktJ2
K =•
^ K
-------
g
0)
4J
I
o
•H
0.30-
0.10
Bulk Density (g/cm )
Cobb Loamy Sand 1.54
Cobb Sandy Loam 1.61
Teller Loam 1.67
Zaneis Loam 1.50
Port Sllty Clay 1.60
Figure 18.
40 80 120
Negative Pressure Head (cm) H^X
Soil-water characteristic curves fo- "ive Oklahoma soils,
—• r
loU
/uu
-------
Physical Characteristics of Soils
of the Southern Region-
Bethany, Konawa, and Tipton Series
D.L. Nofziger
J.R. Williams
A.G. Hornsby
A.L Wood
Project Number S-124 "Movement and Retention of Water and Solutes in Selected Southern Region Field Soils'
-------
45 CM
V*. SILT
"A
SILT CLAY /
v\ \
•W 80 70 60 50
360/
o SILT CLAY X
* SILT CLAY X
SO 40 JO ?0 10
SAND
SAND
Figure 1. Particle size distributions for Bethany soil.
-------
30
60
u
Q. 90
LU
0
120
150
1.4
i.:
1.6
i.;
1.8 1.9
BULK DENSITY, g/cm
3
Figure 2. Mean bulk density as a function of depth for Bethany soil sites.
21
-------
30
60
90
120
130
30
Q.
Ul
Q
90
120
150
30
90
120
150
BETHANY
SITE tl
30
60
90
120
150
SITE «2
SITE «3
30
60
90
120
150
/
SITE «5
.18 .24 .3 .36 .42 .48 .18 .24 .3 .36 .42 .48
.18 .24 .3 .36 .42 .48 .18 .24 .3 .36 .42 .43
.18 .24
90
120 -
150
.36 .42 .48 .13 .24 .3 .36
WATER CONTENT, cm3/cm
Figure 3. Water content profiles of Bethany soils before (open symbols) and after (solid symbols) drainage measured
by neutron scattering.
22
-------
.42
.36
.3
.24
(J
01
_,
u .36
O
O
.
.3
.34
18
48
.42
.36
.3
.24
.18
BETHflMY §1
13 cr»
43 cw
30 60
90
90 en
Meutron Scottenng
.48
.42
.36
.3
.24
i i
30 cn
.18
30 60 90 120 150 0
.48
30 60 90 120 ISO
.42
.36
.3
.24
60 cm
120 ISO ' 0
.48
30 60 90 120 150
.42
.36
.3
.24
.18
120 en
IH-HH
30 60 90 120 150 "~~0 30 60 90 120 150
NEGATIVE PRESSURE HEAD, cm
Figure 4. Soil-water desorption curves for site 1 of Bethany soil.
23
-------
.48
.42
.36
.3
.24
.18
0
.48
, .42
o
'B -36
«k
1—
z
^ -a
(_ .3
0
0
UJ .24
0 0
.48
.42
.36
.3
.24
* 'I8o
.48
.42
.36
.3
.24
.18
50
III!
30 en
•n •
Q
0 a
• U
.^^^7^^ .
4
"°\ o.
3D 60 90 120 IS
DD a a a 60 cw
"li- • i ~M
» I 1 -f
moo o * o
-
-
30 60 90 120 15
I i i I
120 CM
V-5 "-fl
.n-t-t-H
: + « * ****^
-*
1 30 60 90 120 15
NEGATIVE PRESSURE HEAD, cm
Figure 5. Soil-water desorption curves for site 2 of Bethany soil.
24
-------
.42
.36
.3
.24
.18
0
.48
co .42
0
co
w .36
V-
LU
O
0
UJ 94
H~ " *-
3
.48
.42
.36
.3'
.24
.18
IIII
BETHANY §3
15 cn
£H^. •
. ^^rj-ssj^.
-
30 60 90 120 I!
•
oo o 45 cn
DO D D
++ + -t-fc^^.^
till
30 60 90 120 1!
iiii
90 cn
U—U-J
-+V* + V>^SH.
.°° 0 0 0
IIII
) 30 60 90 120 1
.to
.42
.36
.3
.24
.18
>0 0
.48
.42
.36
.3
.24
.18
SO G
.48
.42
.36
.3
.24
.18
JO C
IIII
30 cn
:is s 8 :
_^-*^~^ .
-%
30 60 90 120 131
iiii
60 cn
m 9m
/ V*+
30 60 90* 120 15
iiii
120 cn
JH-H-i
- ** ^ **'
+ Neutrr •, Scattering
So? c&r«
iiii
1 30 60 90 120 13
NEGATIVE PRESSURE HEAD, cm
Figure 6. Soil-water desorption curves for site 3 of Bethany soil.
25
-------
U
.48
.42
.36
.3
.24
.18
.48
.42
BETHANY »4 -
15 CM
.42
.36
.3
.24
30 en
30 60 90 120 150
30 60 90 120
CO
u .36
UJ
o
0£
.3
.24
.18
•o-r
45 CM
I
.48
.42
.36
.3
.24
60 en
.42
.36
.3
..'24
.18
30 60 90 120 150 'l 0
.48
30 60 90 120 150
Neutron Scattering
Cores 90
.42
.36
.3
.24
.18
120 en
30 60 90 120 150 "0 30 60
NEGATIVE PRESSURE HEAD, cm
Figure 7. Soil-water desorption curves for site 4 of Bethany soil.
26
90 120 150
-------
.42
.36
.3
.24
.18
o-i-
BETHftNY «5 -
15 cr>
30 60 90 120
.48
.42
.36
.3
.24
.18
.42
PO
o .36
o
0
_
.3
-24
.18
.48
.42
.36
.3
.24
,18
•~^.
O O 0 O O O
45 en
30 60 90 120 150
.42
.36
.3
.24
.18
D a
•f Neutron Scattering
Corzs
-------
.48
.42
.36
.3
.24
.18
I
.48
.42
i
co
o .36
CO
E
o
LU
O
<_) •
.42
.36
.3
.24
.18
BETHANY *6
15 en
45 on
30 60 90 120
90 crt
I! * $ * •
MT~T^T-T-.
Scot-ten ng
.42
.36
.3
.24
.18
30 60 90 120 150 0
.48
i i
.42
.36
.3
.24
.18
.42
.36
.3
.24
.18
30 cn
30 60 90 120
60 ct'i
150 0 30 60 90 120 150
.48
iLJfi B •
120 cn
30 60 90 120 150 "0 30 60 90 120 15u
NEGATIVE PRESSURE HEAD, cm
Figure 9. Soil-water desorption curves for site 6 of Bethany soil.
28
-------
I I
c •
•' •
"&•
a
10
1-J
o
3
O
.01
.00!
. .1.101
10
.01
. frr.if.1 1
y\ *('. "in \<*f\
•
r
m
.01
.001
30 60
10
.01
.001
NEGATIVE PRESSURE HEAD, cm
Figure 10. Hydraulic conductivity as a function of negative pressure head for Bethany soil. '
29
-------
10
.001
.0001
.001
.0001
1 1
«
••<*<
— .01
S -001
.0001
.1
.01
.001
.29
.44 .48
10
.01
.001
.0001
?0-liO en
.32 .36 .4 .44 .48
WATER CONTENT, cn3/cm3
. 3i
SITE
1 O
3 «
3 a
11-30 c«
10
.1
.01
.0001
60 -.*5 CP.
.4 .44
. 1
.01
.001
.0001
.23
*
.4 .44 .48 .28 .3? . 3t .4
Figure 11. Hydraulic conductivity as a function of volumetric water content for Bethany soil.
30
-------
TADLE 8.1 Volumetric w»t»r content of foil corts
tt ••ltet*d pr«§«ur« htidt for fit* 1
of B* thany toi1.
PRESSURE
HEAD
cm
DEPTH
_
-
-
-
•
-
•V
-
-
-
-
-
_
-8
-8
-8
-8
-8
-8
16
16
16
16
16
16
36
36
36
36
36
36
56
-56
-
-
-
-
_
-
-
56
56
56
56
76
76
76
-76
-
-
_
-
-
-
-
-
-1
-1
-1
-1
-1
-1
76
76
96
96
96
96
96
96
26
26
26
26
26
26
WATER
CONTENT
cm /em
PRESSURE
HEAD
cm
: 15 cm
.0
.0
.0
.0
.0
.0
. t
. 1
. 1
. 1
. 1
. 1
. 0
. 0
.0
.0
. 0
0
. 3
3
. 3
.3
.3
.3
.0
0
.0
.0
.0
0
. 0
. 0
.0
.0
.0
. 0
.0
. 0
. 0
. 0
.0
. 0
.361
.386
.372
.377
.282
.370
.361
386
.372
.375
.277
.370
.361
. 386
.371
.373
.276
.367
.354
.377
.361
. 373
. 267
.358
.341
359
.348
.348
.253
.343
.328
. 343
.336
.336
.240
.328
.314
.324
.322
.320
.240
.312
w
-
-
•»
-
-
_
-
-
-
-
-
_
-
-
-
-
-
-I
-I
-1
-1
-1
-1
-5
-5
-5
-5
-8
-8.
-8.
-8 .
-8
-8
16 .
16 .
16.
16.
16.
16.
55
55 .
55.
S3
55.
55 .
96 .
96 .
96.
96 .
96.
96 .
56.
56.
56 .
56.
56.
56 .
10.
10.
10.
10.
WATER
CONTENT
c.3/e.3
PRESSURE
HEAD
em
30 cm
9
9
9
9
9
9
4
4
4
4
4
4
6
6
6
6
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.452
.384
. 443
.402
.324
.281
.412
.372
.434
.397
.321
.273
.365
.345
399
.371
.290
247
.348
.336
.385
.360
.271
.238
.340
.330
.377
.353
.257
.222
300
.308
.333
.335
*
-
-
-
-
-
..
.
-
-
.
-8.
-8.
-8.
-8.
-8 .
-8.
16.
16.
16.
16.
16.
16.
56 .
56 .
56 .
56.
56.
-56.
_
.
-
.
-
-
-1
96 .
96.
96 .
96.
96.
96.
56 .
-156 .
-1
56 .
-156
-156 .
-1
-5
-5
-5
-5
-
$6.
10.
10.
10.
10.
WATER
CONTENT
em /cm
45 cm
0
0
0
0
0
0
0
0
0
0
0
0
t
0
0
0
0
0
0
0
0
0
0
.372
.441
.369
.405
.423
.395
.372
.441
.369
.405
.420
.395
.365
.420
.361
.396
.411
.384
.356
.403
.354
.389
.399
.378
.350
.379
.348
.384
.386
.372
.341
. 340
.343
.372
94
-------
TABLE 8.1 Continued
PRESSURE
HEAD
cm
DEPTH: 15
-156 .2
-15* . 2
-154 . 2
-156.2
-156 .2
-156.2
PRESSURE
HEAD
em
DEPTH: 60
-8 . 0
-8 .0
-8 .0
-8 .0
-8.0
-8 . Q
-16 . 1
-16.1
-16.1 '
-161
-16 . I
-16.1
-56 .0
-56 . 0
-56 .0
-56. 0
-56 .0
-56. 0
-75 .9
-75. ?
-75 . ?
-75. 9
-75 . 9
-75. 9
-96 .0
-96.0
-96 .0
-76.0
-96 .0
-96.0
WATER
CONTENT
3 3
cm /cm
cm
.301
.306
.308
.304
.240
.296
WATER
CONTENT
3, 3
cm /cm
cm
.361
.361
.409
.369
.361
.412
355
.368
.400
359
.355
.401
.350
.354
.394
.351
.353
.394
.348
.350
. 391
.347
.353
. 392
.346
.347
.389
.344
.352
.390
PRESSURE
HEAD
em
PRESSURE
HEAD
cm
- .0
- .0
- .0
- .0
- .0
-8.0
-16. 3
-16.3
-16 . 3
-16 . 3
-16 .3
-16 . 3
-56.0
-56 .0
-56 .0
-56 .0
-56.0
-56 .0
-76 .0
-76 . 0
-76 . 0
-76 .0
-76 .0
-76.0
-96 . 0
-96 .0
-96.0
-96. 0
-96.0
-96 . 0
WATER
CONTENT
3 3
cm /cm
30 cm
WATER
CONTENT
3, 3
cm /cm
90 cm
.397
.396
.375
.377
.388
.380
. 392
.383
371
. 372
. 382
.374
. 379
.376
.361
.368
.377
.368
.372
.373
. 357
. 366
.375
366
.368
.370
.353
.364
.374
.364
PRESSURE
HEAD
cm
45
PRESSURE
HEAD
cm
120
- .0
- . 0
- .0
- .0
- .0
- .0
-16 .0
-16.0
-16 .0
-16 . 0
-16.0
-16. 0
-36 . 0
-36.0
-36 .0
-36.0
-36.0
-36.0
-56.0
-56 . 0
-56 .0
-56.0
-56 . 0
-56 .0
-76. 1
-76. 1
-76.1
-76. 1
-76. 1
-76. 1
WATER
CONTENT
3 3
cm /cm
cm
WATER
CONTENT
3, 3
cm /cm
cm
.425
.395
.410
.422
.382
.392
.405
.391
.401
.411
.376
.390
.403
.388
.407
.407
.374
.389
.401
.383
.403
.402
372
.388
.397
.379
.399
.398
.369
.383
95
-------
TABLE 8.1 Continued
PRESSURE
HEAD
cm
WATER
CONTENT
3, 3
cm /ca
PRESSURE
HEAD
WATER
CONTENT
3, 3
cm /ca
PRESSURE
HEAD
WATER
CONTENT
CB /ca
DEPTH: 40 em
»0 ca
120 ei
154 .0
154.0
154 0
154.0
154 .0
154 . 0
.343
.342
.384
.340
.350
.387
163. 0
143.0
143 . 0
163 0
143.0
143.0
.354
.361
.343
.354
. 367
354
-94 .0
•96. 0
-94 .0
•94 . 0
-94 . 0
•94.0
.394
.375
.394
394
.344
.380
•510.0
•510. 0
•510 .0
•5100
.341
.385
.373
.330
•510.0
•510.0
•510.0
•510.0
.345
.334
.320
.331
•155
•155
•155
•155
-155
•155
•S10
•510
•510
-510.0
.385
.345
.387
.383
.357
.370
.324
.340
.363
.357
96
-------
TABLE 8.2 Volumetric water content of toil cores
at (elected pressure heads for lite 2
of Be thany toil.
PRESSURE WATER
HEAD CONTENT
cm cm ten
DEPTH:
-8.
-8.
-8 .
-8 .
-8 .
-8 .
-14.
-14.
-14.
-U.
-14.
-U
-34 .
-34
-34 .
-34
-34 .
-34
-54 .
-54.
-54 .
-54.
-54 .
-54.
-74 .
-74.
-74 .
-74
-74 .
-74.
-94 .
-94.
-94 .
-94
-94 .
-94.
-1 24 .
-124 .
-124 .
-124.
-124 .
-124
0
0
0
0
0
0
1
1
1
1
1
I
0
0
0
0
0
0
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
IS cm
.347
.284
.349
.374
.377
.385
. 347
284
.349
.374
.377
385
.343
.284
.349
.361
.340
. 372
. 352
.282
. 337
. 344
.338
348
.340
. 275
.325
.331
.323
.342
.332
.249
.314
. 320
309
.324
.322.
249
.305
304
.294
.309
PRESSURE VATER
HEAD CONTENT
cm cm /cm
-8
-8
-8
-8
-8
-8
-14
-14
-14
-14
-14
-14
-55
-55
-55
-55
-55
-55
-94
-94
-94
-94
-94
-94
-154
-154
-154
-154
-154
-154
-510
-510
-510
-510
30
. 9
. 9
.9
.9
. 9
.9
.
.
.
•
.4
4
.4
.4
.4
.4
.0
.0
.0
.0
. 0
.0
.0
. 0
.0
0
.0
.0
. 0
. 0
.0
. 0
cm
.413
.412
.418
.391
.219
.285
. 402
.404
. 409
.388
.217
.282
383
.375
. 380
343
.195
.243
.372
. 342
347
.351
. 184
.251
344
.351
.354
.340
. 177
.244
.334
.322
334
305
•
PRESSURE VATER
HEAD CONTENT
3, 3
cm cm /cm
-8
-8
-8
-8
-8
-8
-14
-14
-14
-14
-14
-14
-54
-54
-54
-54
-54
-54
-94
-94
-94
-94
-94
-94
-154
-154
-154
-154
-154
-154
-510
-510
-510
-510
45
0
.0
. 0
. 0
.0
. 0
.
,
.
.2
.0
.0
.0
.0
.0
.0
. 1
0
.0
. 0
.0
.0
.0
.0
0
.0
. 0
cm
.443
.440
.459
.459
.479
.454
.443
.440
.459
.459
.471
.454
445
434
.447
.458
.445
.449
.429
.429
.434
449
.444
.438
.415
.420
.423
.435
.432
.427
.405
.392
.389
.401
97
-------
TABLE 8.2 Continued
PRESSURE WATER
HEAD
ea
DEPTH:
-ISA .
-ISA.
-154 .
-154 .
-154
-154 .
2
2
2
2
2
2
CONTENT
3 3
CB /ca
IS CB
.311
.269
.295
.2?2
.281
.273
PRESSURE WATER PRESSURE WATER
HEAD CONTENT HEAD CONTENT
33 33
CB CB /CB CB CB / CB
30 CB 45 CB
PRESSURE WATER
HEAD CONTENT
3, 3
CB CB /CB
DEPTH
-
.
-
-
-
. -8
-14
-14
- 14
-14
-14
-14
-54
-54
-54
-54
-54
-54
-75
-75
-75
-75
-75
-75
-94
-96
-94
-94
-94
-94
: 40
. 0
.0
.0
. 0
0
. 0
1
. 1
. 1
. 1
. 1
. 1
. 0
.0
.0
.0
.0
. 0
. 9
9
. 9
. 9
. 9
. 9
. 0
.0
.0
.0
. 0
. 0
CB
.108
.425
.440
421
348
.413
404
415
453
.413
348
403
400
.410
449
408
.347
.399
.398
. 408
.447
404
.347
.398
397
.405
.444
. 404
.347
.394
PRESSURE WATER
HEAD CONTENT
3, 3
CB CB /CB
- .
- .
•^
- .
- .
-
-14 .
-14
-14 .
-14
-14 .
-14
-54 .
-54.
-54.
-54 .
-54
-54
-74.
-74
-74
-74 .
-74
-74.
-94.
-94.
-94.
-94 .
-94 .
-94.
90
0
0
0
0
0
0
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
ca
347
.371
.377
.397
.404
344
361
348
372
.385
.392
358
357
.362
.363
377
. 386
354
355
340
360
375
.385
353
354
.358
.358
.373
394
352
PRESSURE WATER
HEAD CONTENT
CB CB /CB
-8
•8
-1
-8
-8
-8
-16
-16
- 16
-16
-16
' -16
-36
-36
-36
-36
-34
-36
.-54
-56
-56
-56
-54
-56
-74
-74
-74
-74
-74
-74
120
0
.0
.0
0
0
. 0
.0
. 0
0
.0
.0
0
.0
.0
. 0
0
0
0
.0
.0
0
.0
. 0
. 0
. 1
. 1
. 1
. 1
1
. 1
CB
.38}
.373
.394
.402
394
385
.383
.372
.393
.395
393
.383
381
.371
.390
.394
.391
.382
.380
.371
.389
393
390
.381
374
.370
.384
.392
.388
.380
98
-------
TABLE 8.2 Continued
PRESSURE WATER PRESSURE WATER PRESSURE WATER
HEAD CONTENT HEAD CONTENT HEAD CONTENT
3, 3 3, 3 33
ca cm /ca ea ca 'cm ca ea /cm
DEPTH: 60 ea ?0 ea 120 ea
-154.0 .392 -U3.0 .346 -94.0 .373
-154.0 .399 -143.0 .330 -94.0 .348
-154.0 .441 -143.0 .348 -94.0 .383
-154.0 .398 -143.0 .344 -94.0 .391
-154.0 .344 -143.0 .374 -94.0 .384
-154.0 .391 -143.0 .344 -94.0 .378
-510.0 .341 -510.0 .344 -155.9 .344
-510 0 .345 -510.0 .325 -155.9 .343
-510.0 .425 -510.0 .325 -155.9 .374
-510.0 .372 -510.0 .334 -155.9 .383
-155.9 .379
-155.9 .372
-510.0 .354
-510.0 .349
-510.0 .350
-510.0 .357
99
-------
TABLE 8.3 Volumetric water content of soil core*
at selected pressure heads for site 3
of Be thany soil.
PRESSURE WATER
HEAD CONTENT
ea ca /ca
^
DEPTH
-8
-8
-8
-8
-8
-8
-14
-14.
-14
-14.
-14
-14.
-34
-34.
-34
-34
-34
-34.
-54
-54
-54
-54
-54
-54
-74
-74
-74
-74
-74
-74
-94
-94
-94
-94
-94
-94
-124
-124
-124
-124
-124
-124
: 15
.0
.0
.0
.0
.0
0
1
1
1
1
. 1
1
0
0
0
0
0
o
.3
.3
. 3
3
.3
. 3
.0
.0
.0
.0
0
0
.0
0
.0
0
0
.0
.0
. 0
.0
.0
.0
.0
_ —
ca
.372
.343
.349
.343
.378
.344
.344
.343
.349
.343
.378
.344
.359
.342
.342
.340
.373
.357
.343
.349
.347
. 331
.341
. 344
.328
.334
.334
.321
.346
.327
.314
324
.323
. 31 1
334
. 315
.302
.311
.310
.301
.318
.301
,.,
PRESSURE WATER
HEAD CONTENT
3, 3
ca ca /ca
— ^ — ~ *~
-8
-8
-8
-8.
-8
-8.
-14.
-14 .
-14
-14.
-14
-14.
-55
-55.
-55
-55.
-55
-55
-94
-94
-94
-94
-94
-94
-154
-154
-154
-154
-154
-154
-510
-510
-510
-510
30
9
9
9
9
.9
9
4
4
4
4
.4
4
4
4
4
4
4
4
.0
0
.0
0
.0
0
.0
.0
.0
.0
.0
0
.0
0
.0
0
II.
ca
.399
.403
.394
.405
.234
.194
.391
.401
. 389
.401
.225
.190
.370
.392
.378
.388
. 199
175
.340
.380
.349
.377
. 184
. 144
.354
374
.342
349
. 174
.158
.329
.349
342
.338
PRESSURE WATER
HEAD CONTENT
3, 3
ca cm /ca
-8.
-8
-8 .
-8.
-8.
-8.
-U.
-14.
-14 .
-14.
-U .
-14.
-54.
-54.
-54.
-54.
-54
-54.
-94
-94.
-94
-94 .
-94
-94.
-154
-154
-154
-154
-154
-154
-510
-510
-510
-510
15
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
0
1
1
I
1
1
1
.0
0
.0
.0
. 0
0
.0
0
.0
0
ca
445
.421
.384
483
.425
410
.445
.421
.384
483
.425
.410
442
.421
.384
.474
425
.408
431
.421
.383
. 440
.417
. 399
.419
.415
.374
.448
.407
. 391
.384
.384
343
.389
«
100
-------
TABLE 8.3 Cont tnu«d
PRESSURE WATER
HEAD CONTENT
3 3
ea CB /CB
DEPTH: IS ca
-154.
-ISA.
• 156 .
-134.
-154 .
-156.
.288
.299
.298
292
.301
.292
PRESSURE WATER PRESSURE WATER
HEAD CONTENT HEAD CONTENT
3, 3 3, 3
CB CB /cm ca cm /cm
30 ea 45 ea
PRESSURE WATER
HEAD CONTENT
ca ca /ca
DEPTH:
-a
-8
-a
-a
-a
-a
-14
-14.
-14
-14
-14
-16
-54
-56
-54
-54
-54
-56
-75
-75
-73
-75
-75
-75
-94
-96
•94
-94
-94
-94
60
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
9
9
9
9
9
9
0
0
.0
0
.0
0
ca
.343
364
374
.359
.356
.35?
341
. 342
.372
. 353
.356
.353
.341
.361
.365
350
. 3S6
. 352
341
361
.361
350
356
.352
.340
.360
.360
.350
. 356
.352
PRESSURE WATER
HEAD CONTENT
ca ca /ca
-a
-a
-a
-a
-8
-8.
-16
-16 .
-14
-14.
-14
-14
-54
-54
-56
-56
-54
-54
-74
-74
-74
-74
-74
-74
-94
-94
-94
-94
-96
-96
90
0
0
0
0
0
0
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
o
0
0
.0
0
.0
0
ea
.343
337
354
349
254
347
341
.337
. 350
345
.252
.346
. 335
333
. 340
.333
.248
.338
333
331
.336
328
.244
335
. 331
.329
.333
325
.244
.333
PRESSURE WATER
HEAD CONTENT
ca ca /cm
-
- .
-
-
-
- .
-14
-1
-I
-1
. 1
-1
-34
-36
-36
-36
-36
-36
-56
-56
-56
-56
-56
-56
-76
-76
-74
-76
-76
-76
120
0
0
0
0
0
0
o
0
0
0
0
0
0
o
0
0
0
0
0
0
0
0
0
0
ca
.372
.407
.404
.391
.391
.381
.372
.404
.396
.384
.391
.377
.371
.402
.393
. 383
.391
.374
.370
. 397
390
.381
.390
.372
.369
393
.386
.378
.388
.368
101
-------
TABLE 8.3 Cont inucd
PRESSURE
HEAD
ca
DEPTH
-1
-I
-I
-1
-1
-1
-5
-5
-5
-5
54
54
34
Si
34
Si
10
10
10
10
WATER
CONTENT
ca /ca
PRESSURE
HEAD
CB
40 oa
0
0
0
o
0
o
0
0
0
0
.340
.358
358
.347
334
350
.348
342
.351
.337
-1
-1
-1
-1
-1
-1
-5
-5
-5
-5
43
43
43
43
43
43
10
10
10
10
WATER
CONTENT
ca /ca
PRESSURE
HEAD
ca
90 cm
0
0
0
0
0
0
0
o
0
0
. 325
.325
.324
314
.238
.325
. 225
311
.312
.301
—
-
-
-
-
-
-1
94
96
94
94
94
94
55
WATER
CONTENT
ca / ca
120 ea
0
0
0
0
0
0
-155.
-I
55
-155.
-I
-1
-5
-5
-5
-5
55
55
10
10
10
10
9
.0
0
.0
0
.364
.388
.381
.375
.385
.363
.359
.378
.372
.368
.379
.352
354
.323
.344
.345
102
-------
Table 11-1. Field Studies of Soil Matrix and Water Retention Properties.
Parameter
Porosity
Porosity
Porosity
Porosity
Bulk Density
Bulk density
Bulk density
Bulk density
Bulk density
Bulk density
Bulk density
Bulk density
Bulk density
X sand/X clay
X sand/X clay
X sand/X clay
X sand/X clay
X sand/X clay
.1 bar water
content
.09 bar water
content
.1 bar water
content (9g)
.1 bar water
content
15 bar water
content
15 bar water
content
15 bar water
content
15 bar water
content
15 bar water
content (9g)
pH
pH
PH
PH ,
Kn (cm3/g)
Mean
0.45
0.37
0.53
0.42
1.36
1.30
1.20
1.47
1.26
1.47
1.65
1.59
1.20
24/45
17/32
59/12
83/9
65/28
.37
.37
.27
.45
.166
.041
.193
.074
.095
6.1
6.4
5.8
8.2
2.01
cv
(X)
11
11
7
10
7
7
26
9
6
6
3
6
15
15/33
32/16
37/53
3/34
8/18
4
17.6
20
15
14.4
45
14
19
33
15
7
9
2
31
Field
***•»*«
(ha)
150
0.8
.03
0.4
150
15
3.8
1.3
0.5
0.5
0.34
91.6
40
150
85
15
91.4
0.28
85
150
15
•
40
85
1.3
0.5
3.3
15
.04
.02
.04
85
0.64
Number
of
Soil RepH.
Texture cates
clay loam
sand
clay loam
•
loany sand
clay loam
sandy loam
sandy loam
sandy loam
sllty clay
silt loam
sand
sand
clay loam
clay
sllty clay loam
sandy loam
loamy sand
sandy clay loam
clay loam
clay loam
sandy loam
clay loam
clay loam
sandy loam
silty clay
silt laom
sandy loam
clay loam
loam
sandy loam
clay loam
loamy sand
120
120
20
12
120
64
30
192
144
72
5
5
36
480
100
64
5
35
100
120
64
36
900
172
144
192
64
1,040
640
208
100
36
Method
e
Measurement
Water content at
zero suction
Not given
Water content at
zero suction
Water content at
zero suction
Undisturbed cores
• Not given
Measure volume of
plastic-lined
hole
Undisturbed cores
Undisturbed cores
Undisturbed cores
Undisturbed cores
Undisturbed cores
Undisturbed cores
Hydrometer
Light scattering
Not given
Not given
Not given
Hanging water
table
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Pressure plate
Batch equlibrlum
Reference
[15]
[16]
[17]
[18]
[15]
[19]
[20]
[21]
[21]
[21]
[22]
[22]
[23]
[15]
[24]
[19]
C22]
[25]
[24]
[15]
•
[19]
[23]
[24]
[21]
[21]
[21]
[19]
[26]
[26]
[26]
[24]
[27]
-------
Table 11-2. Field Studies of Water Transport Properties.
Parameter
(cm d'1)
Saturated K
Saturated K
Saturated K
Saturated K
Saturated K
Saturated K
Saturated K
Saturated K
Saturated' K
Saturated K
Saturated K
Saturated K
Saturated K
Saturated K
Infiltration
Infiltration
rate
Infiltration
rate
Infiltration
rate
Inf1 Itration
rate
Infiltration
rate
Infiltration
rate
Unsaturated
K(9)
(8[9-9o])P
KO
8
KO
3
KO
8
KO
8
Mean
20.6
168
316
84
3.6
18.9
11.0
6.9
28.1
55.6
71.2
98.5
24.1
203
14.6
16.3
6.6
8.5
8.5
47
263
22.5
14.6
4.6
89.1
9.6
65.4
4.0
32.9
CV
(*)
120
190
69
69
48
103
118
92
320
118
105
81
178
50
94
40
71
56
23
79
97
343
64
235
41
76
37
46
19
Soil
Texture
Clay loam
Sandy loam
Sand
Loamy sand
Silty clay
loam
Coarse
Fine
Silty clay
Very coarse
Coarse
Loamy sand
Loamy sand
Sandy laom
Silt loam
Clay loam
Loam
Silty clay
loam
Silty clay
Silty clay
loam
7 series
7 series
Clay loam
Clay loam
Silt laom
Loam
Field
Number
of
Size Measure-
(ha)
150
15
0.8
0.4
Composite
SCS date
for a given
soil series
in Imperial
Valley, CA
91.6
91.6
9.6
150
0.9
.004
.004
.004
100 ha
100 ha
150
.66
ments
120
64
90
12
33
330
287
339
36
352
121
5
5
26
20
1,280
625
125
25
20
15
20
20
611
24
Method
of
Measure-
ment
Steady infiltration
20 plots x 6 depths
Lab permeameter
In Situ air-entry
permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
Lab permeameter
0-30 cm infiltration
(double ring)
Steady state
Steady infiltration
(double ring)
Adjacent infiltro-
meters along
transect
Double ring infiltro-
neter
Inverse auger hole
method 150 cm
Instantaneous profile
method
Unit gradient method
Unit gradient method
Instantaneous profile
method 4 plots x 6
depths
Reference
[15]
[19]
[16]
[18]
[28]
[28]
[28]
[28]
[28!
[28!
[28!
[22!
[22:
[29]
[15]
[30]
[31]
[32]
[32]
[33]
[33]
[34]
[35]
-------
Table 11-3.' Field Studies of Chemical Concentrations.
Chemical
1. Chloride
2. Bromide
3. Bromide
4. Chloride
5. EC(l:l
extract)
6. EC(sat
extract)
7. Chloride
8. Chloride
9. Chloride
10. Chloride
Origin
of
Chemical
3 cm pulse
I cm pulse
0.5 cm pulse
Surface
application
Native
•
Sugarcane
Plantation
Fertilized
fields
Native
to
Manure
fertilized
fields
Irrigated-
fertilized
fields
Measure-
ment
Depth (m)
0.65
1.15
0.3
0.6
0.9
0.6
0.12
0.32
0-.025
075-.15
0-1
0-1
0-1
1.8-6
1.8-6
1.0-3.6
1.0-4.2
Surface
bedrock
•v20 cm
1.5-6.3
1.5-6.3
1.5-6.3
.6-1.2
.9-1.5
.6-1.2
Field
Soil Size
Texture (ha)
Loamy 0.64
sand
Loamy 0.64
sand
Sandy 0.2
loam
Loamy 0.3
sand
Mankos
shale
Clay loam- loam
Clay loam-loam
Clay loam-loam
Sandy loam- loan
Sandy loam-loam
Loam-sandy loam
Loam-sandy loam
Various
Sandy loam
Sandy loam
Clay loam
Loam
Fine sandy loam
Fine sandy loam
Number
of
Repli-
cates CV
"127
79
76
118
90
89
100
67
61
128
263
150 91
440 75
445 225
16 22
8 30
20 101
13 21
100-200 12-70
81 19
14 19
14 66
60
8 102
2 87
Method
of
Measure-
ment
Soil cores
Solution
samplers
Soil cores
Soil cores
Soil samples
Soil cores
Soil cores con-
solidated to
depth average
below root zone
Summary of 9
catchment areas
Average concen-
tration in core
Average concentra-
tion in entire
vertical profile
Soil samples
Soil samples
Soil samples
Reference
[36]
[36]
[37]
[38]
[39]
[40] :
[41] ?
«
c
c
[42]
[43]
[44]
-------
SPATIAL VARIABILITY Of SOIL PKOff8TI£S 257
Table 11-5. Sample Sizes Required to Have a 951 Probability of
Detecting a Change of FX 1n the Mean Using a T-Test
with a*5X (Sample CVS are the mean of all field
studies).
Number of
Parameter Studies
Bulk density or
porosity
Percent sand or
clay
0.1 bar water
content
15 bar water
content
PH
Saturated K
Infiltration
rate
IC0 in K(9)
Ponded solute
velocity
Unsaturated
solute velocity
Solute concen-
tration
13
10
4
5
4
13
8
4
1
5
4
F: 20%
40% lOOt
Number of Samples
6
28
9
23
4
502
135
997
1,225
127
119-551
* *
9 *
* *
7 *
* *
127 22
36 8
251 42
308 51
33 7
32-140 7-24
Average
CVtSO
10 t 6
28 ± 18
14 ± 7
25 t 14
8 t 5
124 t 71
64 t 26
175 ± 139
194
52 t 9
60-130
(range)
•Sample size estimates are less than 5 and should not be used.
-------
D
go
/us/«y /*/ v-
-------
* * Jly
-------
Co/u s er
9(
015
Ue I;
tS
-------
Jarcy- Doc ki*>* n
s
u /c»
s
s'+t* u
-------
*, o?
Li
* . * X
3
-------
C
'*>TC
/*>
3t
£
Sx
(«rtg>+£
&/
(k(ti
2h
*/<
(5
TKi
s
-------
T/.I
3
/
he Ids -f
c^ 5
* h-
* h -
-------
A; s e r
5
- CeS (X
is e
<9
-------
Soil Science Fact Sheet
Sept. 1983
SL 40 (Revised)
Pesticides and Their Behavior in Soil and Water
P.S.C. Rao, R.S. Mansell, L.B. Baldwin and M.F. Laurent*
Florid* Cooperative titeruion Service / Initltulr of Food »nd Apiculture Science* / Uoivcrtlty of Hortdi / J. 1. Woeitt, D«tn
Concern for man himself and his late must always lorrr. the
chief interest of all technical endeavor.
Albert Einstein
Pesticides stand out as one of the major
developments of the twentieth century. During the
past twenty years, however, concern has arisen as
to the extent their presence in the environment
poses a threat to wildlife and mankind.
Certainly, pesticides have improved longevity
and the quality of life, chiefly in the area of public
health. Insect control programs have saved
millions of lives by combatting diseases such as
malaria, yellow fever and typhus. The use of
pesticides also constitutes an important aspect
of modern agriculture, for without chemicals to
control various pests like insects, weeds, plant
diseases, worms and rodents, our food supply
would decrease and prices would increase.
Florida's temperate to subtropical climate favors
growth of many harmful insects, weeds and
diseases, thus making this state particularly
dependent on pesticides for economical crop
management.
Unfortunately, pesticides are poisons and can
be particularly dangerous when misused. Fish-
kills, reproductive failure m birds, and acute ill-
nesses in people have all been attributed to
exposure to or ingestion of pesticides — usually
?;. ;;c:i-'/"-iv'-^':';o'j^:'f'iZjjf-^ Ateo'v-'0''*- ;c.f
Figure 1: Pathways of pesticide lost. P'peiticide.
Adapted from Herbifidt Injury Symptoms *nd Diannos:- Skroct. K'. A tnd Sfteen. T. J tfdi.f. North Ctrolint Agriculwrt' Exttnsio:
Servict. AC-S5. Doc. 19S1.
Pro<«».3- of So'.' Scitnct, Profwto; of Soil Sci»nci, Anoititt Prof«vor of Ae'iculturi' Engin«»rif>t »nd Anintr.i ir. Ed to-n
-------
•s § result of misapplication or careless disposal
of unused pesticides and pesticide containers.
Pesticide losses from areas of application and
contamination of non-target sites such as surface
and ground water represent a monetary loss to
the farmer as well as a threat to the environment.
Thus careful management of pesticides In order
to avoid environmental contamlnaion Is desired
by both farmers and the general public.
The purpose of this fact sheet is to explain how
pesticides can move from the area In which they
are applied, and to show how this Information can
be used, along with other factors, to select the
proper pesticide.
PATHWAYS OF PESTICIDE LOSS
There are basically two ways properly-applied
pesticides may reach surface and underground
waters — through runoff and leaching.1 Runofl is
the physical transport of pollutants over the
ground surlace by rainwater which does not
penetrate the soil. Leaching is a process whereby
pollutants are flushed through the soil by rain or
Irrigation water as It moves downward. In many
areas of Florida soils are sandy and permeable
and leaching Is likely to be a more serious prob-
lem than runoff. We now have technology to help
estimate tne potential contamination of water
from a given pesticide. To understand this
technology, It is necessary to know how a
pesticide behaves in soil and water.
Once applied to cropland, a number of things
may happen to a pesticide (Fig. 1). It may be taken
up by plants or Ingested by animals, Insects,
worms, or microorganisms in the soil. It may move
downward In the soil and either adhere to par-
ticles or dissolve. The pesticide may vaporize and
enter the atmosphere, or break down via microbial
and chemical pathways Into other, less toxic com-
pounds. Pesticides may be leached out of the root
zone by rain or irrigation water, or wash off the
surface of land. The fate of a pesticide applied to
soil depends largely on two of Its properties, per-
sistence and solubility.
PERSISTENCE
Persistence defines the "lasting-power" of a
pesticide. Most pesticides break down or "de
grade" over time as a result of several chemical
and micro-biological reactions In soils. Sunlight
breaks down some pesticides. Generally,
chemical pathways result in only partial deactiva
tion of pesticides, whereas soil microorganisms
can completely break down many pesticides to
carbon dioxide, water and other Inorganic const*
tuents. Some pesticides produce Intermediate
substances, called "metabolites" as they
degrade. The biological activity of these
substances may also have environmental signifi-
cance. Because populations of microbes
decrease rapidly beio* the root rone, pesticides
leached beyond this depth are less likely to be
degraded. However, some pesticides will con-
tinue to degrade by chemical reactions alter they
have left the root zont.
Degradation time is measured in "half-life."
Each half-life unit measures the amount of time It
takes for one-halt tne original amount o1 a
pesticide In soil to be deactivated. Half-life is
sometimes defined as the time required for half
the amount of applied pesticide to be completely
degraded end released as carbon dioxide. Usu-
ally, the half-life of a pesticide measured by the
latter basis is longer than that based on deactiva-
tion only. This is especially true If toxic or non-
toxic metabolites accumulate in the soil during
the degradation. Table 1 groups some of the
pesticides used in Florida by persistency, or
length of half-life, on the basis of their deactiva-
tion in soils.
Table 1: Grouping of pttticldes bated on p»r»l»tenct In tolls
Ptrtittent
Non P«rtl«Unt Mo6>r*t«1y P«r»l»ttnt
(halt-lite less (hail-iile greater than
than 30 days) 30 days, tess than 100)
Aldicarb
Captan
Dalapon
Dlcamba
Malalhion
Methyl para
Ihion
Oxamyl
2.4-D
2, 4. 5-T
Aldiin
Atrazine
Carba'y!
Cerbofuran
Diajirt-r.
Endrir.
Fonofos
Glyphosate
Heptachlor
Llnuron
Parathion
Phorate
Simazine
Terbacil
TCA
(n, It-hie
Q'tater than
IOC days)
Btomacil
Chlordane
Line ane
Paraquat
Pidorarn
Tritluralm
SOLUBILITY AND SORPT1ON
Probably the single most important property in-
fluencing a pesticide's movement with water is its
solubility. Soil is a complex mixture of solids, li-
quids and gases that provides the life support
system for roots of growing plants and micro
organisms such as bacteria. When a pesticide
enters soil, some of it will stick to soil panicles.
particularly organic matter, through a process
called adsorption and some will dissolve and mi>
with the water between soil particles, called "soil-
water." As more water enters the soil through rain
or irrigation, the adsorbed pesticide molecules
may be detacher from soil particles through t
process called desorption. The solubility of e
Two othc pcthwiyi of peslteidt Ion »'• throuB1' r«rnov>' in tht hirvvrtec! pltnt »-id by vcpo-Ujtior, (volitilititlon) Into ttu •tmosphfi
Occurrence of p*rttcidt rtiidun in (dibit parti of pl«nu it lignihunt In term of burnt* «npo«-'». whilt pcrticidei rtlttated into the tTrrvoi
pht:« hm «n imptrt on «lr qutlity »nd cr«U probl»-ni wher. *9ricullJr»< wo-V»-i «rt«- tht trtrtKJ §r*»i. Whil» th»M two pithwiyt 1-1
imporum. thty will not b* considered furthe- in this 1»rt*.-.ec<.. which Is devot*-! tc p»r.i:id« b*".r->c.- in toil «r.d wttei.
-------
pesticide and Its sorption on soil are Inversely
related; that is, Increased solubility results In less
sorption.
One of the most useful Indices for quantifying
pesticide adsorption on soils Is the "partition
coefficient" (PC). The PC value Is defined as the
ratio of pesticide concentration In the adsorbed
state (that is, bound to soil particles) and the
solution-phase (that Is. dissolved in the
soil-water). Thus, for a given amount of pesticide
applied, the smaller the PC value, the greater the
concentration of pesticide In solution. Pesticides
with small PC values are more likely to be leached
compared to those with large PC values.
Partition coefficients of several chemicals are
shown in Table 2. Note the wide range of partition
coefficients. Values of partition coefficients
listed in Table 2 are independent of soil type and
are characteristic of each pesticide. The partition
coefficient is determined by a pesticide's
chemical properties such as solubility and
melting point.
1»blt 2: Partition coffficknn (PC) tor tckclron5 occu' *oo- i*tep
to pollute surface or ground water is possible.
Quantitative prediction of pesticide loss via
runoff and leaching requires complex computer
models which utilize site-specific soil, crop, and
climatological information. This would include
the soil type, the date, amount and method of ap-
plication, and the amount, frequency and duration
of rain or irrigation following application.
-------
PESTICIDE SELECTION AND USE
Agricultural use of pesticides should be part of
an overall pest management strategy which in
eludes biological controls, cultural methods, pest
monitoring and other applicable practices, re
ferred to altogether as Integrated Pest Manage
menl or IPM. When a pesticide is needed its selec-
tion should be based on effectiveness, toxicity to
non-target species, cost, end site characteristics,
as well as its solubility and persistence.
Half-lives and partition coefficients are par-
ticularly important when the application site of a
pesticide is near surface waters or is underlain
with permeable subsoil and a shallow aquifer.
Short half-lives and intermediate to large PC's are
best in this situation.
Many areas of Florida have impermeable sub-
soils which impede deep leaching of soluble
pesticides. On such land, soluble pesticides with
low PCs and moderate-to-long half-lives require
cautious application to prevent rapid transport in
drainage water to a nearby lake or stream. Non-
erosive soils are common to much of Florida and
pesticides with large PCs remain on the applica-
tion site for a long time. However, the user should
be cautious of pesticides with long half-lives as
they are likely to build up in the soil.
In addition to the pesticide solubility and soil
permeability it is important that the pesticide's
toxicity to non-target species be considered.
Some of the pesticides listed in Tables 1 and 2
have severely restricted use due to acute toxicity
or long half-life. An important purpose of the
pesticide container's label is to instruct users to
apply the pesticide safely and with minimum
threat to non-target species, both on and off the
application site. Pesticide users assume respon-
sibility to follow label Instructions. It Is unsafe
and unlawful not to do so.
NEED MORE INFORMATION?
Pesticide recommendations for various crops
and pests may be obtained from the Florida Co
operative Extension Service. Contact your count>
Extension office for this information. For more
discussion of some of the ideas presented here.
consult these Extension publications.
IF AS 76 A Clean Water Refresher... answers
frequently asked questions about water quality in
Florida and describes Florida's agricultural wale:
quality program.
SP-19 Pollution Solutions for Florida Farmers
... discusses agricultural water quality problems
in Florida and presents prevention measures.
SL-14 The Soil: Our Number One Waste
Disposal System ... discusses 14 types of
pollutants related to agriculture and explains soil
as a recycling system for treatment.
Si.-37 Soil as a Porous Medium ... part one in
Basics of Soil and Water Relationships series; ex-
plains fundamentals of soil structure, particularly
particle and pore size, total porosity and soil bulK
density.
SL-38 Retention of Water... part two in above
series; explores the influence of soil structure on
retention of water.
SL-39 Movement of Water... part three in
above series; deals with fundamental principles
of water flow in soil.
IPM-1 Integrated Pest Management Primer ...
goals, benefits and implementation of IPM as ar.
alternative to heavy use of pesticides.
I
Best
Management
ices
This public document was promulgated at a cost ot $314.40. or 10.1 cents per copy. 10 help implement
the agricultural element of the Florida wate: quality plan. 7-3-1M-84
COOPERATIVE EXTENSION StRVICE. UMVERSITV oc FLOPIDA. INSTITUTE O' FOOL) A','D AGRICULTURAL
SCIENCES, K. ft. Ttfertllie1, director. Ir, cooperation wlir- the UniteC Slates DtPB'tment o' Ay'k^itu'e. publishes this Info1-
matlor, to further the purpose of the May tanaJune 30.1(14 Acts of Congress. *nc Is authorises to provide r«March, •Oud-
tloni! Information ane other Mrvlces only to Individual! anc Institutions that function without retire to race, color, e*> or
national orlglr.. Single copies of Extension publications (*>dudlng I -H and Youtn publications) ft available fre* to Florida
ras'deMi from County Extension Oftlces Information o* bulk rates or copies fo> out-of-stete pjrcnat«r> Is available from I
C rV. Hint or, PuMiu'io-.i DiKrit jtior. Cente-. IF AS Bui'J.r.j tf t , University o' Flcrlfli Gaines. 'it. ftc'iOt 3 ?£ ! 1 . Before put I:: •>••>( if.,i
put-i'tatlof.. e)dlto-s »^.c~-ic con la:1 tnis aocresi to oete'rrii* ».a liability.
-------
t
orous
4-41«i (
vAirv^ATS
Lratf-
.
|.
Uo
dU.-fjuil
-------
7k
V
WerljL
X t-S
fVc/C JT
-fi'^f
— \/
&, A,
v
Jlts~#fa
A
(
a
iJU.
-------
e.CiT*
U
O
-fW»c^'ox\Jl
£•
OC- fi I )
Ox^v
"
-------
bores
r
L --
-------
Ho
ryy
j, rC n t^ j»U S
CD
vrL
-------
3-
C -
t*
— *o £ X ^-4-<
- O * X- < O
rVr
= 0
r.Cx t ^oy x > o
( X > o )
/o«/C
xCUx.
( A ^ o )
-------
(11)
L
( /-
6°; ^ 0
*
-------
- Hg-fcznJ
09.
- 0
-t
»vj ZEva.
3** C (X) ;
Tka
c«<\(3UL-ksv\ (_
Q
,
J
UA
AAftx W
(7
0 *
Jit
dvuz
(
C/f)
-------
f
J
/rau
> - (A, G) (
A*C, L
L
-------
c * f
At ^
5/1
j)'
(V/0
«• ; jjfTtJi ^ •
- ^
c.
T
-------
Diffusion Cell
-18
Df :0,i00
0 : ADD 1 :
1,06
Esc = HEN
Length (CHS)
fllphaA2 :G,5W
Tine =99999,
-------
•Z
J.
-
J*OL;
C * ^ ) •
= Mr"
\A
tf
ML. r
-j
J(koa
-------
3X
LJLTTWjp
4
«i
S
, "TUusx £, [z]
% -
2. 'u4
-------
;. A/^J
ii
. Lit X; cuJL -t, W
JrMiKLi^
^i
t,
= C x - v.t
= t
C(x/O & CCx,/t,y
at
^ I
ax
T
ac
ax,
s>c
a-t,
ac
= o
-------
= o
;|
l-i
C Cx;t) = O ; X>v0t
BA3
-------
Jfct
-------
UtA
Ae_
C =
n
r
£*•/
. fe^COUK V0
-------
X
Cj,
YX
10
o
2
3
*
5
As
•/
-------
SJMUOU.S cuJ
I
ii 4«.Lbrt d^c^iocJbL -fco
OU
C
-------
'06
V
o
-------
J&JL PlST&fO blSf>*A*£N-E
-------
I •
(
Jttvt
— -JD
t • "3;
60^* "^JUXTj
at:
jH*w - Ji- I D0
at ax
«f
oo
-------
or
ty
»r-
3tr
- v
era
M IT3
LT
~;
T
-------
A Microcomputer-Based Management Tool for
Chemical Movement in Soil1
D.L. Nofzigrr
Associate Professo'
Agronomy Department
Oklahoma State L'r..\ersit\-
Stillwater. OK
A.G. Hornsby
Associate Proicsso-
Soil Science Depaimenl
University of Florida
Gainesville. K
Abstract. A management model i>
presented that can be used to make
informed derisions reparrimc the be-
havior of aprichemicaK in soiK. The
conceptual and mathematica1 ba>e-
of the model are disc ussed. ncludmc
assumption^ and limitation^ Graph-
ical outputs from the mode! illustrate
the impact that soil properties chem-
ical properties, and climatolocic tai-
lors have on chemical movement ir
soil. Data entrx routines permit ap-
plication to an\ area with appropriate
data This software require* an IBM-
PC or compalable computer with
23dK bvles random-access memo'x
one disk dn\e. and PC - or MS-DOi
version 2.0.
Introduction
The objectives of this paper are (I) to illustrate the
influence of soil properties, chemical properties.
and weather patterns upon the movement of organic
chemicals in soils. (2) to present a computer model
for estimating the movement of nonpolar organic
chemicals in soil, and (3) to present the mathemat-
ical basis of the model, assumptions inherent in it.
and its limitations.
The depth to which chemicals move in soils de-
pends in a complex way upon a number of soil.
chemical, and weather factors. Soil properties that
influence chemical movement include: pH. bulk
density, "field capacity" and "permanent wilting
point" volumetric water contents, and soil organic-
carbon content. Properties of chemicals that influ-
ence their movement include: partition coefficient
(Kd or Km). and degradation half-lives. Climatic and
cultural factors include plant root depth, daily rain-
fall and irrigation amounts, and daily evapotrans-
piration amounts.
Due to the large number of chemicals, soils, and
weather patterns of interest, it was deemed desir-
able to develop a model for interactively simulating
the movement of chemicals. The model was to be
based on physical processes involved in the flow
process, to require information for chemicals and
soils that are relatively easy to obtain, to be easy
to use. and to display results in easily understood
1 Approved for publication as Florida Agricultural Ex-
periment Station Journal Series No. 6659.
Address reprint requests to: A.G. Hornsby. 2169
McCartv Hall. University of Florida. Gainesville. FL
32611. U.S.A.
graphical form. The following sections describe the
model, assumptions in the model, use of the model.
and required computer hardware.
Description of Model
Movement of Chemical
The model used to estimate the position of the
chemical in the soil is a modification of one pre-
sented by Rao. Davidson, and Hammond [ I]. In this
model, chemicals move only in the liquid phase in
response to soil-water movement. In the present im-
plementation, the soil is comprised of as many as
25 layers or horizons. The soil properties may vary
in different layers, but they are assumed to be uni-
form within each layer.
Let ds represent the depth of the solute front in
a uniform soil. The change in depth of the solute.
A 0.
if q « 0.
(1)
where q is the amount of water passing the depth
-------
Chemical Movement in Soil
51
|2) and Karickhoff |3. 4] have shown that ihc par-
tition coefficient for a particular organic chemical
in a soil divided by the organic-carbon content of
that soil is nearly constant for a wide range of soils.
Therefore, in this model the partition coefficient is
given by
Klt
. or.
where A'f)( is the linear sorption coefficient nor-
malized by the organic carbon conteni (OC) of Ihc
soil. The use of A'()f as defined in equation (?) is
applicable only to nonionic organic solutes.
To use equation (I) to predict the position of a
chemical in a soil requires that the quantity of water
passing the solute front be determined. The model
estimates this from daily records of evapotranspi-
ration demand and infiltration. The following steps
must be carried out for each day in which flow is
being simulated:
1. Adjust water content in the root zone for the
evapotranspiration on that day.
2. Adjust the water content in the root zone for any
infiltration on that day and determine the quan-
tity of water passing the solute depth.
3. Determine the new solute depth.
These steps are described below for the layered soil
shown in Figure I. Notice that the soil contains two
layers more than the number of horizons. One of
these layers has a lower boundary at the solute
depth, d[s], and an upper boundary at the lower
edge of the layer above the solute front. This layer
changes in thickness and position as the chemical
moves. The second layer has a lower boundary at
the bottom of the rooting zone. c/[RZ]. and an upper
boundary at the lower edge of the layer above this
depth. These layers are inserted for computational
convenience.
Step 1
Each layer in the soil profile is assumed to be at
"field capacity" at the beginning of day 1. As long
as water in the root zone is available to plants, it is
removed from the soil to meet the daily evapotrans-
piration demand. Water is considered available if
the water content in any layer of the root zone is
above the "permanent wilting point" of the soil in
that layer. If Q(j) represents the volumetric water
content of layer j. the available water in that layer.
AWl/). is given by
AW(/) =
(4)
where t(/) is the thickness of the layer and 6PWP0)
is the volumetric water content at the "permanent
«[0]
d[8]
VXl*€TRlC WATER CONTENT
0.1 0.2 0.1 0.4 0.5
d[2] ' *—.—
O
OC
a
S d[3]
o
z
X
t-
Q.
u
o
d[4]
• Siiitiiirrt mint)
little it lirlui I
linn it rut tin
— Itttu itliriin J
llttll it lulni 1
F.C.
Lilt tirilli lltiid<
ti iii| In* till
Fig. 1, Representation of soil layers used in the compu-
tational scheme. The solid vertical line represents the vol-
umetric water conteni at lime /,.
wilting point" of the layer. The total available water
in the root zone. A\V,ota|. is the sum of the amounts
available in each layer in the root zone. If the total
available water is greater than the evapotranspira-
tion (ET) demand for the day. the water content of
each layer in the root zone is decreased in propor-
tion to the amount of water available in that layer.
That is.
8l/) =
- [ET * AW(/)]'
(5)
where 8'(/) is the water content prior to adjustment.
If the total available water is less than the evapo-
transpiration demand.
ei./i = ePWPo") (6)
for all layers in the root zone.
Step 2
The water content of each layer in the root zone
must be adjusted when an infiltration event occurs.
Starting with the la\er closest to the soil surface (j
= 1). the soil-water deficit for that layer. swd(/>. is
determined using the equation
(7)
-------
52
D.L. Nofzipcr and A.G. Hon»>K
where flj.r(.») i«- the volumetric water content of the
layer at "field capaciu." If the infiltrating amount.
/(/). is greater than swd(/) then.
W.M = eK-i/).
and
/
where time ^ the elapsed time since the chemical
was applied ir*J half-life is the biologic degradation
half-life of the chemical.
Assumptions in Model
The following assumptions arc used in this model:
1. All soil waier residing in pore spaces participates
in the transport process. Soil water initiallv
present in the profile is completely displaced
ahead of water entering at the soil surface. Rao
and colleagues 11) present data from different re-
searchers indicating that these assumptions are
valid for many soils. If they are not valid and a
portion of the soil water is bypassed during flow.
this model would tend to underestimate the
depth of the chemical front.
2. Water entering the soil redistributes instanta-
neously to "field capacity." This assumption is
approached for coarse textured soils. If the
water redistributes more slowly as in fine tex-
tured soils, the depths predicted here are likely
to be associated with an elapsed time a few days
later than that specified.
3. Water is removed by evapotranspiration from
each layer in the root zone in proportion to the
relative amount of water available in that layer.
A uniform root distribution with depth is as-
sumed. The validity of this assumption will de-
pend upon the root distribution in the soil. It will
not be strictly valid for many situations. More
precise schemes for dealing with evapotranspi-
ration would require information about the root
distribution and the soil hydraulic properties.
4. Upward movement of water does not occur an>-
where in the soil profile. Water is lost from the
root zone by evapotranspiration. but soil water
in the roo; zone is not replenished from below.
5. The adsorption process can be described b> a
linear, reversible, equilibrium model. If the sorp-
tion coefficient is described by nonlinear iso-
therm, the partition coefficient decreases with
increasing concentration of the chemical. Thus.
the depth to which the chemical will be leached
will depend upon the concentration. This aspect
is probabh not significant for the concentration
range of imerest in most agricultural application?-
-------
Chemical Mo\cmcni in Soil
|5). When adsorption equilibrium is not instan-
taneous, the chemical will be leached to a greater
depth than predicted here. Irreversible sorption
would result in less leaching.
6. The half-life for biologic degradation of the
chemical is constant with time and soil depth.
Degradation rale coefficients arc dependent
upon a variety of environmental factors, pri-
marily temperature and soil-water contcni.
Hence, seasonal changes in rale coefficient can
be expected. Also, with decreasing microbial ac-
tivity at greater soil depths, the degradation rate
coefficient may decrease with depth. Sufficient
data are not available to formulate mathematical
relationships to describe these effects.
wilting point." and the depth of the bottom of the
horizon. Options are provided in the software to
enable the user to enter these data in files, to modify
data previously stored in the files, and to displax
the contents of the file on the screen or printer. The
use of files enable the user to make repeated sim-
ulations without reentcring the data. Tables 1 and 2
illustrate the data displayed by the software for the
soils and chemicals used in Figure 2.
The model also requires daily amounts of effec-
tive rainfall or infiltration and evapotranspiration
(Fig. 3). These data are stored in separate files. In-
formation can be entered in English or metric units.
Options for entering, modifying, and displaying
data are similar to those for the chemical and soil
data.
Use of Model
The computer software for this model is menu
driven with the following options: (I) calculate the
movement of a chemical in a soil. (2) enter, modify.
or display data for soils or chemicals, and (3) enter.
modify, or display daily effective rainfall and evapo-
transpiration amounts. The steps involved in each
of these options are discussed below.
The calculation of chemical movement requires
the user to specify the chemical and soil of interest.
the depth to the bottom of the root zone for the
crop being grown, the names of data files containing
weather data for the location of interest, the depth
of application of the chemical, the date of applica-
tion, and the final data to be included in this sim-
ulation. Depths entered by the user and those cal-
culated can be in either English or metric units. The
calculated depth of the chemical front as a function
of time since application is displayed graphically.
Depths for several chemicals can be displayed on
one graph if desired. If the computer has high res-
olution graphics, bar graphs of daily rainfall as a
function of time are also displayed. Calculated
depths of the chemical front and the relative amount
of chemical remaining in the soil profile can be dis-
played in tabular form.
For each chemical used in the model, the parti-
tion coefficient normalized for organic carbon and
the half-life for biologic degradation are required.
The model includes these data for approximately 40
chemicals. A soil name, identifer. and the number
of horizons in the profile are required for each soil.
For each horizon, the model requires the percent
organic carbon, bulk density, and volumetric water
contents at "field capacity" and "permanent
Hardware and Software Requirements
This software requires an IBM PC or a compatable
computer with 256K bytes of random access
memory and one disk drive. An IBM compatible
color/graphics card is very desirable, but it is not
essential. An 808" numeric coprocessor can be uti-
lized for enhanced speed. (Simulating movement for
one year and drawing the graphs will require ap-
proximately 10 s with the 8087 processor or ap-
proximately 1 min without it). The operating system
must be PC-DOS 2.0 or MS-DOS 2.0 (or a more
recent version). The software is available from the
Institute for Food and Agricultural Sciences. Uni-
versity of Florida.
Use of the Model as a
Management Tool
Increasing the use efficiency of applied agrichemi-
cals (fertilizers and pesticidesl requires a good un-
derstanding of the factors that control their fate in
the environment. Soil-applied agrichemicals and
others reaching the soil as overspray or foliar wash-
off may leach through the soil and pose a threat to
ground water quality, remain at or near the soil sur-
face and be carried by surface runoff to streams or
surface impoundments, or be metabolized by soil
microbes and'or plants, thereby posing no environ-
mental impact.
Agrichemicals are applied to the soil to enhance
crop production and economic return to investment
of land and capital. Knowledge of the fate of applied
agrichemicals can improve nutrient- and pesticide-
-------
54
D.L. Nof/ipci and A.G. Hormtn
Table I. Soil parameters for Tavares fine sand (Typic QuartzipsammcntM and Orangchurp fine sand\ loam (Typic
PaJeudults).
Soil name
Soil identifier
Number of horizons in profile
Horizon
1
t
3
4
5
6
Dcplh
(cm)
10.2
20.?
5?.?
106.7
121.9
203.2
Organic carbon
7,
0.55
0.42
O.oy
0.06
0.04
o.o:
Tax-are-, fine sand
S27-8-II-6I
6
Water content
ul -O.I bar
6.5
7.2
5.2
5.4
6.1
11.9
Water content Bulk dcn-.il>
ai - 15 bar* g cc
1.3
1.5
0.8
0.7
0.8
1.0
.42
.44
.5(1
.5(>
.56
.58
Soil name
Soil identifier
Oranpeburg fine sand> loam
S37-8-II-6)
Number of horizons in profile
Horizon
1
2
3
4
5
6
Depth
(cm)
i3.o
25.0
41.0
102.0
155.0
203.0
Organic carbon
T,
2.48
0.66
0.40
0.14
0.10
0.06
6
Water content
at -O.I bar
21.9
23.7
33.2
30.0
32.8
30.8
Water conten; Bulk density
at -15 bars p cc
9.4
11.5
12.2
14.1
19.3
18.0
.42
.58
.50
.53
.71
.71
Table 2. Chemical data for Diuron and Picloram.
Common name Diuron
Trade name Karmex
Trade name lirox D
Trade name Direx 4L
Trade name Diurol
Partition coefficient (ml/g OC) 383
Half-life (days) 328
Common name Picloram
Trade name Tordon
Trade name Tordon 22K
Trade name Amdon
Trade name Grazon
Partition coefficient (ml/g OCi 26
Half-life (davs) 138
use efficiency as well as reduce unwanted environ-
mental consequences. The software described
herein can provide insight and increased under-
standing of the interactions that influence the fate
of agrichemicals in soil-water-plant systems.
With the exception of volatile compounds, such
as NH3 and fumigants, chemicals move through soil
dissolved in soil water. Wherever the soil water
moves, the dissolved chemicals move with it. The
chemical may lag behind the water front due to re-
tardation as shown by Equation (2). Figure 2 shows
a simulation of the depth distribution of three chem-
icals (diuron. picloram. and nitrate ion) in two con-
trasting soih (Tavares fine sand and Orangeburg
fine sandy loam) under two different periods of rain-
fall and evapotransporation (Fig. 3). The differences
in depth of leaching in a given soil reflect differ-
ences in properties of the chemicals themselves:
namely, the partition coefficients as shown in Table
2. Nitrate nitrogen has a partition coefficient of 0:
that is. no sorption is expected. Comparing Figures
2A and 2B illustrates the significant impact that dif-
ferences in soil properties alone make in the depth
of leaching of a particular chemical. Soil properties
for the two soils used in this example are given in
Table 1. Differences in organic carbon and -0.01
MPa (-0.1 bar) water contents are the principal
contributors to this contrast.
By comparing Figures 2A with 2C. and 2B with
2D, the effect of climatic parameters (rainfall and
evapotranspiration) can be seen for the Tavares and
Orangeburg soils, respectively. The rainfall and
evapotranspiration distributions for both different
time periods are given in figures 3A and B and 3C
and D. respectively. The differences in depth of
leaching reflect the differences in amount and
timing of rainfall versus evapotranspiration and the
resultant soil-water deficit. The total rainfall rep-
resented in Figure 3A is 804.2 mm versus 65S.9 mm
in Figure 3C. Potential evapotranspiration for the
-------
Chemical Movement in Soil
u
1.0
2.0
§ 3'°
(C
u.
-•an
~~ ^ 1
— 1
t
1 — v
\v
s
>\_
A
t-.
Sv
^
-v<
!
TAVARES U,
g °0
£ o
u
u-
x -
0.
Ill
0 2.0
3£
I
30
i i .3
60 90
IjO
2 0
3.0
-, — _,
.^
w^ —
L ^ \ . !
h ~^ 1
- C ;
• TAVARES
i i i i
120 0 30 60 90 120
^-i \ '
. .^
B
^-u
L_
>
t
1
ORANGEBURG
0
60 -
~ 60-
E
£
j 40-
IL
Z
C 20-
n .
,
30
,
60 90
1.0
2.0
3.0
A A
'-^ '
• »-, * I
Ltgtnn tor ni 9niM , Fig. 2. Depth of chemica
i Diuron fronts as a function of time
2 p'cior«T. . since application date. Ap
3Nltrtt"on plication dates for Panels^
D Rcct z.»« and B and for Panels C anc
ORANGEBURG D were 2-1-83 and 4-1-83
i i . t i resncclivelv.
120 0 30 60 90 120
ELAPSED TIME (DAYS)
• A _ . r
1
|
|
A C
|
60-
I
40- 1
2 0 *
i n i ill 1 1 ii jit
40
80
120
40
80
120
100 -r
100 T-
80
60
40
20
120
40
80
120
ELAPSED TIME , (DAYS) ELAPSED TIME . (DAYS)
Fig. 3. Distribution of rainfall and evapotranspiraiion as a function of time since application. Panels A and B are for
the period 2-1-83-5-31-83. Panels C and D are for the period 4-1-83-7-29-83.
-------
D.L. Nof/ipcr and A.G. Hornxb)
same periods was 540.5 mm and M>2.4 mm. respec-
tively. Nci evapotranspiralion varied, due to differ-
ences in the water-holding capacities of the two
soils.
Tabular outputs of data for date of rainfall, rainfall
amount, depth of chemical front, and relative
amount of chemical remaining in the soil profile as
a function of elapsed time arc also provided as an
option in the software. By examining the behavior
of selected alternative chemicals using this pro-
gram, one can make informed choices and thereby
maximize the efficacy of the chemical used.
References
1. Rao. P.S.C.. Davidson. J.M.. Hammond. L.C. Esti-
mation of nonreactive and reactive solute front lo-
cations in soils. In Proc. Hazard. Wastes Res. Symp.
EPA-600 19-76-015. Tucson. AZ. 1976. pp. 235-241.
2. Hamaker. J.W.. Thompson. J.M. Adsorption. In
Goring. C.A.I.. Hamaker. J.W. (eds.). Organic
Chtmirah it: tin Environment. New York: Marcc!
Dckker. 1972. pp. 49-14?.
3. Karickhoff. S.W. Semi-empirical estimation of sorp-
lion of hxdrophobic pollutants on natural sediment*
and soils. Chcmosphcrc 10:833-8-16. I9SI.
4. Karickhoff. S.W. Organic pollutant sorption in
aquatic systems. J. Hydr. Eng. 110:707-735. I9M.
5. Rao. P.S.C.. Davidson. J.M. Estimation ol pesticide
retention and transformation parameters required in
nonpoint source pollution models. In Overcash.
M.R.. Davidson. J.M. (eds.). Envintnnicnttil Imputi
of .\onpoint Source Pollution. Ann Arbor. Ml: Ann
Arbor Science Publishing. 1980. pp. 23-67.
-------
PISTON DISPLACEMENT OF WATER IN SOIL
CONSIDER A SOIL WITH A BULK DENSITY OF 1.58
AND A SATURATED WATER CONTENT OF 0.4 CM3/CM3.
1. AT SATURATION, HOW MUCH WATER WILL BE STORED IN
THE TOP 10 CM OF THIS SOIL? IF THE WATER CONTENT
IS ONLY 0.35 CM3/CM3, HOW MUCH WATER IS STORED IN
THE TOP 10 CM?
2. IF THE SOIL IS INITIALLY DRY AND 5 CM OF WATER IS
APPLIED TO THE SURFACE, APPROXIMATELY HOW DEEP
WILL THE WET FRONT BE AT IMMEDIATELY AFTER
INFILTRATION STOPS? IF THE WATER REDISTRIBUTES TO
A WATER CONTENT OF 0.3 CM3/CM3 VERY QUICKLY AFTER
INFILTRATION, HOW DEEP WILL THE WET FRONT BE?
3. IF THE SOIL HAD AN INITIAL WATER CONTENT OF 0.15
CM3/CM3, WHERE WILL THE WET FRONT BE IMMEDIATELY
AFTER INFILTRATION? WHERE WILL THE WET FRONT BE
AFTER THE WATER REDISTRIBUTES TO A WATER CONTENT
OF 0.3 CM3/CM3?
4. WHERE is THE LEADING EDGE OF THE INFLOWING WATER
IN CASES C AND D ABOVE?
-------
PISTON DISPLACEMENT OF WATER IN SOIL
CONSIDER A SOIL WITH A BULK DENSITY OF 1.58
AND A SATURATED WATER CONTENT OF 0.4 CM^/CM^.
1. AT SATURATION, HOW MUCH WATER WILL BE STORED IN
THE TOP 10 CM OF THIS SOIL? IF THE WATER CONTENT
IS ONLY 0.35 CM3/CM3, HOW MUCH WATER IS STORED IN
THE TOP 10 CM?
-------
PISTON DISPLACEMENT OF WATER IN SOIL
CONSIDER A SOIL WITH A BULK DENSITY OF 1.58
AND A SATURATED WATER CONTENT OF 0.4 CM3/CM^.
2. IF THE SOIL IS INITIALLY DRY AND 5 CM OF WATER IS
APPLIED TO THE SURFACE, APPROXIMATELY HOW DEEP
WILL THE WET FRONT BE AT IMMEDIATELY AFTER
INFILTRATION STOPS? IF THE WATER REDISTRIBUTES TO
A WATER CONTENT OF 0.3 CM^/CM^ VERY QUICKLY AFTER
INFILTRATION, HOW DEEP WILL THE WET FRONT BE?
-------
PISTON DISPLACEMENT OF WATER IN SOIL
CONSIDER A SOIL WITH A BULK DENSITY OF 1.58
AND A SATURATED WATER CONTENT OF 0.4
3. IF THE SOIL HAD AN INITIAL WATER CONTENT OF 0.15
CM^/CM^, WHERE WILL THE WET FRONT BE IMMEDIATELY
AFTER INFILTRATION? WHERE WILL THE WET FRONT BE
AFTER THE WATER REDISTRIBUTES TO A WATER CONTENT
OF 0.3 CM3/CM3?
-------
PISTON DISPLACEMENT OF WATER IN SOIL
CONSIDER A SOIL WITH A BULK DENSITY OF 1.58
AND A SATURATED WATER CONTENT OF 0.4
4. WHERE is THE LEADING EDGE OF THE INFLOWING WATER
IN CASES C AND D ABOVE?
I
I
-------
EVAPOTRANSPIRATION IN CMLS
1. WATER is REMOVED FROM ROOT ZONE ONLY.
2. WATER is REMOVED FROM EACH HORIZON IN
PROPORTION TO "AVAILABLE WATER11 IN THE
ROOT ZONE.
3. NO WATER MOVES UPWARD FROM BELOW THE ROOT
ZONE.
-------
AVAILABLE WATER IN ONE LAYER OF SOIL
THE AVAILABLE WATER IS TAKEN TO BE THE AMOUNT OF
WATER STORED IN THE LAYER ABOVE THE WATER CONTENT
CORRESPONDING TO THE "PERMANENT WILTING POINT11 OF
THE SOIL.
AW = (8 - 6pWP) * T
WHERE
0 IS THE AVERAGE WATER CONTENT IN THE LAYER
0pwp IS THE PERMANENT WILTING POINT
T IS THE THICKNESS OF THE LAYER.
-------
CHANGE IN WATER CONTENT DUE TO EVAPOTRANSPIRATION
(ONE LAYER ONLY)
IF THE LAYER CONTAINS ENOUGH WATER TO MEET THE
EVAPOTRANSPIRATION DEMAND, THAT AMOUNT OF WATER IS
REMOVED FROM THE LAYER AND THE AVERAGE WATER CONTENT
IS ADJUSTED ACCORDINGLY. IF THE LAYER DOES NOT
CONTAIN SUFFICIENT WATER, THE AVERAGE WATER CONTENT
IS SET EQUAL TO THE "PERMANENT WILTING POINT11 OF THE
SOIL.
IF AW < ET THEN 6 = 9PWP
IF AW > ET THEN 8=0'- ET/T
WHERE
0 IS AVERAGE WATER CONTENT AFTER CORRECTING
FOR EVAPOTRANSPIRATION,
0' IS AVERAGE WATER CONTENT BEFORE CORRECTING
FOR EVAPOTRANSPIRATION,
0pwp IS THE PERMANENT WILTING POINT
T IS THE THICKNESS OF THE LAYER.
AW IS THE AVAILABLE WATER IN THE LAYER
ET IS THE AMOUNT OF WATER LOST TO
EVAPOTRANSPIRATION.
-------
CHANGE IN WATER CONTENT DUE TO EVAPOTRANSPIRATION
(MULTIPLE LAYERS)
STEPS:
1. CALCULATE THE AVAILABLE WATER FOR EACH LAYER
IN ROOT ZONE.
2. CALCULATE THE TOTAL AVAILABLE WATER.
3. REMOVE WATER FROM EACH LAYER IN PROPORTION TO
THE AMOUNT OF WATER AVAILABLE IN THAT LAYER
BUT DO NOT LET THE WATER CONTENT DECREASE
BELOW THE PERMANENT WILTING POINT.
FOR LAYER J THEN
9(J) = 9'(j) - [ET*AW(j)]/AWTOTAI_*T(j)
WHERE
9(j) IS THE AVERAGE WATER CONTENT OF LAYER J
AFTER ADJUSTING FOR ET,
6'(j) IS THE AVERAGE WATER CONTENT OF LAYER J
BEFORE ADJUSTING FOR ET,
AW(j) IS THE AVAILABLE WATER IN LAYER J,
AWTQTAL IS THE AVAILABLE WATER IN THE
ROOT ZONE,
T(j) IS THE THICKNESS OF LAYER J.
-------
INFILTRATION IN CMLS
ASSUMPTIONS:
1. WATER INFILTRATES AS PISTON DISPLACEMENT,
2. WATER REDISTRIBUTES TO "FIELD CAPACITY"
INSTANTANEOUSLY.
-------
WATER PASSING SPECIFIED DEPTH
ASSUMPTION: INFILTRATING WATER ACCUMULATES IN
UPPERMOST LAYER UNTIL THE AVERAGE
WATER CONTENT OF THAT LAYER REACHES
FIELD CAPACITY. EXCESS WATER, IF
ANY, FLOWS INTO NEXT LAYER.
COMPUTATIONAL CONVENTION:
SOIL LAYERS CAN BE DIVIDED BY BOUNDARIES
BETWEEN THE NATURAL SOIL HORIZONS OR ANY
OTHER DEPTH OF INTEREST. IN THIS MODEL,
ONE LAYER ALWAYS ENDS AT THE ROOT ZONE DEPTH
AND ONE LAYER ENDS AT THE DEPTH OF THE
CHEMICAL.
PROCEDURE:
SINCE THE MODEL ASSUMES NO UPWARD FLOW AND
\
SINCE THE SOIL IS ASSUMED TO BE AT "FIELD
CAPACITY" WHEN THE SIMULATION BEGINS, ANY
WATER PASSING THE ROOTING DEPTH MOVES
i
DOWNWARD PAST ANY GREATER DEPTH.
-------
1. THEREFORE, IF DEPTH, D > ROOTING DEPTH, THE
AMOUNT OF WATER PASSING THIS DEPTH IS THE
AMOUNT PASSING THE ROOT ZONE DEPTH.
2. FOR DEPTH < ROOT ZONE DEPTH DO THE FOLLOWING:
FOR EACH SOIL LAYER ABOVE THE DEPTH OF
INTEREST,
A. CALCULATE THE AMOUNT OF WATER NEEDED TO
REPLENISH THE LAYER TO FIELD CAPACITY.
B. IF THE INFILTRATING AMOUNT IS LESS THAN
THIS AMOUNT,
A. SET THE WATER CONTENT 6(j) OF THE
LAYER TO ,
6(J) = 6'(J) + I(J)/T(J)
WHERE
9'(j) IS THE WATER CONTENT OF THE
LAYER BEFORE INFILTRATION,
I(j) IS THE WATER INFILTRATING
LAYER J,
T(j) IS THE THICKNESS OF THE LAYER
B. SINCE ALL THE WATER IS USED UP, SET
I(j+l) EQUAL TO ZERO.
-------
C. IF THE AMOUNT INFILTRATING IS GREATER
THAN THE AMOUNT NEEDED TO REPLENISH
THE LAYER,
A. SET THE WATER CONTENT 9(j) OF THE
LAYER TO 6FC(j).
B. CALCULATE THE AMOUNT PASSING THE
BOTTOM OF THE LAYER. THIS IS THE
AMOUNT INFILTRATING THE NEXT LAYER,
I (J+1) .
-------
DEPTH OF CHEMICAL IN CMLS
PROCESS: FOR EACH DAY:
1. ADJUST THE WATER CONTENT IN THE SOIL FOR
THE DAILY EVAPOTRANSPIRATION AND INFILTRATION.
2. CALCULATE THE AMOUNT OF WATER, Q, PASSING THE
DEPTH OF THE CHEMICAL.
3. IF Q > 0, THE NEW DEPTH D IS GIVEN BY
D = D' + Q/(R*8FC)
WHERE
D' IS THE OLD DEPTH OF THE CHEMICAL,
R IS THE RETARDATION FACTOR FOR THE
CHEMICAL IN THIS SOIL, AND
6FC IS THE WATER CONTENT AT FIELD
CAPACITY.
4. IF Q = 0, THE NEW DEPTH D EQUALS THE OLD
DEPTH D'.
-------
RETARDATION FACTOR
ASSUMPTION: THE ADSORPTION OF THE CHEMICAL ON THE
SOIL IS DESCRIBED BY LINEAR,
REVERSIBLE, EQUILIBRIUM MODEL.
THE RETARDATION FACTOR R IS GIVEN BY
R = 1 +
WHERE
IS THE SOIL BULK DENSITY,
KD IS THE LINEAR SORPTION COEFFICIENT,
0FC IS THE WATER CONTENT AT FIELD CAPACITY.
NOTE: IN CMLS, KQ MAY BE ENTERED DIRECTLY FOR
EACH SOIL AND CHEMICAL OR IT CAN BE OBTAINED
USING THE RELATION
K = K * OC
WHERE
KQC IS THE PARTITION COEFFICIENT NORMALIZED
BY THE ORGANIC CARBON CONTENT OF THE
SOIL AND
OC IS THE ORGANIC CARBON CONTENT OF THE SOIL
HORIZON.
-------
DEGRADATION OF CHEMICAL IN CMLS
ASSUMPTIONS:
1. FIRST ORDER DEGRADATION.
2. HALF-LIFE is CONSTANT WITHIN ONE SOIL
HORIZON.
3. HALF- LIFE is CONSTANT OVER TIME.
4. FOR DEGRADATION PURPOSES, ALL OF CHEMICAL IS
ASSUMED TO BE AT THE DEPTH CALCULATED.
CALCULATION:
THE FRACTION OF THE CHEMICAL REMAINING IN THE
SOIL PROFILE AT THE END OF DAY I IS GIVEN BY
= F(I-1)*EXP{-LN(2)/HALF_LIFE(D(I))}
FOR I = 1,2, ...
F(0) = 1
WHERE
F(l) IS THE FRACTION REMAINING,
D(l) IS THE DEPTH OF THE CHEMICAL ON DAY I,
HALF_LIFE(D(l)) IS THE DEGRADATION HALF- LIFE
OF THE CHEMICAL AT DEPTH D(l).
-------
RETARDATION FACTOR IN CHEMRANK
CONCEPT: To RANK THE POTENTIAL FOR CHEMICALS TO
LEACH PAST A SPECIFIED SOIL DEPTH BASED
ON THE TIME REQUIRED FOR THE CHEMICALS TO
MOVE THAT DISTANCE IN THE SOIL. CHEMICALS
WHICH MOVE FASTER ARE MORE APT TO REACH
GROUND WATER.
CALCULATION:
THE DISTANCE TRAVELED BY A CHEMICAL PER UNIT OF
WATER APPLIED IS INVERSELY PROPORTIONAL TO THE
RETARDATION FACTOR FOR THE CHEMICAL. THUS,
CHEMICALS WITH SMALL RETARDATION FACTORS MOVE
MORE RAPIDLY THAN CHEMICALS WITH LARGER VALUES.
-------
RETARDATION FACTOR FOR UNIFORM SOIL
FOR A UNIFORM SOIL, THE RETARDATION FACTOR, RF,
IS GIVEN BY
RF = 1 + {^KD + (f -eFC)KH}/8FC
WHERE
IS THE SOIL BULK DENSITY,
IS THE PARTITION COEFFICIENT,
f IS THE POROSITY OF THE SOIL,
0FC IS THE SOIL WATER CONTENT AT
"FIELD CAPACITY", AND
KH IS THE DIMENSIONLESS HENRY'S CONSTANT
FOR THE CHEMICAL.
-------
RETARDATION FACTOR FOR LAYERED SOIL
PROBLEM: To REACH THE GROUND WATER, A CHEMICAL MAY
NEED TO PASS THROUGH SEVERAL LAYERS. HOW
IS RF TO BE CALCULATED FOR SUCH A SOIL?
SOLUTION:
IN A UNIFORM SYSTEM, THE TIME, T, REQUIRED FOR
A CHEMICAL TO REACH A SPECIFIED DEPTH D IS
T = D * RF * 0FC /Q
WHERE
RF IS THE RETARDATION FACTOR FOR THE CHEMICAL,
9FC IS THE WATER CONTENT AT FIELD CAPACITY,
AND
Q IS THE FLOW RATE IN THE SOIL.
THUS, RF = T * Q / (D * 6FC).
-------
STEPS:
1. CALCULATE RF AND T FOR EACH LAYER ABOVE
THE CRITICAL DEPTH D ASSUMING THE FLOW
RATE IN THE SOIL IS UNIFORM ACROSS ALL
DEPTHS.
2. CALCULATE THE TOTAL TIME, TTOTAL,
REQUIRED TO MOVE TO DEPTH D BY FINDING THE
SUM OF THE TIMES FOR EACH LAYER.
3. CALCULATE RF FOR THE LAYERED SYSTEM USING
= TTOTAL * Q /
WHERE
6FC IS THE DEPTH-WEIGHTED AVERAGE
WATER CONTENT AT FIELD CAPACITY.
-------
ATTENUATION FACTOR IN CHEMRANK
CONCEPT: To RANK THE POTENTIAL FOR CHEMICALS
TO LEACH PAST A SPECIFIED SOIL DEPTH
BASED ON THE RELATIVE AMOUNT OF CHEMICAL
PASSING THAT DEPTH. THE GREATER THE MASS
OF CHEMICAL MOVED BEYOND THE CRITICAL
DEPTH, THE GREATER THE POTENTIAL TO
ADVERSELY AFFECT GROUND WATER.
-------
CALCULATION:
THE RELATIVE AMOUNT OF A CHEMICAL PASSING
THROUGH A SOIL IN TIME T IS GIVEN BY
Mi/Mo = EXP(-K*T)
WHERE
IS THE AMOUNT OF CHEMICAL ENTERING THE
TOP OF THE SOIL AT TIME ZERO,
IS THE AMOUNT OF CHEMICAL LEAVING THE
LAYER OF THE SOIL AT TIME T, AND
K IS THE DEGRADATION CONSTANT FOR THE
CHEMICAL IN THE SOIL.
(K = LN(2)/HALF-LIFE)
THUS THE ATTENUATION FACTOR, AF, FOR THE LAYER
IS GIVEN BY
AF = EXP(-K*T)
-------
IF N SOIL LAYERS EXIST ABOVE THE CRITICAL DEPTH,
THEN
MN/MO =
AND
AF = EXp(-Ki*Ti-K2*T2-...-KN*TN)
WHERE
MN IS THE AMOUNT OF CHEMICAL PASSING THE
CRITICAL DEPTH,
MQ IS THE AMOUNT OF CHEMICAL AT THE SOIL
SURFACE,
Kj; IS THE DEGRADATION CONSTANT FOR LAYER
I, AND
Tj IS THE TIME REQUIRED TO MOVE THROUGH
LAYER i (DETERMINED AS IN RF FACTOR)
-------
ir/EPA
United States
Environmental Protection
Agency
Robert S Kerr Environmental
Research Laboratory
Ada OK 74820
EPA/600-8-88-001
January 1988
Research and Development
Interactive
Simulation of the
Fate of Hazardous
Chemicals During
Land Treatment of
Oily Wastes:
RITZ User's Guide
-------
EPA/600/8-88/001
January 1988
INTERACTIVE S IMULATION
OF THE
FATE OF HAZARDOUS CHEMICALS
DURING
LAND TREATMENT OF OILY WASTES :
RITZ USER'S GUIDE
by
D.L. Nofziger, J.R. Williams,
Department of Agronomy
Oklahoma State University
Stillwater, Oklahoma 74078
and Thomas E. Short
CR-812808
Project Officer
Thomas E. Short
Processes and Systems Research Division
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
-------
DISCLAIMER
The information in this document has been funded wholly or in part by the
United States Environmental Protection Agency under cooperative agreement No.
CR-812808 to the National Center for Ground Water Research. It has been
subjected to the Agency's peer and administrative review, and it has been
approved for publication as an EPA document. Mention of trade names or
commercial products does not constitute endorsement or recommendation for use.
-------
ABSTRACT
An interactive software system was developed to enable decision makers to
simulate the movement and fate of hazardous chemicals during land treatment of
oily wastes. The mathematical model known as the Regulatory and Investigative
Treatment Zone Model or RITZ was developed and published earlier by
Short(1985). The model incorporates the influence of oil in the sludge, water
movement, volatilization, and degradation upon the transport and fate of a
hazardous chemical. This manual describes the conceptual framework and
assumptions used by Short (1985) in developing the model. It then explains the
micro-computer hardware and software requirements, the input parameters for
the model, and the graphical and tabular outputs which can be selected.
Illustrations of the use of the software are also included. The computational
equations developed by Short (1985) are presented for completeness but are not
derived.
,111
-------
FOREWORD
EPA is charged by Congress to protect the Nation's land, air and water
systems. Under a mandate of national environmental laws focused on air and
water quality, solid waste management and the control of toxic substances,
pesticides, noise and radiation, the Agency strives to formulate and implement
actions which lead to a compatible balance between human activities and the
ability of natural systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of
expertise for investigation of the soil and subsurface environment. Personnel
at the Laboratory are responsible for management of research programs to: (a)
determine the fate, transport and transformation rates of pollutants in the
soil, the unsaturated and the saturated zones of the subsurface environment;
(b) define the processes to be used in characterizing the soil and subsurface
environment as a receptor of pollutants; (c) develop techniques for predicting
the effect of pollutants on ground water, soil, and indigenous organisms; and
(d) define and demonstrate the applicability and limitations of using natural
processes, indigenous to the soil and subsurface environment, for the
protection of this resource.
This user's guide serves the purpose of instructing the user to the execution
of a software package based on the Regulatory and Investigative Treatment Zone
(RITZ) model. The guide should allow easy access to information critical to
the development of an understanding of the transport and fate of hazardous
chemicals applied during land treatment.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
av
-------
TABLE OF CONTENTS
Introduction 1
Basic Concepts, Assumptions, and Limitations 1
Software Overview 4
Hardware and Software Requirements . 6
Operating Conventions 6
Getting Started 9
Example of Software Use - . . 11
- Introduction 11
- Parameter Entry 11
- Output Selection 16
- Output Examples 18
File Structure 43
References Cited 44
Appendix
- Mathematical Basis of Model 46
- Input Parameter Estimation 56
- Parameter Averaging 58
Index 60
v
-------
INTRODUCTION
The Regulatory and Investigative Treatment Zone Model, RITZ, (Short, 1985) was
developed to help decision makers systematically estimate the movement and
fate of hazardous chemicals during land treatment of oily wastes. The model
considers the downward movement of the pollutant with the soil solution,
volatilization and loss to the atmosphere, and degradation. The model
incorporates the influence of oil upon the transport and fate of the
pollutant. This RITZ model forms the basis of this interactive software
system. The software enables users to conveniently enter the required soil,
chemical, environmental, and management parameters and checks the validity of
these entries. The user may then select graphical and tabular outputs of the
quantities of interest.
This manual describes the basic concepts of RITZ and lists the inherent
assumptions. The manual, also, describes the use of the interactive software
and the hardware and software requirements for it. Illustrative examples of
the software are presented. The appendix includes a list of the mathematical
equations used in the software.
BASIC CONCEPTS, ASSUMPTIONS, AND LIMITATIONS
A land treatment site is illustrated in Figure 1. The treatment site consists
of two soil layers called the plow zone and the treatment zone. The sludge
(waste material) containing oil and pollutant is applied to the plow zone. It
is thoroughly mixed with the soil in that layer. As time passes the pollutant
and oil are degraded. Some of the pollutant is carried down through the soil
with percolating water. Some of the pollutant is volatilized and moves into
the air above the treatment site.
The following assumptions were made by Short(1985) in developing this model.
1. Waste material is uniformly mixed in the plow zone.
2. The oil in the waste material is immobile. It never leaves the plow
zone. Only the pollutant moves with the soil water.
3. The soil properties are uniform from the soil surface to the bottom of
the treatment zone. This assumption will rarely, if ever, be met in the
field. The user can estimate the impact of non-uniform soils by
comparing results for several simulations covering the range of soil
properties present at the site.
*
A. The flux of water is uniform throughout the treatment site and
throughout time. This assumption will rarely be met in ,the field.
5. Hydrodynamic dispersion is insignificant and can be neglected. This
assumption gives rise to sharp leading and trailing edges in the
pollutant slug. These sharp fronts will not exist in soils. As a result,
-------
Land Treatment Site
Rainfall
Pollutant
Vapor Losses
Evaporation
Sludge Applied to Plow Zone
Volatilization
Degradation
Leaching
- Soil Surface
- Plow Zone Depth
- Treatment Zone Depth
Pollutant
Leaching Losses
Figure 1. Diagram of land treatment site.
the pollutant will likely reach any depth in the treatment zone before
the time predicted and it will remain at that depth longer than
predicted by the model.
6. Linear isotherms describe the partitioning of the pollutant between the
liquid, soil, vapor, and oil phases. Local equilibrium between phases is
assumed.
7. First order degradation of the pollutant and oil are assumed.
Degradation constants do not change with soil depth or time. This
assumption ignores changes in biological activity with soil depth. It
• also ignores the influence of loading rate, temperature, and the quality
of the environment for microorganisms upon the degradation rate.
8. The pollutant partitions between the soil, oil, water, and soil vapor
and does not partition to the remaining fractions of the sludge.
9. The sludge does not measurably change the properties of the soil water
or the soil so the pore liquid behaves as water.
-------
10. The water content of the soil is related to the hydraulic conductivity
as described by Clapp and Hornberger (1978). That is,
k/ks = (e/es)2b+3
where k is the hydraulic conductivity at a volumetric water content of
8, ks is the saturated hydraulic conductivity or the conductivity of the
soil at the saturated water content, 9S, and b is the Clapp and
Hornberger constant for the soil.
Field validation of the model is in progress. The user is cautioned to
consider the assumptions in the model and to apply the model only where
appropriate. The writers are aware the assumptions are only simplistic
approximations to the continuum of nature. Many of the assumptions were made
to either simplify the mathematical solution or because there was insufficient
experimental data to permit more realistic descriptions of the system.
The model presents results for the specific parameters entered without any
measure of uncertainty in the calculated values. The user is encouraged to
compare results for a series of simulations using parameters in the expected
ranges for the site to obtain an estimate of this uncertainty. For example, if
the site contains two soil layers, the user may want to run the simulation
twice, once for the soil properties of each layer.
-------
SOFTWARE OVERVIEW
The software can be divided functionally into the following three parts.
1. Parameter Entry
This part of the program enables the user to define the
land treatment system to be modeled. This includes
specification of the soil parameters, properties of the
pollutant and oil, and environmental and management
parameters. These user inputs can be made by means of a
data entry editor which allows the user to move the cursor
around the screen to enter or modify parameters in any
sequence. These inputs may be saved in disk files for use
at a later time. The values entered are verified as much
as possible as they are entered. When the user has
finished entering the parameters, a final check is made to
determine if the set of parameters is consistent as a
whole.
2. Output Selection
This part of the program enables the user to specify the
desired graphs and tables. The user may also specify the
desired output device. Tabular outputs from the model may
be directed to the screen, printer, or a text file. These
entries are also made by means of the data entry editor.
Graphical outputs available in this software include the
following:
1. A circle graph of mass balance indicating the
portions of the pollutant leached, volatilized, and
degraded.
2. A line graph of the pollutant volatilized as a
function of time.
3. A line graph of the pollutant leached below the
treatment zone as a function of time.
A. A line graph of the position of the top and bottom
of the pollutant as a function of time.
5. A line graph of the concentration of pollutant as a
function of time for selected depths.
6. A line graph of the concentration of pollutant as a
function of depth at selected times.
7. Bar graphs of the concentration of pollutant in
different phases as functions of time and depth.
-------
Tabular outputs include
1. Input soil, pollutant, oil, environmental, and
operational parameters.
2. Calculated parameters relating to the treatment
system.
3. The amount of pollutant volatilized, leached, and
degraded and the computational mass balance error.
A. The quantity of pollutant volatilized as a function
of time.
5. The quantity of pollutant leached below the
treatment zone as a function of time.
6. The position of the top and bottom of the pollutant
as a function of time.
7. The concentration of pollutant in different phases
as a function of time at selected depths.
8. The concentration of pollutant in different phases
as a function of depth at selected times.
3. Computations/Display
This part of the software performs the specified
calculation and displays the desired results.
When the software is executed, an introductory screen is displayed followed by
the parameter entry screens. When the user has finished entering the
parameters and the entries are verified, the output selection screen is
selected. When the desired outputs have been specified, the computations and
outputs are displayed. When all of the outputs have been displayed the system
returns to the output selection screen. This provides the user with the
opportunity to obtain additional outputs for the same input parameters. If no
additional outputs are desired, the user may return to the parameter entry
screen by pressing the key. Each time the user returns to the data entry
editor, the values selected most recently are displayed. Thus, only the
parameters to be changed need to be entered. Thus if a series of pollutants
are to be simulated for one treatment site, the soil, environmental, and
management parameters need to be entered only once. Repeated simulations can
be made easily by simply modifying the properties of the pollutant.
Illustrations of the operation of the software follow a description of the
operating conventions.
-------
HARDWARE AND SOFTWARE REQUIREMENTS
This software requires an IBM^ PC, XT, AT, or a compatible computer with at
least 256K bytes of random access memory, one floppy disk drive, and an 8087
or 80287 math coprocessor. An IBM color/graphics board and a compatible
monitor are required to fully utilize the software with graphics. A monochrome
card and monitor can be used for tabular output only. A printer is useful but
not essential. If the printer is compatible with the IBM graphics printer,
copies of the graphics may be printed.
The operating system must be PC-DOS or MS-DOS version 2.0 or later. The
GRAPHICS.COM file from your DOS diskette must be executed before executing
this software to obtain copies of the graphics on the printer.
OPERATING CONVENTIONS
The following conventions are used throughout this software.
1. Program Interruption; The user may interrupt the program at any time the
system is asking for an input by pressing the key. Control in the
program reverts to the previous data entry screen. If the key is
pressed from within the parameter entry option, the program is
terminated and control is returned to the disk operating system.
2. Special Keys; Cursor control keys and function keys are used in the data
entry editor. The keys and their functions are listed below.
This key is used to move up one line in the editor. If
the cursor is already on the first entry on the
screen, the cursor moves to the last entry on the
screen.
This key is used to move down one line in the editor.
If'the cursor is already in the last entry on the
screen, the cursor moves to the first entry.
This key is used to move the cursor one character to
the right. If the cursor is at the right end of the
entry on the line, this key does nothing.
This key is used to move the cursor one character to
the left. If the cursor is under the left character in
the entry, this key does nothing.
This key moves the cursor from its present position to
the beginning of the last entry on the screen.
2. IBM is a registered trademark of International Business Machines, Inc.
-------
This key moves the cursor from its present position to
the beginning of the first entry on the screen.
The parameter entry process requires three screens.
One screen is for soil properties, one for pollutant
and oil properties, and one for environmental and
operational parameters. In this case, the key
moves to the next screen in thee series. For example,
if the screen for soil properties is displayed,
pressing this key will display the pollutant and oil
properties screen. Pressing it again will display the
operational and environmental screen.
This key is used to move to the previous screen when
entering the land treatment site parameters.
This key is used to obtain brief help messages
relating to the parameter being entered.
This key is used to enter and calculate a weighted
average value of a soil parameter from values for
different soil depths. See the Appendix for details.
If the parameters entered into this model at one time
have been saved in a file, those values can be input
to the system from the file. The key enables the
user to specify the name of the input file. If the
file exists, its values are input and displayed by the
editor. If the file is not found, the values in the
editor remain unchanged. The user may view the
directory of a disk by pressing when the file
name is requested.
Parameters entered into the system can be saved in
disk files for use at another time. Pressing the
key enables the user to specify the name of an output
file. After the file is specified, the present soil,
chemical and environmental parameters are written to
disk. Pressing when the output file is requested
enables the user to view a disk directory.
This key is used to terminate data entry on a
particular screen and to proceed to the next phase of
the program.
This key is used to interrupt the present process and
to return to the previous data entry screen.
This key is used to terminate entry of a particular
parameter. Any characters to the right of the cursor
are truncated when the key is pressed.
-------
This key is used to delete one character to the left
of the cursor. If the cursor is at the beginning of
the entry, nothing is deleted.
This key is used to delete the character at the
present cursor location.
File Names; File names may be any legal MS-DOS file name. File
extensions may be used to facilitate organization of files.
*
Unknown Parameters; When entering parameters into the editor, the user
may signify that a value is unknown by entering only a period or decimal
point. Entering a period for an input parameter defining the land
treatment site will result in further prompting for the entry. In many
cases, the additional prompt will provide additional information about
the required parameter. It may also provide a method of estimating the
parameter from other parameters which may be known.
Specifying No Data; When tables or graphs of concentration as functions
of time or depth are selected as outputs, the user has opportunity to
specify 15 times or depths of interest. If fewer times or depths are
desired, "no data1 can be specified for the remaining entries. No data
is specified by entering a period or decimal point instead of a number.
Copy Graphics On Printer; When graphs are displayed on the screen, they
can be printed on an IBM graphics printer or a compatible machine by
pressing the key or the and keys. The key
results in smaller copies of the screen. The GRAPHICS.COM must be
executed before RITZ if copies of graphs will be made.
-------
GETTING STARTED
Making a Working Copy; The software is distributed on a single diskette. The
first step is to make a working copy of the software. The original copy should
then be placed in a safe place. The following steps can be followed to make a
working copy.
Fixed Disk Systems
1. Make a new directory for the RITZ model using the
MKDIR command of DOS. For example:
MKDIR \RITZ
2. Copy the contents of the distribution diskettevto
the new directory using the COPY command of DOS. If
the distribution diskette is in disk drive A, enter
the following command:
COPY A;*.* \RITZ /V
Floppy Disk Systems
1. FORMAT a new floppy diskette with the /S option. To
do this place your DOS diskette in drive A and a new
diskette in drive B. Then enter
FORMAT B;/S
2. If you have a color/graphics card, copy the
GRAPHICS.COM program from the DOS diskette to the
working diskette using the COPY command. To do this
enter
COPY A;GRAPHICS.COM B; /V
3. Copy the contents of the distribution diskette to
the new diskette using the COPY command. This can be
done by removing the DOS diskette in drive A and
replacing it with the distribution diskette and
entering the command
COPY A:*.* B; /V
Details on the use of the COPY, FORMAT, and MKDIR commands are given in your
DOS manual.
The software is distributed to run on a system with a color graphics card. If
your computer has this card, your working copy is now complete. If your
computer does not have this card, you will need to execute the configuration
program included on the diskette. To configure the software for a monochrome
system
1. In a floppy disk system, place the working diskette in the default disk
drive. In a fixed disk system, use the CD command to make the directory
containing the RITZ software the default directory.
-------
2. Execute program CONFIG by entering
CONFIG
The program will ask you to specify the type of monitor. Specify the
monitor matching that in your system. The program will modify the RITZ
software for your system. The software on the working diskette should
then be ready for use.
Executing the Program; To execute the program,
~ '• ' «
1. Place the floppy diskette in the default disk drive (or define the
directory containing the software to be the default directory).
2. Enter GRAPHICS to install the memory resident software for
printing graphics screens.
3. Enter RITZ to execute the model.
You may find it more convenient to make a batch file to execute steps 2 and 3
as one command. This file would contain the following lines:
GRAPHICS
RITZ
10
-------
EXAMPLE OF SOFTWARE USE
RITZ
REGULATORY AND INVESTIGATIVE TREATMENT ZONE MODEL
This software is designed to estimate the movement and fate of chemicals
applied as oily wastes in land treatment sites. The user is required to
enter the properties of the chemicals and oil in the waste material, the
soil properties of the treatment site, the management practices used,
and the relevant parameters describing the environment at the site. v
Outputs of the model include the quantity of the pollutant degraded,
leached, and volatilized, the concentration of pollutant in the different
phases at different times and depths, and the quantity of pollutant
volatilized and leached as a function of time. Outputs may be displayed
in graphical and tabular forms.
This software was developed by D.L. Nofziger and J.R. Williams, Oklahoma
State University, Stillwater, Oklahoma. The software is based on a
mathematical model of the treatment zone developed by Thomas E. Short,
R.S. Kerr Environmental Research Laboratory, Ada, Oklahoma.
Press any key to continue:
Screen 1. Purpose of the program.
Introduction: The first screen which appears when the software is run is
displayed in Screen 1. This gives the user the purpose of the software and the
individuals responsible for it.
Parameter Entry; This part of the software enables the user to define the
properties of the treatment site and chemicals. The data entry editor is used
for this purpose. (See OPERATING CONVENTIONS for details on the use of the
editor.) Three screens are used for these inputs. The and keys
can be used to move from one screen to another. Values shown in this manual
are for illustration only.
Screen 2 is the screen used for defining the soil properties of the treatment
site. Since the model assumes the soil at the treatment site is uniform with
depth, only one value is entered for each property. If the soil is not uniform
with depth, the user may obtain an average from known values at different
depths by pressing the key. The averaging scheme used is described in the
Appendix. If the site is not uniform from one position to another, the user
may obtain a spatial average for use in this model or the model may be run
several times for different smaller sites. The parameters to be entered on
this screen are
1. Identification.code: This is simply a string of characters which serve
to identify this set of data for the user's reference. It is displayed
with outputs from the program.
11
-------
Identification code
Soil name
Fraction organic carbon
Bulk density, kg/m3
Saturated water content, m3/m3
Sat. hydraulic conductivity, m/day
Clapp and Hornberger constant
Soil Properties
Site //I
Tipton Sandy Loam
0.0050
1500
0.410
5.0000E-001
4.9000
,
Display help for entries
Average across depths
Input parameters from data file
Save parameters in output data file
Proceed - all entries made
Abort program
Edit other entry screens
Screen 2. Data entry screen for soil properties.
2. Soil name: This again serves to identify the soil at the treatment site.
3. Fraction organic carbon (foc): This is the ratio of the mass of organic
carbon in the soil to the mass of soil solids.
4. Bulk density (p): This is the ratio of the mass of soil solids to the
total volume of the soil. That is, it is the ratio of the mass of solids
to the volume of solids, liquids, and gases in the soil.
5. Saturated water content (8S): This is the ratio of the volume of water
in"the soil to the total volume of the soil when the soil pores are
filled with water.
6. Saturated hydraulic conductivity (ks): This is the hydraulic
conductivity of the soil when all of the soil pores are filled with
water. It is the constant of proportionality between the flux density
and the gradient in potential in Darcy's law.
7. Clapp and Hornberger constant (b): This is the constant in the equation
of Clapp and Hornberger (1978) relating the relative saturation of the
soil to the relative conductivity of the soil. That is
e/es = (k/ks)2b+3
where k is the .hydraulic conductivity of the soil at a volumetric water
content 8 and ks is the saturated hydraulic conductivity at the
saturated water content, 9g.
12
-------
Oil and Pollutant Properties
Name of pollutant in sludge
CAS number
Concentration of pollutant in sludge, g/kg
Organic carbon partition coefficient, m3/kg
Oil-water partition coefficient
Henry's law constant
Diffusion coef. of pollutant in air, m2/day
Half-life of pollutant, days
Concentration of oil in sludge, g/kg
Density of oil, kg/m3
Half-life of oil, days
Pollutant^l
123-4567
.OOOOE+000
.2000E-002
.OOOOE+001
.5000E-005
.3000E-001
.OOOOE+001
.5000E+002
.OOOOE+003
4.5000E+001
,
Display help for entries
Input parameters from data file
Save parameters in output data file
Proceed - all entries made
Abort program
Edit other entry screens
Screen 3. Data entry screen for pollutant and oil properties.
Screen 3 is used to enter the properties of the pollutant and the oil in the
waste material. These entries are described below.
1. Name of the pollutant in sludge: This is the name of the pollutant whose
properties are entered below. This name is for identifying output tables
and graphs.
2. CAS number: This unique Chemical Abstracts Number may be entered to
provide positive identification for the pollutant being modeled. This
number is also displayed with the outputs.
3. Concentration of pollutant in sludge (Sp): This is the concentration of
the pollutant in the sludge when it was applied to the soil.
4. Organic carbon-water partition coefficient (KQQ): This is the partition
coefficient between the pollutant in soil and water normalized to the
soil's organic carbon content. That is
CS = KOCfOCcW
where Cg and C^ are the concentrations of pollutant in the soil and
water, respectively, and
is the fraction organic carbon in the soil.
13
-------
5. Oil-water partition coefficient (KQ): This is the partition coefficient
for the pollutant between the oil and water phases.
That is
C0 = KoCW
where CQ and C^ are the concentrations of the pollutant in the oil and
water phases, respectively, and KQ is the oil-water partition
coefficient.
6. Henry's law constant (Kg): This is the constant for partitioning the
pollutant between the vapor and water phases. That is
Cv = KHCW
where Cy and C^ are the concentrations of the pollutant in the vapor and
water phases, respectively.
7. Diffusion coef. of pollutant in air (D^): The diffusion coefficient of
the pollutant in air is used to determine pollutant losses in the vapor
phase.
8. Half-life of the pollutant (tip): This is the time required for one-half
of the original amount of pollutant to be transformed to some other
product. It is based on the assumption that the transformation follows
first-order or pseudo first-order kinetics.
9. Concentration of oil in the sludge (SQ): This is the concentration of
oil in the sludge at the time of application.
10. Density of oil (po): This is the density of the oil in the sludge. That
is, it is the mass of oil per unit volume of oil.
11. Half -life of oil (tio): This is the time required for one-half of the
original amount of oil in the sludge to be biologically degraded. It is
based on the assumption that the transformation of the oil in the sludge
will follow first-order kinetics.
Screen A is used to enter or edit data relating to the operation of the
treatment site and the environment at the site. The parameters needed include
the following:
1. Sludge application rate (SAR): This is the mass of sludge or waste
material -applied per hectare of land area.
2. Plow zone depth (pzd): This is the depth to which the sludge or waste
material is incorporated. See Figure 1 for more information.
3. Treatment zone depth (tzd): This is the depth of the bottom of the soil
considered to be part of the treatment zone. Chemical movement below
this depth is lost from the system and is considered as leached.
A. Recharge rate (V
-------
Operational and Environmental Factors
Sludge application rate, kg/ha
Plow zone depth, m
Treatment zone depth, m
Recharge rate, m/day
Evaporation rate, m/day
Temperature, degrees C
Relative humidity
Diffusion coef. of water vapor in air, m2/day
1.5000E+005
0.150
1.500
0.0060
0.0025
25.0
0.500
2.0000E+000
,
Display help for entries
Input parameters from data file
Save parameters in output data file
Proceed - all entries made
Abort program
Edit other entry screens
Screen 4. Data entry screen for operational and environmental factors.
5. Evaporation rate (E): This is the average flux density of water
evaporating from the soil.
6. Air temperature (T): This is the average air temperature at the site.
7. Relative humidity (RH): This is the average relative humidity at the
site expressed as a fraction (rather than a percent).
8. Diffusion coef. of water vapor in air (Dw): This diffusion coefficient
of water vapor in air is used to estimate the vapor losses of the
pollutant.
The keyboard will be the primary method of entering parameters into the model.
However, the software enables the user to save manually entered values in data
files for use at a later time. This is done from within the data entry editor
by means of the and function keys as explained in the section on
OPERATING CONVENTIONS. When saving data, the system will request the name of
the output file from the user. It will then write the current values of the
input parameters in that file. When reading parameters from a file, the system
will prompt the user for the name of the input file. The data will then be
read and the editing screens updated to those values. When naming input and
output files, the user is advised to develop a system of names and extensions
which will facilitate identification of the file contents. When a file name is
requested, the user may press the key to view a directory of files.
15
-------
Output Options
Graphs:
Mass balance
Pollutant volatilized vs. time
Pollutant leached vs. time
Position of pollutant vs. time
Concentration vs. time at selected depths
Concentration vs. depth at selected times
Concentration bar graphs
Tables:
Input parameters %
Calculated parameters
Mass balance
Pollutant volatilized vs. time
Pollutant leached vs. time
Position of pollutant vs. time
Concentration vs. time at selected depths
Concentration vs. depth at selected times
Output device for tables
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
SCREEN
Display help for entries
Proceed - all entries made
Abort option and return to parameter entry screen
Screen 5. Screen for selection of desired outputs from model.
Output Selection: This portion of the software enables the user to select the
types of outputs desired and the desired output device. This selection process
begins with Screen 5. If any concentration outputs are selected, one or two
additional screens are required to select the depths and times of interest.
The use of the three screens are illustrated in this section.
Screen 5 illustrates the selection of outputs from the model. For each option,
the user enters Y if that option is desired or N if it is not desired. In this
example, all the entries are Y to generate all the possible types of output.
The entries on Screen 5 are as follows:
1. Graphs:
a. Mass balance: This option displays a pie chart of the relative
amount of the pollutant degraded, leached, and volatilized.
b. Pollutant volatilized vs. time: This option displays a graph of
the flux density of pollutant removed from the treatment site in
the vapor phase as a function of time.
c. Pollutant leached vs. time: This option displays a graph of the
flux density of pollutant leached from the treatment zone as a
function of time.
d. Position of pollutant vs. time: This option displays a graph of
the location of the top and bottom of the pollutant as a function
of time.
16
-------
e. Concentration vs. time at selected depths: This option displays a
graph of the concentration of pollutant as a function of time at
one or more depths selected by the user using Screen 6. Graphs of
the total concentration of pollutant and concentrations in water,
soil, vapor, and oil phases are displayed sequentially. For each
phase, the software displays a depth and draws the line for that
depth. It then waits 'for the user to press a key. If that key is
not , , or the system will display the line for the
next depth selected. If is pressed, the remaining depths for
this phase are not drawn and the system proceeds to draw the graph
for the next phase. If is pressed, the screen is printed on
the printer. If is pressed, the system returns to Screen 5.
f. Concentration vs. depth at selected times: This option displays a
graph of the concentration of pollutant as a function of depth for
one or more times selected by the user using Screen 7. This option
operates in the same manner as the concentration vs. time graphs
described above.
g. Concentration bar graphs: This option presents a series of bars
representing the treatment zone. Within each bar the concentration
of pollutant in one phase at a particular time is displayed
qualitatively using one of six patterns. The bars are redrawn for
different times selected by the user (Screen 7). In this way the
user can see the change in depth and concentration of the
pollutant with changes in time. Different bars on the screen
represent the total concentration of pollutant, pollutant
concentration in water, soil, vapor, and oil, and the oil content.
2. Tables:
a. Input parameters: This table displays the parameters entered by
the user to define the current scenario.
b. Calculated parameters: This table contains selected chemical and
physical parameters calculated from the input parameters.
c. Mass balance: This table lists the absolute and relative amounts
of pollutant degraded, volatilized, and leached along with the
mass balance error.
d. Pollutant volatilized vs. time: This is a table of the flux
density of pollutant leaving the treatment site in the vapor phase
as a function of time.
e. Pollutant leached vs. time: This is a table of the flux density of
pollutant leached from the treatment zone as a function of time.
f. Position of pollutant vs. time: This table displays the location
of the top and bottom of the pollutant slug at different times.
17
-------
Dept s of I terest
Depth 1
Depth 2
Depth 3
Depth 4
Depth 5
Depth 6
Depth 7
Depth 8
Depth 9
Depth 10
Depth 11
Depth 12
Depth 13
Depth 14
Depth 15
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
meters
0.00
0.05
0.10
0.15
0.25
0.50
0.75
1.00
1.25
1.50
Display help for entries
Proceed - all entries made
Abort option and return to output option screen
Screen 6. Selection of depths of interest for concentration tables and graphs.
g. Concentration vs. time at selected depths: This table contains the
total pollutant concentration, the concentration of pollutant in
water, soil, vapor, and oil, and the oil content at user selected
times and depths. These tables are structured so that
concentrations for all times at one depth occur on one page.
h. Concentration vs. depth at selected times: This table is similar
to that described above. It differs in that the output is
organized so that concentrations for all depths and one time occur
on one page.
i. Output device for tables: Tabular output can be displayed on the
screen or printer. It may also be saved in disk files for later
use. This line enable the user to specify the desired device.
Entries in this line may be SCREEN, PRINTER, or a legal file name.
If one or more of the concentration options is desired the depths or times
desired are entered using Screens 6 and 7, respectively. In each case the user
enters the depths or times of interest. A period indicates 'no data" or no
value.
Outputs of Model; The following pages illustrate the outputs from the RITZ
model for the inputs shown in screens 2, 3, and 4 and the outputs selected in
screens 5, 6, and 7. Graphical outputs were generated by pressing the key.
18
-------
Times of I terest
Time 1
Time 2
Time 3
Time A
Time 5
Time 6
Time 7
Time 8
Time 9
Time 10
Time 11
Time 12
Time 13
Time 14
Time 15
days
days
days
days
days
days
days
days
days
days
days
days
days
days
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
: Display help for entries
: Proceed - all entries made
: Abort option and return to output option screen
Screen 7. Selection of times of interest for concentration table and graphs,
19
-------
Table 1. Table of input parameters describing land treatment site.
INPUT DATA - SOIL PROPERTIES
Fraction organic carbon : 0.0050
Bulk density (kg/m3) : 1500.0
Saturated water content (m3/m3) : 0.4100
Saturated hydraulic conductivity (m/day) : 5.0000E-001
Clapp and Hornberger constant : 4.9000
INPUT DATA - OIL AND POLLUTANT PROPERTIES
Concentration of pollutant in the sludge (g/kg)
Organic carbon partition constant (m3/kg)
Oil-water partition coefficient
Henry's law constant
Diffusion coefficient of pollutant in air (m2/day)
Half-life of the pollutant (day)
Concentration of oil in the sludge (g/kg)
Density of the oil (kg/m3)
Half-life of the oil (day)
Diffusion coefficient of water vapor in air (m2/day)
1.
2.
5.
5,
4.
3,
2.
1.
4,
OOOOE+000
2000E-002
OOOOE+001
5000E-005
3000E-001
OOOOE+001
5000E+002
OOOOE+003
5000E+001
2.OOOOE+000
INPUT DATA - OPERATIONAL AND ENVIRONMENTAL FACTORS
Sludge application rate (kg/ha)
Plow zone depth (m)
Treatment zone depth (m)
Recharge rate (m/day)
Evaporation Rate (m/day)
Air Temperature (deg C)
Relative humidity
1.5000E+005
0.150
1.500
0.0060
0.0025
25.0
0.500
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
20
-------
Table 2. Table of calculated parameters for site described in Table 1.
CALCULATED PARAMETERS
Ratio of the density of water vapor to liquid
Boundary layer thickness (m)
Soil-water partition coefficient (m3/kg)
Degradation rate constant of pollutant (I/day)
Degradation rate constant of oil (I/day)
Water content of soil (m3/m3)
Soil pore water velocity (m/day)
Initial oil content in the plow zone
Initial pollutant content in the plow zone (g/m3)
Air content of the soil (m3/m3)
Effective diffusion coefficient of
pollutant vapor in soil (m2/day)
Initial pollutant loading (g/m2)
2.3E-005
4.6E-003
.1E-004
.3E-002
1.5E-002
2.9E-001
.1E-002
.5E-002
, OE+002
1.
2.
2.
2.
1.
9.5E-002
9.9E-OOA
1.5E+001
BASIC INFORMATION ABOUT THE SYSTEM
Maximum residence of the pollutant in the plow zone (days) : 35
Maximum residence of the pollutant in the treatment zone (days) : 138
Treatment zone breakthrough time (days) : 102
Retardation factor in the lower treatment zone : 1.6E+000
Velocity of the pollutant in the lower treatment zone (m/day) : 1.3E-002
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
21
-------
Table 3. Mass balance table summarizing the amount of pollutant degraded,
volatilized, and leached as well as the computational error.
Amount loaded
Amount degraded
Amount volatilized
Amount leached
Computational error
MASS BALANCE
Mass of Pollutant
g/m2
1.5E+S01
l.AE+001
7.7E-003
9.4E-001
4.8E-009
Relative Amount
l.OE+002
9.
5.
6.
AE+001
1E-002
3E+000
3.2E-008
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
MASS BALANCE
Le AC lie dl
Vo 1 At i 1 i
i on-a.1 Eif»if*oif»: O . OOOOK
Figure 2. Mass balance graph summarizing information in Table 3.
22
-------
Table 4. The flux density of pollutant lost to the atmosphere as a function
of time.
Time Flux
days g/m2-day
0.00 3.0E-001
1.55 5.7E-004
3.09 2.8E-004
4.60 1.8E-004
6.09 1.3E-004
7.55 1.1E-004
8.99 8.6E-005
10.41 7.3E-005
11.80 6.2E-005
13.18 5.5E-005
14.54 4.8E-005
15.87 4.3E-005
17.19 3.9E-005
18.49 3.5E-005
Identification Code:
VAPOR FLUX
Time
days
19.78
21.04
22.29
23.53
24.75
25.95
27.14
28.32
29.48
30.63
31.77
32.89
34.01
35.11
Site //I
VERSUS TIME
Flux
g/m2-day
3.2E-005
3.0E-005
2.7E-005
2.5E-005
2.4E-005
2.2E-005
2.1E-005
1.9E-005
1.8E-005
1.7E-005
1.6E-005
1.5E-005
1.4E-005
1.4E-005
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
Uapor
g l.OE-002
a
I \
p i.OE-004 N^
F ^-^
1 ^^v
u
X l.OE-006
t . OF-008 1
Flux (g/»2-da«)
-^-^
versus Tine
^— -_
Time Flux
days g/m2-day
42.42 7.0E-006
49.74 4.3E-006
57.05 2.8E-006
64.37 1.9E-006
71.69 -1.4E-006
79.00 l.OE-006
86.32 7.6E-007
93.63 5.8E-007
100.95 4.4E-007
108.27 3.4E-007
115.58 2.6E-007
122.90 2.1E-007
130.21 1.6E-007
137.53 1.3E-007
RITZ
Identification:
Sitettl
Soil Name:
Tipton Sandy Loan
Pollutant Nam:
Pollutant*!
CAS Number:
123-4567
0 25 50 75 100 125 150
Tim (days)
Figure 3. Graph of flux density of pollutant in vapor phase as a function of
time.
23
-------
Table 5. The flux, density of pollutant leached below the treatment zone as a
function of time.
LEACHATE FLUX VERSUS TIME
Time Flux
days g/m2-day
102.42 3.3E-002
103.28 3.3E-002
104.14 3.2E-002
104.99 3.2E-002
105.85 3.2E-002
106.71 3.1E-002
107.56 3.1E-002
108.42 3.1E-002
109.27 3.0E-002
110.13 3.0E-002
110.99 3.0E-002
111.84 2.9E-002
112.70 2.9E-002
113.56 2.9E-002
Identification Code: Site
Time
days
114v41
115.27
116.12
116.98
117.84
118.69
119.55
120.41
121.26
122.12
122.97
123.83
124.69
125.54
//I
Flux
g/m2-day
2.9E-002
2.8E-002
2.8E-002
2.8E-002
2.7E-002
2.7E-002
2.7E-002
2.6E-002
2.6E-002
2.6E-002
2.6E-002
2.5E-002
2.5E-002
2.5E-002
Time
days
126.40
127.26
128.11
128.97
129.82
130.68
131.54
132.39
133.25
134.11
134.96
135.82
136.67
137.53
Flux
g/m2-day
2.5E-002
2.4E-002
2.4E-002
2.4E-002
2.3E-002
2.3E-002
2.3E-002
2.3E-002
2.2E-002
2.2E-002
2.2E-002
2.2E-002
2.1E-002
2.1E-002
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Leachate Flux
versus Tine
J. . V£T WX
L
e l.OE+000
a
c
h
a
t l.OE-001
e
F
1
« l.OE-002
X
i.OE-003
f
— • ,
— b_
— — I 1 1 1— 1 P 1 —
Identification:
Sitettl
Soil Nam:
Tipton Sandy Loan
Pollutant Nam:
Pallutantttl
CAS NuNl*i>:
123-4567
100 105 110 115 120 125
Tim (days)
130 135 140
Figure 4.
Graph of flux density of pollutant leached below the treatment
zone as a function of time.
24
-------
Table 6. The location of the top and bottom of the pollutant as a function
of time.
DEPTH OF BOTTOM AND TOP OF POLLUTANT VERSUS TIME
Time
days
0.00
4.15
8.13
11.94
15.61
19.14
22.54
25.83
29.02
32.11
35.11
Top
m
0.00
0.01
0.03
0.04
0.06
0.07
0.09
0.10
0.12
0.14
0.15
Bottom
m
0.15
0.20
0.26
0.31
0.36
0.40
0.45
0.49
0.53
0.57
0.61
Time
days
35.11
45.35
55.59
65.83
76.08
86.32
96.56
106.80
117.05
127.29
137.53
Top
m
0.15
0.29
0.42
0.56
0.69
0.83
0.96
1.09
1.23
1..36
1.50
Bottom
m
0.61
0.75
0.88
1.02
I.'IS
1.29
1.42
> 1.50
> 1.50
> 1.50
> 1.50
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Slag Position versus Tine
1.50
25
50 75 100
Tim (days)
125
Identification:
Sitettl
Soil Nam:
Tipton Sands Loan
Pollutant Nam:
Pollutant*!
CflS Hunker:
123-4567
150
Figure 5, Location of the top and bottom of the pollutant as a function of
time.
25
-------
Table 7. Concentration of pollutant in different phases and oil content as a
function of time at selected depths.
Depth = 0
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
.000 meters
Total
Pollutant
g/m3
l.OE+002
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
5.9E+001
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
»
Soil
g/kg
6.5E-003
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
Vapor
g/m3
3.2E-003
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
g/m3
2.9E+003
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
Content
m3/m3
2.5E-002
2.1E-002
1.8E-002
1.6E-002
1.4E-002
1.2E-002
7.9E-003
5.4E-003
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Depth - 0.050 meters
CONCENTRATION PROFILE
Pollutant in
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
lotaj.
Pollutant
g/m3
1 . OE+002
7.9E+001
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Water
g/m3
5.9E+001
5.2E+001
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Soil
g/kg
6.5E-003
5.7E-003
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Vapor
g/m3
3.2E-003
2.9E-003
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
g/m3
2.9E+003
2.6E+003
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
U1J.
Content
m3/m3
2.5E-002
2.1E-002
1.8E-002
1.6E-002
1.4E-002
1.2E-002
7.9E-003
5.4E-003
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
26
-------
Table 7. Continued.
Depth = 0
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
.100 meters
Total
Pollutant
g/m3
1 . OE+002
7.9E+001
6.3E+001
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
5.9E+001
5.2E+001
4.6E+001
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
Soil
g/kg
6.5E-003
5.7E-003
5.0E-003
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
Vapor
g/m3
3.2E-003
2.9E-003
2.5E-003
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
Oil
g/m3
2.9E+003
2.6E+003
2.3E+003
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
Oil
Content
m3/m3
2.5E-002
2.1E-002
1.8E-002
1.6E-002
1.4E-002
1.2E-002
7.9E-003
5.4E-003
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Depth = 0.150 meters
CONCENTRATION PROFILE
Pollutant in
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
lotaj.
Pollutant
g/m3
1 . OE+002
7.9E+001
6.3E+001
5.0E+001
0 . OE+000
0. OE+000
0 . OE+000
0 . OE+000
Water
g/m3
5.9E+001
5.2E+001
4.6E+001
4.0E+001
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Soil
g/kg
6.5E-003
5.7E-003
5.0E-003
4.4E-003
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
Vapor
g/m3
3.2E-003
2.9E-003
2.5E-003
2.2E-003
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
Oil
g/m3
2.9E+003
2.6E+003
2.3E+003
2.0E+003
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
Ull
Content
m3/m3
2.5E-002
2.1E-002
1.8E-002
1.6E-002
1.4E-002
1.2E-002
7.9E-003
5.4E-003
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutants/1
CAS Number: 123-4567
RITZ
27
-------
Table 7. Continued.
Depth = 0
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
.250 meters
Total
Pollutant
g/m3
0 . OE+000
2.2E+001
1.9E+001
1.7E+001
1.5E+001
0. OE+000
0 . OE+000
0. OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
0. OE+000
4.8E+001
4.2E+001
3.7E+001
3.3E+001
0 . OE+000
0 . OE+000
0 . OE+000
Soil
g/kg
0 . OE+000
5.3E-003
4.7E-003
4.1E-003
3.6E-003
0 . OE+000
0. OE+000
0. OE+000
Vapor
g/m3
0 . OE+000
2.6E-003
2.3E-003
2.1E-003
1.8E-003
0. OE+000
0. OE+000
0. OE+000
. Oil
g/m3
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
Oil
Content
m3/m3
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
0. OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Depth = 0.500 meters
CONCENTRATION PROFILE
Pollutant in
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
louaj.
Pollutant
g/m3
0. OE+000
0. OE+000
0 . OE+000
1.4E+001
1.2E+001
1.1E+001
0. OE+000
0. OE+000
Water
g/m3
0 . OE+000
0. OE+000
0. OE+000
3.0E+001
2.7E+001
2.4E+001
0 . OE+000
0. OE+000
Soil
g/kg
0. OE+000
0. OE+000
0 . OE+000
3.4E-003
3.0E-003
2.6E-003
0. OE+000
0. OE+000
Vapor
g/m3
0. OE+000
0. OE+000
0 . OE+000
1.7E-003
1.5E-003
1.3E-003
0. OE+000
0. OE+000
Oil
g/m3
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
0 . OE+000
VJ1J.
Content
m3/m3
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
28
-------
Table 7. Continued.
Depth = 0
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
.750 meters
Total
Pollutant
g/m3
0 . OE+000
O.OE+000
0. OE+000
0 . OE+000
0 . OE+000
8.8E+000
6 . AE+000
0 . OE+000
CONCENTRATION' PROFILE
Pollutant in
Water
g/m3
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
1.9E+001
1.4E+001
O.OE+000
Soil
g/kg
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
2.1E-003
1.6E-003
O.OE+000
Vapor
g/m3
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
-1.1E-003
7.8E-004
O.OE+000
Oil
g/m3
O.OE+000 .
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
-O.OE+000
0 . OE+000
Oil
Content
m3/m3
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Depth = 1.000 meters
CONCENTRATION PROFILE
Pollutant in
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
lULcU.
Pollutant
g/m3
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
5.3E+000
0 . OE+000
Water
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
1.2E+001
0 . OE+000
Soil
g/kg
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
1.3E-003
O.OE+000
Vapor
g/m3
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
6.4E-004
O.OE+000
Oil
g/m3
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
U1JL
Content
m3/m3
O.OE+000
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant#l
CAS Number: 123-4567 ,
RITZ
29
-------
Table 7. Continued.
Depth = 1
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
.250 meters
Total
Pollutant
g/m3
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
3 . 2E+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
7 . OE+000
Soil
g/kg
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0 . OE+000
7.7E-004
Vapor
g/m3
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
3.8E-004
Oil
g/m3
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
0. OE+000
Oil
Content
m3/m3
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
0. OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Depth = 1.500 meters
CONCENTRATION PROFILE
Pollutant in
Time
days
0.00
10.00
20.00
30.00
40.00
50.00
75.00
100.00
lotax
Pollutant
g/m3
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
Water
g/m3
O.OE+'OOO
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0 . OE+000
Soil
g/kg
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
Vapor
g/m3
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
Oil
g/m3
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0 . OE+000
U1J.
Content
m3/m3
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
0 . OE+000
0. OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
30
-------
Concentration of Pollutant (s/w3) us Tine
l.OE+003
C l.OE+001
0
n
c
e l.OE-001
n
t
p
a l.OE-003
t
i
0
" l.OE-005
t AF-AA9
Total
,
.
25 50 75 100
Tine (days)
Identification:
Siteftl
Soil Nawe:
Tipton Sandy Loam
Pollutant Nam:
Pollutant*.!
CAS Number:
123-4567
150
Figure 6. Concentration of total pollutant as a function of time for depths
of 0.1, 0.5, 1.0, and 1.5 meters.
Concentration of Pollutant (g/i*3) vs Tine
A. V1TVVO
C l.OE+001
0
n
c
e l.OE-001
n
t
K»
a l.OE-003
i
0
" l.OE-005
1 OF-007
:
Water
Identif icatian:
Sitettl
Soil Nai«e:
Tipton Sandy Loan
Pollutant Nane:
Pollutant*!
CAS NuMber:
123-4567
25 50 75 100
Tine (days)
125
150
Figure 7. Concentration of pollutant in water as a function of time for
depths of 0.1, 0.5, 1.0, and 1.5 meters.
31
-------
Concentration of Pollutant (g/kg) us Tine
J. , UA-UIU
C l.OE-003
0
n
e l.OE-005
n
t
r
» l.OE-007
i
o
n l.OE-009
] .OF-Oll
., Soil
1 —
Identification:
SitetU
Soil Nam:
Tipton Sandy Loan
Pollutant Nane:
Pollutanttti
CAS NUM!I«I>:
123-4567
25 50 75 100
Tine (dags)
125
150
Figure 8. Concentration of pollutant in soil as a function of time for
depths of 0.1, 0.5, 1.0, and 1.5 meters.
Concentration of Pollutant (g/*?) us Time
C l.OE-003
o
n
c
e l.OE-005
n
t
p
J l.OE-007
t
i
o
" l.OE-009
1 AF-At 1
' '-
Uapor
25 50 75 100
Tine (days)
125
Identification:
SiteM.
Soil Nam:
Tipten Sandy Loan
Pollutant Nam:
Pollutant*!
150
Figure 9. Concentration of pollutant in vapor as a function of time for
depths of 0.1, 0.5, 1.0, and 1.5 meters.
32
-------
l.OE+004
Concentration of Pollutant (g/*3) us Tine
C l.OE+002
o
n
e l.OE+000
n
t
p
* l.OE-002
i
o
n l.OE-004
l.OE-006
Oil
25 SO 75 100
Tine (days)
125
Identification:
Sitettl
Soil Nam:
Tipton Sandy Loan
Pollutant Nam:
Pollutant»l
CAS Nunber:
123-4567
150
Figure 10. Concentration of pollutant in oil as a function of,time for depth
of 0.1 meters. Curves for 0.5, 1.0, and 1.5 meter depths are not
visible since the concentration at these depths is zero.
Oil Content (1*3/1*3) us Tine
j. . vn-vvj.
C l.OE-003
0
n
e l.OE-005
n
t
p
» l.OE-007
i
0
n l.OE-009
l.OE-011
*""* ~
0 25 50 75 100 125 15
Identification:
Si tell
Soil Nam:
Tipton Sandy Loan
Pollutant Nam:
Pollutant*!
CAS NuMber:
123-4567
0
Tim (days)
Figure 11. Oil content as a function of time for depths of 0.1 meters. Oil
content curves for 0.5, 1.0, and 1.5 meter depths are not shown
since the oil content is zero below the plow zone.
33
-------
Table 8. Concentration of pollutant in various phases and oil content as a
function of depth at selected times.
Time = 0.
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
00 days
Total
Pollutant
g/m3
1 . OE+002
1. OE+002
1 . OE+002
1 . OE+002
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
5.9E+001
5.9E+001
5.9E+001
5.9E+001
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
>
Soil
g/kg
6.5E-003
6.5E-003
6.5E-003
6.5E-003
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Vapor
g/m3
3.2E-003
3.2E-003
3.2E-003
3.2E-003
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
g/m3
2.9E+003
2.9E+003
2.9E+003
2.9E+003
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
Content
m3/m3
2.5E-002
2.5E-002
2.5E-002
2.5E-002
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Time = 10.00 days
CONCENTRATION PROFILE
Pollutant in
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
luuajL
Pollutant
g/m3
O.OE+000
7.9E+001
7.9E+001
7.9E+001
2.2E+001
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Water
g/m3
O.OE+000
5.2E+001
5.2E+001
5.2E+001
4.8E+001
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Soil
g/kg
0 . OE+000
5.7E-003
5.7E-003
5.7E-003
5.3E-003
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
Vapor
g/m3
O.OE+000
2.9E-003
2.9E-003
2.9E-003
2.6E-003
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
Oil
g/m3
O.OE+000
2.6E+003
2.6E+003
2.6E+003
0 . OE+000
O.OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
U1J.
Content
m3/m3
2.1E-002
2.1E-002
2.1E-002
2.1E-002
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
34
-------
Table 8. Continued.
Time = 20
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
.00 days
rri-. 4. _ 1
LOuai
Pollutant
g/m3
0 . OE+000
0 . OE+000
6.3E+001
6.3E+001
1.9E+001
0. OE+000
- 0 . OE+000
0 . OE+000
0 . OE+000
0. OE+000
CONCENTRATION
PROFILE
Pollutant in
Water
g/m3
0. OE+000
0 . OE+000
4.6E+001
4.6E+001
4.2E+001
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
Soil
g/kg
0 . OE+000
0 . OE+000
5.0E-003
5.0E-003
4.7E-003
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
Vapor
g/m3
0. OE+000
0. OE+000
2.5E-003
2.5E-003
2.3E-003
0. OE+000
0. OE+000
0. OE+000
0 . OE+000
0. OE+000
Oil
g/m3
0 . OE+000
0 . OE+000
2.3E+003
2.3E+003
0. OE+000
0 . OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
f\l T
Ull
Content •
m3/m3 ,<
1.8E-002
1.8E-002
1.8E-002
1.8E-002
0 . OE+000
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Time = 30.00 days
CONCENTRATION PROFILE
Pollutant in
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
lotai
Pollutant
g/m3
0 . OE+000
0 . OE+000
0. OE+000
5.0E+001
1.7E+001
1.4E+001
0 . OE+000
0. OE+000
0. OE+000
0 . OE+000
Water
g/m3
0. OE+000
0. OE+000
0. OE+000
4.0E+001
3.7E+001
3.0E+001
0. OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Soil
8/kg
0. OE+000
0. OE+000
0. OE+000
4.4E-003
4.1E-003
3.4E-003
0. OE+000
0. OE+000
0. OE+000
0. OE+000
Vapor
g/m3
0 . OE+000
0 . OE+000
0. OE+000
2.2E-003
2.1E-003
1.7E-003
0. OE+000
0. OE+000
0. OE+000
0. OE+000
Oil
g/m3
0. OE+000
0. OE+000
0. OE+000
2.0E+003
0 . OE+000
0. OE+000
0 . OE+000
0 . OE+000
0. OE+000
0. OE+000
Ull
Content
m3/m3
1.6E-002
1.6E-002
1.6E-002
1.6E-002
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
0. OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
35
-------
Table 8. Continued.
Time = 40
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
.00 days
Total
Pollutant
g/m3
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
1.5E+001
1.2E+001
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
3.3E+001
2.7E+001
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
Soil
* g/kg
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
3.6E-003
3.0E-003
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
Vapor
g/m3
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
1.8E-003
1.5E-003
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
Oil
g/m3
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
Oil
Content
m3/m3
1.4E-002
1.4E-002
1.4E-002
1.4E-002
O.OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Time = 50.00 days
CONCENTRATION PROFILE
Pollutant in
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
lotaj.
Pollutant
g/m3
0 . OE+000
O.OE+000
O.OE+000
0 . OE+000
0 . OE+000
1.1E+001
8 . 8E+000
0 . OE+000
0 . OE+000
O.OE+000
Water
g/m3
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
2.4E+001
1.9E+001
O.OE+000
O.OE+000
O.OE+000
Soil
g/kg
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
2.6E-003
2.1E-003
0 . OE+000
O.OE+000
O.OE+000
Vapor
g/m3
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
1.3E-003
1.1E-003
O.OE+000
O.OE+000
0 . OE+000
Oil
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
U1J.
Content
m3/m3
1.2E-002
1.2E-002
1.2E-002
1.2E-002
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
Identification Code: Site //I
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
36
-------
Table 8. Continued.
Time = 75
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
.00 days
Total
Pollutant
g/m3
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
6.4E+000
5 . 3E+000
O.OE+000
O.OE+000
CONCENTRATION PROFILE
Pollutant in
Water
g/m3
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
1.4E+001
1.2E+001
0 . OE+000
0 . OE+000
Soil
g/kg
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
1.6E-003
1.3E-003
O.OE+000
O.OE+000
Vapor
g/m3
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
7.8E-004
6.4E-004
0 . OE+000
O.OE+000
Oil
g/m3
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
Oil
Content
m3/m3
7.9E-003
7..9E-003
7.9E-003
7.9E-003
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
0 . OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
Time = 100.00 days
CONCENTRATION PROFILE
Pollutant in
Depth
m
0.000
0.050
0.100
0.150
0.250
0.500
0.750
1.000
1.250
1.500
louaj.
Pollutant
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
3.2E+000
O.OE+000
Water
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
7 . OE+000
O.OE+000
Soil
g/kg
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
O.OE+000
7.7E-004
0 . OE+000
Vapor
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
3.8E«-004
0 . OE+000
Oil
g/m3
0 . OE+000
0 . OE+000
0 . OE+000
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
O.OE+000
O.OE+000
O.OE+000
U1X
Content
m3/m3
5.4E-003
5.4E-003
5.4E-003
5.4E-003
O.OE+000
0 . OE+000
O.OE+000
0 . OE+000
0 . OE+000
0 . OE+000
Identification Code: Site #1
Soil Name: Tipton Sandy Loam
Compound Name: Pollutant//!
CAS Number: 123-4567
RITZ
37
-------
Concentration of Pollutant
* l.OE-003
i
0
n l.OE-005
i (or-<\M
~H
%
Total
Identification:
Sitettl
Soil Name:
Tipton Sandy Loam
Pollutant Nane:
Pollutanttti
CAS Nuhber:
123-4567
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Depth
Figure 12. Concentration of total pollutant as a function of depth for times
of 10, 50, and 100 days.
Concentration of Pollutant (sr/i»3) us Depth
J.. V&TVVO
C l.OE+001
0
n
c
• l.OE-001
n
p
« l.OE-003
i
o
" l.OE-005
l.OE-007
,
Hater
Identification:
Sitettl
Soil Name:
Tipton Sandy Loam
Pollutant Name:
Pollutanttti
CAS Number:
123-4567
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Depth (N)
Figure 13. Concentration of pollutant in water as a function of depth for
times of 10, 50, and 100 days.
38
-------
Concentration of Pollutant (sr/kg) ws Depth
C l.OE-003'
o
n
c
e l.OE-005
n
t
» l.OE-007
t
i
o
» i.OE-009
i AF-AI i
Soil
Identification:
Site«l
Soil Na«e:
Tipton Sandy Loan
Pollutant Nam:
PollutantHl
CAS NuMber:
123-4567
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Depth (N)
Figure 14. Concentration of pollutant in soil as a function of depth for
times of 10, 50, and 100 days.
Concentration of Pollutant (g/i«3) us Depth
i. Vt-WVJ.
C l.OE-003
o
n
• l.OE-005
n
t
r
a l.OE-007
t
i
0
" i.OE-009
1 AC A1 1
Uapor
Identification:
Sitettl
Soil Name:
Tipton Sandy Loan
Pollutant Name:
Pollutant*!
CAS Hunker:
123-4567
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Depth (N)
Figure 15. Concentration of pollutant in vapor as a function of depth for
times of 10, 50, and 100 days.
39
-------
Concentration of Pollutant (g/i»3) us Depth
i . vAi-wn
C l.OE+002
0
n
» l.OE+000
n
t
a l.OE-002
i
0
•> l.OE-004
l.OE-006
0.
—
' Oil '
*
00 0.25 0.50 0.75 1.00 1.25 1.
Identification:
Sitettl
Soil Nane:
Tipton Sandy Loan
Pollutant Nane:
Pollutantttl
CAS NuMbep;
123-4567
50
Depth (M)
Figure 16. Concentration of pollutant in oil as a function of depth for 10
days after application. Note the concentration decreases to zero
at the plow zone depth. The concentration was zero at 50, and 100
days.
Oil Content d*3/i«3) vs Depth
1. VJC.-WJ.
C l.OE-003
0
n
e l.OE-005
n
p
« l.OE-007
i
o
n l.OE-009
l.OE-011
0.
00 0.25 0.50 0.75 1.00 1.25 1.
Identification:
Sitettl
Soil Name:
Tipton Sandy Loan
Pollutant Name:
, Pollutantttl
CAS Nunbep:
123-4567
50
Depth (M)
Figure 17. Oil content as a function of depth for times of 10, 50, and 100
days. The oil does not move downward but the oil content
decreases due to degradation.
AO
-------
Tine: 10.00 days
Depth (H).
'Total
Soil Nane: Tipton Sandy Loan
CflS Hunker: 125-4567
. „ f Pollu
—Concentration o
Mater Soil
llutant '-•
Uapor
Oil
Oil
Content
n
0.00
0.25
0.50
0.75
1.00
1.25
1.50
Pattern description for total concentration of pollutant (g/n3).
H.OE+001 >1.0E+000 M.OE-001 >1.0E-002 >1.0E-003 >=O.OE+000
Figure 18. Concentration bar graphs representing the pollutant and oil in
the treatment zone at a time of 10 days. The concentrations
represented by the patterns in each phase can be displayed by
pressing the key.
Tine: 30.00 days
c&'Ucsi Il5^5n67SandB Loa"
Concentration of Pollutant —
Soil
Uapor
Oil
Oil
Content
n
1.50
Pattern description for total concentration of pollutant (g/n3).
>1.0E+001 H.OE+000 >1.0E-001 >1.0E-002 >1.0E-003 >=O.OE+000
Figure 19. Concentration bar graphs for 30 days.
Al
-------
Tine: 50.00 days
Soil Mane: Tipton Sandy Loan
CAS Number: 123-4567
-Concentration of Pollutant
Total Hater Soil Uapor
^1 ^1 ^^\ ^\
Oil
Oil
Content
0.25
0.50
0.75
1.00
1.25
1.50
Pattern description for concentration of pollutant in water (g/n3).
>5.9E+000 >5.9E-001 >5.9E-002 >5.9E-003 >5.9E-004 >=OTOE+C
Figure 20. Concentration bar graphs for 50 days.
Tine: 100.00 days
0.25
0.50
0.75
1.00
1.25
1.50
Soil NaMe: Tipton Sandy Loan
3-
CAS Number: 123-4567
-Concentration of Pollutant
Hater
Soil
Uapor
Oil
Oil
Content
n
Pattern description for concentration of pollutant in water (g/«3)
>5.9E+000
>5.9E-001 >5.9E-C
>5.9E-003 >5.9E-004 >=O.OE«000
Figure 21. Concentration bar graphs for 100 days.
42
-------
FILE STRUCTURE
Disk files are used in this software for two purposes. The first is to store
input parameters entered at one time for use at another time. The second is
for storing output tables for later printing or display or for use in other
documents.
The input parameter files are made up of a single record of binary
information. The record is composed of parameters in the sequence listed in
screens 2, 3, and A. All numeric entries are stored as floating point values.
All alphanumeric entries are stored as strings.
Tabular data stored in files are written as text in ASCII characters.
-------
REFERENCES CITED
1. Clapp, Roger B. and George M. Hornberger. 1978. Empirical equations for
some soil hydraulic properties. Water Resources Research 14: 601-604.
2. Jury, W.A., W.F. Spencer, and W.J. Farmer. 1983. Behavior assessment
model for trace organics in soil:Model description. J. Environ. Qual.
12:558-564.
>
3. Laskowski, D.A., C.A.I. Goring, P.J. McCall, and R.L. Swann. 1982.
Terrestrial environment. In Environmental Risk Analysis for Chemicals,
R.A. Conway (Ed.). Van Nostrand-Reinhold Co., NY. pp 198-240.
4. Karickhoff, Samuel W. 1981. Semi-empirical estimation of sorption of
hydrophobic pollutants on natural sediments and soils. Chemosphere
10:833-846.
5. Karickhoff, S.W., D.S. Brown, and T.A. Scott. 1979. Sorption of
hydrophobic pollutants on natural sediments and soils. Water Research
13:241-248.
6. Millington, J.R. and J.M. Quirk. 1961. Permeability of porous solids.
Trans Faraday Soc. 57:1200-1207.
7. Ralston, Anthony. 1965. A First Course In Numerical Analysis, McGraw-
Hill Book Co., New York, pp 121-129.
8. Short, Thomas E. 1985. Movement of contaminants from oily wastes during
land treatment. Proceedings of Conference on Environmental and Public
Health Effects of Soils Contaminated with Petroleum Products, Amherst,
MA.
9. Swartzendruber, Dale. 1960. Water flow through a soil profile as
affected by the least permeable layer. J. of Geophysical Research
65:4037-4042.
10. Verschuren, K. 1983. Handbook of Environmental Data on Organic
Chemicals. Van Nostrand Reinhold Co., New York, New York., 1310 pp.
44
-------
APPENDIX
45
-------
MATHEMATICAL BASIS OF RITZ
This section summarizes the mathematical equations used in this version of the
RITZ software. They are presented for your information only. No attempt is
made here to explain the mathematical derivations of these equations. See
Short(1985) for those derivations.
Total Pollutant Concentration; The total concentration of the pollutant
Crri(x,t) at position x and time t is given by
•L ^
Cij(x,t) = 0 for x < top of pollutant slug
Crji(x,t) = C-poexp(-(jpt) for top of pollutant slug < x < pzd
CT(x,t) = CToRexp(-Mpt)/(R + RTexp(-no(t-(x-pzd)/Vp)))
for pzd < x < bottom of pollutant slug
,t) = 0 for x > bottom of pollutant slug
where
C-jo is the initial pollutant concentration,
Mp is the degradation constant for the pollutant
(Up = ln(2)/tip),
Mo is the degradation constant for the oil
(MO = ln(2)/40),
R is the retardation factor for the pollutant in the treatment zone,
R-p is the contribution of oil to the retardation,
Vp is the velocity of the pollutant in the lower treatment zone, and
pzd is the depth of the plow zone .
Cr|i(x,t) is the mass of pollutant per unit volume of soil. In this software
these units are grams of pollutant per cubic meter of soil. The initial
pollutant concentration is given by
CTo = SAR • Sp /
where
SAR is the sludge application rate and
Sp is the concentration of pollutant in the sludge.
46
-------
The retardation factor, R, is given by
R = 1 + (PKD + (9S - 9)KH) / 6
where
p is the bulk density of the soil,
9 is the water content of the soil on a volume basis,
9S is the saturated water content of the soil on a volume basis,
Kj) is the partition coefficient for pollutant in the soil, and
Kg is the dimensionless value of Henry's Law constant, (
The partition coefficient is given by Kp = K0Qf0Q where KQQ is the organic
carbon partition coefficient and f0£ is the fractional organic carbon content
of the soil.
The parameter R-^ is given by
RlJ = ^oCKQ - Kjj) / 9
where
$o is the initial oil content or the volume fraction occupied by oil, and
KQ is the partition coefficient for oil.
The volumetric water content of the soil, 9, is given by
6 = 8s[Vd/k8]1/(2bf3)
where
V^ is the recharge rate,
ks is the saturated conductivity of the soil, and
b is the Clapp and Hornberger constant for the soil.
The velocity of the pollutant in the lower treatment zone, Vp, is given by
Vp = Va / R
where Va = V^/9 is the aqueous or pore water velocity.
47
-------
Pollutant Concentration in Water; The concentration of pollutant in water,
C^(x,t) at position x and time t is given by
Cy(x,t) = 0 for x < top of pollutant slug
Cw(x,t) = CT(x,t) / 9(R + RTexp(-^i0t))
for top of pollutant slug < x < pzd
Cw(x,t) = CT(x,t) / R6 * for pzd < x < bottom of pollutant slug
,t) = 0 for x > bottom of pollutant slug
where all the symbols are those defined for the total pollutant concentration.
C^(x,t) is the mass of pollutant in water per unit volume of water. In this
software these units are grams of pollutant per cubic meter of water.
Concentration of Pollutant in Soil: The concentration of the pollutant in the
soil phase Cg(x,t) at position x and time t is given by
Cs(x,t) = KDCw(x,t)
where
Kp is the soil: water partition coefficient for the pollutant and
C^(x,t) is the concentration of pollutant in water.
Cg(x,t) is the mass of pollutant in water per unit mass of soil solids. In
this software these units are grams of pollutant per kilogram of soil.
Concentration of Pollutant in Vapor; The concentration of the pollutant in the
vapor phase Cy(x,t) at position x and time t is given by
Cv(x,t) = KHCw(x,t)
where
KJJ is the dimensionless (Henry's Law) vapor:water partition coefficient and
C^j(x,t) is the concentration of pollutant in water.
CyCx.t) is the mass of pollutant per unit volume of vapor. In this software
these units are grams of pollutant per cubic meter of vapor.
48
-------
Concentration of Pollutant in Oil; The concentration of pollutant in the oil
phase C0(x,t) at position x and time t is given by
C0(x,t) = K^Cx.t) for x < pzd
C0(x,t) = 0 for x > pzd
where
Ko is the dimensionless oiliwater partition , coefficient for the pollutant,
pzd is the depth of the plow zone, and
C^(x,t) is the concentration of the pollutant in water.
CQ(x,t) is the mass of pollutant per unit volume of oil. In this software
these units are grams of pollutant per cubic meter of oil.
Oil Content: The oil content $(t) in the plow zone at time t is the volume of
oil per unit volume of soil and is given by
= $0exp(-M0t)
where
$0 is the initial oil content in the plow zone and
Mo is the degradation constant for oil.
The oil content is uniform throughout the plow zone at each instant of time.
The oil content is zero below the plow zone at all times. The initial oil
content <&o is given by
-------
RT/R)exp[Moxtop/Vp - F(xtop)] - RT/R}
for 0 < xtop < pzd
(xtop - Pzd)/Vp - G(xtop)
for pzd < xtop < tzd
where
F(xton) = ^aV^lnU + xt?D/g),
{top
top-* = ^oavp lnU + xtop/B-'.
G(xto_) = aV:1ln[(g + xtoJ/(g + pzd)],
g = DS5/DA + a,
a = KHDs/Va8,
DA is the diffusion coefficient of the pollutant vapor in air,
Dg is the diffusion coefficient of the pollutant vapor in the soil,
6 is the thickness of the stagnant boundary layer above the soil, and
tzd is the depth of the treatment zone.
Although the equations above hold for all depths, numerical overflow occurs in
the first equation when Moxtop/^p •"•s verv large. In this case, an approximate
form of the equation is used which is
ttop(xtop) = Mo^MoXtop/Vp - F(xt0p) + ln(1 + RT/R)}
for 0 < xtop < pzd.
The diffusion coefficient of the pollutant in the soil, Dg is given by
DS = DAn10/3/ei
where n is the initial air content of the soil (Millington and Quirk, 1961).
The thickness of the stagnant boundary layer (Jury et al., 1983) is given by
6 = DwPwvCl - RH)/2EpWL
where
Ify is the diffusion coefficient of water vapor in air,
RH is the relative humidity of the air,
E is the evaporation rate,
is the density of water vapor, and
is the density of liquid water.
The ratio of the density of water vapor to the density of liquid water is
given by (Short, 1985)
PWV/PWL = ao + aiT + a2T2 + a3T3
where
T is the temperature in degrees Celsius,
a0 = 4.60843696E-06,
ax = A.0710817E-07,
a2 = 3.02943E-09, and
a3 = 3.9405E-10.
50
-------
Time at Which the Bottom of the Pollutant Slug Reaches a Specified Depth; The
bottom of the pollutant slug is located at the plow zone depth at time zero.
It moves downward through the treatment zone as time increases. The time at
which the bottom of the slug reaches a position xt,ottom is given by
= ° for xbottom * Pzd
= ^bottom " Pzd)/vp
for xbottom > Pzd
where
pzd is the depth of the bottom of the plow zone and
Vp is the velocity of the pollutant in the lower treatment zone.
Flux of Pollutant Vapor for a Specified Position of the Top of the Pollutant
Slug and the Corresponding Time; The flux of pollutant vapor, J(t(xtOD)),
moving upward out of the treatment zone at the time t is given by
J(t) = aVpCToexp(-Mpt)/{(g - a + xtop)[l + (RT/R)exp(-Mot) ] }
for 0 < xtop < pzd
J(t) = aVpCToexp(-npt)/{(g - a + xtop)[l + (RT/R)exp(-noAt)] } ,
for pzd < xtop < tzd
where
t = ttop(xtOp) as defined previously and
Total Amount of Pollutant Lost as Vapor; The amount of pollutant lost in the
vapor form can be obtained by integrating the vapor flux over the time in
which the pollutant is in the plow zone and the treatment zone. That is
r1
Mv - Jo J(t)dt
where t is the time at which the top of the pollutant slug reaches the bottom
of the treatment zone. It is computationally more efficient to change variable
of integration and integrate over distance. This integral then becomes
rpzd tzd
My = JQ J(t(x))(dt/dx)dx + J ^ J(t(x))(dt/dx)dx
The integrands in the above equation are
II = aClo^P^pttopW^B + x) for 0 < x < pzd (term 1)
I2 = aCToexp(-Mpttop(x)/{(g + x)(l + (RT/R)exp(-MoAt))}
for pzd < x < tzd (term 2)
where At = ttop(x) - (x - pzd)/Vp. The integration is carried out numerically
using Romberg integration. Convergence is assumed when the difference between
51
-------
consecutive approximations to the integral is less than l.OE-06 percent of the
pollutant applied.
Total Amount of Pollutant Leached Below the Treatment Zone; The amount of
pollutant leached below the treatment zone, M^, is obtained by integrating the
product of the recharge rate and the pollutant concentration in water at the
treatment zone depth. That is
ft
MT * L V 9C (tzd.t)dt
L J0 a W
where
V&9 = the recharge rate and
C^(tzd,t) is the concentration of pollutant in water defined previously.
This integration is also performed numerically using Romberg integration
(Ralston, 1965). Convergence is assumed when the difference between
consecutive approximations to the integral is less than l.OE-06 percent of the
pollutant applied.
Total Amount of Pollutant Degraded in the Treatment Zone: The amount of the
pollutant degraded, MJJ, within the entire treatment zone is equal to the sum
of the amounts degraded in the plow zone and in the treatment zone. That is
pzd
=
J
(x,t (x))(dt/dx)dx
U p T top
tb
+ I M Acc(t)dt
J0
-
+
J
p
tzd"
u Acc(t)(dt/dx)dx
pzd p
where tb = tto_(pzd) is the time at which the top of the slug reaches the
depth of the plow zone and Acc(t) is the mass of pollutant accumulated in the
lower treatment zone. The first integral represents the degradation within the
plow zone. The second integral represents the degradation in the lower
treatment zone before the top of the slug reaches the lower treatment zone.
The third integral represents the degradation in the lower treatment zone
after the slug is entirely in that zone. These integrals are evaluated by the
Romberg integration with the same convergence criteria as for volatilization
and leaching.
52
-------
The accumulation of pollutant in the lower treatment zone, Acc(t), is given by
Acc(t) = CToexp(-npt){(xbottom - xtop) - VpM-1ln(H(xbottom)/H(xtop))}
where
H(x) = 1 + (RT/R)exp(-M0(xb - x)/Vp)
and
xb = pzd + Vpt.
Mass Balance Error; Pollutant applied to the soil must be volatilized,
leached, or degraded by the time the top the slug reaches the treatment zone
depth. Each of these three components are evaluated above. If the
computational techniques are accurate, the sum of these should be equal to the
amount of pollutant applied. The mass balance computational error is given by
Error = MT - Mv - ML - MD
where Mf is the mass of pollutant applied to the plow zone. The other symbols
were defined previously.
53
-------
Table 9. List of symbols with meaning and units as used in this section.
b Clapp and Hornberger constant, dimensionless
Crp total concentration of pollutant in all phases, g/rn^
Cy concentration of pollutant in water, g/mj
Cg concentration of pollutant in soil, g/kg
Cy concentration of pollutant in vapor, g/m
CQ concentration of pollutant in oil, g/m^
GIJO total concentration of pollutant at time zero, g/m^
D^ diffusion coefficient of pollutant in air, m^/day
Dg diffusion coefficient of pollutant vapor in soil, m^/day
Dy; diffusion coefficient of water vapor in air, m^/day
E evaporation rate, m/day
fgc fractional organic carbon content of soil
J flux of pollutant vapor, g/m^-day
k unsaturated hydraulic conductivity, m/day
ks saturated hydraulic conductivity of soil, in/day
KD soilrwater partition coefficient of pollutant, nrVkg
Kg vapor:water partition coefficient of pollutant
or the dimensionless Henry's law constant, dimensionless
KQ oil:water partition coefficient of pollutant, dimensionless
organic-carbon:water partition coefficient, nrVkg
total amount of pollutant degraded, g/m
ML total amount of pollutant leached below treatment zone, g/m^
My total amount of pollutant lost in vapor form, g/m^
pzd plow zone depth, m
R retardation factor for pollutant (ignoring oil), dimensionless
RP contribution of oil to retardation of pollutant, dimensionless
RH relative humidity, dimensionless
SAR sludge application rate, kg/ha
So initial concentration of oil in the sludge, g/kg
Sp initial concentration of pollutant in the sludge, g/kg
T temperature,- °C
t time, days
tip degradation half-life of the pollutant, days
ti0 degradation half-life of the oil, days
tzd treatment zone depth, m
V^ recharge rate, m/day
Va pore water velocity, m/day
V velocity of the pollutant in the lower treatment zone, m/day
x distance from the soil surface, m
p bulk density of soil, kg/m^
Po density of oil, kg/m^
density of water vapor, kg/rn^
density of liquid water, kg/^
6 water content on a volume basis, itr/nr
6_ saturated water content on a volume basis, nr/mr
54
-------
Table 9. Continued.
oil content (volume fraction of oil) at time t, nrVn
$0 initial oil content (volume fraction of oil), nrVnr
Mp degradation constant of pollutant, days"
Ho degradation constant of oil, days"^-
6 thickness of stagnant boundary layer, m
H initial air content of soil, m-Vm^
55
-------
INPUT PARAMETER ESTIMATION
The user of this software must provide soil, chemical, and environmental
parameters to define the land treatment site. The parameters may be obtained
experimentally for the site, based on published values such as those in
Verschuren (1983), or estimated from related parameters. The software includes
a few built in estimators for certain required parameters. These are intended
for use in situations in which the required parameter is unknown. They should
be used with caution. In this secteion, the approximations available for each
parameter are described briefly. Table 10 contains a list of the numerical
parameters with their units and symbols used in the previous section.
Fractional organic carbon content
If this is not known but the organic matter content of the
soil is known, this is approximately equal to the product
of 0.4 and the fractional organic matter content.
Saturated water content
This can be estimated from the bulk density, p, and
particle density, ps, of the soil using the equation
9S = 1 - p/ps. The particle density for most mineral
soils is between 2600 and 2700 kg/mj. If the particle
density is not known a value of 2650 kg/m3 is usually a
good estimate.
Clapp and Hornberger constant
If this parameter is not known, it can be estimated using
the values presented by Clapp and Hornberger for different
soil textures. This table will be displayed on the screen
if the help key is pressed.
Organic carbon partition coefficient
If this parameter is not known, it can be estimated
(Karickhoff, 1981) from the water solubility, S (g/m3),
the molecular weight, MW (g/mole), and the melting point,
MP (°C) of the pollutant. If
x = -0.921og(S/(55556-MW) -4.404), then the organic carbon
partition coefficient, KQQ, is approximately
KQC ~ 10X if melting point < 25°C
„ 10x - O.OKMP - 25)
if melting,point > 25°C.
If these pollutant properties are not known, KQQ can be
estimated from the octonal-water partition coefficient,
KQW, using the relation of Karickhoff et al. (1979)
56
-------
Table 10. Input parameters required by the RITZ model.
Input Parameter
Fractional organic carbon content
Bulk density
Saturated water content of soil
Saturated hydraulic conductivity
Clapp and Hornberger constant
Concentration of pollutant in sludge
Organic carbon partition coefficient
Oil-water partition coefficient
Henry's law constant
Diffusion coefficient of pollutant in air
Half -life of pollutant
Concentration of oil in sludge
Density of oil
Half-life of oil
Sludge application rate
Plow zone depth
Treatment zone depth
Recharge rate
Evaporation rate
Air temperature
Relative humidity
Diffusion coefficient of water vapor in air
Units
--
kg/m3
m3/m3
m/day
--
g/kg
m3/kg
--
--
m^/day
days
g/kg
kg/m3
days
kg/ha
m
m
m/day
m/day
degrees C
--
m^/day
Symbol
foc
P
9s
ks
b
Sp
K0
%
DA
4?
PO
t50
SAR
pzd
tzd
Vd
E
T,
RH
Dy
Oil-water partition coefficient
If this is not known, it can be approximated by the
octonal water partition coefficient for the pollutant.
Henry's law constant
If the dimensionless Henry's law constant is not known, it
can be determined from the value of the constant in units
of atm-m3/mole by dividing the dimensioned value by 0.024.
If the dimensioned constant is not known, the
dimensionless value of Kg can be estimated according to
Laskowski et al. (1982) from the water solubility,
molecular weight, and vapor pressure of the pollutant
using the relation
KH ~ VP-MW / (760-S)
where S is the solubility of the pollutant (g/m3), MW is
the molecular weight (g/mole), and VP is the vapor
pressure (mm of Hg).
57
-------
PARAMETER AVERAGING
The soil parameters in this model are assumed to be uniform throughout the
treatment site. This will not be true in general. The software includes an
option to calculate a weighted average value for soil properties known for
different layers in the soil. This section outlines the averaging schemes
employed. The software enables the user to enter values of d^ and V.^ for each
layer. It then calculates the average and places it in the data entry screen.
*.
Depth Weighted Average; The average value calculated for all parameters except
the saturated hydraulic conductivity is the depth weighted average of the
values for each layer. Consider a site in which the depth of the soil layer i
is d^ for i = 1, 2, 3, ..., N and dg = 0 and d^ is equal to the treatment zone
depth. If the parameter of interest has a value V^ for i = 1, 2, 3, ..., N,
then the depth-weighted average V is given by
V = E^ 1 w-V-
v ^i=l wivi
where w^ = (d.^ - d^_^)/djj for i = 1, 2, 3, .. ., N.
Average Saturated Hydraulic Conductivity; If d^ contains the depths of each
layer of soil as explained above for depth weighted averages and if k^
contains the corresponding saturated hydraulic conductivities for each layer,
the equivalent conductivity, kg, for the layered soil (Swartzendruber, 1960)
is given by '
ks = dN /
Screen 8 illustrates the use of the averaging feature built in to the
software. In this case, the key was pressed when the user was being
prompted for the fraction organic carbon content. The treatment zone was made
up of 5 layers so the user chose to use this averaging scheme to compute the
average value for the site. In this case, each line includes an entry for the
depth of the layer and the fraction organic carbon content for the layer. The
two numbers must be separated by a comma or a blank space. When the key
is pressed, the average value is calculated and placed in the appropriate line
on Screen 2. The user can then continue entering data there.
NOTE; THE AVERAGE IS CALCULATED TO THE MAXIMUM DEPTH ENTERED. THIS MAXIMUM
DEPTH SHOULD CORRESPOND TO THE DEPTH OF THE TREATMENT ZONE.
58
-------
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
Depth,
m
m
m
m
m
m
m
m
m
m
m
m
m
m
m
,
,
»
,
>
,
,
,
,
,
,
,
»
,
»
and
and
and
and
and
and
and
and
and
and
and
and
and
and
and
Averaging
fraction organic
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
fraction
Display help
Proceed - all
Abort
option
organic
organic
organic
organic
organic
organic
organic
organic
organic
organic
organic
organic
organic
organic
Screen
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
carbon
0
0
0
1
1
.10 0
.15 0
.30 0
.05 0
.50 0
.02
.007
.005
.002
.001
for entries
entries made
and return to parameter
entry screen
Screen 8. Screen for depth wei
59
-------
Index
A.
abort 6
assumptions 1
Clapp and Hornberger
constant 3
computer 6
concentration bar graphs
concentration graphs 17
configuration
graphics card 9
monochrome card 9
cursor keys 6
D
data entry editor 5, 6,
degradation 2, 14
depth-weighted averages
* > 11
directory 15
disk directory 15
disk files 4, 7, 43
dispersion 1
E
editor 5, 6, 11
Esc 5, 6
execution 10
file names 8
file output 18
file structure 43
flux of water 1
function keys 6 -
G
graphs 4, 8
printouts 8
1C
keys
Backspace 8
cursor 6
Delete 8
down arrow 6
End 6
Enter 7
Esc 7
Fl 7
F10 7
F2 7
F7 7, 15
F8 7, 15
function 6
Home 6
left arrow 6
PgDn 7
PgUp 7
right arrow 6
up arrow 6
L
land treatment site 2
M
mass balance 16
model assumptions 1
no data 8, 18
non-uniform soils 11
O
oil 1
oil properties 13
operating system 6
output device 18
output options 4, 16
outputs
graphs 4
tables 5
half life 14
hardware 6
Henry's Law constant 14
hydraulic conductivity
function 3
input parameter 56
installation 9
fixed disk 9
floppy disk 9
graphics card 9
monochrome card 9
parameter entry 4, 11
file 15
keyboard 15
parameter estimation 56
partition coefficient
oil 13
organic carbon 13
vapor 14
plow zone 1
plow zone depth 14
60
-------
pollutant concentration
oil 13, 48
soil 13, 48
total 46
vapor 14, 48
water 13, 14, 47
pollutant properties 13
printer 6
printer graphics 8
printer output 18
program execution 10
program interruption 6
R
recharge rate 14
software operation 5
soil properties 1, 11
T
tables 5
text files 18
treatment zone 1
treatment zone depth 14
U
units 56
unknown parameters 8, 56
W
waste application 1
site description 1
61
-------
DAYS
SATURATED
ZONE
SOLUTE
TRANSPORT
MODELING
MOC
CO
-------
OBJECTIVES
Highlight assumptions, limitations, and
uncertainty in groundwater modeling.
Introduce processes that control fate
and transport of contaminants in the
saturated zone.
Discuss management/regulatory con-
cerns in model application.
Provide an overview on the groundwater
modeling procedure.
Identify data type and quality require-
ments to satisfy the objectives of
modeling.
Provide insight into reviewing a model
application.
Expose EPA personnel to a widely used
solute transport code (MOC).
Provide a basis and foundation (theory)
of MOC.
Provide hands on experience with the
use of MOC.
Cjeoi
Irans, inc
-------
SCHEDULE
8:00 Introduction
- overview of course
- objectives
- schedule
- class notes
- role of modeling
8:15 Modeling Overview
- problem statement
- processes that control fate and transport
- equations
- uncertainty
- management/regulatory concerns
9:15 Solute Transport Process
— source
- velocity variations
- dispersion
- heterogeneity
10:00 Break
10:15 Modeling Procedure/Numerical
Methods
— governing equations
- boundary conditions
- initial conditions
- finite-difference methods
- gridding
- general application procedure
rans, inc.
GKOUNDWATDI SPECIALISTS
-------
SCHEDULE (Continued)
11:15 MOCCode
- features
- data requirements
- application
- solution procedure
- mass balance
- output
12:00 Lunch
1:00 Rocky Mountain Arsenal Case Study
1:30 Data Input Instructions For MOC
2:00 Special Problems
- point sources
- point sinks
- reaction terms
- subgrid option
2:15 Example Problem
- preprocessors
- introduction to problem
- computer facilities
- hands on use
4:00 Discussion
- example problem results
- special problems
- questions
- summary of course
5:00 Adjourn
GeoT
lr«
trans, inc.
GxouNDwmx SPECIALISTS
-------
CLASS NOTES
1. Equation Derivation
2. Model Documentation (MOC)
3. Program Updates
4. Bibliography
5. Perspective on Modeling
6. Case History
7. Selected Slides
8. Class Problem
9. Class Problem (Results)
Geol
Iransjnc.
CJOOKDWATDl SPECIALISTS
-------
BP-F-1-28
MODEL MISUSE
MOST MODELING MISTAKES OCCUR
IN MODEL APPLICATION; COMMON
WAYS TO MISUSE MODELS INCLUDE:
(1) OVERKILL-MAKING THE MODEL
MORE COMPLEX THAN DATA
AND/OR GOALS REQUIRE;
(2) IMPROPER CONCEPTUALIZATION -
BASING THE MODEL ON A POOR
OR INCOMPLETE SITE
CHARACTERIZATION;
(3) IMPROPER MODEL SELECTION -
SELECTING A MODEL WHEN NOT
FULLY UNDERSTANDING ITS
LIMITATIONS;
(4) IMPROPER BOUNDARY CONDITION
AND/OR EQUATION PARAMETER
SPECIFICATION:
(5) APPLICATION OF A GENERIC
MODEL TO A SPECIFIC SITE:
(6) INAPPROPRIATE PREDICTION -
FORECASTING UNDER VASTLY
DIFFERENT CONDITIONS THAN
THOSE USED FOR HISTORY
MATCHING;
-------
BP-F-1-27
MODEL MISUSE (CONT.)
(7) MISINTERPRETATION - POOR
HYDROLOGIC INTERPRETATION
OF COMPUTED RESULTS;
(8) MISUSE OF NUMERICAL
APPROXIMATION (IMPORTANCE
OF MASS BALANCE);
(9) UNDETECTED CODING ERROR
(IMPORTANCE OF MODEL
VERIFICATION).
-------
Bf-F-a-13
QUALITY ASSURANCE
TECHNICAL COMPETENCY
— APPROACH
— SYSTEM CONCEPTUALIZATION
— INTERPRETATION OF RESULTS
PROGRAM USE
PROGRAM MODIFICATIONS
COMMON TO ANY
TECHNICAL PROJECT
SPECIAL CONCERN
WHEN MODELS
ARE USED
LEVEL AND EFFORT OF QUALITY ASSURANCE WILL DEPEND ON
PROJECT NEEDS
-------
BP-F-«-i4
PROGRAM USE - QA CONCERNS
NUMERICAL ACCURACY
— MODEL SELECTION
— GRID SIZE
— TIME STEP SIZE
MODELING ASSUMPTIONS
— BOUNDARIES AND CONDITIONS
— ZONATION
— CALIBRATION CRITERIA
DATA PREPARATION
- REDUCTION FROM FIELD DATA
— KEYPUNCHING
INVOLVE DECISIONS
- DOCUMENT REASONS
- MAKE COMPARISONS
- CHECK
REQUIRES ACCURACY
- CHECK
- MAINTAIN RECORDS
-------
BP-F-6-15
PROGRAM MODIFICATIONS
FOR MANY APPLICATIONS, IT IS NECESSARY TO
MODIFY EXISTING PROGRAMS THAT HAVE BEEN
DOCUMENTED AND TESTED
COSMETIC-CHANGE INPUT OR OUTPUT FORMAT
MAJOR-CHANGE PHYSICAL DESCRIPTION OR
NUMERICAL METHOD
-------
BP-F-6-18
ALL PROGRAM MODIFICATIONS
SHOULD BE DOCUMENTED AND TESTED
DOCUMENTATION SHOULD INCLUDE
• REASON FOR CHANGE
• DESCRIPTION OF CHANGE
• NEW LISTING OF PART OF PROGAM CHANGED
TESTING SHOULD
• BE CONSISTENT WITH CHANGES MADE
(I.E., MAJOR CHANGES REQUIRE EXTENSIVE TESTING
WITH KNOWN SOLUTIONS)
• HAVE DOCUMENTION OF TEST
- DISCUSSION OF TEST PROBLEM SELECTION
- GRAPHICAL COMPARISON
- COMPLETE OUTPUT
-------
BP-F-6-11
SCHEDULING
MODELING EFFORTS SHOULD BE WELL-
COORDINATED WITH OTHER PROJECT TASKS
MAXIMUM TECHNICAL FEEDBACK TO AVOID DELAYS
-------
BP-F-6-12
MAJOR PROJECT TASKS
MODELING APPLICATION
PROJECT
PLANNING
DATA
COLLECTION
DESIGN
DATA
COLLECTION
AND ANALYSIS
QUALITATIVE
CHARACTERIZATION
REPORT
WRITING
MODEL NEED
AND SELECTION
SYSTEM
CONCEPTUALIZATION
SENSITIVITY ANALYSIS
MODEL CALIBRATION
QUANTITATIVE PREDICTION
-------
BP-F-a-4
COMMENTS
THE EFFECTIVE USE OF MODELS USUALLY REQUIRES A
TEAM EFFORT AMONG TECHNICAL PEOPLE HAVING
DIFFERENT SKILLS
COMMUNICATION SKILLS ARE NECESSARY FOR THOSE
RESPONSIBLE FOR MODEL DEVELOPMENT AND
APPLICATION
SKILL LEVELS HIGHER THAN 5 REQUIRE FORMAL
TRAINING, DEDICATED SELF INSTRUCTION, OR
EXPERIENCE WORKING WITH WELL-TRAINED PEOPLE
SKILL LEVELS OF 5 OR LESS CAN BE ATTAINED FROM SELF
INSTRUCTION, SHORT COURSES, OR EXPERIENCE
-------
^$fess>3
j^S^o
-V^CSssC
XO^S^->Q ,xV/ Q
^§§§|oS§
Figure 8.2
Statistical distribution of flow paths around local heterogeneities
leads to dispersion. The process is shown here at a microscopic
scale where pore space surrounds gravel-sized grains. (From R. A.
Freeze and J. A. Cherry, Groundwater,©\919, p. 384. Reprinted by
permission of Prentice-Hall, Inc., Englewood Cliffs, N. J.)
-------
C(jt,0)/N
Longitudinal concentration
profile
Uniform
flow field
Initial
tracer slug
Ellipse of variance
due to dispersion
C(0,y)
Lateral concentration
profile
Figure 8.1
Dispersion of an instantaneous point source in a uniform flow field. The longitudinal
and lateral distributions of concentration in the ellipse are shown by the superimposed
graphs.
-------
v, = 0.1 m day'1, / = 400 days
Figure 8.6
One-dimensional longitudinal dispersion showing effect of changing the
value of the dispersion coefficient.
-------
RP2465-5
EPRI
EPRI EA-4ttO
RP2O5-S
Final Report
August 1M6
A Review of Field-Scale Physical Solute Transport
Processes in Saturated and Unsaturated Porous
Media
Contractor: Ttnnwto Vallty Authority
I O.OOO
1,000
r- IOO
cr
UJ
in
5
I0
10
° A
A
A A
TRACER CWTOM
TEST EVENTS TRACERS
FRACTURED
MEDIA °
POROUS m
MEDIA
10
IOO 1000 10,000 100,000
SCALE (m)
figure 2-1. Sc*le of Observation Versus Longitudinal Dispersivity for the
Saturated Zone
-------
1.0
0.8 ¥-
.0
N
H 0.6
X
o
LU
X
LJ
r 0.4
LU
OC
0.2
0.0
1 CHALK RIVER SITE
I MOBILE SITE
| (RUN 1)
MOBILE SITE
(RUN 2)
I
L
I
Y/////A -
o.o
0.2 0.4 0.6 0.8
RELATIVE CONDUCTIVITY, K/Kmax
1.0
-------
0.2
t=3 days
y-z PLANE
ID
•z.
o
»-
o
UJ
0.2
t = 8.53 days
0 5 10 m
x-z PLANE
-------
' LEVEL 2
300 400 500 600 200
TIME, hrs.
300 400 500
UJ
§ 1-'
0.8
0.6
o
0.0
LEVEL 3
200 400 600
^LEVEL 4-
200 400
TIME, hrs.
200 300
§
_l Z
UJ UJ
oc o
0.6
.
-4
O 0.2
O
0.0
- LEVEL 6
100 200
T I
LEVEL 7
300 200
TIME,.hrs.
FIELD DATA
MODEL PREDICTION
300 400 500
-------
0.20
UJ
oc
0.16
Z
o
ft 0.12
Z
UJ
o
Z
o
o
UJ 0.08
0.04
0.0
o EXPERIMENT
ADJUSTED K(Z)
UNADJUSTED K(Z)
a, =400 cm
12 16 20
TIME, days
24
32
-------
BP-F-2-1
GROUNDWATER
FLOW MODEL
(MATHEMATICAL)
-------
BP-F-2-7
DIAGRAM OF THE MAJOR COMPOMENTS OF
THE GROUNDWATER FLOW EQUATION
WATER
MASS
BALANCE
WATER
MOMENTUM
BALANCE
GROUNDWATER
FLOW
EQUATION
DARCY'S
EQUATION
-------
BASIC EQUATION
BP-F-2-8
rate of
mass in
rate of
mass out
rate of mass
accumulation
ax
w = s
ah
at
CONFINED, ARTESIAN FLOW
-------
•• a
- SP-F-2-9
BASIC EQUATION (CONT.)
PARTIAL DIFFERENTIAL EQUATION
SECOND ORDER
LINEAR
DIFFUSION EQUATION
DEPENDENT VARIABLE - h
INDEPENDENT VARIABLES - x,y,t
EQUATION PARAMETERS - T, W, S
-------
BP-F-2-10
EQUATION PARAMETERS
TRANSMISSIVITY, T
A MEASURE OF AN AQUIFER'S ABILITY TO TRANSMIT
WATER THROUGH ITS ENTIRE THICKNESS
STORAGE COEFFICIENT, S
A MEASURE OF AN AQUIFER'S ABILITY TO TAKE IN AND
RELEASE WATER FROM STORAGE
SOURCE/SINK TERM, W
RECHARGE OR DISCHARGE, SUCH AS PUMPAGE
-------
INDEPENDENT VARIABLES
DISTANCE
• x- AND y- DIRECTIONS
• TWO-DIMENSIONAL
TIME
• TRANSIENT,!
-------
BP-F-2-12
MAJOR ASSUMPTIONS
> POROUS MEDIA
DARCY'S LAW
> SLIGHTLY COMPRESSIBLE FLUID
SMALL VERTICAL VARIATION IN PROPERTIES
AND HEAD
SINGLE AQUIFER WITH AREAL, CONFINED FLOW
LINEAR AQUIFER VERTICAL COMPRESSIBILITY
PRINCIPAL COMPONENTS OF THE TRANSMISSIVITY
ALIGNED WITH COORDINATE AXES
-------
BP-F-3-1
SOLUTE
TRANSPORT
MODEL
(MATHEMATICAL)
-------
BP-F-3-3
DIAGRAM OF THE MAJOR COMPONENTS
OF THE SOLUTE TRANSPORT EQUATION
MASS
BALANCE
FOR SPECIES
WATER
MOMENTUM
BALANCE
SOLUTE
TRANSPORT
EQUATION
DARCY'S
EQUATION
-------
BP-F-3-S
BASIC EQUATION (CONT.)
PARTIAL DIFFERENTIAL EQUATION
SECOND ORDER
LINEAR (CONSTANT DENSITY)
CONVECTION-DIFFUSION EQUATION
DEPENDENT VARIABLE - C
INDEPENDENT VARIABLES - x, y, t
EQUATION PARAMETERS - 0, D, q, RC*
-------
BP-F-3-7
INDEPENDENT VARIABLES
DISTANCE
• x-, y-, AND z- DIRECTIONS
TIME
• TRANSIENT, t
-------
BP-F-3-8 "
EQUATION PARAMETERS
• POROSITY, J0f
A MEASURE OF INTERSTITIAL SPACE CONTAINED
IN THE ROCK. IT IS EXPRESSED AS A RATION OF
VOID SPACE TO THE TOTAL (GROSS) VOLUME OF
THE ROCK
• DARCY VELOCITY, q
• DISPERSION, D
• SOURCE/SINK TERM, RC*
-------
node
/*/• /•/•
123 4
b
T
-------
or- r-3-
+ Q3i + Q4i + Qsi = Ax, Ay, S,
ah,
lit7
3h
=Ax, T2, ( —)21
3y
1* Ax,T21
h2 - h
- -
Ay
! = — Ax2 —
! - hi
at At
Ax2
'•J = T "A? v"'
-------
NODE POINT
>
^r -».
/
\
V
Ay
f
^
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
*. ^
Ax
MESH CENTERED
I
Ay
Ax
BLOCK CENTERED
-------
>'->' - <.' - 12 f-
No Matter Which Numerical
Approach (F.D., F.E., or M.O.C.) is
Chosen, the End Result is a System
of Linear Algebraic Equations that
Must be Solved.
For Steady-State—One Solution
For Transient—Repeated Solutions
-------
Matrix Solution Important to User
• Most Time-Consuming Part of
Computer Calculations
• Controls In-Core Storage
Requirements
• Optimal Choice of Method is
Problem Dependent
-------
Iterative Methods—Use
Convergence—How Many Guesses
Required? Does it Converge? When
has it Converged?
Improving Speed of Convergence—
Acceleration and Other Parameters
• Problem Dependent
• Must be Specified
-------
CONVERGENCE
1 2 3 4 5 6 7 8 9 1011 12 13 14
ITERATION NUMBER
-------
X- --2
BOUNDARY CONDITIONS
Map
View
t
Aquifer
Boundary
The Values of the
Required Solution of
the Problem on the
Aquifer Boundary
-------
BP-F-2-2S
BOUNDARY CONDITIONS (CONT.)
SPECIFIED VALUE
• CONSTANT HEAD AT A LARGE LAKE,
DISTANT BOUNDARY
SPECIFIED FLUX
• WELL
• IMPERMEABLE ROCK
• GROUNDWATER DIVIDE
VALUE-DEPENDENT FLUX
• HEAD-DEPENDENT LEAKAGE FROM
A CONFINING BED, RIVER
-------
Constant
Head Boundary
Recharge
1 1 ill
Confining
1||||||| Artesian 1
Illlll Aquifer |
$v No-Flow
^Boundary
. ••»-.. i -
-------
BP-F-3-18
INITIAL CONDITIONS
CONCENTRATIONS ARE SPECIFIED AT THE BEGINNING
OF THE TIME PERIOD INSIDE THE REGION OF INTEREST
-------
BP-F-1-10
DETERMINE NECESSITY
OF NUMERICAL MODEL
COMPILE & INTERPRET
AVAILABLE DATA
COLLECT DATA AND
OBSERVE SYSTEM
CONCEPTUALIZATION
PREPARE DATA FOR
MODEL USING
ESTIMATED PARAMETERS
INTERPRET RESULTS
IMPROVE
COMPEPTUAL
MODEL
GOOD
COMPARISON
RESULTS
SATISFACTORY
SENSITIVITY RUNS
IS MORE DATA NEEDED?
PREDICTIVE
PREDICTIVE
SCENARIO RUNS
SENSITIVITY RUNS
HISTORY
MATCHING
(FIELD PROBLEM)
PREPARE DATA FOR
MODEL USING
ESTIMATED PARAMETERS
COMPARE RESULTS WITH
OBSERVED DATA
POOR
COMPARISON
YES
-------
BP-F-1-18
MODEL APPLICATION
MODEL APPLICATION HAS THREE
MAIN PHASES:
(1) SYSTEM CONCEPTUALIZATION;
(2) HISTORY MATCHING OR MODEL
CALIBRATION;
(3) PREDICTION.
MOST APPLICATIONS INVOLVE EACH
OF THE THREE PHASES, BUT TO
DIFFERENT DEGREES OF EFFORT.
-------
BP-F-1-20
MODEL APPLICATION (CONT.)
SYSTEM CONCEPTUALIZATION
INVOLVES ORGANIZING AVAILABLE
INFORMATION ON THE GROUND-
WATER SYSTEM IN AN INTERNALLY
CONSISTENT FRAMEWORK. THE
CONCEPTUALIZATION PRODUCES
FACTORS CONTROLLING THE FLOW
SYSTEM SUCH AS STRATIGRAPHY
AND GEOMETRY, BOUNDARY AND
INITIAL CONDITIONS, AND
HYDROLOGIC PARAMETERS.
SYSTEM CONCEPTUALIZATION IS
SUBJECTIVE AND QUANTITATIVE
STANDARDS OF PERFORMANCE ARE
GENERALLY NOT AVAILABLE.
-------
BP-F-1-22
MODEL APPLICATION (CONT.)
HISTORY MATCHING OR MODEL
CALIBRATION IS USED TO REFINE
ESTIMATES OF HYDROLOGIC
PARAMETERS AND BOUNDARY
CONDITIONS BY COMPARING MODEL
RESULTS WITH OBSERVED DATA.
THE HISTORY MATCHING PROCEDURE
CAN BE PERFORMED BY EITHER TRIAL
AND ERROR OR BY AUTOMATIC
REGRESSION. FOR BOTH, SENSITIVITY
ANALYSIS IS PART OF THE MATCHING
PROCESS.
FOR HISTORY MATCHING,
PERFORMANCE CAN BE JUDGED BY
HOW WELL COMPUTED VARIABLES
(E.G., HYDRAULIC HEAD) COMPARE TO
MEASURED VALUES.
-------
MODEL APPLICATION (CONTINUED)
f START J
f START J
mates
Update model
„. parameter esti
1
initial parameter estimates,
model specification
-*• RUN MODEL
1
COMF
CALCUI
ad & OBSE
VALI
<
S
initial parameter
, estimates
MODEL
SPECIFICATION
*~ **• —
1 if
§ II
«' en ^*-
.ATED "°
ERVED |_
\
RUN MODEL
\
CALCULATE
CRITERIA
yes
JES
good
f STOP )
X_ _/ trial and error
converg
ARE RESULTS
ACCEPTABLE
\
yes
I
1
1
1
1
1
1
1
ence? J
no
t STOP J
y J automatic
PROCEDURES FOR MODEL CALIBRATION USING
TRIAL AND ERROR AND AUTOMATIC HISTORY
MATCHING APPROACHES
-------
BP-F-1-25
MODEL APPLICATION (CONT.)
PREDICTION IS USUALLY THE FINAL
AND SHORTEST PORTION OF A MODEL
APPLICATION. PREDICTIONS ARE
BASED ON MODEL RESULTS USING
THE BEST ESTIMATE OF SYSTEM
PARAMETERS OBTAINED BY HISTORY
MATCHING AND FORECASTING THE
EFFECTS OF A SYSTEM CHANGE.
AS WITH SYSTEM CONCEPTUAL-
IZATION, PREDICTION IS SUBJECTIVE
AND QUANTITATIVE STANDARDS OF
PERFORMANCE ARE GENERALLY NOT
AVAILABLE.
-------
FEATURES OF METHOD
OF CHARACTERISTICS CODE
• 2 Dimensional (areal)
Flow and solute transport
Steady state and transient
Finite-difference for flow
Method of characteristics for
transport
Rectangular block centered FD grid
Variety of boundary conditions
Adapted for decay, adsorption
Thoroughly documented (1978)
Extensively tested and used
Adapted for PC use
Preprocessor
GeoT"
Irans, inc.
CTOumimuu SPECIALISTS
-------
DATA REQUIREMENTS
• Grid data
• Time data
• Execution parameters
• Output options
• Porosity
• Storage coefficient
• Dispersivity
• Transmissivity*
• Saturated thickness*
• Diffuse recharge*
• Flux boundary data
• Leakance*
• Initial heads*
• Initial concentrations*
*arrays (data sets)
GeoT
In
rans,mc.
iKXKDWxm mcuum
-------
OUTPUT
Echo of input data
Computed head distribution
Flow mass balance
X and Y velocities
Stability criteria
Computed concentration
distribution
Chemical mass balance
Observation well data
GeoT
In
rans,mc.
QMXMDVXm BfCIALBTS
-------
Summary of MOC Updates
05/16/79 ijiprove accuracy (source/sink representation)
08/26/81 variable length pumping period
10/12/83 double precision; convenient printout; output routine calls
06/10/85 increase number of particles per node (16)
07/26/85 improve calculating dispersive concentration changes
08/02/85 first order decay; linear equilibrium adsorption
08/08/85 smaller transport subgrid
08/12/85 improve output readability
07/02/86 improve particle-velocity calculations
10/20/86 minimize zero divide check errors
03/02/87 mass balance calculations in double precision
03/05/87 add SIP solution routine
05/15/87 ijiprove efficiency
01/29/88 ijiprove operational aspects
-------
0 CUMULATIVE MASS BALANCE -- (IN FT**3)
RECHARGE AND INJECTION
PUMPAGE AND E-T WITHDRAWAL
CUMULATIVE NET PUMPAGE
WATER RELEASE FROM STORAGE
LEAKAGE INTO AQUIFER
LEAKAGE OUT OF AQUIFER
CUMULATIVE NET LEAKAGE
MASS BALANCE RESIDUAL
ERROR (AS PERCENT)
-.63115E+09
.37869E+09
-.25246E+09
.OOOOOE+00
.54938E+09
-.80194E+09
-.25257E+09
-.10783E+06
-.91339E-02
0 RATE MASS BALANCE -- (IN C.F.S.)
LEAKAGE INTO AQUIFER
LEAKAGE OUT OF AQUIFER
NET LEAKAGE (QNET)
RECHARGE AND INJECTION
PUMPAGE AND E-T WITHDRAWAL =
NET WITHDRAWAL (TPUM)
.87043E+00
-.12706E+01
-.40017E+00
-.10000E+01
.60000E+00
-.40000E+00
-------
CHEMICAL MASS BALANCE
MASS IN BOUNDARIES = .54938E+10
MASS OUT BOUNDARIES = -.84234E+10
MASS PUMPED IN = .63115E+12
MASS PUMPED OUT = -.29071E+11
MASS LOST BY DECAY = .OOOOOE+00
MASS ADSORBED ON SOLIDS= .OOOOOE+00
INITIAL MASS ADSORBED = .OOOOOE+00
INFLOW MINUS OUTFLOW = .59915E+12
INITIAL MASS DISSOLVED = .26880E+11
PRESENT MASS DISSOLVED = .62728E+12
CHANGE MASS DISSOLVED = .60040E+12
CHANGE TOTL.MASS STORED= .60040E+12
COMPARE RESIDUAL WITH NET FLUX AND MASS ACCUMULATION:
MASS BALANCE RESIDUAL = -.12501E+10
ERROR (AS PERCENT) = -.19636E+00
-------
• •
B
Figure 9.—Parts of finite-difference grids showing
the initial geometry of particle distribution for the
specification of four (A), five (B), eight (C), and
nine (D) particles per cell.
-------
EXPLANATION
• Initial location of particle
O New location of particle
—^ Flow line and direction of flow
Computed path of particle
Figure 1.—Part of hypothetical finite-
difference grid showing relation of
flow field to movement of points.
-------
./-I./
/'1.7-1
•
o
EXPLANATION
Node o( finite-difference grid
Location of particle p
Xor Y component of velocity
Area of influence for interpolating velocity
in X direction at particle p
Area of influence for interpolating velocity
in Y direction at particle p
Figure 2.—Part of hypothetical finite-difference grid
showing areas over (which bilinear interpolation is
used to compute the velocity at a point. Note that
each area of influence Is equal to one-half of the
nr«n of a mil
-------
or 7/wE-SW/»
-f
or
TINJT
FLOW-
* 77MX}
J fcr //*«/ //
-------
C START ^J
1
READ GEOLOGIC.
HYDROLOGIC.&
CHEMICAL
INPUT
DATA
I
GENERATE UNIFORM
DISTRIBUTION OF
TRACER PARTICLES
COMPUTE HYDRAULIC
GRADIENTS FOR
ONE TIME STEP
COMPUTE DISPERSION
EQUATION COEFFICIENTS
COMPUTE
GROUND-WATER
VELOCITIES
DETERMINE LENGTH
OF TIME INCREMENT
FOR EXPLICIT
CALCULATIONS
I
MOVE PARTICLES
I
GENERATE NEW PARTICLES
OR REMOVE OLD
PARTICLES AT
APPROPRIATE BOUNDARIES
1
COMPUTE AVERAGE
CONCENTRATION IN EACH
FINITE-DIFFERENCE CELL
I
COMPUTE EXPLICITLY
THE CHEMICAL
CONCENTRATION AT
NODES
i
ADJUST CONCENTRATION
OF EACH PARTICLE
i
COMPUTE
MASS BALANCE
END OF
TIME STEP?
SUMMARIZE AND
PRINT RESULTS
END OF
PUMPING
PERIOD
YES ^ £ND OF
SIMULATION?
Figure 8.—Simplified flow chart illustrating the major steps In the calculation
procedure.
-------
o
A
EXPLANATION
Node of finite-difference grid
Previous location of particle p
Computed new location of particle p
Corrected new location of particle p
Flow line and direction of flow
Computed path of flow
Zero transmissivity (or no-flow boundary)
Figure 4.—Possible movement ol particles near
an impermeable (no-flow) boundary.
-------
AT START CX MIT
PARTICLE MOVEMENT
DID f AITICIC
O«ICINAU IN THAT
SOURCE CEU '
It SOUtCf CEU
OCA HO AlOMC EOCf
of
FJ770
OCIMMIXC I -T
COOROINAHS (X MOOf
•Him pAnnciE it
toc*uorM0.SIIION
At OLD rAMlCLl IN
NEW CELL
f J420-M40
IS OLD
OCATiON IN A
SOURCE CELL OR
A SlN« CUL '
J480-JS7
MAI PARtlCLC
CMANCCO CELL
IOCAIION7
CMAIE NEW PAHTlClf
f IS«0
I AND T
COO*OlKATlS OF CELL
Al NEW LOCATION Of
PARTICLE rioM.ll!0
COMPUTi OISTANCC
MOVtO IN I AND »
OIKtCIIONJ
1ACE NEW PARTICLE
AT ORIGINAL LOCATION
Of OLD PARTICLI
S Nf
LOCAIION
IN A PUMTINC
OR CONSTANT -MCAO
COUfUTt OlilANCt
TlUVtllO
MTONO MXJNOAIIT
MJUOv: PARTICLE
FROM CRIO
FM4O-J710
RELOCATE PARTICLE INTO
AQUIFER (T REFLECTION
ACROSS IOUNOART
IES
CALL iUMOUTINE
CNCON TO COMPUTE
NEW CONCENTRATION!
F1JM
STO*f OMEHVATION WELL
MI" F4000-40.0
Flgur* 10.—Generalized How chert of lubroutlrw MOVE. Numbere indicate line numbers where the operation Is executed.
-------
Summary of M3C Updates
05/16/79 inprove accuracy (source/sink representation)
08/26/81 variable length pumping period
10/12/83 double precision; convenient printout; output routine calls
06/10/85 increase number of particles per node (16)
07/26/85 improve calculating dispersive concentration changes
08/02/85 first order decay; linear equilibrium adsorption
08/08/85 smaller transport subgrid
08/12/85 improve output readability
07/02/86 improve particle velocity calculations
10/20/86 minimize zero divide check errors
03/02/87 mass balance calculations in double precision
03/05/87 add SIP solution routine
05/15/87 improve efficiency
01/29/88 iinprove operational aspects
-------
LIST OF SUBROUTINES FOR SOLUTE-TRANSPORT MODEL
NAME PURPOSE
MAIN Control Execution
PARLOD Data Input and Initialization
ITERAT Compute Head Distribution
-*
GENPT Generate or Reposition Particles
VELO Compute Hydraulic Gradients, Velocities,
Dispersion Equation Coefficients, and
Time Increment for Stable Solution to
Transport Equation
MOVE Move Particles
CNCON Compute Change in Chemical Concentrations
and Compute Mass Balance for Transport
Model
OUTPT Print Head Distribution and Compute Mass
Balance for Flow Model
CHMOT Print Concentrations, Chemical Mass Balance,
and Observation Well Data
-------
SECTION 1
EQUATION DERIVATION
-------
DERIVATION OF EQUATIONS DESCRIBING
SOLUTE TRANSPORT IN GROUND WATER
111
U. S. GEOLOGICAL SURVEY
Water-Resources Investigations 77-19
-------
BIBLIOGRAPHIC DATA
SHEET
1. Report No.
3. Recipient's Accession No.
I. Title and Subtitle
DERIVATION OF EQUATIONS DESCRIBING SOLUTE TRANSPORT IN
GROUND WATER
5. Report D*te
April 1977
7. Author(s)
Leonard F. Konikow and David B. Grove
8. Performing Organization Rept.
No- USGS/WRI-77-19
9. Performing Organization Name and Address U.S. Geological Survey
Water Resources Division
Mail Stop 413, Box 25046
Denver Federal Center
Denver, Colorado 80225
10. Project/Task/Work Unit No.
II. Contract/Grant No.
2. Sponsoring Organization Name and Address
Same as 9 above
13. Type of Report & Period
Covered
Final
U.
IS. Supplementary Notes
16. Abstracts
A general equation describing the three-dimensional transport and dispersion of
a reacting solute in flowing ground water is derived from the principle of conserva-
tion of mass. The derivation presented in this report is more detailed but less
rigorous than derivations published previously. The general solute-transport equation
relates concentration changes to hydrodynamic dispersion, convective transport, fluid
sources and sinks, and chemical reactions. Because both dispersion and convective
transport depend on the velocity of ground-water flow, the solute-transport equation
must be solved in conjunction with the ground-water flow equation.
17. Key Words and Document Analysis. 17o. Descriptors
Groundwater, Dispersion, Computer models, Path of pollutants
I7b. Identifiers/Open-Ended Terms
Solute-transport models
17c. COSATI Field.'Group
18. Availability Statement
No restriction on distribution
19. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
Pace
TJNCLASSIFIED
21. No. of Pages
35
22. Price
FORM NTis-39 i«ev. 10-73) ENDORSED BY ANSI AND UNESCO.
THIS FORM MAY BE REPRODUCED
USCOMM-DC S2«8'PT4
-------
DERIVATION OF EQUATIONS DESCRIBING SOLUTE TRANSPORT
IN GROUND WATER
By Leonard F. Konikow and David B. Grove
U.S. GEOLOGICAL SURVEY
Water-Resources Investigations 77-19
April 1977
Revised Jan. 1984
-------
UNITED STATES DEPARTMENT OF THE INTERIOR
CECIL D. ANDRUS, Secretary
GEOLOGICAL SURVEY
V. E. McKelvey, Director
For additional information .write to:
U.S. Geological Survey
Water Resources Division
Mail Stop 413, Box 25046
Denver Federal Center
Denver, Colorado 80225
-------
CONTENTS
Page
Abstract 1
Introduction • 2
Ground-water flow 3
General flow equation 3
Equations of state 4
Flow velocity 5
Simplifying assumptions 6
Homogeneous fluid properties 6
Two-dimensional areal flow 7
Alignment of coordinate axes 9
Solute-transport equation 10
Derivation of general transport equation 10
Two-dimensional areal solute transport 16
Dispersion coefficient 24
Summary 28
References cited 29
ILLUSTRATIONS
Page
Figure 1. Representative elementary volume (REV) of aquifer 11
2. Representative volume of aquifer having variable
saturated thickness *• • 17
iii
-------
DERIVATION OF EQUATIONS DESCRIBING SOLUTE TRANSPORT IN GROUND WATER
By Leonard F. Konikow and David B. Grove
ABSTRACT
A general equation describing the three-dimensional transport and
dispersion of a reacting solute in flowing ground water is derived from
the principle of conservation of mass. The derivation presented in this
report is more detailed but less rigorous than derivations published
previously. The general solute-transport equation relates concentration
changes to hydrodynamic dispersion, convective transport, fluid sources
and sinks, and chemical reactions. Because both dispersion and convective
transport depend on the velocity of ground-water flow, the solute-transport
equation must be solved in conjunction with the ground-water flow equation.
-------
INTRODUCTION
In recent years there has been an increased awareness of problems of
ground-water contamination. Reliable predictions of contaminant movement
can only be made If we understand and can quantitatively describe the
physical and chemical processes that control solute transport in flowing
ground water. Several reports have been published recently that develop
and present solute-transport equations to compute the concentration of a
dissolved chemical species in ground water as a function of space and
time. Examples of these reports include Reddell and Sunada (1970), Bear
(1972), and Bredehoeft and Finder (1973). The three main processes
affecting solute transport, and consequently chemical concentrations, are
convective transport, hydrodynamic dispersion (Including diffusion and
mechanical dispersion), and chemical reactions. Because convective trans-
port and hydrodynamic dispersion depend on the velocity of ground-water
flow, the solute-transport equation must be considered in conjunction with
the ground-water flow equation.
Aquifers generally have heterogeneous properties and complex boundary
conditions. Therefore, the solution of the partial differential equations
that describe the solute-transport processes generally require the use of
a deterministic, distributed parameter, digital simulation model. Among
the reports that describe or present numerical models to solve the solute-
transport equations are Reddell and Sunada (1970), Bredehoeft and Finder
(1973), Finder (1973), Ahlstrom and Baca (1974), Gupta and others (1975),
Grove (1976), and Lantz and others (1976). Furthermore, several documented
case histories show that where adequate hydrogeologic data are available,
solute-transport models can be used to compute the rates and directions of
spreading of contaminants from known or projected sources. Examples of
model applications to field problems include Konikow and Bredehoeft (1974),
Robertson (1974), Robson (1974), Konikow (1976), and Segol and Finder
(1976).
These models use either finite-difference methods, finite-element
methods, or the method of characteristics. The selection of the "best"
numerical method depends largely on the nature of the specific field
problem, but also depends to some extent on the mathematical background
of the analyst. Although solute-transport models are best utilized when
the analyst is thoroughly familiar both with the equations and with the
numerical algorithm, the increasing availability of documented and published
programs affords the opportunity for the use of a model by persons with
only minimal familiarity with both.
The basic purpose of this report is to derive a general form of the
solute-transport equation from general principles in a more detailed,
step-by-step, but less rigorous manner than has been done in previously
published literature. The report is Intended to serve as an introduction
to quantitative modeling of solute-transport processes in ground water.
It will also show how the general solute-transport equation can be modified
or simplified for application to a variety of different types of field
problems. Because of the interrelation between the flow equation and the
solute-transport equation, the former will also be presented in some
-------
detail although not specifically derived. It Is assumed that the mathemat-
_ical background of the reader includes at least a familiarity with partial
differential equations.
GROUND-WATER FLOW
General flow equation
A quantitative description of ground-water flow is a prerequisite to
accurately representing solute transport in aquifers. A general form of
the equation describing the transient flow of a compressible fluid in a
nonhomogeneous anisotropic aquifer may be derived by combining Darcy's Law
with the continuity equation. By following the developments of Cooper
(1966) and of Bredehoeft and Finder (1973), the general flow equation may
be written in cartesian tensor notation as:
^h* fe+pg^)J-pa"
3P
8 dm.
*- Z ^r + 'v* <»
2
where k. . is the intrinsic permeability (a second-order tensor), L ;
•z-j
p is the fluid density, ML~ ;
is the dynamic viscosity, ML T ;
-2
-1 -2
P is the fluid pressure, ML T
g is the gravitational acceleration constant, LT
z* is the elevation of the reference point above a standard
datum, L;
W* = W*(x,y,z,t) is the volume flux per unit volume (positive
sign for outflow and negative for inflow), T ;
« Q
P* is the density of the source/sink fluid, ML~ ;
a is the vertical compressibility coefficient of the medium,
LM"1!2;
p is the fluid density at a reference pressure, temperature, and
and concentration, ML ;
t is the effective porosity (dimensionless);
-1 2
6 is the compressibility coefficient of the fluid, LM T ;
-------
3
VQ is the reference volume of the fluid, L ;
m. is the mass of species i in the reference volume v , M;
7> 0
e is the number of species, (dimensionless);
x. are the cartesian coordinates, L; and
ts
t is time, T.
The summation convention of Cartesian tensor analysis is implied in
equation 1. That is, each term is summed over the range of its subscripts.
Bredehoeft and Finder (1973) note that the derivation of equation 1 is
based on the following assumptions:
1. The porous medium may only deform vertically.
2. Isothermal conditions prevail.
3. The volume of individual grains remains constant during deforma-
tion of the medium.
4. Fluid density is a linear function of pressure and concentration,
as indicated by the following relationship:
v~
0
-1 -2
where P is the reference fluid pressure, ML T ; and
m. is the mass of species i in the reference volume v at the
reference pressure, M.
5. The permeability is independent of pressure, temperature, and
concentration.
6. There is no change in volume caused by mixing fluids of different
ionic concentrations.
7. The proportionality constants a and 3 are independent of pressure
and concentration.
8. Hydraulic head gradients are the only significant driving
mechanism.
9. The vertical velocity of grains is negligible.
Equations of state
The density and viscosity of ground water are both related to its
temperature, pressure, and chemical content. Because isothermal condi-
tions have been assumed, temperature changes need not be considered.
Equation 2 expresses the dependence of density on both the pressure
and the mass concentrations of all species. Equation 2 may be rewritten
-------
in terms of the concentration of a single chemical species of Interest
as:
P - PQ + P0B(P-P0) + Y(C-Co) (3)
where C is the mass concentration per unit volume of solution for the
solute species of interest, ML ;
C is the concentration of the solute at the reference pressure
0 -3
and temperature, ML ; and
Y is the constant of proportionality between concentration and
fluid density (dimensionless).
If the relationship indicated by equation 3 is substituted for
equation 2, then equation 1 may be rewritten as:
9P 3P
+ ey + W*p* (4)
Viscosity may be similarly expressed as a linear function of con-
centration by the following:
y - U0 + A(C - CQ) (5)
where y is the dynamic viscosity of the fluid at the reference pressure,
-1 -1
temperature, and concentration, ML T ; and
A is the constant of proportionality between concentration and
2-1
viscosity, L T .
Flow velocity
The seepage velocity, or average interstitial velocity, of ground-
water flow may be computed as:
v*-r
where V. is the seepage velocity in the direction of x., LT ; and
1, T*
q. is the specific discharge, or specific flux, in the direction
^ _i
of x., LT .
I*
The specific discharge may be computed directly from Darcy's Law,
which is written as:
-------
Simplifying assumptions
The general flow equation written as equation 4 can be simplified
considerably if certain conditions can be satisfied. Several of these are
described next.
Homogeneous fluid properties
When changes in concentrations of dissolved chemical species are
relatively small, the fluid density and viscosity remain essentially
constant. This assumption of homogeneous fluid properties both simplifies
the flow equation and allows it to be solved independently from the solute
transport equation. If density is independent of concentration, then
the third term on the right side of equation 4 can be eliminated from the
flow equation.
We may aim next to express equation 4 in terms of hydraulic head
rather than pressure. Following the development of Hubbert (1940), we may
define the hydraulic head as:
where h is the hydraulic head, L; and
-1 -2
P is atmospheric pressure, ML T .
If we differentiate equation 8 with respect to x., for constant
density we obtain:
3h m 3z* 1_ 3P
3x. " 3x. pg 3x.
Tf If Tr
3P
Solving equation 9 for -r— yields:
3P /3h 3z* \
ax. " P8l 3x. " 3x. I (10)
i \ i i /
-------
We may similarly differentiate equation 8 with respect to time to
obtain:
ui;
at at pg at
Because -r— = 0, we can express equation 11 as:
ot •
3P 3h
If we next substitute the relations indicated by equations 10 and 12
into equation 4, and then divide both sides of the equation by the constant
density, we obtain:
Equation 13 may be further reduced if we consider that
where K.. is the hydraulic conductivity tensor, LT , and that
'
8 - g(pa + p eg) (15)
s o
where S is the specific storage, L
S
By substituting equations 14 and 15 into equation 13, we obtain:
%) -.'.£*«•
Two-dimensional areal flow
In many ground-water studies it can be reasonably assumed that ground-
water flow is areally two-dimensional. This allows the three-dimensional
flow equation to be reduced to the case of two-dimensional areal flow, for
which several additional simplifications are possible. The advantages of
reducing the dimensionality of the equations include less stringent data
requirements, smaller computer storage requirements, and shorter computer
execution times to achieve a numerical solution.
-------
An expression similar to equation 16 may be derived for the two-
dimensional areal flow of a homogeneous fluid and written as:
_** f If H — »-"- 1 • C V\ Y_- J
3x. l ij 3x. I a 3t
* \ " J/
where b is the saturated thickness of the aquifer, L, and it is assumed
that the hydraulic conductivity, specific storage, and hydraulic head
represent vertically integrated mean values (Cooley, 1974).
The transmissivity of the aquifer may be defined as:
1.. = K.. b (18)
2 -1
where T.. is the transmissivity, L T .
tj
Similarly, the storage coefficient of the aquifer may be defined as:
S = SB b (19)
where S is the storage coefficient (dimensionless).
After substituting the relationships indicated by equations 18 and 19
into equation 17, we obtain:
•sr- (t;* ^r\ " s IT + w (20)
where W = W(x,y,t) » W*b is the volume flux per unit area, LT~ .
Although fluid sources and sinks may vary in space and time, they have .
been lumped into one term (W) in the previous development. There are
several possible ways to compute W. If we consider only sources and sinks
such as (1) direct withdrawal or recharge, such as pumpage from a well,
well injection, or evapotranspiration, and (2) steady-state leakage into or
out of the aquifer through a confining layer, streambed, or lake bed, then
for the case of two-dimensional horizontal flow, the source/sink terms may
be specifically expressed as:
K
W(x,y,t) - Q(x,y,t) - -* (H - h) (21)
Ul 0
where Q is the rate of withdrawal (positive sign) or recharge (negative
sign), I/T1;
K is the vertical hydraulic conductivity of the confining layer,
-1
streambed, or lake bed, LT ;
8
-------
m is the thickness of the confining layer, streambed, or lake
bed, L; and
H is the hydraulic head in the source bed, stream, or lake, L.
s
Alignment of coordinate axes
The cross-product terms of the permeability tensor drop out when
the coordinate axes are aligned with the principal axes of the tensor
(Bredehoeft, 1969); that is, k.. = 0 when i t j. Therefore, the only
tj
permeability terms with possible nonzero values are k , k , and k
r •> xx yy zz
This assumption simplifies the general flow equation, which can now be
rewritten to include all permeability terms as:
Darcy's Law may be written similarly for the three flow directions
as:
k
qx = "i \ 3x • H6 3x / (23a)
kyy /3P
qy ~ ~ v \*y ' "B 3y / (23b)
k
zz
qz = ' p V 3z ' "B 3z / (23c)
/3P^ 3z*
(-37 + P8 -3
For the case of two-dimensional areal flow, if the coordinate axes
are aligned with the principal directions of the transmissivity tensor,
equation 20 may be written as:
T + -T =s.
3x xx Zx 3y yy ty & 3t * w
-------
SOLUTE-TRANSPORT EQUATION
Derivation of general transport equation
An equation describing the three-dimensional transport and dispersion
of a reacting dissolved chemical in flowing ground water will be derived
from the principle of conservation of mass (continuity condition). The
derivation presented here is based on the developments of Reddell and
Sunada (1970), Bear (1972), and Bredehoeft and Finder (1973).
The principle of conservation of mass requires that the net mass of
solute entering or leaving a specified volume of aquifer during a given
time interval must equal the accumulation or loss of mass stored in that
volume during the interval. This may be expressed in a verbal equation as:
(Rate of Solute Accumulation)
= (Rate of Solute Inflow) - (Rate of Solute Outflow)
+ (Rate of Chemical Production by Reactions) (25)
This relationship may then be expressed mathematically by considering
all fluxes into and out of a representative elementary volume (REV), as
described by Bear (1972, p. 19). The REV shown in figure 1 is centered
at coordinates (x, y, z) and has dimensions (Ax, Ay, Az).
First we will determine fluxes in the x-direction. We know that at
the center of the REV the mass flux of solute in the x-direction across the
y-z plane (face IJKL) is equal to (CV * eAyAz), where C is the concentration
of the solute (ML ), V * is the instantaneous mass velocity of the solute
(LT~ ), and Ay and Az are the dimensions (L) of face IJKL. Note that the
term (eAyAz) simply represents the total effective cross-sectional area
through which flow is occurring.
We need expressions for the fluxes across the outer faces ABCD and
EFGH. The difference between the mass flux of solute across face ABCD and
face IJKL equals the rate of change of mass flux in the x-direction times
the distance between these two faces. The rate of change of the mass flux
3
of solute in the x-dlrection equals -5— (CV * eAyAz), and the distance from
OX X
the center to face ABCD is (-Ax/2). Thus, the mass flux through face ABCD
equals
CV * eAyAz - |- (CV * eAyAz )-^
X oX X f-
Similarly, the distance from the center to face EFGH is (+Ax/2) and the
mass flux through face EFGH is given by
10
-------
Figure 1.—Representative elementary volume (REV) of aquifer.
11
-------
eAyAz + (CV* eAyAz
The net mass flux of the solute entering or leaving the REV in the
x-direction equals the difference (input-output) between the two previous
terms:
(Net Mass Flux) = fcv * eAyAz - |- (CV * eAyAz )|^
x L x «x x i
* eAyAz +
(26)
This equation can also be derived by writing a Taylor series for the mass
flux term about the point (x, y, z) (Reddell and Sunada, 1970, p. 39).
Note that if the value of the derivative in the x-direction (equation 26)
is negative, then the mass flux of solute entering through face ABCD is
greater than the mass leaving through face EFGH. If all other fluxes
balance, there will then be a positive accumulation of solute mass in the
REV. Conversely, if the derivative is positive, there will be a decrease
over time of solute mass stored in the REV.
It can similarly be shown that for the y-direction:
(Net Mass Flux) - - J- (CV * eAxAz)Ay (27a)
and for the z-direction:
(Net Mass Flux) - - j- (CV * eAxAy)Az (27b)
z dz z
Solute may also enter or leave the REV as a-flux through a source or
sink (W). This may be expressed mathematically as:
(Source/Sink Mass Flux)REy - C'W*AxAyAz (28)
where C' is the concentration of the solute in the source or sink
fluid, ML~3.
12
-------
If a sink (withdrawal) is considered positive in sign and a source
(recharge or injection) is considered negative in sign, then when all other
fluxes balance, a positive W must be balanced by a decrease over time of
3C
solute mass stored in the REV (negative -r-), and vice versa. Note that
for a sink C' is equivalent to the concentration in the aquifer at the
location of the sink.
A particular solute may also be added to or removed from solution
within the REV by the effects of chemical reactions. Examples of such
reactions include radioactive decay, ion exchange, and adsorption. The
amount of solute that is produced (that is, added to or removed from
solution) within the REV is equal to the rate of production of the solute
times the volume of solution and may be expressed as :
8
(Solute Mass Produced )REV - eAxAyAz
where R« is the rate of production of the solute in reaction k of 8
different reactions (positive for addition of solute and
negative for removal), ML~ T~ .
The conservation of mass for a given solute may be expressed in a
continuity equation by combining the terms in equations 26, 27a, 27b, 28,
and 29, resulting in:
j- (CeAxAyAz) - - ^ (CVx* eAyAz)Ax
- - (CV * eAxAz)Ay - -- (CV * eAxAy)Az
«y y dz z
- C'WAxAyAz + EAxAyAz R. (30)
fc-1 *
If we assume that changes over time in porosity of the aquifer are
not significant and Ax, Ay, and Az are constants, then their derivatives
equal zero. Using an indicial notation to represent directions in
which x.., x,, and x. correspond to the x-, y-, and z-dlrections respec-
tively, equation 30 can be rewritten as:
eAXlAx2Ax3 || - - AXlAx2Ax3 -gjy (CV^* e) - C'WAx^x^
7c
8
+ eAx1Ax2Ax3 £ *fc (31)
13
-------
Dividing both sides of equation 31 by (Ax-Ax-Ax-) to remove the common
factors results in:
(32)
The instantaneous mass flux of the solute is given as CV>*. As shown
by Bear (1972, p. 101), this flux can be separated into two parts:
o
CV.* = CV. + CV. (33)
o
where V . is the deviation of the mass average velocity of the solute from
*£"
the average insterstitial velocity of the fluid
(V. = V.* - V.), LT'1.
Is i* V
The term CV. represents the convective flux of solute carried by the
1^
average fluid motion through the REVv Neglecting diffusion, the term
o
CV. represents the dispersive flux resulting from velocity fluctuations.
'Z'
Bear (1972, p. 101) also shows that the dispersive flux can be
approximated by:
CV. = - D.. I0- (34)
^ ^3 3x.
3
where D . . is the coefficient of mechanical dispersion (a second-order
3 2-1
tensor), L T .
Equation 34 indicates that the dispersive flux is directly proportional
to the concentration gradient and occurs in a direction from higher
concentrations towards lower concentrations. The form of equation 34 is
analogous to Pick's Law describing diffusive flux, as described by Bear
(1972, p. 78). In considering flowing ground water, diffusive fluxes are
assumed to be negligible in comparison to dispersive fluxes. If diffusion
is negligible, the coefficient of mechanical dispersion is equivalent to
the coefficient of hydrodynamic dispersion described by Bear (1972,
p. 606).
Coupling between forces of one type and fluxes of another type are
discussed by Bear (1972, p. 85-90). By following the development of
Bredehoeft and Finder (1973), and by assuming that the only significant
driving mechanism is the gradient of hydraulic head and that Darcy's Law
is fully valid, we eliminate the necessity of considering coupled
processes.
14
-------
As a result of substituting equation 34 into equation 33, the instan-
taneous mass flux may be expressed in terms of the dispersion coefficient
•as:
CV. * = CV . - D. . -r-^—
J
Equation 35 can next be substituted into equation 32 to yield:
** ^1 II f i
-------
Two-dimensional areal solute transport
A solute-transport equation for problems Involving two-dimensional
areal flow may be derived in a manner analogous to the previous derivation
of a general three-dimensional equation by assuming that vertical varia-
tions in head and concentration are negligible. Consider the total volume
of aquifer under a representative square area, as shown in figure 2.
Note that the vertical dimension is represented by the saturated thick-
ness, b, and that b may vary within the representative area. In this
case the mass flux through face ABCD is approximately equal to
<
***> - !; (
-------
Figure 2.—Representative volume of aquifer having variable saturated
thickness.
17
-------
Similarly, the mass flux through face EFGH may be given by
Ax
Ix" (°V £Ayb)
p £Ayb • a^ | «•„ (-"/wi 2
The net mass flux of the solute entering or leaving the representative
volume thus equals the difference between the two previous terms:
(Net Mass Flux>x - - |^ (w^* eAyb\Ax (43)
It can also be shown In the same manner that for the y-directlon:
(Net Mass Flux) = - y- { CV * eAxbJAy (44)
In the case of two-dimensional areal flow, It Is assumed that any
flux across the upper or lower faces of the representative volume is
included in the source/sink term. Solute entering or leaving the represen-
tative volume through a source or sink may be expressed mathematically
as:
(Source/ Sink Mass Flux) - C'WAxAy (45)
Solute added to or removed from solution within the representative
volume by the effects of chemical reactions may be expressed as:
8
(Solute Mass Produced) « eAxAyb Y) R,, (46)
fc-1 *
The conservation of mass for a given solute may be expressed in a
continuity equation by combining the terms in equations 43, 44, 45, and
46, resulting in:
J£ (CeAxAyb) - - |j (cVx* eAyb) Ax
e
C'WAxAy + eAxAyb £ Rfc ^7^
fe-1
18
-------
Tf E, Ax, and Ay are constants, equation 47 may be rewritten as:
• - eAxAy \- ( CV * b]
{?(*/*)
8
EAxAyb 2* •** •
-------
The left side of equation 49 may be expanded as:
1 C -57 + b !£ (52)
Substituting equation 52 into equation 51 and solving for dC/dt
results in:
i£-i-i-/hn 3C \ 1 J_ /hrv \
3t b 3x^ ( b°tj 3Xj. j " b 3x^ ( bCVt )
C 3b C^ f,
b 3t " eb + A fe (53)
If the saturated thickness is constant in space, the spatial deriv-
atives of b are equal to zero. Under these conditions, equation 53 can
be further simplified to:
at
CH/.C ab ., f .
eb b at + 1* ^ (54)
The two-dimensional solute-transport equation can be reduced further
if changes in saturated thickness over time are negligible and if the
solute is not affected by chemical reactions. Under these conditions
equation 54 may be simplified to:
C'W
20
-------
The difference between equation 53 and equation 54 can be presented
more explicitly by expanding the first two terms on the right side of
equation 53. After combining terms, equation 53 may then be rewritten
as:
at
Cl T1 ^ ^L.
W C ob , ^-« _ /CAN
~!b " b "3T+ ^ ^ (56)
Thus,'the difference between equations 53 and 54 is equal to:
In other words, the error in computed concentrations caused by assuming
that the saturated thickness is uniform, when it actually varies in space,
is inversely proportional to the saturated thickness and directly propor-
tional to the divergence of the saturated thickness. If the rate of
change in saturated thickness is small compared to the total saturated
thickness, the simpler equation 54 can be used as a reasonable approxi-
mation to equation 53.
If we consider c as a spatial variable, then equation 48 could
instead be divided by (AxAy). Following the steps that led to equation
51 then results in:
8
C'W + eb 2 R. (57)
fe-1 ^
21
-------
The equation of continuity for water may be written as:
•air (pebV + pw • ° (58)
^»
For homogeneous fluids, density (p) is constant. We may therefore divide
through by p to obtain:
+ 3 (eby } + w = o (59)
31 3x • t-
We may rewrite equation 57 by expanding the term on the left side,
expanding the second term on the right side, and rearranging to obtain:
3C . „ 3(eb)
C'M
8
- .eb T Rfc - 0 (60)
'fi
After adding the term CW to both sides of equation 60 and after
further factoring and rearranging of terms, we obtain:
22
-------
8C
+ c'w
.] - cw - «£
|9(cW.)
^ + -gf- + w'• " w " rt£ R* " °
From equation 59 it is apparent that the fifth term on the left
side equals zero. Rearranging terms and dividing through by cb
results in the following general solute-transport equation:
3C 1 3 /_ 3C
It = lb"5
\
)
H
If porosity is constant in space, equation 62 reduces to:
W(C-C')
— - (63)
It is interesting to note that when W represents withdrawal only, then
C' = C and the third term on the right side of equation 63 becomes
equal to zero. Therefore, withdrawals from the aquifer produce
concentration changes only indirectly through the effects of the
withdrawals on the velocity field, rather than by any direct effect on
the mass or concentration of solutes.
If vertical variations of head or concentration are significant,
then the two-dimensional equations previously derived would not precisely
describe areal solute transport. Cooley (written commun. , 1976) shows
that when a two-dimensional solute-transport equation is derived with a
more rigorous vertical integration of the three-dimensional equation,
the third dimension is not actually eliminated in converting to areal
coordinates but instead is transformed to boundary conditions.
23
-------
Dispersion coefficient
The solution of the solute- transport equation requires consideration
of the dispersion coefficient. Because of its tensorial properties, its
consideration may not appear to be straightforward. Hence, we will next
consider this coefficient in more detail.
Bear (1972, p. 580-581) states that hydrodynamic dispersion is the
macroscopic outcome of the actual movements of individual tracer particles
through the pores and that it includes two processes. One process is
mechanical dispersion, which depends upon both the flow of the fluid and
the nature of the pore system through which the flow takes place. The
second process is molecular and ionic diffusion, which because it depends
on time, is more significant at low flow velocities. Bear (1972) further
states that the separation between the two processes is artificial. In
developing our model we assume for flowing ground-water systems that the
definable contribution of molecular and ionic diffusion to hydrodynamic
dispersion is negligible.
The relationship between the dispersion coefficient, the fluid flow,
and the nature of the pore system is given in tensor notation by Scheidegger
(1961, p. 3275) as:
V V
where o... is the dispersivity of the porous medium (a fourth-order
ifjmrl
tensor), L;
V and V are the components of the flow velocity of the fluid in
fit rl »
the m and n directions, respectively, LT ; and
|v| is the magnitude of the velocity vector, LT~ .
Scheidegger (1961, p. 3275) states that the dispersivity tensor
possesses 81 components, but that even in the case of an anisotropic medium,
symmetry properties reduce the number of components to 36. Both Scheidegger
(1961) and Bear (1972) show that the dispersivity of an isotropic porous
medium can be defined by two constants. These are the longitudinal dis-
persivity of the medium, a, , and the transverse dispersivity of the medium
a . For an isotropic porous medium the components of the dispersivity
tensor in three dimensions (i,j <" 1,2,3) are:
a (68a)
(68b)
-------
a.... » a.... • a.... » a.... e 0
I (aL - V (68d)
The components of the dispersion coefficient for three-dimensional
flow may be stated explicitly by expanding equation 67 for a range of
three on i and J. After eliminating terms with coefficients that equal
zero (shown by equation 68c), we obtain:
v v v V V V
11 99 V
V V V V V V
11 99 ^
oo = aoon ~±-A + ao90o ~£-£ + a->->i* -*-
22 2211 |y| 2222 jyj 2233 jy|
V V VV V V
-.,... ,,,. ,,,
33 3311 3322 3333
a. -- +-:- (69c)
|v| |y| |y|
V V V V
D., = D,. = a191, -^ +a1,,1-?-i (69d)
12 21 1212 |v| 1221 |V.
V V V V
._ = D,. -a.,., -^- + a, „, -^ (69e)
13 31 1313 |vj 1331 jv|
V V V V
D,, = D., = a,,,, -^ + a -± (69f)
23 32 2323
If we substitute the identities presented in equations 68a and b
into equations 69a, b, and c, we obtain directly:
V1V1 V2V2 V3V3
-^-^ +0.-^-^ +aT-^^ (70a)
T T
25
-------
V V V V V V
TT + *' T7 + *T TT <70b>
|v| • Ivl * |vl
V V V V V V
11 22 33
-X - -, -
Next, by substituting the identities given by equation 68d into equations
69d, e, and f, we see that:
- V
V V
- V
D23 " °32 * <*L - V
Scheidegger (1961) and Bachmat and Bear (1964) also show that for a
Cartesian coordinate system x« in which one of the axes, say x., coincides
with the direction of the average velocity, then V.. = |v| and \^ = 0.
Substituting these relations into equations 70 and 71 we obtain:
DL (72.)
where D. and D are respectively the longitudinal and transverse
2-1
dispersion coefficients, L T
26
(72b)
D12 ' D21 " D13 - D31 C D23 " D32 " ° (72c)
-------
Solving equations 72a and b for a, and a., results in:
a - -f- (73a)
L V
DT
a - -T
Introducing equations 73a and b into equations 70 and 71 produces:
(V.)2 (V)2 (V.)2
"n • ° + °T -7 + "T -fl
(v,)2
V V
D. - D«. - (D. - D_) -i-3- (7Ae)
13 31 L T jv|2
D23 " D32 ' (DL * DT) l (7Af )
v
2
Equation 74 defines the local transformation of D.. from orthogonal
«v
axes, in which x, is parallel to V., to global cartesian axes. Note that
while D.., D.., and D__ must have positive values, it is possible for the
cross-product terms (equations 74d, e, and f) to have negative values.
27
-------
For the case of two-dimensional flow, all components and terms in equa-
tion 74 that have a subscript 3 are eliminated.
The magnitude of the velocity, |v|, is defined as:
2 + v 2 + v 2
L V2 + V3
(75)
In summary, the components of the dispersion tensor that must be
evaluated for three-dimensional flow in an isotropic porous medium are:
Dll D12 D13
D21 D22 D23
D31 D32 D33
D D D
xx xy xz
D D D
yx yy yz
zx zy zz
(76)
SUMMARY
A general equation describing the three-dimensional transport and
dispersion of a reacting dissolved chemical in flowing ground water was
derived nonrigorously from the principle of conservation of mass. The
general equation relates concentration changes to hydrodynamic dispersion,
convective transport, fluid sources and sinks, and chemical reactions.
Concentration changes caused by dispersion are assumed to be a
function of both the dispersion coefficient and the concentration gradient.
The dispersion coefficient is a second-order tensor and is related to
the dispersivity of the porous medium and to the flow velocity of the
ground water. If solute concentrations are affected by chemical reactions',
specific mathematical expressions describing the rates of reactions must
be incorporated into the general solute-transport equation.
Because both the dispersion coefficient and convective transport
depend on the flow velocity, the solution of the solute-transport equation
requires the definition of the velocity field, which in the general case
requires that the flow and solute-transport equations be solved simul-
taneously. However, the solution of these equations can be considerably
simplified if conditions of homogeneous fluid properties and (or) two-
dimensional flow can be validly assumed.
28
-------
REFERENCES CITED
Ahlstrom, S. W., and Baca, R. G., 1974, Transport model user's manual:
Battelle Pacific Northwest Laboratories rept. BNWL-1716, 25 p.
Bachmat, Y., and Bear, J., 1964, The general equations of hydrodynamic
dispersion in homogeneous, isotropic, porous mediums: Jour. Geophys.
Research, v. 69, no. 12, p. 2561-2567.
Bear, J., 1972, Dynamics of fluids in porous media: New York, Am. Elsevier
Publishing Co., 764 p.
Bredehoeft, J. D., 1969, Finite difference approximations to the equations
of ground-water flow: Water Resources Research, v. 5, no. 2,
p. 531-534.
Bredehoeft, J. D., and Pinder, G. F., 1973, Mass transport in flowing
groundwater: Water Resources Research, v. 9, no. 1, p. 194-210.
Cooley, R. L., 1974, Finite element solutions for the equations of
ground-water flow: Hydrology and Water Resources Pub. no. 18,
Desert Research Inst., Univ. Nevada, 134 p.
Cooper, H. H., Jr., 1966, The equation of groundwater flow in fixed and
deforming coordinates: Jour. Geophys. Research, v. 71, no. 20,
p. 4785-4790.
Grove, D. B., 1976, The use of Galerkin finite element methods to solve
mass transport equations: unpub. Ph. D. thesis, Colorado School of
Mines, Golden, Colo., 152 p.
Gupta, S. K., Tanji, K. K., and Luthin, J. N., 1975, A three-dimensional
finite element ground water model: California Water Resources Center,
contr. no. 152, 119 p.
Hubbert, M. K., 1940, The theory of ground-water motion: Jour. Geology,
v. 48, no. 8, pt. 1, p. 785-944.
Konikow, L. F., 1976, Modeling solute transport in groundwater: Internat.
Conf. on Environmental Sensing and Assessment, Las Vegas, Nev., Proc.,
art. 20-3.
Konikow, L. F., and Bredehoeft, J. D., 1974, Modeling flow and chemical
quality changes in an irrigated stream-aquifer system: Water Resources
Research, v. 10, no. 3, p. 546-562.
Lantz, R. B., Pahwa, S. B., and Grove, D. B., 1976, Development of a
subsurface waste disposal simulation model [abs]: EOS, Am. Geophys.
Union Trans., v. 57, no. 4, p. 249.
Pinder, G. F., 1973, A Galerkin-finite element simulation of ground-water
contamination on Long Island, New York: Water Resources Research,
v. 9, no. 6, p. 1657-1669.
29
-------
Reddell, D. L., and Sunada, D. K., 1970, Numerical simulation of dispersion
in groundwater aquifers: Colorado State Univ. Hydrology Paper 41,
79 p.
Robertson, J. B., 1974, Digital modeling of radioactive and chemical waste
transport in the Snake River Plain aquifer at the National Reactor
Testing Station, Idaho: U.S. Geol. Survey open-file rept., 41 p.
Robson, S. G., 1974, Feasibility of digital water-quality modeling illus-
trated by application at Barstow, California: U.S. Geol. Survey
Water-Resources Inv. 46-73, 66 p.
Scheidegger, A. E., 1961, General theory of dispersion in porous media:
Jour. Geophys. Research, v. 66, no. 10, p. 3273-3278.
Segol, G., and Finder, G. F., 1976, Transient simulation of saltwater
intrusion in southeastern Florida: Water Resources Research, v. 12,
no. 1, p. 65-70.
30
-------
SECTION 2
MODEL DOCUMENTATION
-------
Techniques of Water-Resources Investisations
oF the United States Geological Survey
Chapter C2
COMPUTER MODEL OF TWO-DIMENSIONAL
SOLUTE TRANSPORT AND DISPERSION
IN GROUND WATER
By L F. Konikow and J. D. Bredehoeft
Book 7
AUTOMATED DATA PROCESSING AND COMPUTATIONS
-------
DEPARTMENT OF THE INTERIOR
WILLIAM P. CLARK, Secretary
U.S. GEOLOGICAL SURVEY
Dallas L. Peck, Director
First printing 1978
Second printing 1984
UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1978
For sale by the Books and Open-File Reports Section, U.S. Geological Survey,
Federal Center, Box 25425, Denver, CO 80225
-------
PREFACE
The series of manuals on techniques describes procedures for plan-
ning and executing specialized work in water-resources investigations.
The material is grouped under major headings called books and further
subdivided into sections and chapters; section C of Book 7 is on computer
programs.
This chapter presents a digital computer model for calculating
changes in the concentration of a dissolved chemical species in flowing
ground water. The computer program represents a basic and general
model that may have to be modified by the user for efficient application to
his specific field problem. Although this model will produce reliable cal-
culations for a wide variety of field problems, the user is cautioned that in
some cases the accuracy and efficiency of the model can be affected sig-
nificantly by his selection of values for certain user-specified options.
m
-------
CONTENTS
Abstract -
Introduction _
Theoretical background
Flow equation
Transport equation
Dispersion coefficient
Review of assumptions
Numerical methods
Flow equation
Transport equation
Method of characteristics
Particle tracking
Finite-difference approximations
Stability criteria
Boundary and initial conditions
Mass balance
Special problems
Computer program
General program features
Program segments
MAIN
Subroutine PARLOD _
Subroutine ITERAT
Subroutine GENPT
Subroutine VELO
Subroutine MOVE
Pure
1
1
2
2
3
3
4
4
4
5
6
6
7
11
13
14
15
19
20
21
21
22
22
22
23
23
Page
Computer program—Continued
Program segments—Continued
Subroutine CNCON 26
Subroutine OUTPT 26
Subroutine CHMOT . 25
Evaluation of model 25
Comparison with analytical solutions — 26
Mass balance tests 28
Test problem 1—spreading of a tracer
slug 28
Test problem 2—effects of wells 31
Test problem 3—effects of user
options 32
Possible program modifications 34
Coordinate system and boundary
conditions 36
Basic equations 36
Input and output 36
Conclusions 87
References cited „ 87
Attachment I, Fortran IV program listing 41
Attachment II, Definition of selected program
variables 74
Attachment III, Data input formats 76
Attachment IV, Input data for test problem 3 79
Attachment V, Selected output for test
problem 3 80
FIGURES
Page
1. Part of hypothetical finite-difference grid showing relation of flow field to movement of points... 7
2. Part of hypothetical finite-difference grid showing areas over which bilinear interpolation is used
to compute the velocity at a point 7
8. Representative change in breakthrough curve from time level fc—1 to k 11
4. Possible movement of particles near an impermeable (no-flow) boundary 15
B. Replacement of points in source cells adjacent to a no-flow boundary 16
6. Replacement of points in source cells not adjacent to a no-flow boundary for negligible regional
flow (a) and for relatively strong regional flow (b) 17
7. Relation between possible initial locations of points and indices of adjacent nodes 19
8. Simplified flow chart illustrating the major steps in the calculation procedure 21
9. Parts of finite-difference grids showing the initial geometry of particle distribution for the specifi-
cation of four (a), five (b), eight (c), and nine (d) particles per cell 28
10. Generalized flow chart of subroutine MOVE 24
11. Comparison between analytical and numerical solutions for dispersion in one-dimensional,
steady-state flow 26
-------
VI CONTENTS
FIGURES—Continued
P.«e
12. Comparison between analytical and numerical solutions for dispersion in plane radial steady-
state flow 28
13. Grid, boundary conditions, and flow field for test problem 1 29
14. Mass-balance errors for test problem 1 30
15. Grid, boundary conditions, and flow field for test problem 2 30
16. Mass-balance errors for test problem 2 31
17. Grid, boundary conditions, and flow field for test problem 3 32
18. Effect of NPTPND on mass-balance error for test problem 3; CELDIS=0.50 in all cases 33
19. Effect of CELDIS on mass-balance error for test problem 3; NPTPND=9 in all cases 34
TABLES
Page
1. List of subroutines for solute-transport model 20
2. Model parameters for test problem 1 29
3. Model parameters for test problems 2 and 3 31
4. Effect of NPTPND on accuracy, precision, and efficiency of solution to test problem 3 33
5. Effect of CELDIS on accuracy, precision, and efficiency of solution to test problem 3 33
-------
COMPUTER MODEL OF TWO-DIMENSIONAL SOLUTE TRANSPORT
AND DISPERSION IN GROUND WATER
By L F. Konikow and J. D. Bredehoeft
Abstract
This report presents a model that simulates solute
transport in flowing ground water. The model is
both general and flexible in that it can ba applied
to a wide range of problem types. It is applicable
to one- or two-dimensional problems involving
steady-state or transient flow. The model computes
changes in concentration over time caused by the
processes of convective transport, hydrodynamic
dispersion, and mixing (or dilution) from fluid
sources. The model assumes that the solute is non-
reactive and that gradients of fluid density, viscos-
ity, and temperature do not affect the velocity dis-
tribution. However, the aquifer may be hetero-
geneous and (or) anisotropic.
The model couples the ground-water flow equa-
tion with the solute-transport equation. The digital
computer program uses an alternating-direction im-
plicit procedure to solve a finite-difference approxi-
mation to the ground-water flow equation, and it
uses the method of characteristics to solve the
solute-transport equation. The latter uses a particle-
tracking procedure to represent convective transport
and a two-step explicit procedure to solve a finite-
difference equation that describes the effects of hy-
drodynamic dispersion, fluid sources and sinks, and
divergence of velocity. This explicit procedure has
several stability criteria, but the consequent time-
stop limitations are automatically determined by the
program.
The report includes a listing of the computer pro-
gram, which is written in FORTRAN IV and con-
tains about 2,000 lines. The model is based on a
rectangular, block-centered, finite-difference grid. It
allows the specification of any number of injection
or withdrawal wells and of spatially varying diffuse
recharge or discharge, saturated thickness, trans-
missivity, boundary conditions, and initial heads and
concentrations. The program also permits the desig-
nation of up to five nodes as observation points, for
which a summary table of head and concentration
versus time is printed at the end of the calculations.
The data input formats for the model require three
data cards and from seven to nine data sets to de-
scribe the aquifer properties, boundaries, and
stresses.
The accuracy of the model was evaluated for two
idealized problems for which analytical solutions
could be obtained. In the case of one-dimensional
flow the agreement was nearly exact, but in the
case of plane radial flow a small amount of nu-
merical dispersion occurred. An analysis of several
test problems indicates that the error in the mass
balance will be generally less than 10 percent. The
test problems demonstrated that the accuracy and
precision of the numerical solution is sensitive to
the initial number of particles placed in each cell
and to the size of the time increment, as determined
by the stability criteria. Mass balance errors are
commonly the greatest during the first several time
increments, but tend to decrease and stabilize with
time.
Introduction
This report describes and documents a
computer model for calculating transient
changes in the concentration of a nonreac-
tive solute in flowing ground water. The
computer program solves two simultaneous
partial differential equations. One equation
is the ground-water flow equation, which de-
scribes the head distribution in the aquifer.
The second is the solute-transport equation,
which describes the chemical concentration
in the system. By coupling the flow equation
with the solute-transport equation, the model
can be applied to both steady-state and tran-
sient flow problems.
The purpose of the simulation model is to
compute tiie concentration of a dissolved
chemical species in an aquifer at any speci-
fied place and time. Changes in chemical
concentration occur within a dynamic
ground-water system primarily due to four
-------
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
distinct processes: (1) convective transport,
in which dissolved chemicals are moving
with the flowing ground water; (2) hydro-
dynamic dispersion, in which molecular and
ionic diffusion and small-scale variations in
the velocity of flow through the porous media
cause the paths of dissolved molecules and
ions to diverge or spread from the average
direction of ground-water flow; (3) fluid
sources, where water of one composition is
introduced into water of a different composi-
tion; and (4) reactions, in which some
amount of a particular dissolved chemical
species may be added to or removed from the
ground water due to chemical and physical
reactions in the water or between the water
and the solid aquifer materials. The model
presented in this report assumes (1) that no
reactions occur that affect the concentration
of the species of interest, and (2) that gra-
dients of fluid density, viscosity, and tem-
perature do not affect the velocity distribu-
tion.
This model can be applied to a wide
variety of field problems. However, the user
should first become aware of the assumptions
and limitations inherent in the model, as
described in this report. The computer pro-
gram presented in this report is offered as a
basic working tool that may have to be
modified by the user for efficient application
to specific field problems. The program is
written in FORTRAN IV and is compatible
with most high-speed computers. The data
requirements, input format specifications,
program options, and output formats are all
structured in a general manner that should
be readily adaptable to many field problems.
This report includes a detailed description
of the numerical method used to solve the
solute-transport equation. The reader is as-
sumed to have (or can obtain elsewhere) a
moderate familiarity with finite-difference
methods and ground-water flow models.
Theoretical Background
Flow equation
By following the derivation of Finder and
Bredehoeft (1968), the equation describing
the transient two-dimensional areal flow of
a homogeneous compressible fluid through a
nonhomogeneous anisotropic aquifer can be
written in Cartesian tensor notation as
W
3*
(i)
where
Tit is the transmissivity ten-
sor, Lf/T\
h is the hydraulic head, L;
S is the storage coefficient,
(dimensionless);
t is the time, T;
W= W(x,y,t) is the volume flux per unit
area (positive sign for
outflow and negative
for inflow), L/T; and
x( and Xj are the Cartesian coordi-
nates, L.
If we only consider fluxes of (1) direct with-
drawal or recharge, such as well pumpage,
well injection, or evapotranspiration, and
(2) steady leakage into or out of the aquifer
through a confining layer, streambed, or
lakebed, then W(x,y,t) may be expressed
as
W(x,y,t)=*Q (x.y.t) ~(H.- h) (2)
//»
where
Q is the rate of withdrawal (posi-
tive sign) or recharge (negative
sign),L/r;
K, is the vertical hydraulic conductiv-
ity of the confining layer, stream-
bed, or lakebed, L/T;
m is the thickness of the confining
layer, streambed, or lakebed, L;
and
H, is the hydraulic head in the source
bed, stream, or lake, L.
Lohman (1972) shows that an expression
for the average seepage velocity of ground
water can be derived from Darcy's law. This
expression can be written in Cartesian ten-
sor notation as
3h
(3)
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
3
where
Vt is the seepage velocity in the direc-
tion of xlt L/T;
KH is the hydraulic conductivity tensor,
L/T; and
c is the effective porosity of the aqui-
fer, (dimensionless).
Transport equation
The equation used to describe the two-di-
mensional areal transport and dispersion of
a given nonreactive dissolved chemical spe-
cies in flowing ground water was derived by
Reddell and Sunada (1970), Bear (1972),
Bredehoeft and Finder (1973), and Konikow
and Grove (1977). The equation may be
written as
C'W
t,/=l,2 (4)
where
C is the concentration of the dissolved
chemical species, M/L3;
DtJ is the coefficient of hydrodynamic
dispersion (a second-order ten-
sor), L»/T;
b is the saturated thickness of the
aquifer, L; and
C' is the concentration of the dissolved
chemical in a source or sink fluid,
•Qt
The first term on the right side of equa-
tion 4 represents the change in concentra-
tion due to hydrodynamic dispersion. The
second term describes the effects of convec-
tive transport, while the third term repre-
sents a fluid source or sink.
Dispersion coefficient
Bear (1972, p. 580-681) states that hydro-
dynamic dispersion is the macroscopic out-
come of the actual movements of individual
tracer particles through the pores and that
it includes two processes. One process is
mechanical dispersion, which depends upon
both the flow of the fluid and the nature of
the pore system through which the flow takes
place. The second process is molecular and
ionic diffusion, which because it depends on
time, is more significant at low flow veloci-
ties. Bear (1972) further states that the
separation between the two processes is arti-
ficial. In developing our model we assume for
flowing ground-water systems that the de-
finable contribution of molecular and ionic
diffusion to hydrodynamic dispersion is
negligible.
The dispersion coefficient may be related
to the velocity of ground-water flow and to
the nature of the aquifer using Scheidegger's
(1961) equation:
VmV(.
**\i= CUfwm |»ri * •* '
In
where
«
-------
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
w^ <«>
Note that while DZI and !>„„ must have
positive values, it is possible for the cross-
product terms (eq 10) to have negative
values if V, and V, have opposite signs.
Review of assumptions
A number of assumptions have been made
in the development of the previous equa-
tions. Following is a list of the main assump-
tions that must be carefully evaluated before
applying the model to a field problem.
1. Darcy's law is valid and hydraulic-head
gradients are the only significant driv-
ing mechanism for fluid flow.
2. The porosity and hydraulic conductivity
of the aquifer are constant with time,
and porosity is uniform in space.
3. Gradients of fluid density, viscosity, and
temperature do not affect the velocity
distribution.
4. No chemical reactions occur that affect
the concentration of the solute, the
fluid properties, or the aquifer proper-
ties.
5. Ionic and molecular diffusion are negli-
gible contributors to the total disper-
sive flux.
6. Vertical variations in head and concen-
tration are negligible.
7. The aquifer is homogeneous and isotropic
with respect to the coefficients of longi-
tudinal and transverse dispersivity.
The nature of a specific field problem may
be such that not all of these underlying as-
sumptions are completely valid. The degree
to which field conditions deviate from these
assumptions will affect the applicability and
reliability of the model for that problem. If
the deviation from a particular assumption
is significant, the governing equations will
have to be modified to account for the ap-
propriate processes or factors.
Numerical Methods
Because aquifers have variable properties
and complex boundary conditions, exact ana-
lytical solutions to the partial differential
equations of flow (eq 1) and solute trans-
port (eq 4) cannot be obtained directly.
Therefore, approximate numerical methods
must be employed.
The numerical methods require that the
area of interest be subdivided by a grid into
a number of smaller subareas. The model
developed here utilizes a rectangular, uni-
formly spaced, block-centered, finite-differ-
ence grid, in which nodes are defined at the
centers of the rectangular cells.
Plow equation
Finder and Bredehoeft (1968) show that
if the coordinate axes are alined with the
principal directions of the transmissivity
tensor, equation 1 may be approximated by
the following implicit finite-difference equa-
tion:
h*-ij,k — ht,i.k I
"-"•"I (AX)» J
(ID
where
i,j,k are indices in the x, y, and
time dimensions, respec-
tively;
Az,Ay,At are increments in the x, y,
and time dimensions, re-
spectively; and
qw is the volumetric rate of with-
drawal or recharge at the
(i,j) node, L*/T.
Note that k represents the new time level
and fc-1 represents the previous time level.
To avoid confusion between tensor sub-
-------
MODEL OP SOLUTE TRANSPORT IN GROUND WATER
scripts and nodal indices, the latter are sep-
arated by commas.
The finite-difference equation (eq 11) is
solved numerically for each node in the grid
using an iterative alternating-direction im-
plicit (ADI) procedure. The derivation and
solution of the finite-difference equation and
the use of the iterative ADI procedure have
been previously discussed in detail in the
literature. Some of the more relevant refer-
ences include Finder and Bredehoeft (1968),
Prickett and Lonnquist (1971), and Tres-
cott, Finder, and Larson (1976).
After the head distribution has been com-
puted for a given time step, the velocity of
ground-water flow is computed at each node
using an explicit finite-difference form of
equation 3. For example, the velocity in the
x direction at node (i,j) would be computed
as
The velocity in the x direction can also be
computed on the boundary between node
(i,j) and node (t+1,;) using the following
equation :
(13)
where the hydraulic conductivity on the
boundary is computed as the harmonic mean
of the hydraulic conductivities at the two
adjacent nodes.
Expressions similar to equations 12 and 13
are used to compute the velocities in the y
direction at (t,/) and (t,/+Vfc) respectively.
Note that equation 13, which computes the
head difference over a distance Ax, is more
accurate than equation 12, which computes
the head difference over 2Ax.
Transport equation
Method of characteristics
The method of characteristics is used in
this model to solve the solute-transport equa-
tion. This method was developed to solve
hyperbolic differential equations. If solute
transport is dominated by convective trans-
port, as is common in many field problems,
then equation 4 may closely approximate a
hyperbolic partial differential equation and
be highly compatible with the method of
characteristics. Although it is difficult to
present a rigorous mathematical proof for
this numerical scheme, it has been success-
fully applied to a variety of field problems.
The development of this technique for prob-
lems of flow through porous media has been
presented by Carder, Peaceman, and Pozzi
(1964), Finder and Cooper (1970), Reddell
and Sunada (1970), and Bredehoeft and
Finder (1973). Carder, Peaceman, and
Pozzi (1964) state that this technique does
not introduce numerical dispersion (artifi-
cial dispersion resulting from the numerical
calculation process). They and Reddell and
Sunada (1970) also compared solutions ob-
tained using the method of characteristics
with those derived by analytical methods
and found good agreement for the cases in-
vestigated. Applications of the method to
field problems have been documented by
Bredehoeft and Finder (1978), Konikow
and Bredehoeft (1974), Robertson (1974),
Robson (1974), and Konikow (1977).
The approach taken by the method of char-
acteristics is not to solve equation 4 directly,
but rather to solve an equivalent system of
ordinary differential equations. Konikow and
Grove (1977, eq 61) show that by consider-
ing saturated thickness as a variable and by
expanding the convective transport term,
equation 4 may be rewritten as
-V.
W(C - C')
tb
• (14)
Equation 14 is the form of the solute-trans-
port equation that is solved in the computer
program presented in this report. For con-
venience we may also write equation 14 as
(15)
-------
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
where
F -
(16)
Next consider representative fluid par-
ticles that are convected with flowing ground
water. Note that changes with time in prop-
erties of the fluid, such as concentration, may
be described either for fixed points within
a stationary coordinate system as successive
fluid particles pass the reference points, or
for reference fluid particles as they move
along their respective paths past fixed points
in space. Aris (1962, p. 78) states that "as-
sociated with these two descriptions are two
derivatives with respect to time." Thus
"dC/fit is the rate of change of concentration
as observed from a fixed point, whereas
dC/dt is the rate of change as observed when
moving with the fluid particle. Aris (1962)
calls the latter the material derivative.
The material derivative of concentration
may be defined as
dx
_ dy
dt "ftt "Qx dt "Qy dt
Note the correspondence of the second and
third terms on the right side of equation 15
with the second and third terms on the right
side of equation 17. The latter includes the
material derivatives of position, which are
defined by velocity. Thus for the x and y
components, respectively, of position and
velocity we have
and
dt
dy
~dt
(18)
(19)
If we next substitute the right sides of
equations 15, 18, and 19 for the correspond-
ing terms in equation 17, we obtain
—=— — (bDi^-)+F. (20)
dt b 3x1 fiXf
The solutions of the system of equations
comprising equations 18-20 may be given as
(21)
and are called the characteristic curves of
equation 15.
Given solutions to equations 18-20, a solu-
tion to the partial differential equation (eq
15) may be obtained by following the char-
acteristic curves. This is accomplished nu-
merically by introducing a set of moving
points (or reference particles) that can be
traced within the stationary coordinates of
the finite-difference grid. Garder, Peaceman,
and Pozzi (1964, p. 27) state, "Each point
corresponds to one characteristic curve, and
values of x, y, and C are obtained as func-
tions of t for each characteristic." Each point
has a concentration and position associated
with it and is moved through the flow field
in proportion to the flow velocity at its loca-
tion. Intuitively, the method may be visual-
ized as tracing a number of fluid particles
through a flow field and observing changes
in chemical concentration in the fluid par-
ticles as they move.
Particle tracking
The first step in the method of character-
istics involves placing a number of trace-
able particles or points in each cell of the
finite-difference grid to form a set of points
that are distributed in a geometrically uni-
form pattern throughout the area of inter-
est. It was found that placing from four to
nine points per cell provided satisfactory re-
sults for most two-dimensional problems.
The location or position of each particle is
specified by its x- and y- coordinates in the
finite-difference grid. The initial concentra-
tion assigned to each point is the initial con-
centration associated with the node of the
cell containing the point.
For each time step every point is moved a
distance proportional to the length of the
time increment and the velocity at the loca-
tion of the point. (See fig. 1.) The new posi-
tion of a point is thus computed with the fol-
lowing finite-difference forms of equations
18 and 19:
(22)
and
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
L
I
EXPLANATION
• Initial location of particle
O New location of particle
—^- Flow line and direction of flow
Computed path of particle
Figure 1.—Part of hypothetical finite-
difference grid showing relation of
flow field to movement of points.
(23)
where
p is the index number for
point identification ; and
Bxf and &yf are the distances moved in
the x and y directions, re-
spectively.
The x and y velocities at the position
of any particular point p, indicated as
V•»<,.»,]» for time k are calculated through
bilinear interpolation over the area of half
of a cell using the x and y velocities com-
puted at adjacent nodes and cell boundaries.
For example, figure 2 illustrates that the
velocity in the x direction of point p, located
in the southeast quadrant of cell (i,j) , would
be computed using bilinear interpolation be-
tween the x velocities computed with equa-
tions 12 and IS at (i,j), (t,; + l), (t + VW),
and (t-r-V6 ,;'+!). Similarly, the velocity in
the y direction of point p would be based on
the y velocities computed at (tj), (t +!,/),
.jf The time index is distinguished
with an asterisk here because this tempo-
rarily assigned average concentration rep-
resents the new time level only with respect
to convective transport. The moving points
simulate convective transport because the
concentration at each node of the grid will
change with each time step as different
points having different concentrations enter
and leave the area of that cell.
Finite-difference approximations
The total change in concentration in an
aquifer may be computed by solving equa-
tions 18-20. Equations 18 and 19, which are
related to changes in concentration caused
-------
8
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
by convective transport alone, are solved
by the movement of points as described
previously. The changes in concentration
caused by hydrodynamic dispersion, fluid
sources, divergence of velocity, and changes
in saturated thickness are calculated using
an explicit finite-difference approximation to
equation 20, which can be expressed as
f~ 1 3 3C ~\
fl -- (60V— ) +F .
L b 3*< 3z, J
(24)
Note that a solution to equation 20 re-
quires the computation of the change in con-
centration at the tracer particles. However,
primarily because of the difficulty in comput-
ing the concentration gradient at a large
number of moving points, the change in con-
centration represented by equation 20 is
solved at each node of the grid rather than
directly at the location of each point. The
material derivative of concentration on any
characteristic curve (or for any tracer par-
ticle) is then related to the change in con-
centration for a node during one time step,
which was computed with the solution to
equation 24.
The right side of equation 24 can be con-
sidered as the sum of two separate terms,
as follows :
ACijU = ( ACU,*) ! + ( AC,,M) „ (25)
where
k) i is the change in concentration
caused by hydrodynamic
dispersion, and is defined
as
and
(26)
(ACu.k)n is the change in concentra-
tion resulting from an ex-
ternal fluid source and
changes in saturated thick-
ness, and from equation 16
is defined as
. (27)
= A/
W(C - C')
€/)
First we will examine the change in con-
centration due to dispersion, partly follow-
ing the development of Reddell and Sunada
(1970). The right side of equation 26 can be
expanded according to the summation con-
vention of tensor notation to obtain
.$ *.{wje+wj£.}
T -
3»
(28)
A finite-difference approximation for the
derivative in the z direction at (i,j) may be
written as
2-(M)j£
3z Qz
)
AZ
AZ
(29)
In the following expansion of equation 29
it is implied that concentrations (C) are
known from the previous (fc-1) time level;
hence, equation 29 is an explicit finite-differ-
ence equation. The spatial derivatives of con-
centration at (i+Vz,j) may be approximated
by
+HJ
and
AZ
C —C
H-H./+1
(30)
vu 2Ay
(31)
Because concentrations are defined only at
nodes, we must express the right side of
equation 31 in terms of concentrations at
nodes. Assuming that the concentration at a
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
cell boundary is approximately equal to the
average (arithmetic mean) of the concentra-
tions at adjacent nodes, we have
+C
<+K.H->
and
H-KJ-i
(32)
(33)
Substitution of equations 32 and 33 into
equation 31 results in:
(34)
Similarly, the spatial derivatives of con-
centration at (i-l/2,j) are
(—\
\dx)i-
Ax
(35)
and
(36)
After substituting equations 30, 34, 35, and
36 into equation 29, we have
bD
(AX)'
J) ' U+l
(AX)'
-C«-,-Cl
wrH-HJP <-
+
4AXAV
(37)
A finite-difference approximation for the
derivative in the y direction in equation 28
may be developed for node (i,/) in an analo-
gous manner to equation 37 to produce
"dv
AJ/
^
(Atf)«
-C, .. -C.
~ «-U-t~ <-U'
(38)
4AXAV
Equation 28 may then be solved explicitly
by substituting the relationships expressed
by equations 87 and 38 for the terms within
brackets on the right side of equation 28.
-------
10
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
Next we will examine the change in con-
centration denoted by equation 27. Substi-
tuting explicit finite-difference approxima-
tions for tiie terms in equation 27, we have
(39)
Equations 28, 37, 38, and 39 together pro-
vide a solution to equation 24, which in turn
allows us to solve equation 20 and complete
the definition of the characteristic curves of
equation 15.
Because the processes of convective trans-
port, hydrpdynamic dispersion, and mixing
are occurring continuously and simultane-
ously, equations 18, 19, and 20 should be
solved simultaneously. However, equations
18 and 19 are solved by particle movement
based on implicitly computed heads while
equation 20 is solved explicitly with respect
to concentrations. Because the change in con-
centration at a source node due to mixing is
proportional to the difference in concentra-
tion between the node and the source fluid
(see eq 27), the accuracy of estimating the
concentration at the node during a time in-
crement will clearly affect the computed
change. Similarly, because the change in con-
centration due to dispersion is proportional
to the concentration gradient at a point, the
accuracy of estimating the concentration
gradient will clearly affect the accuracy of
the numerical results. As the position of a
front or breakthrough curve advances with
time, say from the k-1 to k time level, the
concentration gradient at any fixed reference
point and the concentration differences at
sources are continuosly changing. The con-
sequent limitations imposed by estimating
nodal concentrations in a strict explicit man-
ner can be minimized by using a two-step
explicit procedure in which equation 24 is
solved at each node by giving equal weight
to concentration gradients computed from
the concentrations at the previous time level
(k-1) and to concentration gradients com-
puted from concentrations at time level (k*),
which represents the convected position of
the front at the new time level (k) prior to
adjustments of concentration for dispersion
and mixing. Figure 3 illustrates the sequence
of calculations to solve equations 18-20 over
a given time increment. First the concentra-
tion gradients at the previous time level
(k-1) are determined at each node. Then
the front is convected to a new position for
time level k* based on the velocity of flow
and length of the time increment. Next the
concentration gradients at each node are re-
computed for the new position of the front.
The concentration distribution for the new
frontal position is then adjusted at each node
in two steps: first based on concentration
gradients at k-1 and second based on con-
centration gradients at k*.
The finite-difference approximation to
equation 24 may thus be expressed as
0.5
b
0.5 A/
dxi
a.v,
(bD:
ac
/,M
* '-
(40)
in which the appropriate finite-difference ap-
proximations for the terms within brackets
are indicated by equations 37, 38, and 39.
The new nodal concentrations at the end
of time increment k are computed as
» (41)
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
11
0.6
RELATIVE DISTANCE
1.0
Figure 3.—Representative change in breakthrough curve from time level It—1 to k. Note that concentration
changes are exaggerated to help Illustrate the sequence of calculations.
where £«./,»• is the average of the concentra-
tions of all points in cell (ij) after equations
22 and 28 were solved for all points for time
step k, and ACM-t is the change in concentra-
tion caused by hydrodynamic dispersion,
sources, and sinks, as calculated in equation
40.
Because the concentrations of points in a
cell vary about the concentration of the node,
the change in concentration computed at a
node using equation 40 cannot be applied
directly in all cases to the concentrations of
the points. If the change in concentration at
the node (AC1J(») is positive, the increase is
simply added to the point concentrations.
But if the concentration change is negative,
it is applied to points in that cell as a per-
centage decrease in concentration at each
point that is equal to the percentage decrease
at the node. This technique preserves a mass
balance within each cell, but when a decrease
in concentration is computed for a node, it
will also prevent a possible but erroneous
computation of negative concentrations at
those points that had a concentration less
than that at the node.
Stability criteria
The explicit numerical solution of the
solute-transport equation has a number of
stability criteria associated with it. These
may require that the time step used to solve
the flow equation be subdivided into a num-
ber of smaller time increments to accurately
solve the solute-transport equation.
First, Reddell and Sunada (1970, p. 62)
show that for an explicit finite-difference
solution of equation 26 to be stable,
-------
12
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
(A*)' (Ay)' 2
Solving equation 42 for At, we see that
0.5
Min
(over grid)
(AZ)
(42)
. (43)
Because the solution to equation 26 is ac-
tually written as a set of N equations for N
nodes, the maximum permissible time incre-
ment is the smallest At computed for any in-
dividual node in the entire grid. The smallest
At will then occur at the node having the
largest value of
(A*)' (Ay)*
Next consider the effects of mixing ground
water of one concentration with injected or
recharged water of a different concentra-
tion, as represented by the source terms in
equation 39. The change in concentration in
a source node cannot exceed the difference
between the source concentration (C' . ) and
»>/
the concentration in the aquifer (C
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
13
(55)
where y is the fraction of the grid dimen-
sions that particles will be allowed to move
(0
and
Because these criteria are governed by the
maximum velocities in the system, and since
the computed velocity of a tracer particle
will always be less than or equal to the
maximum velocity computed at a node or cell
boundary, we have to check only the latter.
Substituting the grid velocities and solving
equations 56 and 57 for At results in
and
(V.)t
(58)
(59)
If the time step used to solve the flow
equation exceeds the smallest of the time
limits determined by equations 43, 49, 58, or
69, then the time step will be subdivided into
the appropriate number of smaller time in-
crements required for solving the solute-
transport equation.
Boundary and initial conditions
Obtaining a solution to the equations that
describe ground-water flow and solute trans-
port requires the specification of boundary
and initial conditions for the domain of the
problem. Specifications for solving the flow
equation must be compatible with the solu-
tion of the solute-transport equation. Several
different types of boundary conditions can
be incorporated into the solute-transport
model. Two general types are incorporated
in this model; these are constant-flux and
constant-head conditions. These can be used
to represent the real boundaries of an
aquifer as well as to represent artificial
boundaries for the model. The use of the
latter can help to minimize data require-
ments and the areal extent of the modeled
part of the aquifer.
A constant-flux boundary can be used to
represent aquifer underflow, well with-
drawals, or well injection. A finite flux is
designated by specifying the flux rate as a well
discharge or injection rate for the appro-
priate nodes. A no-flow boundary is a spe-
cial case of a constant-flux boundary. The
numerical procedure used in this model re-
quires that the area of interest be sur-
rounded by a no-flow boundary. Thus the
model will automatically specify the outer
rows and columns of the finite-difference grid
as no-flow boundaries. No-flow boundaries
can also be located elsewhere in the grid to
simulate natural limits or barriers to
ground-water flow. No-flow boundaries are
designated by setting the transmissivity
equal to zero at appropriate nodes, thereby
precluding the flow of water or dissolved
chemicals across the boundaries of the cell
containing that node.
A constant-head boundary in the model
can represent parts of the aquifer where the
head will not change with time, such as re-
charge boundaries or areas beyond the in-
fluence of hydraulic stresses. In this model
constant-head boundaries are simulated by
adjusting the leakage term (the last term on
the right side of equation 11) at the appro-
priate nodes. This is accomplished by setting
the leakance coefficient (K./m) to a suffi-
ciently high value (such as 1.0 «-') to allow
the head in the aquifer at a node to be im-
plicitly computed as a value that is essen-
tially equal to the value of H,, which in this
case would be specified as the desired con-
stant-head altitude. The resulting rate of
leakage into or out of the designated con-
stant-head cell would equal the flux required
to maintain the head in the aquifer at the
specified constant-head altitude.
If a constant-flux or constant-head bound-
ary represents a fluid source, then the chemi-
cal concentration in the source fluid (C')
must also be specified. If the boundary rep-
resents a fluid sink, then the concentration
of the produced fluid will equal the concen-
m
-------
14
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
tration in the aquifer at the location of the
sink.
Because solute transport directly depends
upon hydraulic and concentration gradients,
the head and concentration in the aquifer at
the start of the simulation period must be
specified. The initial conditions can be deter-
mined from field data and (or) from previ-
ous simulations. It is important to note that
the simulation results may be sensitive to
variations or errors in the initial conditions.
In discussing computed heads, Trescott,
Finder, and Larson (1976, p. 30) state:
If initial conditions are specified so that transient
flow is occurring in the system at the start of the
simulation, it should be recognized that water levels
will change during the simulation, not only in re-
sponse to the new pumping stress, but also due to
the initial conditions. This may or may not be the
intent of the user.
Mass balance
Mass balance calculations are performed
after specified time increments to help check
the numerical accuracy and precision of the
solution. The principle of conservation of
mass requires that the cumulative sums of
mass inflows and outflows (or net flux) must
equal the accumulation of mass (or change
in mass stored). The difference between the
net flux and the mass accumulation is the
mass residual (Rn) and is one measure of
the numerical accuracy of the solution. Al-
though a small residual does not prove that
the numerical solution is accurate, a large
error in the mass balance is undesirable and
may indicate the presence of a significant
error in the numerical solution.
The model uses two methods to estimate
the error in the mass balance. Both are based
on the magnitude of the mass residual, Rm>
which is computed from
fl.=AM,-M, (60)
where
AM. is the change in mass stored in the
aquifer, M; and
Mf is the net mass flux, M.
The two mass terms, AM. and Mf, are
evaluated using the following equations:
AM.
(61a)
where
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
15
Special problems
There are a number of special problems
associated with the use of the method of
characteristics to solve the solute-transport
equation. Some of these problems are asso-
ciated with the movement and tracking of
particles, while other problems are related to
the computational transition between the
concentrations of particles within a cell and
the average concentration at that node. We
will next describe the more significant prob-
lems and the procedures used to minimize
errors that might result from them.
One possible problem is related to no-flow
boundaries. Neither water nor dissolved
chemicals can be allowed to cross a no-flow
boundary. However, under certain conditions
it might be possible for the interpolated
velocity at the location of a particle near a
no-flow boundary to be such that the particle
will be convected across the boundary during
one time increment. Figure 4 illustrates such
a possible situation, which arises from the
deviation between the curvilinear flow line
and the linearly projected particle path. If
a particle is convected across a no-flow
boundary, then it is relocated within the
aquifer by reflection across the boundary, as
also shown in figure 4. This correction thus
will tend to relocate the particle closer to the
true flow line.
Fluid sources and sinks also require special
treatment. Because they tend to represent,
singularities in the velocity field, the use of
a central difference formulation (eq 12) to
compute the velocity at a node may indicate
zero or very small velocities at the nodes.
Therefore, the velocity components at a
source or sink node cannot be used for in-
terpolation of the velocity at a point within
or adjacent to that cell. To help maintain
radial flow to or from a sink or source, re-
spectively, the velocities computed on the
boundaries of source or sink cells are as-
signed to that node. The appropriate bound-
ary velocities are determined on the basis of
the quadrant of interest. This can be illus-
trated by referring again to figure 2. If a
point is located in the southeast quadrant of
cell (f,j), the x velocity at node (t,/) would
o
A
EXPLANATION
Node of finite-difference grid
Previous location of particle p
Computed new location of particle p
Corrected new location of particle p
Flow line and direction of flow
Computed path of flow
Zero transmissivity (or no-flow boundary)
Figure 4.—Possible movement of particles near
an impermeable (no-flow) boundary.
be set equal to V.(H_H j>(and the y velocity to
^»(U+W)' Corresponding adjustments are
made for points in other quadrants, so that
the magnitude and direction of velocity at
the node are not fixed for a given time in-
crement, but depend on the relative location
of the point of interest within the cell. A
similar approximation is made when a point
of interest is located in a cell adjacent to a
source or sink. Thus, if the same point, p, in
figure 2 were located in an unstressed cell
but the adjacent cell (t+l,j) represented a
source or sink, then the y velocity at
node (t'+l,;) would be approximated by
V,(i+l i+V4) in order to estimate the y velocity
at point p. A corresponding approximation
for the x velocity at node (t,; + l) would be
made using ^t(i+^J+D^ a source or sink
were located at (t,/+1).
The maintenance of a reasonably uniform
and continuous spacing of points requires
special treatment in areas where sources and
sinks dominate the flow field. Points will con-
tinually move out of a cell that represents a
source, but few or none will move in to re-
-------
16
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
place them and thereby maintain a continuous
stream of points. Thus, whenever a point
that originated in a source cell moves out of
that source cell, a new point is introduced
into the source cell to replace it. Placement
of new points in a source cell is compatible
with and analogous to the generation of fluid
and solute mass at the source.
The procedure used to replace points in
source cells that are adjacent to no-flow
boundaries is illustrated in figure 5. Here a
steady, uniformly spaced stream of points is
maintained by generating a new point at the
same relative position in the source cell as
the new position in the adjacent cell of the
point that left the source cell. As an example,
point 7 was convected from cell (t-1,;) to
cell (i,j). So the replacement point (22) was
placed at a location within cell (t-1,;) that
is identical to the new location of point 7
within cell (t,/).
The procedure used to replace points in
source cells that lie within the aquifer and
not adjacent to a no-flow boundary is illus-
trated in figure 6. Here a steady, uniformly
spaced stream of particles is maintained by
generating a new point in the source cell at
the original location of the point that left
the source cell. When a relatively strong
source is imposed on a relatively weak re-
gional flow field, as illustrated in figure 6a,
then radial flow will be maintained in the
area of the source, and all initial and replace-
ment points will move symmetrically away
from node (t,/). For example, after point 7
moves from cell (t,;) to (t+1, ;-l), the re-
placement point (18) is positioned at time k
in cell ({,;') at the same location as the ini-
tial position of point 7. Although the re-
placement procedure illustrated earlier by
figure 5 would work just as well for the case
illustrated in figure 6a, it would not be satis-
factory for the situation presented in figure
6b, which illustrates the imposition of a rela-
tively weak source in a relatively strong
regional flow field. In this case the velocity
distribution within the source cell does not
possess radial symmetry, and the velocity
within the upgradient part of the source cell
is much lower than the velocity within the
downgradient part of the source cell. Re-
placement of points at original locations in
source cells, as illustrated in figure 6b, will
maintain a steady stream of points leaving
the source cell in proportion to the velocity
field. However, the use of the procedure illus-
trated in figure 5 for the case presented in
figure 6b would result in the accumulation of
lima *-1
tim *
-3 —-4
1J 14
*»
°2 °3
°7 °8
"19
EXPLANATION
• NodaoKinita-dlttaranc* 0/id
•p Initial location of panic to •
Of Naw location o* panicla a
Aa Location of raplacamant partlela •
n
Conatant-haad aewca
Zaro oanamitaivity (or no-flow bondary)
Hgur* 5.—Replacement of points in source cells adjacent to a no-flow boundary.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
17
tiim *-1
\ Vl /
\ 4
/ M./-1
12"
10°
•Pis
lima*
°2 V/-1 °3
/
°M
time *
i
£A
03
012
(b)
EXPLANATION
• Nodi of finite -diffaranca ftrid
•p Initial location of particla p
Op Naw location of paftiela p
Ap Location of laplacamant panlela p
Fluid aourca
Figure 6.—Replacement of points In source cells not adjacent to a
no-flow boundary for negligible regional flow (a) and for relatively
strong regional flow (b).
points in the low-velocity area of the source
cell (i,/), with few points being replaced into
the high-velocity area, where convective
transport is the greatest.
Although we normally expect points to be
convected out of source cells, figure 6b also
demonstrates the possibility that points may
sometimes enter a source cell. This can also
occur when two or more source cells of dif-
ferent strengths are adjacent to each other.
An erroneous multiplication of points might
then result if points that did not originate
in a particular source cell are replaced when
they in turn are convected out of that source
cell. Therefore, points leaving a source cell
are replaced only if they had originated in
that source cell.
Hydraulic sinks also require some special
treatment. Points will continually move into
a cell representing a strong sink, but few or
none will move out. To avoid the resultant
crowding and stagnation of tracer points,
any point moving into a sink cell is removed
from the flow field after the calculations for
that time increment have been completed.
The numerical removal of points which enter
-------
18
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
sink cells is analogous to the withdrawal of
fluid and solute mass through the hydraulic
sink. The combination of creating new points
at sources and destroying old points at sinks
will tend to maintain the total number of
points in the flow field at a nearly constant
value.
Both the flow model and the transport
model assume that sources and sinks act
over the entire cell area surrounding a
source or sink node. Thus, in effect, heads
and concentrations computed at source or
sink nodes represent average values over the
area of the cell. Part of the total concentra-
tion change computed at a source node repre-
sents mixing between the source water at
one concentration and the ground water at a
different concentration (eq 39). It can be
shown from the relationship between the
source concentration (C'..k ) and the aquifer
concentration (Cw.*_,), as indicated by
equation 44, that the following constraints
generally must be met in a source cell :
and
for
If it is assumed that the sources act over
the area of the source cell and that there is
complete vertical mixing, then these same
constraints should also apply to all points
within the cell. Because of the possible devia-
tion of the concentrations of individual
points within a source cell from the average
concentration, the change in concentration
computed at a source node (AC(i>.k) should
not be applied directly to each of the points
in the cell. Rather, at the end of each time
increment the concentration of each point in
a source cell is updated by setting it equal
to the final nodal concentration. Although
this may introduce a small amount of nu-
merical dispersion by eliminating possible
concentration variations within the area of a
source cell, it prevents the adjustment of the
concentration at any point in the source cell
to a value that would violate the constraints
indicated by equation 65.
In areas of divergent flow there may be a
problem because some cells can become void
of points where pathlines become spaced
widely apart. This would result in a calcula-
tion of zero change in concentration at a
node due to convective transport, although
the nodal concentration would still be ad-
justed for changes caused by hydrodynamic
dispersion (eq 28). Also, some numerical
dispersion is generated at nodes in and ad-
jacent to the cells into which the convective
transport of solute was underestimated be-
cause of the resulting error in the concentra-
tion gradient. This might not cause a serious
problem if only a few cells in a large grid
became void or if the voiding were transitory
(that is, if upgradient points were convected
into void cells during later or subsequent
time increments). Figure 6a illustrates
radial flow, which represents the most severe
case of divergent flow. Here it can be seen
that when four points per cell are used to
simulate convective transport, then in the
numerical procedure four of the eight sur-
rounding cells would erroneously not receive
any solute by convection from the adjacent
source. If eight points per cell were used
initially, then at a distance of two rows or
columns from the source only 8 of 16 cells
would be on pathlines originating in the
source cell. So, while increasing the initial
number of points per cell would help, it is
obvious that for purely radial flow, an im-
practically large initial number of points
per cell would be required to be certain that
at least one particle pathline passes from the
source through every cell in the grid.
The problem of cells becoming void of par-
ticles can be minimized by limiting the num-
ber of void cells to a small percentage of the
total number of cells that represent the
aquifer. If the limit is exceeded, the numeri-
cal solution to the solute-transport equation
is terminated at the end of that time incre-
ment and the "final" concentrations at that
time are saved. Next the problem is reini-
tialized at the time of termination by re-
generating the initial particle distribution
throughout the grid and assigning the "final"
concentrations at the time of termination as
new "initial" concentrations for nodes and
particles. The solution to the solute-transport
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
19
equation is then simply continued in time
from this new set of "initial" conditions until
the total simulation period has elapsed. This
procedure preserves the mass balance within
each cell but also introduces a small amount
of numerical dispersion by eliminating vari-
ations in concentration within individual
cells.
To help minimize the amount of numeri-
cal dispersion resulting from the regenera-
tion of points, the program also includes an
optimization routine that attempts to main-
tain an approximation of the previous con-
centration gradient within a cell. The opti-
mization routine aims to meet the following
constraints:
C* is the concentration of the nth
point in cell ({,/), M/L8;
Nf is the total number of points ini-
tially placed in a cell; and
Ci,m is the concentration at node (l,m),
which represents a cell adjacent
to (t,?) and on a line that starts
at ({,/) and extends through the
coordinates of the point (n) of
interest, as illustrated in figure
7, M/L».
Note that equation 66a simply indicates
that a mass balance must be preserved in a
cell regardless of the range in variation of
point concentrations within the cell. Equa-
tions 66b and c indicate that the concentra-
tion of any point must lie between Cu and
the concentration at the node adjacent to
particle n. The coordinates of the adjacent
node would take on values of l=i or Z=t±l
and m=; or m=;±l. For example, figure 7
shows that for point 2, the coordinates (l,m)
would equal ({,;'-!), while for point 3, (l,m)
would equal (t+l,/-l). The optimization
.'•/-1
•4 *u -6
•e "7 -a
EXPLANATION
• Node of finite -difference grid
•„ Location of particle n
Figure 7.—Relation between possible Ini-
tial locations of points and indices of ad-
jacent nodes.
routine is written so that if equations 66a-c
cannot be satisfied simultaneously for node
(i,j) within two iterations, then to avoid fur-
ther computational delay all C* are simply
set equal to Ctil.
Computer Program
The computer program serves as a means
of translating the numerical algorithm into
machine executable instructions. The pur-
pose of this chapter is to describe the overall
structure of the program and to present a
detailed description of its key elements,
thereby providing a link between the numeri-
cal methods and the computer code. We hope
that this link will make it easier for the
model user to understand and, if necessary,
modify the program. The FORTRAN IV
source program developed for this model is
listed in attachment I and includes almost
2,000 lines. For reference purposes columns
73-80 of each line contain a label that is
numbered sequentially within each sub-
routine. The definition of selected variables
used in the program is presented in attach-
ment II; this glossary therefore also serves
as a key for relating the program variables
-------
20
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
to their corresponding mathematical terms.
The computer program is compatible with
many scientific computers; it has been suc-
cessfully run on Honeywell, IBM, DEC, and
CDC computers.
General program features
The program is segmented into a main
routine and eight subroutines. The name and
primary purpose of each segment are listed
in Table 1. Each program segment will be
described in more detail in later sections of
this chapter.
Table 1.—List of subroutines for solute-transport model
Name
ParpoM
MAIN Control execution.
PARLOD ..Data input and initialization.
ITERAT ...Compute head distribution.
GENPT Generate or reposition particles.
VELO Compute hydraulic gradients, velocities,
dispersion equation coefficients, and
time increment for stable solution to
transport equation.
HOVE Move particles.
CNCON Compute change in chemical concentra-
tions and compute mass balance for
transport model.
OUTPT Print head distribution and compute
mass balance for flow model.
CHMOT —Print concentrations, chemical mass
balance, and observation well data.
The major steps in the calculation pro-
cedures are summarized in figure 8, which
presents a simplified flow chart of the over-
fill structure of the computer program. The
flow chart illustrates that the tracer particles
may have to be moved more than once to
complete a given time step. In other words,
the time step used to implicitly solve the flow
equation may have to be subdivided into a
number of smaller time increments for the
explicit solution of the solute-transport
equation. The maximum time increments al-
lowable for the explicit calculations are com-
puted automatically by the model. Thus, the
model user cannot specify an erroneously
large increment or an inefficiently small in-
crement for solving the solute-transport
equation. For transient flow problems, some
discretion is still required in the specifica-
tion of the initial time step and of the time-
step multiplier, as discussed by Trescott,
Finder, and Larson (1976, p. 38-40).
The general program presented here is
written to allow a grid having up to 20 rows
and 20 columns. Because the numerical pro-
cedure requires that the outer rows and col-
umns represent no-flow boundaries, the
aquifer itself is then limited to maximum
dimensions of 18 rows and 18 columns. If a
problem requires a larger grid, then the ap-
propriate arrays must be redimensioned ac-
cordingly. These arrays are contained
in COMMON statements PRMK, HEDA,
HEDB, CHMA, CHMC, and DIFUS, and in
DIMENSION statements on lines C170,
G200, H140, and 1160.
The program allows the specification of
one pumping well per node. The wells can
represent injection (recharge) or withdrawal
(discharge). If more than one well exists
within the area of a cell, then the flux spe-
cified for that node should represent the net
rate of injection or withdrawal of all wells
in that cell. The model assumes that stresses
are constant with time during each pumping
period (NPMP). But the total number of
wells, as well as their locations, flux rates,
and source concentrations, may be changed
for successive pumping periods. The pro-
gram also allows the specification of obser-
vation wells at as many as five nodes in the
grid. For nodes that are designated as ob-
servation wells, at the end of the simulation
period or after every 50 time increments the
model will print a summary table of the head
and concentration at the previous time in-
crements.
The program also includes a node identi-
fication array (NODEID), which allows cer-
tain nodes or zones to be identified by a
unique code number. This feature can save
much time in the preparation of input data
by easily equating each code number with a
desired boundary condition, flux, or source
concentration.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
21
START
\ READ GEOLOGIC.
\ HYOROLOGIC.&
\ CHEMICAL
\ INPUT
DATA
j
GENERATE UNIFORM
CtlCTDlDl ITl/"*M f\C
I/IS IKIbU I ION Or
TRACER PARTICLES
COMPUTE DISPERSION
EQUATION COEFFICIENTS
DETERMINE LENGTH
OF TIME INCREMENT
FOR EXPLICIT
CALCULATIONS
*
MOX/P PARTlPI FQ
j
ftFKlFRATF MF\I/ PARTlPl FC
OR REMOVE OLD
DADTIPI CC AT
rMn 1 lULfca A I
APPROPRIATE BOUNDARIES
COMPUTE AVERAGE
CONCENTRATION IN EACH
FINITE-DIFFERENCE CELL
|
COMPUTE EXPLICITLY
THE CHEMICAL
NODES
|
\SUMMARIZE AND /
DQlfUT DCCIIITC /
rnlN 1 KcbULTS /
i
1 Ji
( STOP J
COMPUTE HYDRAULIC
»b fltl A FMCKJTC CfiO
ONE TIME STEP
|
— COMPUTE
* GROUND-WATER
t/Cl rtfMTICG
VcLOUITIcS
|
ADJUST CONCENTRATION
OF EACH PARTICLE
COMPUTE
MASS BALANCE
t'
^
.
^
JL
S ,x EN° O^X NO
to
iO
Plgur* 8.—Simplified flow chart Illustrating the major steps In the calculation
procedure.
Program segments
MAIN
The primary purpose of the MAIN routine
is to control the overall execution sequence
of the program. Subroutines for input, ex-
ecution, and output are called from MAIN
and the elapsed time simulated is compared
with the desired total simulation period.
Also, lines A500-A580 serve to store (or
-------
22
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
record)" observation well data for transient
flow problems.
Subroutine PARLOD
All input data are read through subroutine
PARLOD. These data define the properties,
boundaries, initial conditions, and stresses
for the aquifer, as well as spatial grid and
time-step factors. The values of many vari-
ables are also initialized here. After the data
are read, some preliminary calculations are
made, such as (1) determining time incre-
ments for the flow model (lines B780-B890),
(2) computing the harmonic mean Jrans-
missivities in the x and y directions (B1670-
B1800), (3) adjusting transmissivity for
anisotropy (B1810-B1820), (4) computing
iteration parameters (B1840-B1910 and
B2880-B2980),and (5) checking for possible
inconsistencies among the input data
(B3140-B3290). A printout is also provided
of all input data so that the data may be re-
checked and each run identified.
Subroutine ITERAT
This subroutine solves a finite-difference
approximation of the flow equation (eq 11)
using an iterative ADI procedure. The ma-
trix generated by the finite-difference ap-
proximation is solved using the Thomas
algorithm, as described by von Rosenberg
(1964, p. 113). Row calculations are made in
lines C270-C610, and column calculations are
made in lines C630-C970. The calculations
are assumed to have converged on a solution
if the maximum difference at all nodes be-
tween heads computed along rows and heads
computed along columns is less than the spec-
ified tolerance. Convergence is checked on
lines C940-C950. Note that here (for ex-
ample, lines C380, C700, C930, and C1150)
and in other subroutines the thickness array
(THCK) is used to check whether a node is
in the aquifer.
It should also be noted here that the flow
model, as written, assumes that the trans-
missivity of the aquifer is independent of the
head (or saturated thickness) and remains
constant with time. If this assumption is not
appropriate to the particular aquifer system
being modeled, then the solution algorithm
presented in this subroutine should be modi-
fied accordingly. For example, flow models
published by Prickett and Lonnquist (1971,
p. 43-45) and Trescott, Pinder, and Larson
(1976) include such a modification.
All parameters involved in the calculation
of heads are defined as double precision vari-
ables and all calculations involving these
parameters are performed in double pre-
cision. The number of double precision vari-
ables and operations can be reduced sig-
nificantly if the program is to be executed on
a high-precision scientific computer, thereby
improving the efficiency of the model by re-
ducing computer storage requirements and
execution time.
The iterative ADI procedure used to solve
the finite-difference equations is not neces-
sarily the best possible solution technique for
all problems. For example, it may be difficult
to obtain a solution using the iterative ADI
procedure for cases of steady-state flow when
internal nodes in the grid have zero trans-
missivity and for cases in which the trans-
missivity is highly anisotropic. In such cases,
a strongly implicit procedure, such as the
one documented by Trescott, Pinder, and
Larson (1976), should be substituted for the
solution algorithm contained in subroutine
ITERAT.
Subroutine GENPT
The primary purpose of subroutine
GENPT is to generate a uniform initial
distribution of tracer particles throughout
the finite-difference grid. This is done either
at the start of a simulation period or at an
intermediate time when too many cells have
become void of particles. In the latter case,
the program attempts to preserve an ap-
proximation of the previous concentration
gradient within each cell (lines D1420-
D2040).
The placement of particles is accomplished
in lines D510-D1410. The program allows
the placement of either four, five, eight, or
nine particles per cell. Of course each option
will result in a slightly different geometry
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
23
Figure 9.—Parts of finite-difference grids showing
the Initial geometry of particle distribution for the
specification of four (A), five (8), eight (C), and
nine (0) particles per cell.
and density of points, as illustrated by figure
9. The most regular or uniform patterns are
produced when four or nine particles per cell
are specified. If a different number of par-
ticles per cell or a different placement geom-
etry are desired, this subroutine could be
modified accordingly.
As particles are moved or convected
through the grid during the calculation pro-
cedure, there is a need to remove particles at
fluid sinks and create particles at fluid
sources. A buffer array (called LIMBO) is
created on lines D430-D480 that contains
particles that can be added later to the grid
at sources and that also contains space to
store particles removed at sinks or discharge
boundaries.
Subroutine VELO
Subroutine VELO accomplishes three ob-
jectives. First, it computes the flow velocities
at nodes and on cell boundaries by solving
equations having the form of equations 12
and 13. The velocities are computed on lines
E420-E680. Second, the dispersion equation
coefficients are calculated. These coefficients
represent terms factored out of equations 37
and 88, as follows:
DISP(IX,IY,1) = (bD..),<+HJ)/(A*)* (67a)
DISP(IX,IY,2) = (bDn) ,tt^,/(*V)* (67b)
(67c)
DISP(IX,IY,8)-
DISP(IX,IY,4).
Note that each dispersion coefficient (/)„,
£>,,, !?„, D,z) is computed on cell boundaries
using the relationships expressed in equa-
tions 8-10. Therefore, the equation coeffi-
cients computed by equation 67 are stored
as forward values from the indicated node in
the DISP array. Third, this subroutine com-
putes (on lines E1050-E1240 and E1800-
E1930) the minimum number of particle
moves (NMOV) required to solve the trans-
port equation for the given time step so that
the maximum time increment for the trans-
port equation solution will not exceed any of
the criteria indicated by equations 43, 49,
58, and 59.
Subroutine MOVE
Although this subroutine has only one main
function, which is to move the tracer par-
ticles in accordance with equations 22 and
23, it is the longest and perhaps the most
complex segment of the program. The com-
plexities are mainly introduced by the treat-
ment of particles at the various types of
boundary conditions. To help illustrate the
calculation procedure followed within sub-
routine MOVE, a flow chart is presented in
figure 10. The numbers in the flow chart in-
dicate the corresponding lines in subroutine
MOVE where the indicated operation is
executed.
If a node represents a fluid source or sink,
then particles must be respectively created or
destroyed in these cells. If the value of
pumpage (REG) at a node dees not equal
zero, then the node is assumed to represent
either a fluid source (for REC<0) or a fluid
sink (for REC>0). Recharge or discharge
can also be represented by the RECH array.
But it is assumed that this type of flux is
sufficiently diffuse so that it does not induce
areas or points of strongly divergent or con-
vergent flow and therefore particles need not
be created or destroyed at these nodes. Note
that here and in other subroutines the pres-
ence of a constant-head boundary is tested
by checking the value of leakance (VPRM)
-------
COMPUTE ELAPSED TIME
AT START Of NEXT
PARTICLE MOVEMENT
F210
START NEXT MOVE
F2I
1
SELECT NEI
r PARTICLE L
F 3101
YES
DETERMINE «-»
COORDINATES OF NODE
WHERl PARTICLE IS
LOCATED FM0.4TO
DETERMINE IN WHICH
QUADRANT OF CELL THE
PARTICLE IS LOCATED
F MO-1740
IS
U ADMAN
LOCATED IN OK
ADJACENT TO A
SOURCE OR
SINK?
SET VELOCITY AT
SOURCE /SINK NODE
•VELOCITY ON
ADJACENT CELL
BOUNDARY
USE BILINEAR
INTERPOLATION TO
COMPUTE X AND V
VELOCITY OF PARTICLE
F 1770 -2030
COMPUTE X AND Y
COORDINATES OF CELL
AT NEW LOCATION OF
PARTICLE F20M-2110
COMPUTE DISTANCE
MOVED IN > AND Y
DIRECTIONS
F 2040 -2050
COMPUTE DISTANCE
PARTICLE TRAVELED
KYOND BOUNDARY
F2150-2320
RELOCATE PARTICLE INTO
AQUIFER BY REFLECTION
ACROSS BOUNDARY
F2210-23 BO
DID PARTICLE
ORIGINATE IN THAT
SOURCE CELL ?
If SOURCE CELL
TED ALONG EDGE
OF AQUIFER 7
F2720
7
SUM NUMBER OF
PARTICLES AND
CONCENTRATIONS
IN CELL AT
NEW LOCATION
F2420-2430
CREATE NEW PARTICLE
F2S80-2690
SOURCE OH SINK 7
2480-2620
PLACE NEW PARTICLE IN
OLD CELL AT SAME
RELATIVE POSITION
AS OLD PARTICLE IN
NEW CELL
F3420-3460
ISOLD
OCATION IN A
SOURCE CELL OR
A SINK CELL >
2480-2
HAS PARTICLE
CHANGED CELL
LOCATION?
CREATE NEW PARTICLE
F2580-2680
PLACE NEW PARTICLE
AT ORIGINAL LOCATION
OF OLD PARTICLE
F 2770-3380
S N
LOCATION
IN A PUMPING
OR CONSTANT-HEAD
SINK?
580-36
REMOVE PARTICLE
FROM GRID
F3640-1710
CALL SUBROUTINE
CNCON TO COMPUTE
NEW CONCENTRATIONS
F39SO
STORE OBSERVATION WELL
DATA FOR STEADY -FLOW
CASES
3
o
a
M
CO
W
w
09
O
CS
8
w
CO
co
H
o
z
CO
Figure 10.—Generalized flow chart of subroutine MOVE. Numbers indicate line numbers where the operation Is executed.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
25
at each node. If VPRM exceeds 0.09, it is as-
sumed that the node represents a constant-
head boundary condition and is treated as a
fluid source or sink accordingly. At a con-
stant-head node the difference in head be-
tween the aquifer and the source bed is used
to determine whether the node represents a
fluid source or sink (for example, lines
F2500-F2520).
Subroutine CNCON
This subroutine computes the change in
concentration at each node and at each par-
ticle for the given time increment. Equation
39, which denotes the change in concentra-
tion resulting from sources, divergence of
velocity, and changes in saturated thickness,
is solved on lines G350-G610. On the G520
the value of the storage coefficient is checked
to determine whether the aquifer is confined
or unconfined. It assumes that if S<0.005,
then the aquifer is confined and
If S^O.005, the model assumes that
•= 'dh/'dt. If this criterion is not appropriate
to a particular aquifer system, then line
G520 should be modified accordingly. The
change in concentration caused by hydro-
dynamic dispersion is computed on lines
G640-G770 as indicated by equations 37 and
38.
The nodal changes in concentration caused
by convective transport are computed on
lines G850-G940. The number of cells that
are void of particles at the new time level
are also counted in this set of statements on
lines G880-G910, and then compared with
the critical number of void cells (NZCRIT)
to determine if particles should be regen-
erated at initial positions before the next
time level is started (lines G960-G1020).
The new (time level k) concentrations at
nodes are computed on the basis of the previ-
ous concentration at time fc-1 and the
change during fc-1 to k. The adjustment at
nodes is accomplished on lines G1060-G1180,
while the concentration of particles is ad-
justed on lines G1210-G1S60.
A mass balance for the solute is next com-
puted (lines G1400-G1730) at the end of
each time increment. In computing the mass
of solute withdrawn or leaking out of the
aquifer at fluid sinks, the concentration at
the sink node is assumed to equal the nodal
concentration computed at time level fc-1.
Subroutine OUTPT
This subroutine prints the results of the
flow model calculations. When invoked, the
subroutine prints (1) the new hydraulic
head matrix (lines H190-H260), (2) a nu-
meric map of head values (H300-H890), and
(3) a drawdown map (H510-H710). This
subroutine also computes a mass balance for
the flow model and estimates its accuracy
(H420-H820). A mass balance is performed
both for cumulative volumes since the initial
time and for flow rates during the present
time step. The mass balance results are
printed on lines H840-H930.
Subroutine CHMOT
This subroutine prints (1) maps of con-
centration (lines 1250-1380), (2) change in
concentration from initial conditions (1440-
1580), and (3) the results of the cumulative
mass balance for the solute (1670-1860).
The accuracy of the chemical mass balance is
estimated on lines 1610-1660 using equations
62 and 64. The former is not computed if
there was no change in the total mass of
solute stored in the aquifer. The latter is not
computed if the initial concentrations were
zero everywhere. Lines 1890-11140 serve to
print the head and concentration data re-
corded at observation wells. These data are
recorded after each time step for a transient
flow problem and after each particle move-
ment for a steady-state flow problem. The
data are printed after every 50 time incre-
ments and at the end of the simulation
period.
Evaluation of Model
Comparison with analytical solutions
The accuracy of the numerical solution to
the solute-transport equation can be evalu-
-------
26
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
ated in part by analyzing relatively simple
problems for which analytical solutions are
available and then comparing the numerical
calculations with the analytical solution.
Figure 11 presents such a comparison for a
problem of one-dimensional steady-state flow
through a homogeneous isotropic porous
medium. The analytical solution is obtained
with the following equation presented by
Bear (1972, p. 627) :
C(x,t)-C0
C.-C,
(68)
where
erfc
is the complimentary error func-
tion, and
q-.iV is the specific discharge, LT~l.
Bear (1972, p. 627) shows that equation 68
is subject to the following initial conditions:
-oo
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
27
equation 68. In the analysis of one-dimen-
sional test problems, it was assumed that
porosity equals 0.35, velocity equals 3.0x10-'
ft/a (9.1 x 10-" m/s), and time equals 10.0
days.
As shown in figure 11, comparisons be-
tween the analytical and numerical solutions
were made for two different values of dis-
persivity. For the higher dispersion there
was essentially an exact agreement between
the two curves. In the case of low dispersion,
there is a very small difference at some nodes
between the concentrations computed analyt-
ically and those computed numerically. This
difference is caused primarily by the error in
computing the concentration at a node as the
arithmetic average of the concentrations of
all particles located in that cell. This is not
considered to be a serious problem since this
error is not cumulative. Also note in the case
of low dispersion that the grid spacing (10
ft or 3.05 m) was coarse relative to the
width of the breakthrough curve between
concentrations of 0.05 and 0.95. Neverthe-
less, the numerical model still accurately
computed the shape and position of the front.
In computing the numerical solutions
shown in figure 11 the program was executed
using nine particles per cell and with
CELDIS = 0.50 (y in equations 54-55). The
10-day simulation required 52 time incre-
ments and used about 40 seconds of cpu on
a Honeywell 60/68 computer.
An analytical solution is also available for
the problem of plane radial flow in which a
well continuously injects a tracer at constant
rate qK and constant concentration C0. Bear
(1972, p. 638) indicates that the following
equation is appropriate for this problem (al-
though there are some limitations discussed
by Bear):
C 1 ^ (r'/2-Gt )
=-prfr{— } (69)
Co 2 lV4/3«1P )
where
G
r
••Vr;
is the radial distance from
the center of the well,
L; and
r= (ZGt) * is the average radius of the
body of injected water,
L.
Again, the general computer program had
to be somewhat modified to permit a suit-
able comparison to be made between the
analytical solution and the numerical model.
One change involved the direct calculation of
velocity at any point based on its distance
from the well using the following equation:
(70)
The other significant change was made in
subroutine GENPT to allow the initial place-
ment of 16 particles per cell, rather than the
present maximum of 9. In the analysis of
test problems for radial flow, it was assumed
that porosity equals 0.35, the injection rate
(gw) equals 1.0 ftVs (0.028 mVs), saturated
thickness equals 10.0 ft (3.05 m), and longi-
tudinal dispersivity equals 10.0 ft (3.05 m).
The application of the method of character-
istics, which was written for two-dimen-
sional Cartesian coordinates, to a problem
involving radially symmetric divergent flow
represents a severe test of the model. Never-
theless, it can be seen in figure 12 that there
is good agreement between the analytical and
numerical solutions after both relatively
short and long times. However, the presence
of some numerical dispersion is evident, par-
ticularly for the longer time. The numerical
dispersion is introduced in part during the
regeneration of particles after the number of
cells void of particles has exceeded the criti-
cal number. The geometry of initial particle
placement minimized this problem in cells
that lay in the same row or column of the
grid as the injection well. The circles in fig-
ure 12, which indicate concentration values
computed at these nodes, agree closely with
the analytical solution. The greatest errors
occur at nodes on radii from the injection
well that are neither parallel to nor 45° from
the main axes of the grid. These results in-
dicate that this Cartesian coordinate model
is not best suited for application to purely
radial flow problems. However, if radially
divergent flow is limited to areas of several
-------
28
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
1.0
0.9
0.8
0.7
P 0.4
0.2
0.1
0.0
EXPLANATION
— Analytical solution
Numerical solution:
• Nodra on radii pinll*) too/Id
• Nods* on radii 45°to grid
A NodM on intennodlata radii
100
200
300 400 600
RADIAL DISTANCE. IN FEET
(00
700
800
Figure 12.—Comparison between analytical and numerical solutions for dispersion in plane radial steady-state flow.
rows and columns within a more uniform
regional flow field, the model will accurately
compute concentration distributions. To ap-
ply the method of characteristics to a prob-
lem of plane radial flow, it would be best to
rewrite the program in a system of radial
coordinates, which should improve the ac-
curacy for those problems to the same order
shown in figure 11 for the analysis of one-
dimensional flow.
Mass balance tests
The accuracy and precision of the numeri-
cal solution can also be partly evaluated by
computing the magnitude of the error in the
mass balance. The mass balance error will
depend on the nature of the problem and will
vary from one time step to the next. During
the development of the program, the model
was applied to a variety of hypothetical
solute-transport problems to assure its flexi-
bility, transferability, and accuracy under a
wide range of conditions. To illustrate the
range in mass balance errors that might be
expected and some of the factors that affect
it, several of these problems are presented
here.
Test problem 1—spreading of a tracer slug
The first test described here was designed
to evaluate the accuracy of simulating the
processes of convective transport and disper-
sion independent of the effects of chemical
sources. Thus, a slug of tracer was initially
placed in four cells of a grid whose boundary
conditions generated a steady-state flow field
that was moderately divergent in some places
and moderately convergent in other places,
as illustrated in figure 13. The aquifer was
assumed to be homogeneous and isotropic.
Because flow was assumed to be in steady
state, the storage coefficient was set equal to
0.0. The parameters used to define problem
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
29
EXPLANATION
HP No-flow boundary
||:i:Pr| Constant- head boundary
[ + I Initial concentration (Co) equals
I* ±1 100; elaewhera Co=0
• 90— Computed potentiometric altitude.
Contour interval 2.0 foet
(0.61 meter)
A/= 900 feet (274 meters)
A/r 900 feet (274 meterg)
Figure 13.—Grid, boundary conditions, and flow field for test problem 1.
1 are listed in table 2. The slug of known
mass was then allowed to spread down-
gradient for a period of 2.0 years.
Table 2.—Model parameters for test problem 1
Aquifer propertie*
Numerical parameter*
£=0.005 ft/a
(1.6x10'm/s)
ft =20.0 ft
(6.1 m)
5=0.0
i=0.80
.,/.*=O.SO
Ax =900 ft
(274 m)
Ay =900 ft
(274 m)
CELDIS=0.49
NPTPND=9
The model first computed a steady-state
head distribution, shown in figure 13, and
velocity field. The model required 12 time
increments (or particle movements) to simu-
late a 2.0-year period. The model was run to
simulate conditions of no dispersion (a/,=0.0
ft) as well as moderate dispersion (at=100
ft or 30.6 m). The mass balance error com-
puted using equation 64 is shown in figure
14 for both conditions. In these tests the
error averages 1.9 percent and is always
within a range of ±8 percent. Much of the
error is related to the calculation of nodal
concentrations based on the arithmetic mean
of particle concentrations in each cell. When
a particle moves across a cell boundary, its
area of influence shifts entirely from the first
node to the second. Thus, depending on the
local density of points and local concentra-
tion gradients, the use of an arithmetic mean
to compute nodal concentrations may give
too much weight to some particles and too
little weight to others. The use of a weighted
mean, in which the weighting factor is a
function of the distance between a node and
a particle, reduced the error to some degree.
But the improvement in precision was small
compared with the increase in computational
requirements, so this algorithm was not in-
cluded in the general program. Because the
error caused by using an arithmetic mean is
not cumulative, it is not considered a serious
-------
30
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
1 1 1
K A :
' N ' \ '
1.0
TIME. IN YEARS
Figure 14.—Mass balance errors for test problem 1.
1.5
N -I
2.0
EXPLANATION
No-flow boundary
Constant-head boundary
G Injection well
© Withdrawal well
—90- Computed potentiometric altitude.
Contour interval 2.0 feet
(0.61 meter)
A X= 900 feet (274 meter*)
£/= 900 feet (274 meters)
Figure 15.—Grid, boundary conditions, and flow field for test problem 2.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
31
problem. Furthermore, figure 14 shows that
the error decreases for a higher dispersivity
because dispersion smooths out sharp
fronts and minimizes strong concentration
gradients.
Test problem 2—effects of wells
The second problem was designed to eval-
uate the application of the model to prob-
lems in which the flow field is strongly in-
fluenced by wells. The grid and boundary
conditions used to define this problem are
illustrated in figure 15. The problem con-
sists of one injection well and one with-
drawal well, whose effects are superimposed
on a regional flow field controlled by two
constant-head boundaries. The parameters
for problem 2 are defined in table 3. The
aquifer was also assumed to be homogeneous
and isotropic. The model simulated a period
of 2.4 years and assumed steady-state flow.
The model required 18 time increments
(or particle movements) to simulate a 2.4-
year period of solute transport. Problem 2
was also evaluated for conditions of no dis-
persion (o£, = 0.0 ft) as well as moderate dis-
persion (aL=100 ft or 30.5 m). The mass bal-
ance error was computed using equation 62
and is shown in figure 16 for both conditions.
The average of the 36 values shown in figure
16 is -0.06 percent; the error always falls
within the range of. ± 8 percent. It can be
10.0
Table 3.—Model parameters for test problems 2 and 3
Aquifer properties
•nd stresses
Numerical parameters
K =0.005 ft/s
(1.5x10' m/8)
6=20.0 ft
(6.1 m)
S=0.0
e=0.30
or/oi=0.30
C'=100.0
c.=o.o
g.=1.0 ftVs
(0.028 mVs)
Ax =900 ft
(274 m)
Ay =900 ft
(274 m)
CELDIS=0.50
NPTPND=9
seen that in this case the errors are essen-
tially coincident for almost 1 year, after
which the error appears to be dependent on
the magnitude of dispersion. However, the
model output showed that when ot = 100 ft
(30.5 m), the leading edge of the break-
through curve (or chemical front) reaches
the constant-head sink just prior to 1.0 year.
When at = 0.0 ft, the leading edge of the
breakthrough curve still had not entered the
constant-head sink after 2.4 years. Because
the two curves in figure 16 are essentially
coincident prior to 1.0 year, it thus appears
that the divergence of the two curves is not
caused directly by the difference in disper-
sivity. Rather, it is related to the difference
in arrival times at the hydraulic sinks and is
a direct effect of the manner in which con-
0.6
1.0 1.6
TIME, IN YEARS
2.0
2.6
Figure 16.—Mass balance errors for test problem 2.
-------
32
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
centrations are computed at sink nodes and
(or) the method of estimating the mass of
solute removed from the aquifer at sink
nodes during each time increment.
Test problem 3—effects of user options
In addition to the input options that con-
trol the form or frequency of the output,
there are two execution parameters that
must be specified by the user and influence
the accuracy, precision, and efficiency (or
computational cost) of the solution to a par-
ticular problem. These execution parameters
are the initial number of particles per node
(NPTPND) and the maximum fraction of
the grid dimensions that particles are al-
lowed to move (y in equations 54-55 or
CELDIS in the program). The third test
problem was designed to allow an evaluation
of both of these parameters. As illustrated
in figure 17, this problem consists of one
withdrawal well located in a regional flow
field that is controlled by two constant-head
boundaries. The contamination sources are
three central nodes along the upgradient
constant-head boundary. The model param-
eters for test problem 3 are the same as for
test problem 2, as listed in table 3. However,
for test problem 3 solutions were obtained
using a range in values for CELDIS and
NPTPND.
The solution to this problem was found to
be sensitive to the density of tracer particles
used in the simulation. Figure 18 shows how
the error in the mass balance varied with
time for cases of NPTPND equal to 4, 5, 8,
and 9. Table 4 lists the execution time and
the mean and standard deviation of the mass
balance error for each case. These data clear-
ly indicate that the accuracy and precision
EXPLANATION
No •flow boundary
{Illll Constant -head boundary
a Constant*head boundary
and contaminant source
$ Withdrawal well
—90.0— Computed potentlometrlc altitude.
Contour interval 2.5 feet
(0.76 meter)
& *= 900 feet (274 meters)
A/= 900 feet (274 meters)
Figure 17.—Grid, boundary conditions, and flow field for test problem 3.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
33
20.0
EXPLANATION
• • NPTPND* 4
O— —O NPTPNDs 5
6 A NPTPND'8
O O NPTPND* 9
-10.1
1.0 1.6
TIME. IN YEARS
2.0
2.6
Figure 1B.—Effect of NPTPND on mass balance error for test problem 3; CELDIS=0.50 in all cases.
Table 4.—Effect of NPTPND on accuracy, precision,
and efficiency of solution to test problem 3
Han balance error
(percent)
NPTPND
4
5
8
9
epu-ceeonda '
12.8
14.0
17.9
19.2
Memn
1.49
.90
.48
.26
Standard
deviation
6.83
2.29
1.53
.69
'The program wa> executed on a Honeywell 60/68 computer;
CELDIS = 0.60.
of the solution are directly proportional to
particle density, while the efficiency of the
solution is inversely related to NPTPND. In
other words, a better solution will cost more.
It is important to note that the oscillations
or scatter shown in figure 18 decrease with
time and that there is essentially no differ-
ence among the solutions and among the
mass balance errors for times greater than
about 1.5 years.
Next the effect of CELDIS (or y) was
evaluated for test problem 3 by setting
NPTPND=9 and running the model with
several possible values of CELDIS. Figure
19 shows how the error in the mass balance
varied with time for cases of CELDIS equal
to 0.25, 0.50, 0.75, and 1.00. Table 5 lists the
Table 5.—Effect of CELDIS on accuracy, precision.
and efficiency of solution to test problem 3
Mass balance error
(percent)
CELDIS
0.26
.60
,75
1.00 ... .
epu-eeeonda '
84.6
19.2
14.4
12.1
Mean
1.50
.26
.66
.25
Standard
deviation
2.99
.69
.69
1.48
1 The program wai executed on a Honeywell (0/68 computer;
NPTPND=».
execution time and the mean and standard
deviation of the mass balance error for each
case. These data indicate that the relation-
ship between CELDIS and the mass balance
error is not as simple and straightforward
as for NPTPND. It is apparent that the re-
sults for 0.50, 0.75, and 1.00 are similar, and
of these, the results for CELDIS=0.50 ap-
-------
34
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
16.0
CELDIStO.25
O -o CELDIS xO.50
ft A CELDIS:0.75
D— -
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
85
Coordinate system and boundary conditions
After the finite-difference grid is designed,
the first program modification that should be
made is to modify the array dimensions for
the specific grid used. This will permit the
most efficient use of computer storage. The
array sizes should be set equal to NX, NY,
and NPMAX, which are specified on Input
Card 2. The maximum number of particles,
NPMAX, may be computed from the follow-
ing equation:
NPMAX==(NX-2) (NY-2) (NPTPND)
+ (N.) (NPTPND) + 250 (71)
where
N, is the number of nodes that repre-
sent fluid sources, either at wells
or at constant-head cells.
The values of NX and NY should be substi-
tuted for the 20-by-20 arrays contained
in COMMON statements PRMK, HEDA,
HEDB, CHMA, CHMC, and DIFUS, and in
DIMENSION statements on lines C170,
G200, H140, and 1160. The value of NPMAX
should replace 3200 in the PART array in
all the CHMA COMMON statements.
Although this program is designed for ap-
plication to two-dimensional areal flow prob-
lems, it can be applied directly to two-di-
mensional cross sections. In this case the z-
coordinate would replace the ^-coordinate.
Then the user would have to assume and
specify unit width (THCK array) for Ay
and substitute hydraulic conductivity for
transmissivity in data set 3 of attachment'
III. If the problem involves transient flow,
then specific storage (S,) should be substi-
tuted for the storage coefficient. Also, if re-
charge or discharge is to be specified through
the RECH array (data set 5), values should
be divided by the thickness of the layer (Az)
to reduce the dimensionality of the stress
rate to (T~l) rather than (LT-1) as indi-
cated in the documentation. In applying the
cross-sectional model to a field problem it is
important that conditions meet the inherent
assumption that there exist no significant
components of flow into or out of the plane1
of the section. Because this assumption
would probably be impossible to meet in the
vicinity of a pumping well, the use of the
REC array (data set 2) should usually be
limited to representing special or known-flux
boundary conditions.
The program can also be applied directly
and simply to one-dimensional problems. In
this case one of the dimensions (NX or NY)
should be reduced to a value of 3, of which
the outer two are used to represent the no-
flow boundaries around the one-dimensional
row or column.
The most complex type of change would
involve rewriting the program for applica-
tion to other than a two-dimensional rectan-
gular grid. One possibility includes problems
of flow to or from wells in which radial
symmetry can be assumed. This would allow
variables to be expressed in terms of r-z co-
ordinates. Another possibility is to simulate
three-dimensional flow in x-y-z coordinates.
A three-dimensional finite-difference flow
model is available (Trescott, 1975) and would
be compatible with the method-of-character-
istics solution to the solute-transport equa-
tion.
It is sometimes convenient to separately
associate certain parts of the grid or certain
boundary conditions with corresponding field
conditions or hydrologic units. The analysis
of flow patterns and water-quality changes
may then be aided by performing separate
mass balances (or budgets) for each char-
acteristic type of node. The nodal types
or zones can be conveniently identified
through the NODEID array. Then the mass
balance routines in subroutines CNCON and
(or) OUTPT would have to be modified to
tally fluxes separately for each NODEID; for
an example, see Konikow (1977). Similarly,
if a coupled stream-aquifer system is being
considered, a separate subroutine may be
added to route streamflow downstream and
progressively account for ground-water
gains and losses and for tributary inflow or
diversions. An example of such a modifica-
tion is discussed by Konikow and Bredehoeft
(1974).
For certain types of problems it may be
desirable to be able to specify a constant-
concentration boundary condition. The pro-
-------
36
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
gram could be modified to allow this by using
a predetermined value or range in values of
NODEID to identify this type of boundary.
Then a statement could be added between
lines G1090 and G1100 to reset the concen-
tration at the node equal to the constant con-
centration where this condition is specified.
The value of the constant concentration can
be stored in the CNRECH array. Note that
the mass balance calculation as presently
written will not account for the mass of
solute added or removed at a constant-con-
centration boundary.
Basic equations
The basic equations that are solved by this
model were derived under a number of limit-
ing assumptions. Some of these assumptions
can be overcome through modifications of the
basic equations and corresponding changes
in the program.
The program assumes that molecular dif-
fusion is negligible. But if it is necessary to
consider the process of molecular diffusion in
a particular problem, the coefficient of hy-
drodynamic dispersion (Dtl) can be redefined
as the sum of the coefficient of mechanical
dispersion, which is defined by the right side
of equation 5, and a coefficient of molecular
diffusion. The consequent program modifica-
tion would have to be made only in sub-
routine VELO (lines E1280-E1680).
The solute-transport equation can also be
modified to include the effects of first-order
chemical reactions, as was done by Robert-
son (1974). The reaction term could be in-
cluded in the right side of equation 39. The
corresponding program modification would
be required in subroutine CNCON.
In certain problems the range in concen-
trations may be so great that the dependence
of fluid properties, such as density and vis-
cosity, on the concentration may have to be
considered because of the dependence of fluid
flow on variations in fluid properties. In this
case the flow equation (eq 1) would have to
be rewritten in terms of fluid pressure,
rather than hydraulic head, such as equation
15 of Bredehoeft and Finder (1973, p. 197).
Then the program can be modified to iterate
between the solutions to the flow and solute-
transport equations if the change in fluid
properties at any node exceeds some criterion
during one time increment.
The flow equation can also be modified for
application to unconfined aquifers in which
the saturated thickness is a direct function
of water-table elevation. This would require
the inclusion of steps in subroutine ITERAT
to correct the transmissivity for changes in
saturated thickness. Such a feature is in-
cluded in the two-dimensional flow model
documented by Trescott, Finder, and Larson
(1976).
Input and output
The input and output formats have been
designed for flexibility of use and general
compatibility with the analysis of a variety
of types of flow problems. If any of the for-
mats are not suitable for use with a par-
ticular problem, they should be modified ac-
cordingly. All input formats are described
in attachment III and contained in sub-
routine PARLOD in the program.
It has been assumed that several aquifer
parameters are constant and uniform in
space, such as storage coefficient, effective
porosity, and dispersivity. If any of these are
known to vary in space, they should be re-
defined as two-dimensional arrays. Then
statements to allow these arrays to be read
into the program should be added to sub-
routine PARLOD. Similarly, values of leak-
ance and source concentrations (CNRECH)
are only read in data set 7, where values can
be associated only with a limited number of
unique node identification codes. If the varia-
tions of these parameters are known on a
more detailed scale, then they too can be read
as additional data sets by adding appropriate
statements to subroutine PARLOD. For ex-
ample, a typical sequence of statements for
reading one data set is represented by lines
B2650-B2750, where the initial water-table
elevations (data set 8) are read. This se-
quence of statements can then be replicated
for reading in a different data set and in-
serted into subroutine PARLOD.
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
37
A labeled listing of the input data deck for
test problem 3 is provided in attachment IV.
This example illustrates the use of the data
input formats specified in attachment III and
shows that only a few data cards are re-
quired by the model to simulate a relatively
simple problem. This example will also allow
the user to verify that his program deck and
computer yield essentially the same results
as obtained by the documented program.
Thus, selected parts of the output for test
problem 3 are included in attachment V. Not
all of the printed output from test problem
3 has been duplicated in attachment III. In-
stead, it contains only a sufficient selection to
illustrate the type and form of output pro-
vided by the model, as well as to allow the
user to compare his calculated values of cri-
tical parameters, such as head, velocity, and
concentration, with the values computed by
the documented model.
Conclusions
The model presented in this report can
simulate the two-dimensional transport and
dispersion of a nonreactive solute in either
steady-state or transient ground-water flow.
The program is general and flexible in that
it can be readily and directly applied to a
wide range of types of problems, as defined
by aquifer properties, boundary conditions,
and stresses. However, some program modi-
fications may be required for application to
specialized problems or conditions not in-
cluded in the general model.
The accuracy of the numerical results can
be evaluated by comparison with analytical
solutions only for relatively simple and ideal-
ized problems; in these cases there was good
agreement between the numerical and analy-
tical results. Mass balance tests also help to
evaluate the accuracy and precision of the
model results. The error in the mass balance
is generally less than 10 percent. The range
in mass balance errors is commonly the
greatest during the first few time incre-
ments, but tends to decrease and stabilize
with time. For some problems the accuracy
and precision of the numerical results may
be sensitive to the initial number of particles
placed in each cell and to the size of the time
increments, as determined by the stability
criteria for the solute-transport equation.
The results of several numerical experiments
suggest that the accuracy and precision of
the results are essentially independent of the
magnitude of the dispersion coefficient, and
comparable accuracies are attained for high,
low, or zero dispersivities.
References Cited
Aris, Rutherford, 1962, Vectors, tensors, and the
basic equations of fluid mechanics: Englewood
Cliffs, N. J., Prentice-Hall, 286 p.
Bear, Jacob, 1972, Dynamics of fluids in porous
media: New York, Am. Elsevier Publishing Co.,
764 p.
Bredehoeft, J. D., and Finder, G. F., 1973, Mass
transport in flowing ground water: Water Re-
sources Research, v. 9, no. 1, p. 194-210.
Carder, A. 0., Peaceman, D. W., and Pozzi, A. L.,
Jr., 1964, Numerical calculation of multidimen-
sional miscible displacement by the method of
characteristics: Soc. Petroleum Engineers Jour.,
v. 4, no. 1, p. 26-36.
Konikow, L. P., 1977, Modeling chloride movement
in the alluvial aquifer at the Rocky Mountain
Arsenal, Colorado: U.S. Geol. Survey Water-
Supply Paper 2044, 43 p.
Konikow, L. F., and Bredehoeft, J. D., 1974, Model-
ing flow and chemical quality changes in an
irrigated stream-aquifer system: Water Re-
sources Research, v. 10, no. 3, p. 646-662.
Konikow, L. F., and Grove, D. B., 1977, Derivation
of equations describing solute transport in
ground water: U.S. Geol. Survey Water-Re-
sources Investigatons 77-19, 30 p.
Lohman, S. W., 1972, Ground-water hydraulics: U.S.
Geol. Survey Prof. Paper 708, 70 p.
Finder, G. F., and Bredehoeft, J. D., 1968, Applica-
tion of the digital computer for aquifer evalua-
tion: Water Resources Research, v. 4, no. 6,
p. 1069-1093.
Finder, G. F., and Cooper, H. H., Jr., 1970, A nu-
merical technique for calculating the transient
position of the saltwater front: Water Re-
sources Research, v. 6, no. 8, p. 876-882.
Prickett. T. A., and Lonnquist, C. G., 1971, Selected
digital computer techniques for groundwater re-
source evaluation: Illinois Water Survey Bull.
65, 62 p.
-------
38
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Reddell, D. L., and Sunada, D. K., 1970, Numerical
simulation of dispersion in groundwater aqui-
fers: Colorado State Univ. Hydrology Paper
41, 79 p.
Robertson, J. B., 1974, Digital modeling of radio-
active and chemical waste transport in the
Snake River Plain aquifer at the National Re-
actor Testing Station, Idaho: U.S. Geol. Survey
Open-File Rept. IDO-22054, 41 p.
Robson, S. G., 1974, Feasibility of digital water-
quality modeling illustrated by application at
Barstow, California: U.S. Geol. Survey Water-
Resources Investigations 46-73, 66 p.
Scheidegger, A. E., 1961, General theory of disper-
sion in porous media: Jour. Geophys. Research,
v. 66, no. 10, p. 3273-3278.
Trescott, P. C., 1975, Documentation of finite-dif-
ference model for simulation of three-dimen-
sional ground-water flow: U.S. Geol. Survey
Open-File Rept. 75-438, 32 p.
Trescott, P. C., Finder, G. F., and Larson, S. P.,
1976, Finite-difference model for aquifer simu-
lation in two dimensions with results of numeri-
cal experiments: U.S. Geol. Survey Techniques
of Water-Resources Investigations, Book 7, Chap.
Cl, 116 p.
von Rosenberg, D. U., 1969, Methods for the nu-
merical solution of partial differential equa-
tions: New York, Am. Elsevier Publishing Co.,
128 p.
-------
COMPUTER PROGRAM AND RELATED DATA
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
41
C
C
C
C
C
C
C
C
C
C
C
C
C
C
Attachment I
FORTRAN IV Program Listing
***»******•••*•**<
i***********************
SOLUTE TRANSPORT AND DISPERSION IN A POROUS MEDIUM
NUMERICAL SOLUTION METHOD OF CHARACTERISTICS
PROGRAMMED BY J. D. BREDEHOEFT AND L. F. KONIKOW
110
•A**************************************************************
DOUBLE PRECISION DMIN1/DEXP/DLOG/DABS
REAL •8TMRX,VPRM/HI,HR,HC/HK,HT/REC»RECH,TIM,AOPT,TITLE
REAL *8XDEL/YDEL/S/AREA,SUMT,RHO*PARAM,TEST/TOL»PINT,HMIN,PYR
REAL *8TINT«ALPHA1*ANITP
COMMON /PRMI/ NT1H/NPMP/NPNT/N1TP/N/NX/NY/NP/NREC/1NT/NNX/NNY/NUMO
1BS»NMOV,IMOV»NPMAX/ITMAX,NZCRIT/IPRNT/NPTPND,NPNTMV*NPNTVL»NPNTD»N
2PNCHV/NPDELC
COMMON /PRMK/ NODEID(20/20)/NPCELL(20/20)/L1NBO(500)/IXOBS(5)/IYOB
1S(5)
COMMON /HEDA/ THCK<20/20>/PERM(20,20)/TMWL<5/50)/TMOBS(50)/ANFCTR
COMMON /HEOB/ TMRXC20/20/2)/VPRM<20/20>/HK20/20>,HR<20/20>/HC<20/
120>/HK(20/20)/WT(20/20>,REC(20/20)/RECH(20/20)/TIM(100)/AOPT(20)/T
2iTLEdO)»XDEL*YDEL/S/AREA*SUMT,RHO*PARAM,TEST»TOL/PINT*HMIN*PYR
COMMON /CHMA/ PART(3/3200),CONC(20/20)/TMCN<5*50)/VX(20/20)/VY(20*
120)/CONINT(20/20)/CNRECH(20/20)/POROS/SUMTCH/BETA/T1HV/STORM/STORM
2I/CMSIN/CMSOUT,fLMlN/FLMOT,SUMIO/CELDIS/DLTRAT/CSTORM
A**************************************************************
LOAD DATA —
INT«0
CALL PARLOO
CALL 6ENPT
START COMPUTATIONS
COMPUTE ONE PUMPING PERIOD- —
150 INT«1/NPMP
(INT.GT.1) CALL PARLOD
COMPUTE ONE TIME STEP
130 N«1/NTIM
IPRNT«0
LOAD NEW DELTA T
TINT'SUMT-PYR*(INT-1>
TDEL«DMINKTIM(N),PYR-TINT)
SUMT»SUMT+TDEL
TIM(N)«TDEL
REMN«MOD(N/NPNT)
A******************••**••*»•••A**************************** ***
-------
42 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
C OUTPUT ROUTINES
120 IF (REMN.Efl.O.O.OR.N.EO.NTIM.OR.MOD(N,50).EQ.O) CALL CHMOT
IF (SUMT.GE.(PYR*INT)> 60 TO 140
130 CONTINUE
C SUMMARY OUTPUT
UO CONTINUE
IPRNT«1
CALL CHMOT
150 CONTINUE
STOP
r **»**»*»•**••••***•*»•
•it************************************************************
END
SUBROUTINE PARLOO
DOUBLE PRECISION OMINl,DEXP,DLOG,DA8S
590
600
610
620
630
640
6SO
660
670
680
690
700
710
720
730-
10
20
REAL *8TMRX,VPRM,HI,HR,HC,HK,WT,REC,RECH,TIM,AOPT,TITLE B 30
REAL *8XOEL,YDEL,S,AREA,SUMT,RHO,PARAH,TEST,TOL,PINT,HMIN,PYR B 40
REAL *8FCTR,TIHX,TINIT,PIES,YNS,XNS,RAT,HMX,HMY 8 SO
REAL *8TINT,ALPHA1,ANITP B 60
COMMON /PRMI/ NTIM,NPMP,NPNT,NITP,N,NX,NY,NP,NREC,INT,NNX,NNY,NUMO B 70
1BS,NMOV,IMOV,NPMAX,1TMAX,NKRIT,IPRNT,NPTPND»NPNTMV,NPNTVL,NPNTD,N B 80
2PNCHV/NPOELC B 90
COMMON /PRMK/ NODE ID(20,20),NPCEIL(20,20),L1MBO(500),IXOBS(5),IYOB B 100
1S<5) B 110
COMMON /HEOA/ THCK(20,20),PERM(20,20),TMWL(5,50),TMOBS(50),ANFCTR B 120
COMMON /HEOB/ TMRX(20,20,2>,VPRM(20,20),H1(20,20),HR(20,20),HC(20, B 130
120),HK(20,20),WT(20,20),REC(20,20),RECH(20,20),TIM(100),AOPT(20),T B UO
2ITLE(10),XDEL,YDEL,S,AREA,SUMT,RHO,PARAM,TEST,TOL,PINT,HMIN,PVR B 150
COMMON /CHMA/ PART(3,3200),CONC(20,20),TMCN(5,50),VX(20,20),VY(20, B 160
120>*CONINT(20,20)»CNRECH(20,20)»POROS,SUMTCH,BETA,TIMV,STORM*STORM B 170
2l*CMSIN,CMSOUT,FLMIN,FLMOT»SUMIO,CELDIS*DLTRAT»CSTORM B 180
COMMON /BALM/ TOTLQ B 190
COMMON /XINV/ OXINV,DYINV,ARINV,PORINV B 200
COMMON /CHMC/ SUMC(20,20),VXBOY(20,20),VYBOY(20,20) B 210
IF (1NT.GT.1) GO TO 10 B 230
WRITE (6,750) B 240
READ (5*720) TITLE 8 250
WRITE (6,730) TITLE B 260
C INITIALIZE TEST AND CONTROL VARIABLES B 280
STORMI«0.0 B 290
TEST-0.0 B 300
TOTLO-0.0 B 310
SUMT-0.0 B 320
SUMTCH-0.0 B 330
INT»0 B 340
IPRNT-0 B 350
NCA-0 B 360
N»0 B 370
1MOV«0 B 380
NMOV-0 B 390
C LOAD CONTROL PARAMETERS B 410
READ (5,7*0) NTIM,NPMP,NX,NY,NPMAX,NPNT,N1TP,NUMOBS,ITMAX,NREC,NPT B 420
1PND,NCOOES,NPNTMV,NPNTVL,NPNTO,NPOELC,NPNCHV B 430
READ (5/800) PINT,TOL,POROS,BETA,S,T1)1X,T1N1T,XDEL,YOEL,DLTRAT,CEL B 440
1DIS,ANFCTR B 450
PTR>PINT*86400.0*365.25 B 460
NNX«NX-1 B 470
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
43
FORTRAN IV program listing—Continued
NNY«NY-1
NP-NPMAX
DX1NV"1.0/XDEL
DYINV-1.0/YDEL
ARINV=OXINV*DYINV
PORINV'1.0/POROS
C PRINT CONTROL PARAMETERS
WRITE (6/760)
WRITE (6/770) NX/NY/XDEL/YDEL
WRITE (6/780) NTIM/NPMP/PINT/TIMX/TINIT
WRITE (6/790) S/POROS/BETA/DLTRAT/ANFCTR
WRITE (6/870) NITP/TOL/ITMAX/CELDIS/NPMAX/NPTPND
IF (NPTPND.LT.4.0R.NPTPND.GT.9.0R.NPTPND.E0.6.0R.NPTPND.E«.7> WRIT
1E (6/880)
WRITE (6/890) NPNT/NPNTMV/NPNTVL/NPNTD/NUMOBS/NREC/NCODES/NPNCHV/N
1POELC
IF (NPNTMV.EQ.O) NPNTMV999
GO TO 20
C READ DATA TO REVISE TIME STEPS AND STRESSES FOR SUBSEQUENT
C PUMPING PERIODS
10 READ (5/1060) ICHK
IF (ICHK.LE.O) RETURN
READ (5/1070) NT IM/NPNT/NITP/1TMAX/NREC/NPNTMV/NPNTVL/NPNTD/NPDELC
1/NPNCHV/PINT/TIMX/TINIT
WRITE (6/1080) INT
WRITE (6/1C90) NTIM/NPNT/NITP/ITMAX/NREC/NPNTMV/NPNTVL/NPNTD/NPDEL
1C/NPNCHV/PINT/TIMX/TINIT
*•***••<
LIST TIME INCREMENTS
20 DO 30 J«1/100
TIM(J>«0.0
30 CONTINUE
TIM(1)«TINIT
IF (S.EO.0.0) GO TO 50
DO 40 K'2/MT1M
40 TIM(K)«T1MX*TIM(K-1>
WRITE (6/470)
WRITE (6/490) TIM
GO TO 60
50 TIM(1)»PYR
WRITE (6/480) TIMd)
c
c
••••»»»*****»***»*i
.**•***••,
60
INITIALIZE
IF (INT.GT.1)
DO 70 IY-1/NY
00 70 IX«1/NX
VPRM(IX/IY)'0.0
PERH(IX/IY)»0.0
THCK(IX/IY)»0.0
RECH(IX/1Y)»0.0
CNRECH(IX/IY)*0
REC(IX/IY)«0.0
NODEIO(IX/IV)«0
TMRX(IX/IY/1>«0
THRX(IX/I Y/2)"0
HI(1X/IY)«0.0
HR(IX,1Y)«0.0
HC(IX/IY)«C.C
HK(IX/IY)«0.0
WT(IX/IY)«0.0
VX(IX/IY)«0.0
MATRICES
GO TO 100
B 480
B 490
B SOO
B 510
B 520
B 530
B 540
B 550
B 560
B 570
B 580
B 590
B 600
B 610
B 620
B 630
6 640
B 650
B 660
B 670
B 680
B 690
B 700
B 710
B 720
B 730
B 740
B 750
B 760
B 770
B 780
B 790
B 800
B 810
B 820
B 830
B 840
B 850
B 860
B 870
B 880
B 890
B 900
6 910
B 920
B 930
B 940
B 950
B 960
8 970
B 980
B 990
B1000
81010
B1020
B1030
B1040
B1050
B1060
B1070
B1080
B1090
-------
44
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
70
C
c
80
90
100
110
120
130
140
ISO
160
C
C
i A****************
170
FORTRAN IV program listing—Continued
VYdx* I v)»0.0
VXBDY(IX,IY)=0.0
VYBDY(IX*IY)»0.0
CONC(IX*IY)'0.0
CONINT(IX*IY)*0.0
SUMC(IX*IY)«0.0
CONTINUE
*************************************i
READ OBSERVATION WELL LOCATIONS
IF (NUMOBS.LE.O) GO TO 100
WRITE (6*900)
DO 80 J»1*KUMOBS
READ (5*700) IX*1V
WRITE (6*810) J*IX*IY
IXOBS(J)-IX
IV08S(J)»IV
DO 90 I*1*NUMOBS
DO 90 J«1*50
TMWL(I*J)»C.O
TMCN(I*J)>0.0
******<
READ PUKPAGE DATA — (X-Y COORDINATES AND RATE IN CFS)
SIGNS : WITHDRAWAL * POS.; INJECTION » NEG.
IF INJ. WELL* ALSO READ CONCENTRATION OF INJECTED WATER
IF (NREC.LE.O) GO TO 120
WRITE (6*910)
DO 110 I*1*NREC
READ (5*710) IX*IV*FCTR*CNREC
IF (FCTR.LT.0.0) CNRECH(IX*IY)«CNREC
REC(IX*IY)»FCTR
WRITE (6*820) IX*IV*REC(IX*IY)*CNRECH(IX*IY)
IF (INT.GT.1) RETURN
AREA'XDEL'YOEL
WRITE (6*690) AREA
WRITE (6*600)
WRITE (6*610) XDEL
WRITE (6*610) VDEL
****•*•**!
-—READ TRANSMISSIVITY IN FT**2/SEC INTO VPRM
FCTR « TRANSMISSIVITY MULTIPLIER >
WRITE (6*530)
READ (5*550) INPUT*FCTR
DO 160 IY«1*NY
IF (INPUT.£0.1) READ (5*560) (VPRM(IX*IY)*IX«1* NX>
00 ISO IX"1*NX
IF (INPUT.NE.1) GO TO 130
VPRM(IX*IY)*VPRM(IX*IY)*FCTR
GO TO 140
VPRM(IX*IY)»FCTR
IF (IX.EQ.1.0R.IX.EO.NX) VPRM(I X*IY)«0.0
IF (IV.EQ.1.0R.IV.EO.NY) VPRM(IX* IV)*0.0
CONTINUE
WRITE (6*520) (VPR«UX,1Y)*IX«1*NX)
SET UP COEFFICIENT MATRIX BLOCK-CENTERED GRID
AVERAGE TRANSMISSIVITY HARMONIC MEAN
IF (ANFCTR.NE.0.0) GO TO 170
WRITE (6*1050)
ANFCTR«1.0
PIES-3.1415927*3.1415927/2.0
YNS»NY*NY
ARRAY
FT«*2/SEC
B1100
B1110
B1120
81130
81140
81150
81160
B1170
B1180
81190
81200
81210
B1220
81230
B1240
81250
81260
81270
81280
81290
B1300
81310
81320
B1330
81340
B1350
B1360
81370
B1380
B1390
• B1400
81410
B1420
81430
B1440
B1450
B1460
81470
81480
81490
81500
81510
81520
B1530
81540
81550
81560
B1570
81580
81590
81600
81610
81620
81630
81640
81650
81660
B1670
61680
B1690
B1700
B1710
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
45
.EO.0.0) 60 TO 180
,0*VPRM(IX/lY)*VPRM(IX»1/I Y)/(VPRM(IX/IY)*XDEL+VPRM
180
190
200
210
220
230
240
FORTRAN IV program listing—Continued
XNS«NX*NX
HMIN«2.0
00 180 IY-2/NNY
DO 180 IX«2/NNX
IF (VPRMUX/IY) ,
TMRX(IX/1Y/1)«2,
1(IX41/IV)*XDEL>
THRX(IX/IV,2>«2.0*VPRM(IX/IY)«VPRM(IX/IY*1)/(VPRM(IX/IY>*YDEL*VPRM
1(1X/IY*1)«YDEL)
ADJUST COEFFICIENT FOR ANISOTROPY
TMRX(IX/1V/2)>TMRX(IX/IY/2)*ANFCTR
COMPUTE MINIMUM ITERATION PARAMETER (HMIN)
IF (TMRX(IX/IY/1).EQ.O.O> 60 TO 180
IF (TMRXdX/IY/2).EO.0.0) 60 TO 180
RAT=TMRX(IX/IY/1>*YDEL/(TMRX(IX/IY/2)*XDEL>
HMX«PIES/(XNS«(1.0*RAT))
HMY»PIES/(YNS«(1.0*(1.0/RAT>))
IF (HMX.LT.HM1N) HMIN'HMX
IF (HMV.LT.HMIN) HM1N«HMY
CONTINUE
• •**»»«**«**»**»»**»*»*»**»*»**«****«t»***«*»*«»i
READ AQUIFER THICKNESS
WRITE (6/510)
READ (5/550) INPUT,FCTR
DO 210 IY«1/NY
IF (INPUT.EQ.1) READ (5/540) ( THCK( I X/I Y>/IX«1,NX>
DO 200 IX'1/NX
IF (INPUT.NE.1) 60 TO 190
THCK(IX/IY)BTHCK(IX/IY)*FCTR
60 TO 200
IF (VPRMUX/IY).NE.0.0) THCK(IX/IY)«FCTR
CONTINUE
WRITE (6/500) (THCK(1X/IY)/IX«1/NX)
READ DIFFUSE RECHARGE AND DISCHARGE
WRITE (6/830)
READ (5/550) INPUT/FCTR
DO 240 IY-1/NY
IF (INPUT.EQ.1) READ (5/560)
DO 230 IX»1/NX
IF (INPUT.NE.1) 60 TO 220
RECH(IX/IV)*RECH(IX/IY)*FCTR
60 TO 220
IF (THCK(IX/IY).NE.O.O) RECH(I X,IY)«FCTR
CONTINUE
WRITE (6/840) (RECH(IX/IY)/IX'1/NX)
COMPUTE PERMEABILITY FROM TRANSMISSIVITY
COUNT NO. OF CELLS IN AQUIFER
SET N2CRIT « 2X OF THE NO. OF CELLS IN THE AQUIFER
DO 250 IX-1/NX
DO 250 IY«1/NY
IF (THCK(IX/IY).EQ.O.O)
250
(RECH(IX,IY)/IX»1 /NX)
60 TO 250
260
PERM(IX/IV)-VPRM(IX/IV)/THCK(IX/IY>
NCA«NCA*1
VPRM(IX/IY)»0.0
AAO«NCA*AREA
NZCRIT«(NCA*25)/SO
URITE (6/620)
DO 260 IY-1/NY
WRITE (6/650) (PERM(IX/I Y)/IX«1/NX)
B1720
B1730
B1740
81750
B1760
B1770
B1780
B1790
B1800
B1810
B1820
81830
B1840
B1850
81860
81870
B1880
81890
B1900
B1910
B1920
B1930
B1940
B1950
B1960
B1970
81980
B1990
82000
82010
B2020
82030
62040
B2050
82060
82070
82080
82090
B2100
82110
82120
82130
82140
82150
82160
B2170
B2180
82190
82200
82210
B2220
82230
82240
82250
82260
B2270
62280
82290
B2300
82310
82320
B2330
-------
46 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
WRITE (6*630) NCA*AAQ*NZCRIT 82340
C READ NODE IDENTIFICATION CARDS — - B2360
C -—SET VERT. PERM.* SOURCE CONC.* AND DIFFUSE RECHARGE — - B2370
C SPECIFY CODES TO FIT TOUR NEEDS B2380
WRITE (6*570) 82390
READ (5/550) INPUT,FCTR 82400
00 280 IY»1,NY 82610
IF (INPUT.EQ.1) READ (5*640) (NODEID(IX*IY)* IX*1*NX) 82420
DO 270 IX«1*NX 82430
270 IF (INPUT.NE.1.AND.THCK(I X*IV).NE.0.0) NODE ID(IX/IY)•FCTR 82440
280 WRITE (6*580) (NODE 1D(1X*IY)*IX«1*NX) 82450
WRITE (6*920) NCODES 82460
IF (NCODES.IE.0) 60 TO 310 82470
WRITE (6*930) 82480
DO 300 IJ-1/NCODES 82490
READ (5*850) 1COD E * FCTR1 *FCU2*FC TR3*OVERRD 82500
DO 290 IX*1*NX 82510
DO 290 IY«1*NY 82520
IF (NOOEIO(IX*IY).NE.ICODE) 60 TO 290 82530
VPRM(IX*IY)*FCTR1 82540
CNRECH(IX*IY)»FCTR2 82550
IF (OVERRD.NE.O) RECH( I X* I Y)«FCTR3 82560
290 CONTINUE 82570
WRITE (6*860) ICODE*FCTR1*FCTR2 82580
300 IF (OVERRD.NE.O) WRITE (6*1100) FCTR3 82590
310 WRITE (6*590) 82600
DO 320 IY»1/NY 82610
320 WRITE (6*520) (VPRMIX*IY)*IX«1*NX) 82620
C READ WATER-TABLE ELEVATION 82640
WRITE (6*670) 82650
READ (5*550) INPUT*FCTR 82660
DO 350 IY«1*NY 82670
IF (INPUT.EQ.1) READ (5*660) IHT(IX*I V)* IX*1*NX) 82680
DO 340 IX«1,NX 82690
IF (INPUT.(HE.1) 60 TO 330 82700
WT(lX*IV)*bT(IX*IY)*FCTR 82710
GO TO 340 82720
330 IF (THCK(IX*IV).NE.O.O> UT(IX*IV)>FCTR 82730
340 CONTINUE B2740
350 WRITE (6*680) (WT(IX*IY>*IX«1*NX) 82750
C A*************************************************************** B 2 760
C SET INITIAL HEADS 82770
00 360 1X«1,NX 82780
DO 360 1Y»1*NY 82790
HI(IX*IY)«WTHI(IX*IY) 82830
C B2840
CALL OUTPT 82850
C •*•»•••*•••»*»•**••»»•*•*•••»•*••••»••***•••••••••*•»•»»**•»••• 82860
C COMPUTE ITERATION PARAMETERS 82870
DO 370 10*1*20 82880
AOPT(1D)«0.0 82890
370 CONTINUE 82900
ANITP-NITP-1 82910
ALPHA1«DEXP(OLOG(1.0/HNIN)/ANITP> B2920
AOPT(1)»HMIN 82930
DO 380 IP*2*NITP 82940
380 AOPT(IP)«AOPT(IP-1)*ALPHA1 82950
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
FORTRAN IV program listing—Continued
47
(6/450)
(6/460) AOPT
C
c
I **•****•**•*****••»**••******»•***•*****••
390
400
410
420
WRITE
WRITE
* * i
READ INITIAL CONCENTRATIONS AND COMPUTE INITIAL MASS STORED—-
READ (5/550) INPUT/FCTR
DO 420 IY-1/NY
IF (INPUT.EG.1) READ (5/660) (CONC(IX,IY)/IX«1/NX)
DO 410 IX-1/NX
IF (INPUT.NE.1) GO TO 390
CONC(1X/IY)«CONC(IX/IY)*FCTR
60 TO 400
IF (THCK(IX/IY).NE.O.O) CONC(IX/IV)»FCTR
CON I NT (IX/IY)«CONC(IX/IY)
STORMI«STORK1»CON1NT(IX/IY)*THCK(IX/IY)*AREA*POROS
CONTINUE
C
C
C
C
c
c
CHECK DATA SETS
DO 440 1X-1/NX
DO 440 IY«1/NY
IF (THCK(IX/IY).GT
IF (TMRX(IX/IY/1).
IF (TMRXdX/IY/2).
IF (NODEID(IX/IY).
IF (WT(IX/IY).NE.O
IF (RECH(IX/IY).NE
IF (REC(IX/IV).NE.
IF (PERMdX/IY) .GT
IF (NODEID(IX/IV).
IF (WT(1X/IY).NE.O
IF (RECH(IX/IY).NE
IF (REC(IX/IY).NE.
IF (THCK(IX/IY).GT
440 CONTINUE
••****<
RETURN
••***•I
430
FOR INTERNAL CONSISTENCY
.0.0) GO TO 430
GT.0.0) WRITE (6/940) IX/IY
GT.0.0) WRITE (6/950) IX/IY
GT.O) WRITE (6/960) IX/IY
.0) WRITE (6/970) IX/IY
.0.0) WRITE (6/980) IX/IY
0.0) WRITE (6/990) IX/IY
.0.0) GO TO 440
GT.0.0) WRITE (6/1000) IX/IY
.0) WRITE (6/1010) IX/IY
.0.0) WRITE (6/1020) IX/IY
0.0) WRITE (6/1030) IX/IY
.0.0) WRITE (6/1040) IX/IY
i *****
t*****************
450 FORMAT (1H1/20HITERATION PARAMETERS)
460 FORMAT (3H /1G20.6)
470 FORMAT (1H1/27HTIME INTERVALS (IN SECONDS))
480 FORMAT (1H1/15X/17HSTEADY-STATE FLOW//5X/57HTIME
1 FOR SOLUTE-TRANSPORT SIMULATION • /G12.5)
490 FORMAT (3H /10G12.5)
500 FORMAT (3H /20FS.1)
S10 FORMAT (1H1/22HAQUIFER THICKNESS
S20 FORMAT (3H /20F5.2)
S30 FORMAT (1H1/30HTRANSMISSIV1TY MAP
S40 FORMAT (20G3.0)
5SO FORMAT (11/610.0)
560 FORMAT (2064.1)
570 FORMAT (1H1/23HNODE IDENTIFICATION
S80 FORMAT (1H /20I5)
590 FORMAT (1H1/4SHVERTICAL PERMEABILITY/THICKNESS
600 FORMAT (1HO/10X/12HX-Y SPACING:)
610 FORMAT (1H /12X/1061 2. 5 ).
620 FORMAT (1H1/24HPERMEABILTV MAP (FT/SEC))
630 FORMAT (1HO/////10X/44HNO. OF FINITE-DIFFERENCE
1 /I4//10X/28HAREA OF AQUIFER IN MODEL
20X/47HNZCRIT (MAX. NO. OF CELLS THAT
INTERVAL (IN SEC)
(FT))
(FT«FT/SEC»
MAP//)
(FT/(FT*SEC)>)
CELLS IN AQUIFER «
• /612.5/10H SQ. FT.////1
CAN BE VOID OF/20X/56HPARTI
B2960
62970
B2980
62990
63000
63010
B3020
63030
B3040
B3050
63060
63070
63080
63090
63100
63110
63120
83130
83140
83150
63160
63170
63180
63190
63200
63210
63220
63230
63240
83250
63260
63270
63280
83290
B3300
63310
83320
83330
63340
63350
B3360
63370
83380
83390
83400
83410
B3420
B3430
63440
B34SO
B3460
63470
B3480
83490
83500
B3510
83520
B3S30
B3S40
B3550
B3560
83570
-------
48
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
• I*/)
CELL • *612.4)
FORTRAN IV program listing—Continued
3CLES; IF EXCEEDED* PARTICLES ARE REGENERATED) <
640 FORMAT (2011)
650 FORMAT (3H *20F5.3)
660 FORMAT (2064.0)
670 FORMAT (1H1*11HWATER TABLE)
680 FORMAT (1H *20F5.0)
690 FORMAT (1HO»10X*19HAREA OF ONE
700 FORMAT (212)
710 FORMAT (212*268.2)
720 FORMAT (10A8)
730 FORMAT (1HO*10A8)
740 FORMAT (1714)
7SO FORMAT (1H1/77HU.S.G.S. METHOD-OF-CHARACTER1STICS MODEL FOR SOLUTE
1 TRANSPORT IN GROUND WATER)
760 FORMAT (1H0*21 X,21 HI N P U T DATA)
770 FORMAT (1HO*23X*1 6H6RI0 DESCRIPTORS//13X*30HNX (NUMBER OF COLUM
1NS) • *I4/13X*28HNY (NUMBER OF ROWS) »*16/13X*29HXDEL (X
2-OISTANCE IN FEET) * *F7.1/13X*29HYDEL (V-DISTANCE IN FEET) • *F7
3.1)
780 FORMAT (1HO*23X*1 6HTINE PARAMETERS//! 3X»40HNTIM (MAX. NO. OF TI
1ME STEPS) • *I6/13X*40HNPMP CNO. OF PUMPING PERIODS)
2 * *I6/13X*39HPINT (PUMPING PERIOD IN YEARS) «*F10.2/13X,39
3HTIMX (TIME INCREMENT MULTIPLIER) »*F10.2/13X*39HTINIT (INIT
4IAL TIME STEP IN SEC.) **F8.0)
790 FORMAT (1HO*14X*34HHYDROL06IC AND CHEMICAL PARAMETERS//!3X,1HS*7X*
129H(STORA6E COEFFICIENT) »*5X*F9.6/13X»28HPOROS (EFFECTIVE
2 POROSITY)*8X,3H* *F8.2/13X*39HBETA (CHARACTERISTIC LEN6TH)
3 • *F7.1/13X*31HDLTRAT (RATIO OF TRANSVERSE TO/21 X*30HLONGITUO I
4NAL DISPERSIVITY) « *F9.2/13X*39HANFCTR (RATIO OF T-YY TO T-XX)
5 • *F12.6)
800.FORMAT (1265.0)
810 FORMAT (1H *16X*I 2*5X*I2*4X*I 2)
820 FORMAT (1H *7X*214*3X*F7.2*5X*F7.1)
830 FORMAT (1H1,39HDIFFUSE RECHARGE AND DISCHARGE (FT/SEC))
840 FORMAT (1H *1P10E10.2>
850 FORMAT (12*3610.2*12)
860 FORMAT (1HO*7X*I2*7X*E10.3*SX*F9.2)
870 FORMAT (1HO*21X*20HEXECUTION PARAMETERS//13X*39HNITP (NO. OF ITE
1RATION PARAMETERS) « * 14/13X*39HTOL (CONVERGENCE CRITERIA - ADI
2P) • *F9.4/13X*39HITMAX (MAX.NO.OF ITERATIONS - ADIP) • *14/13X*3
34HCELDIS (MAX.CELL DISTANCE PER MOVE/24X*28HOF PARTICLES - H.O.C.)
4 • *F8.3/13X*30HNPMAX (MAX. NO. OF PARTICLES)*7X*2H> *I4/12X*3
S2H NPTPND (NO. PARTICLES PER NOOE)*6X*3H* *I4)
880 FORMAT (1HO*SX*47H*** WARNING •** NPTPND MUST EQUAL 4*5*8* OR 9.)
890 FORMAT (1HO*23X*15HPR06RAM OPTIONS//1 3X*30HNPNT (TINE STEP INTER
1VAL FOR/21X*18HCOMPLETE PR1NTOUT)*7X*3H» *I4/1 3X*31HNPNTMV (MOVE
2INTERVAL FOR CHEM./21X*28HCONCENTRAT10N PRINTOUT) • *I4/13X*29HN
3PNTVL (PRINT OPTION-VELOCITV/21X*24HO"NO; 1-FIRST TIME STEP;/21X*1
47H2*ALL TIME STEPS)*8X*3H« * I 4/13X*31HNPNTD (PRINT OPT ION-D ISP.C
50EF./21X,24HO«NO; 1-FIRST TIME STEP;/21X*17H2-ALL TIME STEPS)*8X*3
6H« *I4/13X*32HNUMOBS (NO. OF OBSERVATION WELLS/21X*28HFOR HVDR06R
7APH PRINTOUT) • * 14/13X*35HNREC (NO. OF PUMPING WELLS) • *I5
8/13X*24HNCOOES (FOR NODE IDENT.)*9X*2H* * 15/13X*25HNPNCHV (PUNCH V
9ELOCITIES)*8X*2H« * 15/13X*36HNPDELC (PRINT OPT.-CONC. CHANGE) • *
SI4)
900 FORMAT (1HO*10X*29HLOCATION OF OBSERVATION WELLS//17x»3HNO.*5X,1HX
1*5X*1HY/I
910 FORMAT (1HO*10X*28HLOCATION OF PUMPING WELLS//11X*28HX Y RA
1TEUN CFS) CONC./>
920 FORMAT (1HO»5X*37HNO. OF NODE IDENT. CODES SPECIFIED • *I2)
930 FORMAT (1HO*10X*41HTHE FOLLOWIN6 ASSIGNMENTS HAVE BEEN MAOE:/5X*51
1HCOOE NO. LEAKANCE SOURCE CONC. RECHARGE)
83580
B3S90
B3600
63610
B3620
B3630
B3640
B3650
83660
83670
B3680
B3690
B3700
83710
83720
83730
B3740
83750
83760
83770
83780
83790
B3800
B3810
B3820
83830
B3840
B3850
B3860
83870
B3880
B3890
83900
B3910
B3920
B3930
B3940
83950
B3960
B3970
B3980
B3990
B4000
B4010
84020
B4030
84040
84050
84060
B4070
B4080
84090
84100
84110
B4120
B4130
B4140
B4150
84160
84170
84180
84190
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
49
FORTRAN IV program littmg—Continued
940 FORMAT <1H ,5X,61H*«* WARNING ••* THCK.EQ.0.0 AND TMRX(X).GT.0.0
1 AT NODE IX «,I4,6H, IV «,I4)
950 FORMAT (1H /5X/61H*«* WARNING **• TNCK.EQ.0.0 AND TMRX(V).6T.O.0
1 AT NODE IX «,I4,6H, IY »»14)
960 FORMAT (1H /5X/61H*** WARNING *•* THCK.EQ.0.0 AND NODE ID .G~T .0.0
1 AT NODE IX «,I4,6H, IV «,I4>
970 FORMAT <1H ,5X,56H««« WARNING *** THCK.EQ.0.0 AND WT.NE.0.0 AT N
10DE IX «/I*,6H/ IV «/!*>
980 FORMAT (1H ,5X,58H**« WARNING «•• THCK.EQ.0.0 AND RECH.NE.0.0 AT
1 NODE IX «,I4,6H, IV «,I4>
990 FORMAT (1H ,5X,58H**« WARNING *•*
1 NODE IX »,I4,6H, IV «,14>
1000 FORMAT (1H ,5X»61H*** WARNING **•
1 AT NODE IX «,I4,6H, IV «,I4>
1010 FORMAT (1H ,5X,56H*** WARNING *•* PERM.EQ.0.0 AND WT.NE.0.0 AT N
10DE IX »,I4,6H* IV «/!*)
1020 FORMAT (1H »5X,58H*** WARNING • •'• PERM.EQ.0.0 AND RECH.NE.0.0 AT
1 NODE IX >,14,6H, IV «,I4)
1030 FORMAT (1H /5X,58H««* WARNING *** PERM.EQ.0.0 AND REC.NE.0.0 AT
1 NODE IX »,I4,6H* IV »/!*>
1040 FORMAT (1H »5x,58H,*«* WARNING ••• PERM.EQ.0.0 AND THCK.GT.0.0 AT
1 NODE IX «,14,6H, IV «,I4)
1050 FORMAT (1HO,5X,45H**« WARNING **• ANFCTR
1X,34HDEFAULT ACTION: RESET ANFCTR • 1.0)
1060 FORMAT (ID
1070 FORMAT (1014,365.0)
1080 FORMAT (1H1,5X,25HSTART PUMPING PERIOD NO.
1G TIME STEP* PUMPAGE* AND PRINT PARAMETERS
1090 FORMAT (1HC,14X,9HNTIM > •14/15X,9HNPNT
1I4/15X»9HITMAX * ,I4/15X/9HNREC • ,I 4/15X,9HNPNTHV « ,I4/15X,9H
2NPNTVL • ,I4/15X,9HNPNTD » 114/1SX»9HNPDELC * •I4/15X»9HNPNCHV •
3»14/15X,9HPINT « 'F10.3/15X/9HTIMX • ,f10.3/15X,9MT1NIT • ,F1
40.5/5
1100 FORMAT (1H ,46X,E10.5)
END
SUBROUTINE HERAT
DOUBLE PRECISION DMIN1»DEXP,DLOG,DABS
REAL *8TMRX,VPRM,H1/HR,HC»HK,WT»REC»RECH/TIM,AOPT,TITLE
REAL »8XDEL»YDEL/S/AREA,SUMT,RHO,PARAM,TEST,TOL,PtNT/HMIN,PYR
REAL *8B/G/U/AxC/E/f»DR/DC/T8AR/TMK*COEF/BLH/BRK/CHK*QL#BRH
COMMON /PRMI/ NTIM/NPMP/NPNT/N1TP,N,NX,NY,NP,NREC»1NT/NNX/NNY/NUMO
1BS.NMOV/IMCV/NPMAX,ITMAX/NZCRIT,IPRNT,NPTPND/NPNTMV/NPNTVL»NPNTD/N
2PNCHV/NPDELC
COMMON /PRCIK/ NODE I 0 ( 20/?0)/NPC ELL (20*20)/L IM80 ( 500) / IXOB S ( 5 ) / IYOB
1S(5)
COMMON /HE DA/ THCK(20/20>»PERH(20*20)»TNWL(5,50)/TMOBS(50),ANFCTR
COMMON /HEDB/ TMRX(20,20,2),VPRM(20,20),HI(20,20),HR(20,20),HC(20,
120),HK(20,20),WT(20,20),R£C(20,20),R£CH(20,20),TIM(100),AOPT(20>,T
2ITLE(10),XDEL,Yi>EL,S,AREA,SUMT,RHO,PARAM,TEST,TOL,PlNT,HMIN,PYR
COMMON /BALM/ TOTLQ
COMMON /XINV/ DXINV,DYINV,ARINV,PORINV
DIMENSION b(20), 8(20), G(20>
C **•*•*<
KOUNT'O
COMPUTE ROW AND COLUMN
CALL NEW ITERATION PARAMETER
10 REMN«MOD(KOUNT,NITP)
IF (REMN.EQ.O) NTH»0
NTH«NTH*1
PARAM«AOPT(NTH)
THCK.EQ.0.0 AND REC.NE.0.0 AT
PERM.EQ.0.0 AND NODE ID.GT.0.0
WAS SPECIFIED AS 0.0/23
,I2//2X,75HTHE FOLLOWIN
HAVE BEEN REDEFINED:/)
• ,14/15X,9HN1TP • ,
C
C
C
C
B4200
B4210
B4220
B4230
B4240
B4250
84260
84270
84280
B4290
B4300
B4310
B4320
B4330
84340
B4350
84360
84370
84580
B4390
84400
B4410
B4420
64430
84440
84450
B4460
B4470
B4480
B4490
B4SOO
84510
B4520
B4530
84540-
,**•»•***•**•»•*•
ROW COMPUTATIONS
10
20
30
40
50
60
70
80
90
C 100
C 110
C 120
C 130
C 140
C 150
C 160
C 170
C 180
C 190
C 200
C 210
C 220
C 230
C 240
C 250
C 260
C 270
-------
50 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program toting—Continued
TEST«0.0 C 280
RHO»S/TIM(N) C 290
BRK»-RHO C 300
00 50 IY«1,NY C 310
00 20 M«1,NX C 320
W.EQ.O.O> 60 TO 30 C 380
COEF*VPRM(IX/IY> C 390
QL«-COEF*WTUX,IV) C 400
A«TMRX*DY1NV C 440
TBAR*A«C*E«F C 450
THK«T8AR*PARAM C 460
BLH — A-C-RHO-COEF-TMK C 470
BRHȣ*F-TMK C 480
OR«BRH*HC(IX/IY)+BRK*HK(IX,IY)-E*HC(IX,lr-1>-F*HC C 510
B(IX)-C/U(IX) C 520
G(IX)«(OR-A*G(IX-1))/W(IX) C 530
30 CONTINUE C 540
C C 550
C BACK SUBSTITUTION C 560
00 40 J»2,hX C 570
IJ-J-1 C 580
IS«NX-IJ C 590
40 HR-e*HR(IS + 1*IY> C 600
50 CONTINUE C 610
W W^WWWWWWWWWWwWWWKWWW W ^ Q ^ \J
C COLUMN COMPUTATIONS C 630
DO 90 IX«1,NX C 640
00 60 M«1,NY C 650
U(M)«0.0 C 660
8(N)>0.0 C 670
60 G(M)«0.0 C 680
DO 70 IY»1/NY C 690
IF (THCK(IX^IV).EO.O.O) GO TO 70 C 700
COEF'VPRMUXsIV) C 710
QL--COEF*WT(1X,IY> C 720
A»TNRX{ IX, IY-1»2)«OYINV C 730
C«TMRXTBAR»PARAM C 780
BLH«-A-C-RHO-COEF-TMK C 790
8RH«E+F-TNK C 800
OC«BRH«HR( 1X/IY) + BRK«HK(IX,IY)-E«HR(IX-1,1Y)-F*HR(IX»1/IY) + OL»RECH C 810
1(IX/IY)*REC(IX,1Y)«ARINV C 820
H
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
51
FORTRAN IV program listing—Continued
80
90
100
110
IJ-J-1
IB«NY-IJ
H'c(ix,iB)«G(iB>-B(ie)*Hc(ix/iB*i)
IF (THCK(IX,IB).EO.O.O> GO TO 80
CHK»DABS(HC(1X/IB)-HR(IX/IB>>
IF (CHK.GT.TOL) TEST«1.0
CONTINUE
CONTINUE
• * **
KOUNT*KOUNT*1
IF (TEST.EO.0.0) GO TO 120
IF (KOUNT.GE.ITMAX) GO TO 100
GO TO 10
••••*•**•••*•**•*****»»•»*•*•<
TERMINATE PROGRAM — ITMAX
WRITE (6/160)
DO 110 IX«1/NX
DO 110 IY«1/NY
HK(IX/IY)«HC(IX/IY>
CALL OUTPT
STOP
120
C
c
130
r *••*
•ft********************************
EXCEEDED
*****•<
r**********************************************
SET NEW HEAD (HK)
DO 130 IY«1»NY
DO 130 1X-1/NX
IF (THCK(IX/1Y).EO.O.O> GO TO 130
HR(IX/IY)aHK(lX/IY)
HKUX/I Y)»HC(IX/I Y)
COMPUTE LEAKAGE FOR MASS BALANCE
IF (VPRMUX/m.EO.0.0) GO TO 130
DELQ«VPRM(1X/IY)*AREA*(WT(IX/IY)-HK(IX/IY))
TOTLO«TOTLQ*DELO*TIM(N)
CONTINUE
WRITE
WRITE
(6/140)
(6/150)
N
KOUNT
*******************i
RETURN
****•*****!
i *****
i*********<
MAX. NO. ITERATION
140 FORMAT (1HC//3X/4HN a /1I4)
ISO FORMAT (.IN /2X/23HNUMBER OF ITERATIONS « /1I4)
160 FORMAT (1HO/SX/64H*** EXECUTION TERMINATED --
1S EXCEEDED ***/26X/21HFINAL OUTPUT FOLLOWS:)
END
SUBROUTINE GENPT
REAL *8THRX/VPRH/HI,HR/HC/HK/UT/REC/RECH,TIH/AOPT/TITLE
REAL *8XDEL/YDEL/S/AREA/SUMT/RHO/PARAM/TEST/TOL/PINT/HMIN/PYR
COMMON /PRMI/ NTIM/NPMP/NPNT/NITP/N/NX/NY/NP/NREC/INT/NNX/NNY/NUMO
1BS/NMOV/IMCV/NPMAX/ITMAX/NZCRIT/IPRNT/NPTPND/NPNTMV/NPNTVL/NPNTD/N
2PNCHV/NPDELC
/PRftK/ NODEID<20/20)/NPCELL(20/20)/LIM80(500)/IXOBS(5),IrOB
COMMON
1S(5)
COMMON
COMMON
/HE DA/ THCK(?0/20>/PERM(20/20)/TMWL(5/50)/TMOBS(50)/ANFCTR
/HEDB/ TMRX(20/20/2)/VPRM(20/20)/HI(20/20)/HR(20/20)/HC(20/
120),HK(20/20)/WT(20«20>/REC(20/20)/RECH(20,20)/TIM(100)/AOPT(20)*T
2ITLE(10)/XDEL/YDEL/S/AREA/SUMT/RHO/PARAM/TEST/TOL/PINT/HMIN/PYR
COMMON /CHMA/ PART(3/3200)/CONC(20/20)/TMCN(5/50)/WX(20/20)/VY(20/
120)/CONINT (20/20)/CNRECH(20/20)/POROS/SUMTCH/BETA/TIMV/STORM/STORM
C
C
C
C
c
c
c
c
c
c
900
910
920
930
940
950
960
970
980
990
C1000
C1010
C1020
C1030
C1040
C10SO
C1060
C1070
C1080
C1090
C1100
C1110
C1120
C1130
C1140
C1150
C1160
C1170
C1180
C1190
C1200
C1210
C1220
C1230
C1240
C1250
C1260
C1270
C1280
C1290
C1300
C1310
C1320
C1330
C1340
C1350
C1360
C1370-
10
20
30
40
50
60
70
80
90
100
110
120
130
140
-------
52 TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program luting—Continued
2I«CMSIN,CMSOUT«FLMIN»FLMOT,SUMIO*CEL01S*OLTRAT«CSTORM 0 150
DIMENSION RP(8)/ RN<8>, IPT(8) 0 160
F1*0.30 0 180
F2«1.0/3.0 0 190
IF (NPTPND.E0.4) F1-0.25 0 200
IF (NPTPNO.EQ.9) F1>1.0/3.0 0 210
IF (NPTPND.E0.8) F2»0.25 0 220
NCHK»NPTPND 0 230
IF (NPTPNO.EQ.5.0R.NPTPND.E0.9) NCHK>NPTPND-1 D 240
IF (TEST.GT.98.) GO TO 10 D 250
C INITIALIZE VALUES 0 270
STORM»0.0 0 280
CMSIN«0.0 D 290
CMSOUT'0.0 0 300
FLMIN»0.0 - 0 310
FLMOT*0.0 D 320
SUMIO-0.0 D 330
C •*»••*»•»***•••**»**»«»«»»*»***«»*»******»*********«*«•*•*»•«»* D 340
10 00 20 10-1*3 D 350
00 20 IN-1/NPMAX D 360
20 PART(ID»IN)«0.0 0 370
DO 30 IA«1,8 D 380
RP(IA)«0.0 0 390
RN(IA)»0.0 D 400
30 1PT(IA)«0 D 410
C SET UP LIMBO ARRAY D 420
00 40 IN»1,500 0 430
40 LIMBO(IN)»0.0 0 440
INO-1 D 450
DO 50 IL»1,500/2 D 460
LIMBO( ID-1NO 0 470
SO 1NO-INO+1 0 480
C ---INSERT PARTICLES D 500
00 410 IX-1/NX 0 510
00 410 IY-1/NY 0 520
IF (THCK(1X/IV).EQ.O.O) GO TO 410 D 530
KR-0 0 540
TEST2-0.0 0 550
METH-1 D 560
NPCELL(IX,IY>«0 0 570
C1«CONC.EG.O.O.OR.THCK(IX + 1,IY-1).EQ.O.O.OR.THCK(IX-1 / D 620
1IY»1).£0.0.0.OR.THCK(IX-1/IY-1).£8.0.0) TEST2«1.0 0630
IF «THCKUX/IY»1) ,EO.O.O.OR-.THCMIX,1Y-1 ).EQ.O.O.OR.THCK.EO.O.O>.AND.NPTPND.GT.5) TEST2-1.0 0 650
CNOOE"C1*<1.0-F1) 0 660
IF (TEST.LT.98.0.OR.TEST2.6T.0.0) GO TO 70 D 670
SUMC»CONC*CONC*CONC
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
FORTRAN IV program lifting—Continued
53
80
90
100
110
120
130
140
150
160
EVET«(-1.0)**IT
DO UO IS«1/2
EVES«<-1.0)**IS
PART(1 /INO)»IX*F1*EVET
PART(2/IND)»IY+F1*EVES
PART (2 /I NO) «-PART (2, J NO)
PART(3/1ND)«C1
IF (TEST. LT. 98.0. OR. TEST2.GT. 0.0) 60 TO 130
IXO«IX*EVET
IYO«IY*EVES
KR«KR+1
IPT(KR)>INO
IF (METH.EO.Z) CO TO 80
PART<3/INO)«CNODE»CONC
IF ) 100/110/120
RP(KR)«CONC»C1-PART<3/INO)
GO TO 130
RP(KR)»0.0
RN(KR)»0.0
60 TO 130
RP(KR)»C1-PART<3/INO)
RN(KR)«CONC(IXO/IYO)-PART<3/INO)
1ND-1NO+1
CONTINUE
IF (NPTPNO.EO. 5. OR. NPTPNO.ee. 9) 60 TO 150
GO TO 160
--- PUT ONE PARTICLE AT CENTER OF CELL ---
PART(1,INO) — IX
PART<2/INO)»-IY
PART<3/1NO)«C1
INO«IND+1
--- PLACE NORTH/ SOUTH/ EAST/ AND WEST PARTICLES ---
IF (NPTPNO.LT.8) GO TO 290
CNOOE"C1«(1.0-F2)
00 280 1T»1,2
EVET»<-1.0)**IT
PART (1/INO)>IX«F2*E VET
PART(2/INO)«-IV
PART(3/IND)'C1
IF (TEST. LT. 98.0. OR. TEST2.6T. 0.0) 60 TO 220
IXO»IX*EVET
170
180
190
200
210
220
IPT(KR)«INO
IF (HETH.EQ.2) 60 TO 170
PART(3/IND)*CNODE*CONCUXD/IY)*F2
60 TO 180
PART(3/IND)*2.0*C1*CONC(IXD/IY)/ 190/200/210
RP(KR)»CONC(IXO/IY)-PART(3/INO)
RN(KR)«C1-PART(3/IND)
60 TO 220
RP(KR)«0.0
RN(KR)«0.0
60 TO 220
RP(KR)-C1-PART(3/IND)
RN(KR)«CONC(IXO/IY)-PART(3/IND)
1ND-INO»1
PART(1/INO)»IX
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
9SO
960
970
980
990
01000
01010
01020
01030
01040
010SO
01060
01070
01080
01090
01100
01110
01120
01130
01140
01150
01160
01170
01180
01190
01200
01210
01220
01230
01240
01250
01260
01270
01280
01290
01300
01310
01320
01330
01340
013SO
01360
01370
01380
-------
54 - TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program luting—Continued
PART(2/INO)«IY+F2*EVET D1390
PART(2/IND)*-PART(2/IND> OUOO
PART(3/INO)«C1 01410
IF (TEST.LT.98.0.OR.TEST?.6T.0.0) GO TO 380 OUZO
IVO«IY*EVET OU30
KR»KR+1 01440
IPT(KR)«INO 01450
IF (METH.E0.2) 60 TO 230 01460
PART(3/IND)«CNODE*CONC(IX,IYO)*F2 01470
GO TO 240 01480
230 PART(3/IND)«2.0*C1*CONC(IX/1YD>/(C1+CONC(IX/IYO)> 01490
240 IF (C1-CONC(IX/IYD)) 250*260/270 01500
250 RP(KR)«CONC(1X/IYD)-PART(3/INO> 01510
RN(KR)»C1-PART(3/INO) 01520
GO TO 280 01530
260 RP(KR>*0.0 01540
RN((CR)«0.0 - 01550
GO TO 280 01560
270 RP(KR>«C1-PART(3/IND) 01570
RN(KR)»CONC(IX/IYO)-PART(3/IND) 01580
280 IND«IND*1 01590
C 01600
290 IF (TEST.LT.98.0.OR.TEST2.GT.0.0) GO TO 410 01610
SUMPT=0.0 01620
C —COMPUTE CONC. GRADIENT WITHIN CELL 01630
00 300 KPT«1/NCHK 01640
IK«IPT(KPT> 01650
300 SUMPT»PART(3/IK)+SUMPT 01660
CBAR*SUMPT/NCHK 01670
C CHECK MASS BALANCE WITHIN CELL AND ADJUST PT. CONCS. 01680
SUMPT-0.0 01690
IF (CBAR-C1) 310/410/330 01700
310 CRCT«1 .0-UBAR/C1) 01710
IF (METH.EQ.1) CRCT«CBAR/C1 01720
DO 320 KPT*1/NCHK 01730
IK«IPT(KPT) 01740
PART(3/IK)«PART(3/IK>*RP(KPT)*CRCT 01750
320 SUMPT«SUMPT*PART(3/IK> 01760
CBARN'SUMPT/NCHK 01770
GO TO 350 01780
330 CRCT«1,0-(C1/CBAR) 01790
IF (METH.EQ.1) CRCT=C1/CBAR 01800
00 340 KPT-1/NCHK 01810
IK»IPT(KPT) D1820
PART(3/IK>*PART(3/1K)+RN(KPT)*CRCT 01830
340 SUMPT«SUMPT*PART(3/IK) 01840
CBARN'SUMPT/NCHK 01850
350 IF (CBARN.Ea.C1) GO TO 410 01860
C CORRECT FOR OVERCOMPENSATION D1870
CRCT-C1/CBARN 01880
00 380 KPT'1/NCHK 01890
IK'IPT(KPT) 01900
PART(3/IK)«PART(3/IK)«CRCT 01910
C CHECK CONSTRAINTS 01920
IF (PART(3/IK)-C1) 360/380/370 01930
360 CL1M«C1-RP(KPT)+RN(KPT) 01940
IF (PART(3/IK).LT.CLIM> GO TO 390 D1950
GO TO 380 01960
370 CLIM«C1*RP(KPT)-RN(KPT) 01970
IF (PART(3/IK).GT.CLIM) GO TO 390 01980
380 CONTINUE 01990
GO TO 410 02000
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
55
FORTRAN IV program listing— Continued
390 TEST2-1.0
DO (00 KPT«1,NCHK
IK«IPT(ICPT>
400 PART(3*1IO»C1
410 CONTINUE
NP«INO
IF (INT.EO.O) CALL
r * * * 1
RETURN
CHMOT
I**********************************
END
SUBROUTINE VELO
DOUBLE PRECISION DM IN1/DEXP/DLOG/DABS
REAL •8TMRX/VPRM/HI/HR/HC/HK/WT/REC/RECHVTIM/AOPT/TITLE
REAL *8XDEL/YDEL/S,AREA,SUMT,RHO,PARAM/TEST/TOL/PINT/HMIN/PVR
REAL *8RATE/SLEAK/D1V
COMMON /PRMI/ NTIM/NPMP/NPNT/NITP/N/NX/NY/NP/NREC/INT/NNX/NNY/NUMO
1BS/NMOV/IMCV/NPMAX/ITMAX/NZCRIT/IPRNT/NPTPND/NPNTMV/NPNTVL/NPNTD/N
2PNCHV,NPDELC
COMMON /PRMK/ NODE ID(20,20)/NPCELL(20/20)»LIMBO(500),IXOBS(5),IYOB
1S(S>
COMMON /HEDA/ THCK(20,20),PERM(20,20)/TMWL(5/50>/TMOBS(50)/ANFCTR
COMMON /HEDB/ TMRX(20/20/2)/VPRM(20/20)/HI(20/20),HR(20/20)/HC(20/
120)/HK(20/20)/UT(20/20)/REC(20/20)/RECH(20,20)/TIM(100)/AOPT(20)/T
2ITLE(10),XDEL/YDEL/S,AREA,SUMT/RHO,PARAM,TEST/TOL/PINT/HMIN/PVR
COMMON /X1NV/ DXINV/DYINV,ARINV/PORINV
COMMON /CHMA/ PART(3,3200),CONC(20,20)/TMCN(5/50)/VX(20/20),VY(20/
120)/CONINT(20/20)/CNRECH(20/20)/POROS/SUMTCH/BETA,TIMV/STORM/STORM
21/CMS IN/CMSOUT/FLMIN/FLMOT/SUMIO/CELDIS/DLTRAT/CSTORM
COMMON /CHKC/ SUMC(20/20>/VXBDY(20/20)/VYBDY(20/20)
COMMON /DIFUS/ DISP (20/20/4)
COMPUTE VELOCITIES AND STORE
VMAX = 1 .OE-10
VMAY*1.OE-10
VMXBO=1.OE-10
VMYBD»1.OE-10
TMV«TIM(N)
LIM«0
DO 20 IX*1/NX
DO 20 IY«1/NY
DO 10 1Z-1/4
10 OISP(IX/IY/H)«0.0
IF (THCKUX,IV).EQ.0.0) GO TO 20
RATE«REC(IX/IY)/AREA
SLEAK«(HK(IX/IY)-WT(IX/1Y))*VPRM(IX/IY)
D1V=RATE*SIEAK*RECH(IX/IY>
VELOCITIES AT NODES
X-DIRECTION
GRDX«(HK(1X-1,IY)-HK(IX+1,IY))*DXINV*0.50
IF (THCK(IX-1/IY).EQ.0.0) GRDX = (HK(IX/IY)-HK(I X»1/IY))«DXIN V
IF (THCKUX + 1/IY).EQ.0.0) GRDX«(HK(IX-1/IY)-HK(I X/IY))•DXINV
IF (THCK(IX-1/IY).EQ.0.0.AND.THCK(IX»1/IY).EQ.0.0) 6RDX«0.0
VX(IX/IY)«PERM(IX,IY)*GROX«PORINV
ABVX«ABS(VX(IX/IY))
IF (ABVX.GT.VMAX) VMAX'ABVX
Y-DIRECTION
GRDY«(HK(IX/IY-1)-HK(1X,IY+1))*DYINV«0.50
IF (THCK(IX/IY-1).EQ.0.0) GROY«(HK(IX,IY)-HK(IX/IY*1))*DYINV
02010
D2020
D2030
D2040
D20SO
D2060
D2070
D2080
D2090
02100
02110-
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
E 210
E 220
230
?40
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
SOO
S10
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
-------
56
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
C
C
20
C
C
FORTRAN IV program listing—Continued
IF (THCK(IX/IV«1).EQ.O.O) 6ROY»(HK( I X/I Y-1 )-HK ( I X/I Y» *DY 1NV
IF (THCK(IX/IY-1).EQ.O.O.AND.THCK(IX/IV+1).EQ.O.O) GRDY-0.0
VY(IX/IV)*PERM(IX/IV)*6ROV*PORINV*ANFCTR
ABVY«ABS(VY(IX/IY)>
IF (ABVY.6T.VMAY) VMAY-ABVY
— VELOCITIES AT CELL BOUNDARIES — -
GRDX"(HK(IX/IY)-HK(IX»1, IV»*OXINV
PERNXa2.0*PERM(IX/IY>*PERM(IX*1/IY)/(PERM(IX/IV)+PERM(IX«1/IV)>
VXBDY(IX/IY)*PERMX*GRDX*PORINV
GRDY«(HK(IX/IY)-HK(IX/IV«1))*DVINV
PERMY>2.0*PERM(IX/IY)*PERM(IX/ir+1)/(PERM(IX/IY)«PERM(IX/IV+1)>
VYBOY(IX/IY)«PERMY*GRDY*PORINV*ANFCTR
A8VX«ABS(VX80Y(IX/IY)>
ABVY*ABS(VYBDY(IX/IY))
IF (ABVX.GT.VMXBD) VHXBO=ABVX
IF (ABVY.GT.VMYBD) VMYBD«ABVY
IF (OIV.GE.0.0) GO TO 20
TDIV»(POROS*THCK(IX/1Y))/DABS(DIV)
IF (TOIV.LT.TMV) TMV«TOIV
CONTINUE
******
PRINT VELOCITIES—-
IF (NPNTVL.EO.O) GO TO 80
,2) GO
,1 .AND
TO 30
.N.EQ.1)
GO TO 30
(VX(1X/IY)/IX«1/NX)
(VXBDYUX/IV)/IX«1/NX)
(VYUX/I Y)/1X«1,NX)
(VVBDY(IX/IV)/IX«1/NX)
C
C
IF (NPNTVL.EO.
IF (NPNTVL.EQ.
GO TO 80
30 WRITE (6/220)
WRITE (6/330)
DO 40 IY»1/NY
40 WRITE (6/350)
WRITE (6*340)
00 50 IY«1/NY
50 WRITE (6/350)
WRITE (6/360)
WRITE (6/330)
DO 60 IY-1/NY
60 WRITE (6/350)
WRITE (6/340)
DO 70 IY-1/NY
70 WRITE (6/3SO)
PUNCH VELOCITIES
80 IF (NPNCHV.EQ.O) GO TO 110
IF (NPNCHV.EQ.2) GO TO 90
IF (NPNCHV.EQ.1.AND.N.EQ.1) 60 TO 90
GO TO 110
90 WRITE (7/510) NX/NV/XDEL/VDEL/VNAX/VNAV
DO 100 IY-1/NY
WRITE (7/520) (VX(IX/IY)/IX»1,NX)
100 WRITE (7/S20) (VY(1X/IY)/IX-1/NX)
A***************************************
COMPUTE NEXT TIHE STEP
110 WRITE (6/390)
WRITE (6/400) VHAX/VHAY
WRITE (6/410) VMXBD/VNVBD
TOELX»CELDIS*XDEL/VMAX
TDELY-CEtOIS*YDEL/VMAY
TDELXB»CELOIS«XOEL/VHX8D
TDELYB*CELDIS*YOEL/VHYBD
TIMV«AHIN1(TDELX/TOELV/TDELXB/TOELVB>
WRITE (6/310) TMV/TIHV
>A****************
E 520
E 530
E 540
E 550
E 560
E 570
E 580
E 590
E 600
E 610
E 620
E 630
E 640
E 650
E 660
E 670
E 680
E 690
E 700
E 710
E 720
E 730
E 740
E 750
E 760
E 770
E 780
E 790
E 800
E 810
E 820
E 830
E 840
E 850
E 860
E 870
E 880
E 890
E 900
E 910
E 920
E 930
E 940
E 950
E 960
E 970
E 980
E 990
El 000
£1010
E1020
El 030
E1040
E1050
E1060
E1070
E1080
E1090
E1100
E1110
£1120
E1130
-------
MODEL OP SOLUTE TRANSPORT IN GROUND WATER 57
FORTRAN IV program listing—Continued
IF (TMV.LT.TIMV) GO TO 120 E1140
LIH—1 E1150
60 TO 130 E1160
120 TIHV-TNV E1170
LIM«1 ~ E1180
130 NTIMV«TIf1(N)/TIMV £1190
NMOV»NTIMV«1 E1200
WRITE (6/420) TIHV,NTI«V»NHOV £1210
TIKV«TIM(N)/NNOV E1220
WRITE (6/370) TIH(N) £1230
WRITE (6/380) TINV £1240
C E12SO
IF (BETA.CO.0.0) 60 TO 200 £1260
C COMPUTE DISPERSION COEFFICIENTS E1280
ALPHA-BETA £1290
AINGMLPHA E1300
TRAN>DLTRAT*ALPHA £1310
XX2-XOEL*XDEl E1320
YY2»YDEL*YDEl E1330
XY2«4.0«XOEL<>YDEL E1340
00 1SO IX»2,NNX E1350
00 150 IY-2/NNY E1360
IF (THCK(IX/IY).EQ.O.O) GO TO 150 E1370
VXE»VXBDY(IX,IY) E1360
VYS»VYBOV(IX*IV) £1390
IF (THCK(IX»1/IY).EO.O.O) 60 TO 140 EUOO
C FORWARD COEFFICIENTS: X-DIRECTION £1410
WYE»(VY8DY(IX/IY-1)*VYBDV(IX + 1.IY-1)+VYS*VYBDY(1X*1/I V))/4.0 E1420
VXE2*VXE*VXE £1*30
VVE2»VYE*VYE E1440
VMGE»SORT(VXE2+VY£2) E14SO
IF (VHGE.LT.1.0E-20) GO TO 140 £1460
DALN»AING*VNGE £1470
DTRN*TRAN*VMGE £1480
VMGE2=VMGE«VMGE £1490
C XX COEFFICIENT E1500
DISP(IX,IV,1)»(DALN*VXE2«DTRN*VYE2)/(VMGE2*XX2) £1510
C XY COEFFICIENT-— E1520
DISP(IX,IY»3)«(DALN-DTRN)*VXE*VYE/(VMGE2«XY2) El 530
C FORWARD COEFFICIENTS: Y-DIRECT10N E1540
140 IF (THCK(IX,IV«1).EQ.O.O) 60 TO 150 £1550
VXS*(VXBDY(IX-1sIV)«VXE«VXBDY(lX-1«IY«1)+VXBDV(IX/IY*1))/400 E1560
VYS2*VYS*VYS E1570
VXS2>VXS*VXS E1580
VMGS«SORT(VXS2»VYS2) £1590
IF (VMGS.LT.1.0E-20) GO TO 150 £1600
DALN«ALNG*VNGS £1610
DTRN'TRAN*VMGS E1620
VMGS2«VMGS*VMGS £1630
C YY COEFFICIENT — - E1640
DISP(IX/1Y/2)«(DALN*VYS2+DTRN*VXS2)/(VMGS2*YV2) E1650
C YX COEFFICIENT E1660
DISP(IX,IV,4)c(DALN-DTRN)*VXS*VYS/(VMGS2*XY2) £1670
150 CONTINUE E1680
C ADJUST CROSS-PRODUCT TERNS FOR ZERO THICKNESS £1700
00 160 IX»2»NNX £1710
00 160 IY«2*NNY E1720
IF (THCK(IX«IY«1>.EQ.O.O.OR.THCK(IX+1,IY+1).EQ.O.O.OR.THCK(IX/IY-1 E1730
1).EQ.O.O.OR.THCK(IX + 1,1Y-1).EO.O.O) DISP(IX/1Y/3)«0.0 E1740
IF (THCK(IX+1,IV).Ee.O.O.OR.THCK(IX+1,IV«1).EQ.O.O.OR.THCK(IX-1,IV E17SO
-------
58
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
1).Ea.O.O.OR.THCK(IX-1*IY*1).EQ.O.O) DISP(IX*IY*4)»0.0
160 CONTINUE
C *********»***»*****»*************************»*l
C CHECK FOR STABILITY OF EXPLICIT METHOD
TIMDIS'0.0
00 170 IX»2»NNX
00 170 IY«2*NNY
TOCO«DISP(IX*IV*1)+DISP(IX*IY*2)
170 IF (TDC0.6T.TIMDIS) TIMOIS-TDCO
TIMOC«0.5/TIMDIS
WRITE (6*4*0) T1MOC
NT1MD«TIM(N)/TIMDC
NOISP«NTIMD+1
IF (NDISP.LE.NMOV) 60 TO 180
NMOV»NOISP
TIMV«TIM(N)/NMOV
LIM«0
180 WRITE (6*430) TIMV*NTIMD*NHOV
C ********««***************************»*i
C ADJUST OISP. EQUATION COEFFICIENTS FOR SATURATED THICKNESS
00 190 IX»2*NNX
DO 190 IY«2»NNY
BAVX«0.5»(THCK(IX*IY)*THCK(IX*1*1Y))
BAVY«0.5*(THCK(IX,IY)+THCK(IX*IV*1))
DISP(IX*IY*1)«DISP(IX»IY*1)*BAVX
D1SP(IX*IY*2)«OISP(1X*IY*2)*BAVY
DISP(IX*IY*3)«DISP(IX*IY*3)*BAVX
OISP(IX*IY*4)»DISP(IX*IY,4)*BAVY
*******************i
190
200
210
220
230
240
r***********************
2SO
260
270
280
290
IF (LIM) 210/220*230
WRITE (6/530)
GO TO 240
WRITE (6/540)
60 TO 240
WRITE (6*550)
****
--- PRINT DISPERSION EQUATION COEFFICIENTS
IF (NPNTD.EQ.O) 60 TO 300
IF (NPNTO.EQ.2) GO TO 250
IF (NPNTD.EQ.1.AND.N.E0.1) 60 TO 250
GO TO
WRITE
(OISP(IX*IY*1)*IX«1*NX)
300
(6*450)
WRITE (6*460)
00 260 IY«1*NY
WRITE (6*500)
WRITE (6*470)
00 270 IY"1*NY
WRITE (6*5CO) (OISP(IX*IY*2)*IX*1*NX)
WRITE (6*480)
DO 280 IY-1/NY
WRITE (6*500) (OISP(IX*IY*3)*IX*1*NX)
WRITE (6*490)
00 290 IY'1*NY
WRITE (6*500) (OISP(IX*IY*4)*IX«1*NX)
****** i
C
C
C
C
300 RETURN
*••***<
310 FORMAT (1H *19H TMV (MAX. INJ.) • *612.S/20H
112.5)
TIMV (CELDIS)
• *6
E1760
61770
E1780
E1790
E1800
E1810
E1820
E1830
E1840
E1850
E1860
E1870
E1880
E1890
E1900
E1910
E1920
E1930
E1940
E1950
E1960
E1970
E1980
E1990
E2000
E2010
E2020
E2030
E2040
E2050
E2060
E2070
E2080
E2090
£2100
E2110
E2120
E2130
E2140
E2150
E2160
E2170
E2180
E2190
E2200
E 2-210
E2220
E2230
E2240
E2250
E2260
E2270
E2280
E2290
E2300
E2310
E2320
E2330
E2340
E2350
E2360
E2370
-------
MODEL OP SOLUTE TRANSPORT IN GROUND WATER
59
320 FORMAT
330 FORMAT
340 FORMAT
350 FORMAT
360 FORMAT
370 FORMAT
380 FORMAT
390 FORMAT
400 FORMAT
410 FORMAT
420 FORMAT
430 FORMAT
440 FORMAT
450 FORMAT
1MGRID
460 FORMAT
470 FORMAT
480 FORMAT
490 FORMAT
SOO FORMAT
510 FORMAT
520 FORMAT
530 FORMAT
540 FORMAT
550 FORMAT
1ECT10N
FORTRAN IV program listing—Continued
(1H1/12HX VELOCITIES)
(1H ,25X,8HAT NODES/)
(1HO/25X/1JHON BOUNDARIES/)
(1H /10G12.3)
<1H1,12HY VELOCITIES)
(3H ,11HTIM » ,1612.5)
(3H ,11HTIMEVELO « ,1612.5)
<1H1,10X,29HSTAB1L1TY CRITERIA — M.O.C.//)
<1HC,8H VMAX « ,1PE9.2,5X,7HVMAY • /1PE9.2)
(1H ,8H VMXBD" ,1PE9.2,5X,7HVMYBD« ,1PE9.2)
(1HO/8H TIMV « ,1PE9.2,5X,8HNTIMV • ,\5»5X/7HNMOV * ,!5/>
<1HO/8H TIMV * »1PE9.2,5X,8HNTIMD • /15,5X/7MNMOV « »I5)
(3H /11HTIMEDISP • ,1E12.5>
<1H1,32HDISPERSION EQUATION COEFFICIENTS,10X,25H«<0-IJ>«
(2I4,2F10.1,2F10.7)
(8F10.7)
<1HO,10X,42HTHE LIMITING
<1HC»10X»40HTHE LIMITING
<1HO,10X,58HTHE LIMITING
RATE)
STABILITY
STABILITY
STABILITY
CRITERION
CRITERION
CRITERION
IS
IS
IS
CELDIS)
BETA)
MAXIMUM
INJ
10
c
c
END
SUBROUTINE MOVE
REAL *8TMRX,VPRM,H1*HR,HC,HK,WT,REC,RECH,T1M*AOPT,T1TLE
REAL *8XOEL,YDEL,S,AREA,SUMT,RHO,PARAM,TEST,TOL,PINT,HMIN,PYR
COMMON /PRMI/ NTIM,NPMP,NPNT,NITP,N,NX,NY,NP,NREC,INT,NNX,NNY,NUMO
1BS/NMOV,IMOV,NPMAX,ITMAX/NZCRIT»IPRNT,NPTPND,NPNTHV,NPNTVL,NPNTO,N
2PNCHV,NPDELC
COMMON /PRMK/ NODEID(20,20),NPCELL(20,20),LIMBO(500),IXOBS(5),IVOB
1S(5>
COMMON /HEDA/ THCK < 20, 20) ,P-ERM (20,20) ,TMWL( 5,50) ,TMOBS(50)# ANF CTR
COMMON /HEOB/ TMRX(20,20,2),VPRM(20,20),HI(20,20>,HR(20,20),MC(20,
120),HK(20,20),UT(20,20),REC(20,20),RECH(20,20),TIM(100),AOPT(20),T
2ITLE(10),XDEL,YOEL,S,AREA,SUMT,RHO,PARAM,TEST,TOL,PINT,HMIN,PYR
COMMON /XIMV/ DXINV,OYINV,ARINV,POR1NV
COMMON /CHMA/ PART(3,3200),CONC(20,20),TMCN(5,50),VX(20,20),VY(20,
120),CONINT(20,20),CNR£CH(20,20),POROS,SUMTCH,BETA,TIMV,STORM,STORM
2I,CMSIN,CMSOUT,FLMIN,FLMOT,SU«IO,CEH>IS,DLTR»T,CSTORK
COMMON /CHMC/ SUMC(20,20 ) ,VXBOY(20,20),VYBDY(20,20)
DIMENSION XNEW(A), YNEW(A), DIST(4)
WRITE (6,680) NMOV
SUMTCHBSUMT-TIM(N)
FlsO.249
IF (NPTPND.E0.5) F1«0.299
IF (NPTPND.EQ.9) F1-0.333
CONST1«TIMV*DXINV
CONST2'TIMV«DYINV
MOVE PARTICLES 'NMOV TIMES
DO 650 IMOV«1,NHOV
NPTM«NP
MOVE EACH PARTICLE
DO 590 IN«1,NP
IF (PART(1,1N).EQ.O.O) GO TO 590
KFLAG'O
i *i
COMPUTE OLD LOCATION
E2380
E2390
E2400
E2410
E2420
E2430
E2440
E2450
E2460
E2470
E2480
E2490
E2500
E2510
E2520
E2530
E2540
E2550
E2560
E2570
E2580
E2590
E2600
E2610
E2620
E2630
E2640-
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
-------
60
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
JFLAG«1
IF GO TO 30
IFLAG»-1
PART(2»IN)»-PART<2»IN)
30 VOLD*PART(2*IN)
IY«YOLD+0.5
IF (THCK(1X,IV).EQ.O.O) 60 TO 560
C ••••*••****•*»**•*•*»»*•«**»»*»***»•»«*****•••*•*•••»•»**••*»*•
C COMPUTE NEW LOCATION AND LOCATE CLOSEST NODE
C LOCATE NORTHWEST CORNER- —
1VX»XOLD
IVY-TOLD
IXE*IVX*1
IVS»IVY*1
C LOCATE QUADRANT, VEL. AT 4 CORNERS/ CHECK FOR BOUNDARIES—
CELDX»XOLD-IX
CELDY»VOLD-IY
IF (CELDX.EQ.O.O.ANO.CELDY.EQ.O.O) 60 TO 280
IF (CELDX.6E.O.O.OR.CELOY.6E.O.O) 60 TO 70
C PT. IN NH QUADRANT
VXNW«VXBDY
VXSU»VXBDY(IVX«IVS)
VXSE»VX(IXE*1VS)
VYNU*VYBDY(IVX,IVV)
VVNE"VYBDV(IXE»IVY)
VVSW»VV(IVX»IYS)
VYSE«VY(1XE,IYS)
IF (THCKdVX,IVY).£0.0.0) 60 TO SO
IF (RECdXE/IVY).EQ.0.0.AND.VPRHUXE,IVY).LT.0.09) 60 TO 40
VXNE-VXNW
40 IF (REC(IVX«IVS).EQ.0.0.AND.VPR«(IVX,IYS).LT.0.09) 60 TO SO
VYSU«VYNW
SO IF 60 TO 270
VYSE-VYNE
GO TO 270
C
70 IF (CELOX.LE.O.O.OM.CELOY.6E.O.O) 60 TO 130
C PT. IN NE QUADRANT —
80 VXNU»VX(IVX»IVY)
VXNE«VXBDY(IVX,IVY)
VXSU«VX(IVX,IYS)
VXSE-VXBOY(IVX,IYS)
VYNH«VYBDY(IVX,IVY)
VYNE«VYBDY(IXE,IVY)
VYSW«VYUVX,IY$)
VYS6«VY(IXE,IYS)
IF (CELDJT.EQ.O.O) 60 TO 120
IF (THCK(1XE,IVV).EQ.O.O) 60 TO 100
IF (RECUVX,IVY).EQ.0.0.AND.VPRMUVX,IVY).LT.0.09) 60 TO 90
VXNU'VXNE
90 IF (REC(IXE»IYS).EO.0.0.AND.VPR«(IXE/IYS).LT.0.09) 60 TO 100
360
370
380
390
400
410
420
430
440
4SO
460
470
480
490
SOO
510
S20
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER 61
FORTRAN IV program lifting—Continued
VYSE-VYNE F 980
100 IF (REC(IVX,IYS>.EQ.0.0.AND.VPRM(IVX,IVS).LT.0.09) 60 TO 270 F 990
IF (THCK(IXE*IVS).EQ.O.O) GO TO 110 F1000
VXSU-VXSE - F1010
110 IF (THCKC1VX,IVY).£0.0.0) 60 TO 270 F1020
VYSU*VYNU F1030
60 TO 270 F1040
120 IF 60 TO 270 F1060
VYSW'VVNU F1070
60 TO 270 F1080
F1090
130 IF (CELOY.LE.O.O.OR.CELDX.GE.O.O) GO TO 190 F1100
PT. IN SW QUADRANT ~ F1110
140 VXNW«VXBDY(IVX,IVY) F1120
VXNE«VX.Efi.0.0.AND.VPRM.LT.0.09) 60 TO 160 F1240
VXSE'VXSW F1250
160 IF (REC(1XE,IVY).EO.0.0.AND.VPRMCIXE,IVY).LT.0.09) 60 TO 270 F1260
IF 60 TO 170 F1270
VXNE*VXNU F1280
170 IF (THCK(IXE»IYS>.EQ.O.O) 60 TO 270 F1290
VYNE'VYSE F1300
GO TO 270 F1310
180 IF (RECUXE/1VY).EO.0.0.AND.VPRMUXE,IVY).LE.0.09) GO TO 270 F1320
IF .Ee.O.O.AND.VPRMUVX,IVY).lT.0.09> 60 TO 270 F1540
IF (THCK(IXE«IVV).EQ.O.O) 60 TO 230 F15SO
VXNW-VXNE F1560
230 If (THCK(IVXtirS).EO.O.O) 60 TO 270 F1570
VYNU-VYSU F1580
60 TO 270 F1S90
-------
62 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program toting—Continued
240 IF (RECUVX,IVY).EO.0.0.AND.VPRMUVX,IVY) .LE.0.09) GO TO 270 F1600
IF (THCK(IXE/IVY).EO.O.O) 60 TO 270 F1610
VXNW'VXNE F1620
60 TO 270 F1630
2SO IF (RECUVX/IVY).EO.0.0.AND.VPRMIVX,IVY).LE.0.09) GO TO 270 F1640
IF (THCK(IVX,IYS>.EO.0.0) 60 TO 270 F16SO
VYNW-VYSW F1660
60 TO 270 F1670
C F1680
260 IF (CELDX.EQ.0.0.AND.CELOV.LT.0.0) 60 TO 80 F1690
IF (CELDX.LT.0.0.AND.CELDY.EO.0.0) GO TO 140 M700
IF (CELDX.6T.0.0.AND.CELDY.EQ.0.0) 60 TO 200 F1710
IF (CELOX.EQ.0.0.AND.CELDY.GT.0.0) 60 TO 200 F1720
WRITE (6*690) IN/IXsIV F1730
270 CONTINUE F1740
C BILINEAR INTERPOLATION F1760
CELXDsXOLO-IVX F1770
CELOXH«AMOO.EQ.0.0) VXN«VXNW*VXNE F1840
VXS«VXSW*(1.0-CELOX)*VXSE«CELDX F1850
IF (THCK(IVX,IYS).EO.0.0.OR.THCK( IXE,IVS).EQ.0.0) VXS«VXSW*VXSE F1860
XVEL«VXN*(1.0-CELOY)*VXS*CELDY F1870
IF (THCKUVX/IVY). EQ.0.0. AND. THCK(IXE/IVY). EQ.0.0) XVEL«VXS F1880
IF (THCKUVX/1YS).EQ.0.0.AND.THCKUXE/IYS).EQ.0.0) XVEL-VXN F1890
C Y VELOCITY F1900
CELDYH«AMOD F2020
YVEL«VY(IX,IY) F2030
290 DISTX«XVEL*CONST1 F2040
DISTY»YVEL*CONST2 F2050
C BOUNDARY CONDITIONS F2070
TEMPX-XOLO+OISTX F2080
T£MPY»YOLD*DISTY F2090
INX«TEHPX*0.5 F2100
INY*TE«PY*0.5 F2110
IF (THCK(INX/INY).GT.O.O> GO TO 330 F2120
( A*************************************************************** F2130
C X BOUNDARY F2140
IF (THCK(INX,IY).EO.0.0) GO TO 300 F2150
PART(1/IN)«TEMPX F2160
GO TO 310 F2170
300 BEYON-TERPX-1X F2180
IF (BEVON.LT.0.0) BEYON«BEYON+0.5 F2190
IF (8EVON.GT.O.O) BEYON«6EYON-0.5 F2200
PARTd#IN>«TEMPX-2.0*BEYOM F2210
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
68
310
320
330
340
FORTRAN IV program listing—Continued
INX«PART(1,1N)*0.5
TEMPX=PART(1/IN)
**************************************************<
Y BOUNDARY
IF 60 TO 330
PART(2»IN)«TEMPY
GO TO 340
*********<
BEYONsTEMPY-IY
IF (BEYON.LT.0.0) BEYON«BEYON*0.5
IF (BEYON.GT.0.0) BEYON«BEYON-0.5
PART(2,IN)»TEMPY-2.0«BEYON
INY«PART(2*IN>+0.5
TEMPY«PART<2/IN>
GO TO 340
PARTd ,IN)«TEMPX
PART(2»IN)«TEMPY
CONTINUE
****** *********************************** 1
SUM CONCENTRATIONS AND COUNT PARTICLES
SUNC*1 .
C
c
****** 1
I ****** 1
AT OLD LOCATION—>-
CHECK FOR CHANGE IN CELL LOCATION
IF UX.EQ.INX.AND.IY.EO.INY) GO TO 580
C CHECK FOR CONST.-HEAD BDY. OR SOURCE
IF (REC(IX/IY).LT.O.O) GO TO 350
IF (REC(1X/IY).GT.O.O) GO TO 360
IF (VPRH< IX,1Y).LT.0.09) GO TO 540
IF .LT.HK(IX,IY>> GO TO 360
GO TO 540
C CREATE NEW PARTICLES AT BOUNDARIES
350 IF (IFLAG.GT.O) GO TO 550
KFLAG-1
360 DO 370 IL«1,500
IF (LIMBO(IL).EO.O) GO TO 370
IP'LIMBOdL)
IF (IP.LT.IN) GO TO 380
370 CONTINUE
C GENERATE NEW PARTICLE
IF (NPTH.EO.NPMAX) GO TO 600
NPTM«NPTH+1
IP-NPTM
GO TO 390
380 LIKBOUD-O
C
390 IF (KFLAG.EQ.O) GO TO 520
IF .EQ.O.O.OR.THCK.EQ.O.O.OR.THCK GO TO 520
IF .EO.O.O.OR.THCK.EQ.O.O) GO TO 520
C IF CENTER SOURCE
IF (JFLAG.LT.O) GO TO 500
JJ«4
AN-TENPY-YOLD
AD'TEMPX-XOLD
DISTMV»SQRT((AD*AD)*(AN*AN))
IF (AD.EO.0.0) GO TO 410
SLOPE-AN/AD
F2220
F2230
F2240
F2250
F2260
F2270
F2280
F2290
F2300
F2310
F2320
F2330
F234Q
F2350
F2360
F2370
F2380
F2390
F2400
F2410
F2420
F2430
F2440
F2450
F2460
F2470
F2480
F2490
F2500
F2510
F2520
F2530
F2540
F2550
F2560
F2570
F2580
F2590
F2600
F2610
F2620
F2630
F2640
F26SO
F2660
F2670
F2680
F2690
F2700
F2710
F2720
F2730
F2740
F2750
F2760
F2770
F2780
F2790
F2800
F2810
F2820
F2830
-------
64
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
NEW COORDINATES AND VERIFY
420
FORTRAN IV program listing—Continued
BI«VOLD-SLOPE*XOLO
XC1-IX-F1
XC2»IX*F1
YC1-IY-F1
YC2»IY*F1
COMPUTE
DO 400 IK»1»4
YNEW(1K)«0.0
XNEU(IK)«0.0
400 DIST(IK)«0.0
VNEUd )» (SLOPE*XC1>*BI
XNEVd)*XC1
VNEU(2>*(SLOPE»XC2>«8I
XNEW(2)»XC2
IF (SLOPE.EO.0.0> 60 TO
YNEW<3)«YC1
XNEU(3)*(VC1-BI)/SLOPE
YNEU(4)«YC2
XNEW<4)«/SLOPE
60 TO 430
410 YNEW(1)*1Y-F1
XNEW(1)=XOLD
YNEW<2)«1Y-»F1
XNEW<2)»XOLD
420 JJ«2
430 DO 440 II«1,JJ
440 DIST**2«(VNEW-TE»1PY)**2>*1.00001
IACOO
DISTCK-2.0
DO 460 IG»1,JJ
IF (DIST(1G).GE.D1STHV.AND.D1STUG>.IT.DISTCK> GO TO 450
60 TO 460
IXC«XNEW*0.50
IYC«YNEWdG>+0.50
IF (IXC.NE.IX.OR.IYC.NE.IY) GO TO 460
I»CC«I6
DISTCK-OISTdG)
CONTINUE
IF (IACC.LT.1.0R.IACC.6T.4) GO TO S10
(XNEW(IACC).EQ.XC1.0R.XNEU(IACC).EO.XC2) 60 TO 470
(YNEU 60 TO 480
TO 510
VNEU(IACC)«YC1
YNEW(IACC)«YC2
C
C
450
460
470
480
490
500
510
520
IF
IF
GO
IF
IF
GO
IF
IF
(YNEW(IACC).LT.VCI)
(VNEU(IACC).6T.YC2)
TO 490
(XNEUdACO.CT.XC1)
(XNEW(IACC).GT.XC2)
PARTd ,IP)«XNEW(IACC)
PART(2»1P>«YNEW(1ACC)
GO TO 530
PART(1,IP)«-IX
PART(2»IP)»IY
60 TO 530
PARTd »IP)«XOLD
PART(2,IP)-YOLO
60 TO 530
IF EDGE SOURCE OR
— X POSITION
OLX-INX-IX
PARTd,IP)*TEMPX-DLX
V POSITION
DLY-INY-lt
XNEW(IACC)»XC1
XNEW(IACC)"XC2
SINK
F2840
F28SO
F2860
F2870
F2880
F2890
F2900
F2910
F2920
F2930
F2940
F29SO
F2960
F2970
F2980
F2990
F3000
F3010
F3020
F3030
F3040
F3050
F3060
F3070
F3080
F3090
F3100
F3110
F3120
F3130
F3140
F3150
F3160
F3170
F3180
F3190
F3200
F3210
F3220
F3230
F3240
F3250
F3260
F3270
F3280
F3290
F3300
F3310
F3320
F3330
F3340
F3350
F3360
F3370
F3380
F3390
F3400
F3410
F3420
F3430
F3440
F3450
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER 65
FORTRAN IV program listing—Continued
PART(2*1P)»TEMPY-DLY F3460
IF (KFLA6.6T.O) 60 TO 530 F3470
C IF SINK F3480
SUMC(IX*IY)>SUMC(IX,1V)«CONC(IX,IV) _ F3490
NPCELL (IX*1Y»NPCELL(IX*IY>*1 F3500
C F3510
530 PART(2»IP)«-PART(2»IP) F3520
PART<3*IP>»CONCUX*IY> F3S30
IF (REC(IX*IV).EQ.O.O) 60 TO 540 F3540
C •*«»•*»••***••*•»»»•••*»***»*»*******•••*••••*•*»»••««*••••»•••• F3550
C CHECK FOR DISCHARGE BOUNDARY AT NEW LOCATION F3S60
540 IfLAG-1.0 F3570
550 IF .LT.HKC INX*1 NY)> 60 TO 56 F3580
10 F3S90
IF (REC(INX'INY).GT.O.O) 60 TO 560 F3600
60 TO 590 F3610
C PUT PT. IN LIMBO F3630
560 PARTU »IN>«0.0 F3640
PART(2,IN)»0.0 F3650
PART(3*IN>«0.0 F3660
DO 570 1D»1*500 F3670
IF (LIMBO(1D).6T.O) 60 TO 570 F3680
LIMBO(ID)*IN F3690
60 TO 590 F3700
570 CONTINUE F3710
C F3720
580 IF (IFLAG.LT.O) PART<2*IN)"-TEMPY F3730
IF (JFLAG.LT.O) PART(1,IN)»-TEMPX F3740
590 CONTINUE F37SO
C END OF LOOP F3760
C «•••»•*•••»•••»*•»*•••**»»»»«**»*•*»***»•»*»••»•»*••»••****•«•*• F 3770
60 TO 620 F3780
C RESTART MOVE IF PT. LIMIT EXCEEDED F3790
600 WRITE (6*700) IMOV*IN F3800
TEST*100.0 F3810
CALL 6ENPT F3820
DO 610 IX»1*NX F3830
DO 610 IY«1,NY F3840
SUMC(IX*IY)«0.0 F38SO
610 NPCELL (IX*m«0 F3860
TEST'0.0 F3870
60 TO 10 F3880
620 SUMTCH*SUMTCH«TIHV F3900
C ADJUST NUMBER OF PARTICLES F3910
NP'NPTM F3920
WRITE (6*670) NP*IHOV F3930
CALL CNCON F3950
C STORE DBS. WELL DATA FOR STEADY FLOW PROBLEMS F3970
IF (S.6T.O.O) 60 TO 640 F3980
IF (NUMOBS.LE.O) 60 TO 640 F3990
J«MOD(IMOV*50) F4000
IF (J.EQ.O) J-50 F4010
TMOBS(J)*SUNTCH F4020
00 630 I-1*NUMOBS F4030
TMWL(I»J)>HK(IXOBS(I)*IVOBS(I)> F4040
630 TNCN(I*J)'CONC(IXOBS(I)*IYOBS(I)) F4050
C PRINT CHEMICAL OUTPUT F4060
640 IF (IMOV.6E.NMOV) 60 TO 660 F4070
-------
66 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
650 IF .EQ.O.OR.MOO(IMOV,50).EO.O> CALL CHMOT F4080
660 RETURN F4100
C **•***»*•*•«*******•*»**»**•****»*»•*»»»»»**•**•*»»***»••*•»«*•* F4110
C F4120
C F4130
C F4140
670 FORMAT <1HC/2X,2HNP/7X/2H* ,8X, 14,10X,11H1MOV • /8X,!4) F4150
680 FORMAT (1HO»10X,61HNO. OF PARTICLE MOVES REQUIRED TO COMPLETE THIS F4160
1 TIME STEP « ,I4//> F4170
690 FORMAT (1HO/5X/53H**• WARNING • •* QUADRANT NOT LOCATED FOR PT. F4180
1 NO. *I5,11H , IN CELL »2IO F4190
700 FORMAT (1HO/5X/17H *** NOTE ***,10X,23HNPTM.EQ.NPMAX 1MOV« F4200
1,I4,5X,8HPT. NO.=,I4,5X,10HCALL GENPT/) F4210
END F4220-
SUBROUTINE CNCON G 10
REAL *8TMRX,VPRM,HI,HR,HC/Hr>WT,REC»RECH,TIM,AOPT,TITLE G 20
REAL *8XDEL,YDEL»S,AREA,SUMT,RHO,PARAM,TEST,TOL,PINT,HMIN/PYR G 30
REAL *8FLW G 40
COMMON /PRMI/ NTIM,NPMP,NPNT,NITP,N,NX,NY,NP,NREC,INT,NNX,NNY,NUMO G SO
1BS,NMOV,IMOV,NPMAX,ITMAX,N2CR1T,IPRNT,NPTPND,NPNTMV,NPNTVL,NPNTD/N G 60
2PNCHV,NPDELC G 70
COMMON /PRMK/ NODE I 0(20,20),NPCELL(20,20),LIMBO<500),IXOBS(5),IY06 G 80
1S(5) G 90
COMMON /HEDA/ THCK(20,20)/PERM(20,20),TMWL(5,50),TMOBS(50),ANFCTR G 100
COMMON /HEDB/ TMR X(20,20/2),VPRM(20,20)/HI(20,20),HR(20,20),HC(20, G 110
120)/HK(20/20)/WT(20,20),REC(20,20),RECH(20,20),TIH(100),AOPT(20)/T G 120
2ITLE(10),XOEL,YDEL,S,AREA/SUMT/RHO,PARAM,TEST,TOL,PINT,HMIN,PYR G 130
COMMON /XIKV/ OXINV/OYINV/ARINV,PORINV G 140
COMMON /CHHA/ PART(3/3200)/CONC(20,20),THCN(5/50)/VX(20,20),VY(20, G 150
120),CONINT(20,20),CNRECH(20,20),POROS,SUMTCH,BETA,T1MV/STORM,STORM G 160
2I/CMSIN/CMSOUT/FLMIN/FLHOT/SUMIO/CELDIS/OLTRAT/CSTORM G 170
COMMON /DIFUS/ DISP(20,20/4) G 180
COMMON /CHMC/ SUMC(20/20)/VXBDY(20/20)/VYBDY(20/20) G 190
DIMENSION CNCNCC20/20)/ CNOLD(20,20) G 200
ITEST'O G 220
DO 10 IXM/NX G 230
DO 10 IY=1,NY G 240
CNOLO( IX,IY)«CONC(IX/IY) G 250
10 CNCNC(1X*IY)*0.0 G 260
APC«0.0 G 270
N2ERO«0 G 280
TVA*AREA*TIMV G 290
ARPOR«AREA*POROS G 300
C •••»*••••••*»•**»*•***•••»••••**»•••**••••**•****••••••******** G 310
C CONC. CHANGE fOR 0.5*TIHV DUE TO: G 320
C RECHARGE* PUMPING, LEAKAGE, DIVERGENCE OF VELOCITY... G 330
CONST»0.5*TIMV G 340
20 DO 60 IX=1/NX G 350
DO 60 IY»1,NY G 360
IF (THCK(IX,IY>.EQ.O.O) GO TO 60 G 370
EQFCT1«CONST/THCK(IX,IY) G 380
EQFCT2«EQFCT1/POROS G 390
C1«CONC(1X,IY) G 400
CLKCN*0.0 G 410
SLEAK'(HK(IX,IY)-UT(IX,IY»*VPRM(IX,IY) G 420
IF (SLEAK..LT.O.O) C LKCN = CNREC H ( I X ,1 Y) G 430
IF (SLEAK.GT.0.0) CLKCN-C1 G 440
CNREC-C1 G 450
RATE'RECd X/I Y)*ARINV 6 460
IF (RATE.LT.0.0) CNREC«CNRECH(I X,IY) G 470
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
67
FORTRAN IV program litting— Continued
DIV«RATE+SLEAK«RECH(IX/IV)
IF (S.EQ.0.0) 60 TO 30
DERH«-HR(IX/IY)>/TIM(N)
DIVsDIV*S*DERH
IF (S.LT. 0.005) GO TO 30
...NOTE: ABOVE STATEMENT ASSUMES THAT S«0.005 SEPARATES CONFINED
FROM UNCONFINEO CONDITIONS; THIS CRITERION SHOULD BE
CHANGED IF FIELD CONDITIONS ARE DIFFERENT.
DELC«EaFCT2*(C1«(DIV-POROS*OERH)-RATE*CNREC-SLEAK*CLKCN-RECH(IX/IV
1>*CNRECH(IX/IY»
GO TO 40
30 DELC«E«FCT2*(C1*DIV-RATE*CNREC-SLEAK*CLKCN-RECH(IX/IY)*CNRECH(IX/I
40
CNCNC(IX/1Y)«CNCNC(1X/IY)*DELC
--- CONC. CHANGE DUE TO DISPERSION FOR 0.5*TIMV ---
-—DISPERSION WITH TENSOR COEFFICIENTS"-
IF (BETA. EQ. 0.0) GO TO 50
Xl«DISP(IX/IY/1)*(CONC(IX«1/IY)-C1)
X2«DISP(IX-1/IY/1)*(CONC(IX-1/IY)-C1)
Y1*DISP
XX1«D1SP-CONC(IX-1/IY)-C
10NCUX-1/1Y-1))
50 CNCNC(IX/IY)«CNCNC(IX/IY)*EOFCT1*
IF (APC.GT.0.0) GO TO 80
IF (REC(IX/IY).NE.O.O.OR.VPRM(1X/IY).GT.0.09) GO TO 90
NZERO-NZERO+1
GO TO 90
CONC(IX,IY)«SUMC(IX,IY)/APC
CONTINUE
--- CHECK NUMBER OF CELLS VOID OF PTS. ---
IF (N2ERO.GT.O) URITE (6/290) NZEROsIMOV
IF (NZERO.LE.NZCRIT) GO TO 20
TEST«99.0
URITE (6/3CO)
WRITE (6/320)
DO 100 IY«1/NY
WRITE (6/330) (NPCELL(IX/IY)/IX-1/NX)
GO TO 20
--- CHANGE CONCENTRATIONS AT NODES ---
DO 130 IX-1/NX
DO 130 IY*1/NY
IF (THCKUX/m.EQ.O.O) GO TO 120
CONC(IX/IV)'CONC(IX/IV)+CNCNC(IX/IY)
6
6
G
G
480
490
SOO
510
G 520
G 530
G 540
G 550
G 560
G 570
G 580
G 590
G 600
G 610
G 620
G 630
G 640
G 650
6 660
G 670
G 680
G 690
G 700
G 710
6 720
G 730
G 740
G 750
G 760
G 770
G 780
G 790
6 800
G 810
G 820
830
840
850
G 860
G 870
G 880
6 890
G 900
6 910
6 920
G 930
6 940
G 950
G 960
970
980
990
G1000
G1010
61020
61030
61040
61050
61060
61070
61080
G1090
6
6
6
6
6
6
-------
68
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program lifting—Continued
120
130
C
c
no
ISO
160
170
180
c
c
190
200
210
220
230
C
C
240
250
260
270
r••*»*****•*»»»•«**•***•
NPCELL(IX*IY)*0
SUMC(IX*IY)«0.0
IF (CONC(IX*IY).LE.O.O) 60 TO 130
CNCPCT-CNCNC(IX*IY)/CONC(IX*IY)
SUMC(IX*IV)>CNCPCT
60 TO 130
IF (CONC(IX,IY).GT.O.O) WRITE (6*310) I X*IY*CONC(IX*IV)
CONC(IX/IY)«0.0
CONTINUE
**•»*•*•»!
CHAN6E CONCENTRATION OF PARTICLES
00 180 IN«1*NP
IF (PART(1*IN).EO.O.O) GO TO 180
1NX«A8S(PART(1*IN)>*0.5
INY*A8S(PART(2*IN))*0.5
UPDATE CONC. OF PTS. IN SINK/SOURCE CELLS
IF (REC(INX*INV).NE.O.O) GO TO 140
IF (VPRM(INX*INY).LE.0.09) 60 TO 150
PART(3*IN)*CONCUNX*INV)
60 TO 180
IF (CNCNC(1NX*INY).LT.O.O) 60 TO 170
PART(3*IN)*PART(3*IN>+CNCNC(INX*INY>
60 TO 180
IF (CONC(INX*INY).LE.O.O) 60 TO 160
IF (SUMC(INX*INY).LT.-1.0) 60 TO 160
PART(3*IN)*PART(3*IN)«PART(3*IN)*SUMC(INX*INV)
CONTINUE
WRITE (6*280) TIM(N)*T1MV*SUMTCH
•»•******»*••••**•**»**»»*»»•••*••**»«**»*•*•*•••»»•**••*•*•••••
COMPUTE MASS BALANCE FOR SOLUTE
CSTORM«0.0
STORM'0.0
00 270 1X«1/NX
00 270 IY«1/NY
IF (THCK(IX*IY).EO.O.O) GO TO 270
SUMC(IX*IV)*0.0
COMPUTE MASS OF SOLUTE IN STORAGE
STORM«STORH + CONe) 200*210*190
CMSOUT»CMSOUT+REC(IX*IY)*CNOLO(IX,IY)*TIMV
GO TO 210
CMSIN'CMSIN*REC(IX*IY)*CNRECH(IX*IV)*TIMV
IF (RECH(IX*IY)) 230*240*220
CMSOUT>CMSOUT+RECH(IX*IV)*CNOLD(IX*IY)*TVA
GO TO 240
CHSIN»CMSIN«RECH(1X*IY)*CNRECH(IX*IV)*TVA
**»•••••*•»»»»«»»•**•••**»•**•••**•***•*•*•.
—-ACCOUNT FOR BOUNDARY FLOW
IF (VPRM(IX*IY).EO.O.O) GO TO 270
FLW»VPRH(IX*IV)*(WT(IX*IV)-HK(IX*IV»
IF (FLW.6T.O.O) 60 TO 250
IF (FLU.LT.0.0) GO TO 260
60 TO 270
MASS IN BOUNDARY DURING TIME STEP
FLNIN«FLMIK«FLW*CNRECH(IX*IY)*TVA
GO TO 270
MASS OUT DURING TIME STEP
FLNOT»FLMOT+FLW*CNOLD(IX*IV)*TVA
CONTINUE
!•••••<
COMPUTE CHANGE IN MASS OF SOLUTE STORED
I DISCHARGED
61100
61110
G1120
61130
61140
61150
61160
61170
61180
61190
61200
61210
G1220
61230
61240
G1250
61 260
61270
G1280
61290
G1300
61310
61320
61 330
61340
61350
61 360
61370
61380
61390
61400
61410
61420
61430
G1440
G1450
61460
61470
61480
G1490
61 500
G1510
61520
61530
G1S40
G1550
G1S60
61570
G1S80
61590
61600
61610
G1620
61630
61640
61650
61660
G1670
61680
61690
G1700
61710
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
FORTRAN IV program listing—Continued
CSTORN-STORM-STORMI
SUMIO»FLM1N»FLMOT-CMSIN-CMSOUT
C
c
C
c
** I
I ••••••*•I
REGENERATE PARTICLES IF 'NZCRIT* EXCEEDED-
IF (TEST.6T.98.0) CALL GENPT
TEST-0.0
******i
RETURN
• *1612.5»10X*11HTIMV
i •***««*
* *1G12.5*10X*
CALL GENPT ••*/>
AT NODE • *2I4*4X,7HC
280 FORMAT (3H ,11HTIM(N>
19HSUMTCH « *G12.5)
290 FORMAT (1HO»5X*40HNUMBER OF CELLS WITH ZERO PARTICLES • *I4*5X*9
1HIMOV « *I4/>
300 FORMAT (1HO*5X*44H*** NZCRIT EXCEEDED
310 FORMAT (1H *5X* 37H***CONC.GT.O. AND*. THCK .E«. 0
10NC « *G10.4,4H •**)
320 FORMAT (1HO*2X*6HNPCELL/>
330 FORMAT (1H *4X*20I3)
END
SUBROUTINE OUTPT
REAL *8TMRX,VPRM,HI*HR,HC*HK,WT*REC»RECH*TIH»AOPT*TITLE
REAL *8XDEL*YDEL*S*AREA*SUMT*RHO*PARAM*TEST*TOL*PINT*HMIN,PVR
COMMON /PRMI/ NTIM*NPMP*NPNT*N1TP*N*NX*NY*NP*NREC*INT*NNX*NNY*NUMO
1BS*NMOV*IMOV*NPMAX»ITMAX*NZCRIT*IPRNT*NPTPND*NPNTMV*NPNTVL»NPNTO*N
2PNCHV/NPDELC
/PRMK/ NODEID(20*20)*NPCELL(20*20),LINBO(500)*IXOBS(5)»IYOB
COMMON
1S(S)
COMMON
COMMON
/HEDA/ THCK(20*20)/PERM(20*20>*TMHL<5*50)*TMOBS<50)»ANFCTR
/HEDB/ TMRX(20/20*2)»VPRM(20/20)»HI(20/20),HR(20/20)/HC(20<.
C
C
120),HK(20/20)/WT(20,20)/REC(20,20)/RECH(20,20)/TIM(100)*AOPT(20)/T
2ITLE(10)»XDEL*YDEL*S»AREA»SUMT»RHO»PARAM,TEST»TOL»PINT»HMIN»PtR
COMMON /BALM/ TOTLO
DIMENSION IHC20)
»**•*<
TIMD'SUMT/86400.
TIMYmSUMT/(86<.00.0*365.25)
PRINT HEAD VALUES
WRITE (6*120)
C
c
WRITE (6*130) N
WRITE (6*UO) SUMT
WRITE (6*150) TIMO
WRITE (6*160) TIMY
WRITE (6*170)
DO 10 1Y«1*NY
10 WRITE (6*180) (HK(IX*I
IF (N.EO.O) GO TO 110
Y),IX«1,NX)
•A*********************************************
- — PRINT HEAD MAP
WRITE (6*120)
WRITE (6*130) N
WRITE (6*140) SUMT
WRITE (6*150) TIND
WRITE (6*160) TIMY
WRITE (6*170)
00 30 IY«1,NY
DO 20 IX«1*NX
20 IH(IX)«HK(IX,IY)+0.5
30 WRITE (6*190) (IH(ID)*
ID»1*NX)
I****************************
G1720
G1730
61740
G17SO
G1760
G1770
61780
61790
61800
61810
61820
61830
61840
61850
61860
61870
61880
61890
61900
61910
61920
61930-
H 10
20
30
40
50
60
70
80
90
H 100
H 110
H 120
H 130
H 140
H 150
H 160
H 170
H 180
H 190
.H 200
H 210
H 220
H 230
H 240
H 250
H 260
H 270
H 280
H 290
H 300
H 310
H 320
H 330
H 340
H 350
H 360
H 370
H 380
H 390
H 400
-------
70
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program listing—Continued
40
50
60
70
80
90
100
COMPUTE WATER BALANCE AND DRAWDOWN
QSTR=0.0
PUMPsQ.O
TPUM«0.0
QINsO.O
OOUT=0.0
QNET*0.0
DELO«0.0
PCTERR=0.0
WRITE (6/290)
DO 80 IY»1/NY
DO 70 IX*1/NX
IHUX)=0.0
IF (THCK( IX/IY).EQ.0.0) GO TO 70
TPUM=REC(IX/IY)+RECH(IX/IY)«AREA+TPUM
IF (VPRM(IX/IY).EQ.0.0) GO TO 60
DELQ=VPRM(IX/IY)»AREA*(WT(1X/IY)-HK(1X/IY))
IF (DtLQ.GT.0.0) GO TO 40
QOUTsQOUT+DELQ
GO TO 50
QIN=QIN*DELQ
ONET«ONET»DELO
DDRWsHI(IX/lY)-HKUX/lY)
IH(IX>»DDRW+0.5
OSTR=OSTR*DDRW*AREA*S
CONTINUE
PRINT DRAWDOWN HAP
WRITE (6/300) (1H(IX)/IX«1/NX)
CONTINUE
PUMP«TPUM*SUMT
DELSs-aSTR/SUMT
ERRMB=PUMP-TOILQ-QSIR
DEN=PUMP+TOTLU
IF (ABS(DEN).EO.ABS(ERRMB)> JCK=1
IF (DEN.EQ.O.U) GO TO 100
IF (JCK.E0.1) GO TO 90
PCTERR=ERRH6*20G.O/DEN
GO TO 100
IF (QIN.EQ.0.0) GO TO 100
PCTERRs100.0*QNET/bIN
PRINT MASS BALANCE DATA FOR FLOW MODEL
WRITE (6/240)
PUMP
QSTR
TOTLU
E RRME
WRITE (6/280) PCTERR
Q1N/QOUT/QNET
TPUM
DELS
WRITE (6/280) PCTERR
WRITE
WRITE
WRITE
WRITE
(6/2SO)
(6/230)
(6/260)
(6/270)
IF (JCK.EQ.O)
WRITE (6/200)
WRITE (6/210)
WRITE (6/220)
IF (JCK.EQ.1)
110
RETURN
••••**i
i ******* t
i*****************
120 FORMAT
130 FORMAT
140 FORMAT
(1H1/23HHEAD DISTRIBUTION - ROW)
(1X/23HNUMBEK OF TIME STEPS • /1IS)
(8X/16HTIME(SECONOS) » /1G12.S)
H 410
H 420
H 430
H 440
H 4SO
H 460
H 470
H 480
H 490
H 500
H 510
H 520
H 530
H 540
H SSO
H 560
H 570
H 580
H 590
H 600
H 610
H 620
H 630
H 640
H 650
H 660
H 670
H 680
H 690
H 700
H 710
K 720
H 730
H 740
h 750
H 760
H 770
H 780
H 790
H 8UO
H 810
H 820
H 830
H 840
H 850
H 860
H 870
H 880
H 890
H 900
H 910
H 920
H 930
H 940
M 950
H 960
H 970
H 980
H 990
H1000
H1010
H1020
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
71
FORTRAN IV program listing—Continued
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
FORMAT (8X,16HTIME = /1E12.5)
FORMAT <8X,1oHTIME(YEARS) = /1E12.5)
FOKMAT <1H )
FORMAT (1HO/10F12.7/1CF12.7)
FORMAT (1HO/20I4)
FORMAT <1HG,2X,33HRATE MASS BALANCE -- (IN
1 /G12.5/10X/8HQOUT * /G12.5/10X/8HQNET «
FORMAT (1H /17X/8HTPUM * /G12.5)
(1H /17X/8HDELS * /G12.S/)
(4X/29HWATER RELEASE FROM STORAGE
C.F.S.) //10X/8HQIN
/G12.5/)
FORMAT
FORMAT (4X/29HWATER RELEASE FROM STORAGE * /1E12.5)
FORMAT (1HO,2X,23HCUMULATIVE MASS BALANCE//)
FORMAT (4X/29HCUMULATIVE NET PUMPAGE « /1E12.5)
FORMAT (4X/29HCUMULATIVE NET LEAK.AGE • /1E12.5)
FORMAT (1HO/7X/25HMASS BALANCE RESIDUAL * /G12.5)
FORMAT (1H /7X/25HERROR (AS PERCENT) * /G12.5/)
FORMAT (1H1/8HDRAWDOWN)
FORMAT OH /20I5)
END
SUBROUTINE CHMOT
REAL *8TMRX/VPRMrHI/HR/HC/HK/WT/REC,RECH,TIM,AOPT/TITLE
REAL •8XDEL/YDEL/S/AREA/SUMT/RHO/PARAM/TEST/TOL/PINT/HMIN/PYR
COMMON /PRMI/ NTIM/NPMP/NPNT/NITP/N/NX/NY/NP/NREC/INT/NNX/NNY/NUMO
1BS/NMOV/IMCV/NPMAX/1TMAX/NZCRIT/1PRNT/NPTPND/NPNTMV/NPNTVL/NPNTD/N
2PNCHV/NPDELC
COMMON /PRMK/ NODE ID(20/20)/NPCELL(20/20)/LIMBO(500>/IXOBS(5)/IYOB
1S(5)
COMMON /HE DA/ THCK(20/20 ) /PERM(20/20)/TMWL(5/50)/TMOBS(50)/ANFCTR
COMMON /HE OB/ THRX(20,20/2)/VPRM(20/20)/HI{20/20)/HR(20/20)/HC(20/
120)/HK(20/20)/WT(20/20)/REC(20/20)/RECH(20/20)/TIM(100)/AOPT(20)/T
2ITLE(10)/XDEL/YDEL/S/AREA/SUMT/RHO/PARAM/TEST/TOL/PINT/HMIN/PYR
COMMON /CHMA/ PART(3/3200)/CONC(20/20)/TMCN(5/50)/VX<20/20)/VY(20/
120)/CONlNT(20/20)/CNRECH(20/20)/POROS/SUMTCH/BETA/TIMV/STORM/STORM
2I/CMSIN/CMSOUT/FLMIN/FLMOT/SUMIO/CELDIS/DLTRAT/CSTORM
DIMENSION IC(20)
I
TMFY«86400. 0*365.25
TMYR»SUMT/TNFY
TCHD-SUMTCH/86400.0
TCHYR«SOMTCH/TMFY
IF (IPRNT.GT.O) GO TO 100
PRINT CONCENTRATIONS
WRITE (6,160)
WRITE (6/170) N
IF (N.GT.O) WRITE (6/180) TIM(N)
(6/190) SUMT
SUMTCH
TCHD
TMYR
TCHYR
I MOV
10
20
C
C
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
DO 20
DO 10
IC(IX)»CONC(IX/IY)*0.5
WRITE (6/240) (IC(IX)/IX*1/NX)
IF (N.EO.O) GO TO 150
IF (NPDELC.EO.O) 60 TO 50
PRINT CHANGES IN CONCENTRATION
WRITE (6/230)
(6/450)
(6/200)
(6/210)
(6/460)
(6/380)
(6/220)
IY-1/NY
IX-1/NX
i »********•»***'
H1030
HlOtO
H1050
H1060
H1070
H1080
H1090
H1100
H1110
H1120
H1130
H1140
H1150
H1160
H1170
H1180
H1190
H1200-
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
160
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
-------
72
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
FORTRAN IV program toting—Continued
C
C
C
C
(6*170)
(6,180)
(6/190)
(6/450)
(6,200)
(6/210)
(6/460)
(6/380)
(6/220)
IY»1/NY
IX«1/NX
N
TIM(N)
SUMT
SUMTCH
TCHO
TMYR
TCHYR
I MOV
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
00 40
00 30
CN6>CONC(IX/IY)-CONINT(IX/IY)
30 IC(IX)*CN6
40 WRITE (6/240) (1C( I X)/IX*1/NX)
>*»**•
PRINT MASS BALANCE DATA FOR SOLUTE
50 RESID«SU«iO-CSTORM
IF (SUMIO.EO.0.0) GO TO 60
RESID-SUM10-CSTORM
ERR1-RESI 0*200.0/(SUMIO+CSTORM)
60 IF (STORMI.EO.0.0) 60 TO 70
ERR3--100.0*RES10/(STORM1-SUMJO)
70 WRITE (6/220)
WRITE (6/2SO)
WRITE (6/220)
WRITE (6/260) FLMIN
WRITE (6/270) FLMOT
RECIN--CMSIN
RECOUT«-CMSOUT
WRITE (6/290) RECIN
WRITE (6/280) RECOUT
WRITE (6/300) SUMIO
WRITE (6/310) STORMI
WRITE (6/320) STORM
WRITE (6/330) CSTORM
IF (SUMIO.EQ.0.0) 60 TO 80
WRITE (6/340)
WRITE (6/3SO) RESIO
WRITE (6/360) ERR1
80 IF (STORMI.EO.0.0) 60 TO 90
WRITE (6/370)
WRITE (6/360) ERR3
A****************************************
PRINT HYOR06RAPHS AFTER 50 STEPS
90 IF (MODUMOV,50).EO.O.AND.S.£0.0.0)
IF (MOD(N/50).EQ.O.AND.S.6T.O.O) 60
60 TO 1SO
100 WRITE (6/390) TITLE
IF (NUMOBS.LE.O) 60 TO 150
WRITE (6/400) INT
IF (S.6T.O.O) WRITE (6/410)
IF (S.EO.0.0) WRITE (6/420)
TABULATE HVOR06RAPH OATA
M02«0
IF (S.6T.O.O) 60 TO 110
NTO-NMOV
IF (NNOV.6T.50) NTO*MOD(IMOV/SO)
60 TO 124)
110 NTO-NTIM
IF (NTIN.6T.SO) NTO»MOD(N/50>
120 IF (NTO.EO.O) MTO-50
00 140 J»1/NUMOBS
****••**••***»***•»**•
OR END OF SIMULATION
60 TO 100
TO 100
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
11000
11010
11020
11030
11040
11050
11060
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
73
FORTRAN IV program listing—Continued
130
no
150
TMYR-0.0
WRITE (6*430) J»IXOBS(J>,IYOBS•**•*
C
c
C
c
RETURN
****** I
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
1TION:)
350 FORMAT
360 FORMAT
370 FORMAT
>*»****(
(1H1/13HCONCENTRATION/)
(1X/23HNUMBER OF TIME STEPS > »115)
(8X/16HDELTA T • /1G12.5)
(8X,16HTIME(SECONDS) • ,1612.5)
(3X,21HCHEM.TIME(OAYS> • /1E12.5)
(8X,16HT1ME(YEARS) « /1E12.S)
(1H )
(1H1/23HCHANGE IN CONCENTRATION/)
(1HO/20I5)
(1H /21HCHEMICAL MASS BALANCE)
(8X/25HMASS IN BOUNDARIES /1E12.5)
(8X/25HMASS OUT BOUNDARIES /1E12.5)
(8X/25HMASS PUMPED OUT /1E12.5)
(8X/25HMASS PUMPED IN /1E12.5)
(8X/25HINFLOW MINUS OUTFLOW /1E12.5)
(8X/25H1NITIAL MASS STORED /1E12.S)
(8X/25HPRESENT MASS STORED /1E12.5)
(8X/25HCHANGE MASS STORED /U12.5)
(1H /5X/S3HCOMPARE RESIDUAL WITH NET FLUX
AND MASS ACCUMULA
(8X/25HMASS BALANCE RESIDUAL • /1E12.5)
(8X/25HERROR (AS PERCENT) • /1E12.5)
(1H /5X/55HCOMPARE INITIAL MASS STORED WITH
CHANGE IN MASS
COMPLETED • ,115)
ISTORED:)
380 FORMAT (1X/23H NO. MOVES
390 FORMAT (1H1/10A8//)
400 FORMAT (1HO/5X/65HTIME VERSUS HEAD AND CONCENTRATION AT SELECTED 0
1BSERVATION POINTS//1Sx/19HPUMPING PERIOD NO. »I4////)
410 FORMAT (1HO/16X,19HTRANSIENT SOLUTION////)
420 FORMAT (1HO/15X/21HSTEAOY-STATE SOLUTION////)
430 FORMAT (1HO/20X,22HOBS.WELL NO. X Y,17X/1HN,6X,40HHEAD (FT)
1 CONC.(MG/L) TIME (YEARS)//24X/I3/9X,\2/3X/IIII)
440 FORMAT (1H /58X,I 2/6X/F7.V8X/F7.1/8X,F7. 2)
450 FORMAT (1H /2X/21HCHEM.TIME(SECONDS) • /E12.S)
460 FORMAT (1H /2X/21HCHEM.TIME(YEARS) * /E12.5)
END
11070
11080
11090
11100
11110
11120
11130
11140
11150
11160
11170
11180
11190
11200
11210
11220
11230
11240
11250
11260
11270
11280
11290
11300
11310
11320
11330
11340
11350
11360
11370
11380
11390
11400
11410
11420
11430
11440
11450
11460
11470
11480
11490
11500
11510
11520
11530
11540
11550
11560-
-------
74
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Attachment II
Definition of Selected Program Variables
AAQ area of aquifer in model
ALNG BETA
ANFCTR anisotropy factor (ratio of T,, to Tu)
AOPT iteration parameters
AREA area of one cell in finite-difference grid
BETA longitudinal dispersivity of porous
medium
CELDIS maximum distance across one cell that
a particle is permitted to move in
one step (as fraction of width of
cell)
CLKCN concentration of leakage through con-
fining layer or streambed
CMSIN mass of solute recharged into aquifer
CMSOUT mass of solute discharged from aquifer
CNCNC change in concentration due to disper-
sion and sources
CNCPCT change in concentration as percentage
of concentration at node
CNOLD concentration at node at end of pre-
vious time increment
CNREC concentration of well withdrawal or
injection
CNRECH concentration in fluid source
CONG concentration in aquifer at node
CONINT concentration in aquifer at start of
simulation
Cl CONG at node (IX.IY)
DALN longitudinal dispersion coefficient
DDRW drawdown
DELQ volumetric rate of leakage across a
confining layer or streambed
DELS rate of change in ground-water storage
DERH change in head with respect to time
DISP dispersion equation coefficients
DISTX distance particle moves in ^-direction
during time increment
DISTY distance particle moves in y-direction
during time increment
DLTRAT ratio of transverse to longitudinal
dispersivity
DTRN transverse dispersion coefficient
FCTR multiplication or conversion factor
FLMIN solute mass entering modeled area
during time step
FLMOT solute mass leaving modeled area
during time step
GRDX hydraulic gradient in ^-direction
GRDY hydraulic gradient in y-direction
HC head from column computation
HI initiaLhead in aquifer
HK computed head at end of time step
HMIN minimum iteration parameter
HR head from row computation in sub-
routine ITERAT; elsewhere HR
represents head from previous time
step
IMOV particle movement step number
INT pumping period number
IPRNT print control index for hydrographs
ITMAX maximum permitted number of
iterations
IXOBS x-coordinate of observation point
IYOBS y-coordinate of observation point
KOUNT iteration number for ADIP
LIMBO array for temporary storage of
particles
N time step number
NCA number of aquifer nodes in model
NCODES number of node identification codes
NITP number of iteration parameters
NMOV number of particle movements (or time
increments) required to complete
time step
NODEID node identification code
NP total number of active particles in grid
NPCELL number of particles in a cell during
time increment
NPMAX maximum number of available particles
NPHP number of pumping periods or simu-
lation periods
NPNT number of time steps between printouts
NPTPND initial number of particles per node
NREC number of pumping wells
NTIM number of time steps
NUMOBS number of observation wells
NX number of nodes in x-direction
NY number of nodes in y-direction
NZCRIT maximum number of cells that can be
void of particles
NZERO number of cells that are void of
particles at the end of a time
increment .
PARAM iteration parameter for current
iteration
PART 1. x-coordinate of particle; 2. y-coordi-
nate of particle; 3. concentration of
particle. Also note that the signs of
coordinates are used as flags to store
information on original location of
particle.
PERM hydraulic conductivity (in LT1)
PINT pumping period in years
POROS effective porosity
PUMP cumulative net pumpage
PYR total duration of pumping period
(in seconds)
QNET net water flux (in LT ')
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
75
Definition of teleeted program variables—Continued
QSTR cumulative change in volume of water
in storage
REG point source or sink; negative for in-
jection, positive for withdrawal
(in L'T')
RECH diffuse recharge or discharge; negative
for recharge, positive for discharge
(in LT-1)
RN range in concentration between regen-
erated particle and adjacent node
having lower concentration
RP range in concentration between regen-
erated particle and adjacent node
having higher concentration
S storage coefficient (or specific yield)
SLEAK rate of leakage through confining
layer or streambed
STORM change in total solute mass in storage
(by summation)
STORMI initial mass of solute in storage
SUMC summation of concentrations of all
particles in a cell
SUMIO change in total solute mass in storage
(from inflows—outflows)
SUMT total elapsed time (in seconds)
SUMTCH cumulative elapsed time during
particle moves (in seconds)
THCK saturated thickness of aquifer
TIM length of specific time step
(in seconds)
TIMD elapsed time in days
TIMY elapsed time in years
TIMV length of time increment for particle
movement (in seconds)
TIMX time step multiplier for transient flow
problems
TINIT size of initial time step for transient
flow problems (in seconds)
TITLE problem description
TMCN computed concentrations at observation
points
TMOBS elapsed times for observation point
records
TMRX transmissivity coefficients (harmonic
means on cell boundaries; forward
values are stored)
TMWL computed heads at observation points
TOL convergence criteria (ADIP)
TOTLQ cumulative net leakage through con-
fining layer or streambed
TRAN transverse dispersivity of porous
medium
VMAX maximum value of VX
VMAY maximum value of VY
VMGE magnitude of velocity vector
VMXBD maximum value of VXBDY
VMYBD maximum value of VYBDY
VPRM initially used to read transmissivfty
values at nodes; then after line
B2270, VPRM equals leakance factor
for confining layer or streambed
(vertical hydraulic conductivity/
thickness). If VPRM^0.09, then the
program assumes that the node is a
constant-head boundary and is flag-
ged for subsequent special treat-
ment in calculating convective trans-
port.
VX velocity in x-direction at a node
VXBDY velocity in x-direction on a boundary
between nodes
VY velocity in y-direction at a node
VYBDY velocity in {/-direction on a boundary
between nodes
WT initial water-table or potentiometric
elevation, or constant head in
stream or source bed
XDEL grid spacing in x-direction
XOLD x-coordinate of particle at end of pre-
vious time increment
XVEL velocity of particle in x-direction
YDEL grid spacing in y-direction
YOLD ^-coordinate of particle at end of pre-
vious time increment
YVEL velocity of particle in y-direction
-------
76
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
Attachment III
Data Input Formats
Card Column
1 1-80
2 1-4
6- 8
9-12
13-16
17-20
21-24
26-28
29-32
33-36
Format
10A8
14
14
14
14
14
14
14
14
14
Variable
TITLE
NTIM
NPMP
NX —illy' &
Btffl&L
NY y<&++
NPMAX
NPNT
NITP
NUMOBS
ITMAX
Definition
Description of problem
Maximum number of time steps in «
pumping period (limit=100)*.
Number of pumping periods. Note
that if NPMP>1, then data set
jj * /i 10 must be completed.
1b($j~~5WD- Number of nodes in x direction
^ (limit=20)*.
(J Number of nodes in y direction
(limit=20)*.
Maximum number of particles
(limit=3200) *. (See eq 71.)
Time-step interval for printing
hydraulic and chemical output
data.
Number of iteration parameters
(usually 4^NITPs^7).
Number of observation points to be
specified in a following data set
(limit=6)*.
Maximum allowable number of it-
erations in ADIP (usually 100
37-40
41-44
45-48
49-62
63-66
67-60
61-64
66-68
14
14
14
14
14
14
14
14
NREC
NPTPND
NCODES
NPNTMV
NPNTVL
NPNTD
NPDELC
NPNCHV
Number of pumping or injection
wells to be specified in a following
data set
Initial number of particles per node
(optiems=4, 6, 8, 9).
Number of node identification codes
to be specified in a following data
set (limit=10)*.
Particle movement interval (IMOV)
for printing chemical output data.
(Specify 0 to print only at end of
time steps.)
Option for printing computed veloci-
ties (0=do not print; l=print for
first time step; 2=print for all
time steps).
Option for printing computed dis-
persion equation coefficients (op-
tion definition same as for
NPNTVL).
Option for printing computed
changes in concentration (0=do
not print; l=print).
Option to punch velocity data (op-
tion definition same as for
NPNTVL). When specified, pro-
gram will punch on unit 7 the
velocities at nodes.
Set footnote* at rad of UbU.
-------
MODEL OP SOLUTE TRANSPORT IN GROUND WATER
77
Data input formate—Continued
Card Column
8 1-6
6-10
11-15
16-20
21-26
26-30
81-55
36-40
41-46
46-60
61-66
66-60
Date Number
•et of eardi
Format
G5.0
G6.0
G6.0
G6.0
G6.0
G6.0
G6.0
G6.0
G6.0
G5.0
G6.0
G5.0
Format
Variable
PINT
TOL
POROS
BETA
S
TIMX
TINIT
XDEL
YDEL
DLTRAT
CELDIS
ANFCTR
Variable
Definition
Pumping period in years.
Convergence criteria in ADIP
(usually TOL^O.Ol).
Effective porosity.
Characteristic length, in feet
(=longitudinal dispersivity).
Storage coefficient (set 5=0 for
steady flow problems).
Time increment multiplier for trans-
ient flow problems. TIMX is dis-
regarded if 5=0 .
Size of initial time step in seconds.
TINIT is disregarded if 5=0.
Width of finite-difference cell in
x direction, in feet.
Width in finite-difference cell In
y direction, in feet.
Ratio of transverse to longitudinal
dispersivity.
Maximum cell distance per particle
move (value between 0 and 1.0).
Ratio of T,, to T...
Definition
1 Value of NUMOBS 212
(limit=5)*
2 Value of NREC
a. 1
b. Value of NY
(limit=20)*
a. 1
b. Value of NY
(limit=20)*
a. 1
b. Value of NY
(limit=20)*
a. 1
b. Value of NY
(limit=20)»
212,
2G8.2
IXOBS, IYOBS
IX, IY, REG, CNRECH
II, GlO.O INPUT, FCTR
20G4.1 VPRM
II, GlO.O INPUT, FCTR
20G3.0 THCK
II, GlO.O INPUT, FCTR
20G4.1 RECH
II, GlO.O INPUT, FCTR
2011 NODEID
x and y coordinates of observation
points. This data set is eliminated
if NUMOBS is specified as =0.
x and y coordinates of pumping (+)
or injection (—) wells, rate in
ft'/s, and if an injection well, the
concentration of injected water.
This data set is eliminated if
NREC=0.
Parameter card t for transmissivity.
Array for temporary storage of
transmissivity data, in ff/s. For
an anisotropic aquifer, read in
values of T,, and the program will
adjust for anisotropy by multi-
plying Tn by ANFCTR.
Parameter cardt for THCK.
Saturated thickness of aquifer, in
feet.
Parameter cardt for RECH.
Diffuse recharge (—) or discharge
(+),inft/s.
Parameter cardt for NODEID.
Node identification matrix (used to
define constant-head nodes or
other boundary conditions and
stresses).
8e* footnotes at end of table.
-------
78
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Data input formats—Continued
Data
get
Number
of cards
Format
Variable
Definition
Value of NCODES
(limit=10)»
I2.3G10.2, ICODE, FCTR1,
12 FCTR2, FCTR3,
OVERRD
10
a. 1
b. Value of NY
(limit=20)*
a. 1
b. Value of NY
(limit=20)*
II, G10.0 INPUT, FCTR
20G4.0 WT
II, G10.0
20G4.0
INPUT, FCTR
CONG
a. 1
II
ICHK
b. 1 10I4.3G5.0 NTIM, NPNT, NITP,
ITMAX, NREC,
NPNTMV, NPNTVL,
NPNTD, NPDELC,
NPNCHV, PINT, T1MX,
TINIT
c. Value of NREC 212, 2G8.2 IX, IY, REC, CNRECH
Instructions for using NODEID
array. When NODEID=ICODE,
program sets Ieakance=FCTRl,
CNRECH=FCTR2, and if
OVERRD is nonzero, RECH
=FCTR3. Set OVERRD=0 to
preserve values of RECH specified
in data set 5.
Parameter cardt for WT.
Initial water-table or potentiometric
elevation, or constant head in
stream or source bed, in feet.
Parameter cardt for CONG.
Initial concentration in aquifer.
This data set allows time step param-
eters, print options, and pump-
age data to be revised for each
pumping period of the simulation.
Data set 10 is only used if NPMP
>1. The sequence of cards in data
set 10 must be repeated (NPMP
—1) times (that is, data set 10
is required for each pumping
period after the first).
Parameter to check whether any re-
visions are desired. Set ICHK=1
if data are to be revised, and then
complete data set lOb and c. Set
ICHK=0 if data are not to be re-
vised for the next pumping period,
and skip rest of data set 10.
Thirteen parameters to be revised
for next pumping period; the
parameters were previously de-
nned in the description of data
cards 2 and 3. Only include this
card if ICHK=1 in previous part
a.
Revision of previously defined data
set 2. Include part c only if
ICHK=1 in previous part a and
if NREC>0 in previous part b.
• These HmiU can be modified if necessary by changing the corresponding array dimensions in the COMMON statements of the
program.
f The parameter card must be the first card of the Indicated data sets. It is used to specify whether the parameter is constant
and uniform, and can be defined by one value, or whether it varies in space and must be defined at each node. If INPUT = 0, the
data set has a constant value, which la defined by FCTR. If IN PUT =1, the data set la read from cards as described by part b.
Then FCTR is a multiplication factor for the values read In the data set
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
79
Attachment IV
Input Data for Test Problem 3
Card I
Card 2
Card3
Data Set 1 •
Data Set 2
Data Set 3
Data Set 4
Data Set 5
Data Set 6
TEST PROBLEM NO. 3 (STEADY FLOW, 1 WELL/ CONSTANT-HEAD BOUNDARIES)
1 1 9 103200 1 7 2 100 1 9 2 10 1 0 0
2.5.0001 0.30 100. 0.0 0.0 0.0 900. 900. 0.3 0.50 1.0
5 4
5 7
A 7 1.0
0 0.1
0 20.0
0 0.0
1 1.0
OOOOOOOOO
022111220
OOOOOOOOO
coooooooo
ooooooooo
ooooooooo
ooooooooo
ooooooooo
022222220
OOOOOOOOO
Data Set 7 •
Data Set 8
1 1.0
1 1.0
100. U
ii.O
0.0100.100.100.100.100.100.100. 0.0
0.0 75. 75. 75. 75. 75. 75. 75. 0.0
Data Set9 0 0.0
-------
80
TECHNIQUES OP WATER-RESOURCES INVESTIGATIONS
Attachment V
Selected Output for Test Problem 3
U.S.&.S. METHOD-OF-CHARACTERIST1CS MODEL FOR SOLUTE TRANSPORT IN GROUND WATER
TEST PROBLEM NO. 3 (STEADY FLOW, 1 WELL. CONSTANT-HEAD BOUNDARIES)
INPUT DATA
GRID DESCRIPTORS
NX (NUMBER OF COLUMNS) « 9
NY (NUMBER OF ROWS) a 10
XDEL (X-OISTANCE IN FEET) * 900.0
YDEL (Y-OISTANCE IN FEET) = 900.0
TIME PARAMETERS
NTIM (MAX. NO. OF TIME STEPS)
NPMP (NO. OF PUMPING PERIODS)
PINT (PUMPING PERIOD IN YEARS)
TIMX (TIME INCREMENT MULTIPLIER)
TINIT (INITIAL TIKE STEP IN SEC.)
HYDROLOGIC AND CHEMICAL PARAMETERS
S (STOWAGE COEFFICIENT) '
POROS (EFFECTIVE POROSITY) =
BETA (CHARACTERISTIC LENGTH) •
DLTRAT (KATIO OF TRANSVERSE TO
LONGITUDINAL 01SPERSIVITY) «
ANFC1K (RATIO OF T-YY TO T-XX) •
EXECUTION PARAMETERS
NITP (NO. OF ITERATION PARAMETERS)
TOL (CONVERGENCE CRITERIA - ADIP)
ITMAX (MAX.NO.OF ITERATIONS - ADIP)
CELDIS (MAX.CELL DISTANCE PER M3VE
OF PARTICLES - M.O.C.)
NPMAX (MAX. NO. OF PARTICLES)
NPTPND (NO. PARTICLES PER NODE)
PROGRAM OPTIONS
NPNT (TIME STEP INTERVAL FOR
COMPLETE PRINTOUT)
NPNTKV (MOVE INTERVAL FOR CHEM.
CONCENTRATION PRINTOUT)
NPNTVL (PRINT OPTION-VELOCITY
0«NO; 1«F1RST TIME STEP.'
2 = ALL T-IME STEPS)
NPNTD (PRINT OPTION-DJSP.COEF.
0«NO; 1»F1RST TIME STEP.'
2»ALL TIME STEPS)
NUMObS (NO. OF OBSERVATION WELLS
FOR HYDROGRAPH PRINTOUT)
NREC (NO. OF PUMPING WELLS)
NCODtS (FOR NODE IOENT.)
NPNCHV (PUNCH VELOCITIES)
NPDELC (PRINT OPT.-CONC. CHANGE)
1
1
2.50
0.00
0.
0.000000
0.3U
100.0
0.30
1.000000
7
0.0001
100
o.sou
3200
9
1
10
2
1
2
0
0
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
Selected output for test problem 8—Continued
STEADY-STATE FLOW
TIME INTERVAL (IN SEC) FOR SO'LUTE-TRANSPORT SIHULATION « 0.768944*06
LOCATION OF OBSERVATION WELLS
NO. X Y
81
5
5
LOCATION OF PUhPING WELLS
X Y RATEdN CFS) CONC.
4 7 1.00 0.0
AREA OF ONE CELL = 0.81004*06
X-Y SPACING:
900.00
90C.OO
TRANSnISSIVI
0.00 0.00
0.00 0.10
0.00 0.10
0.00 0.10
0.00 0.10
0.00 0.10
0.00 0.10
0.00 0.10
0.00 0.10
0.00 O.OU
TY MAP
0.00
0.10
0.10
0.11
0.10
0.10
0.10
0.10
0.10
o.cc
(FT«FT/SEC)
0.00 0.00 0.00
0.10 0.1C 0.10
0.10 0.10 0.10
0.10 0.10 0.10
(J.10 0.10 0.10
0.10 0.10 0.10
0.10 0.10 0.10
0.10 0.10 0.10
0.10 0.10 0.10
0.00 0.00 0.00
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
00
10
10
10
10
10
10
10
10
00
0
0
0
0
0
0
0
0
0
0
.00
.10
.10
.10
.10
.10
.10
.10
.10
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
AQUIFER
0
0
0
0
0
0
0
0
0
0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
THICKNESS
0.0
20.0
2U.O
20.0
20. U
20.0
20.0
20.0
20.0
0.0
0.0
20. C
20.0
20.0
20.0
20. U
20.0
20. C
20.0
0.0
(FT)
tl.C
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
0.0
0
20
20
20
20
20
20
20
20
0
.U
.0
.0
.0
.0
.0
.0
.0
.0
.0
0
20
20
20
20
20
20
20
20
0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
0.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
0.0
0.0
20.0
20.0
20.0
20.0
20. U
20.0
20.0
20.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-------
82
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Selected output for teat problem S—Continued
DIFFUSE RECHARGE AND
O.OOd+OU
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOa+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
DISCHARGE
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
(fT/SEC)
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.DOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+UO
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
O.OOd+00
3.30d+00
0.30d»00
3.30d+00
O.DOd+00
O.DDd+00
0.33d+00
0.30d+00
0.30d+00
0.30d+00
3.334+00
PERMEABILTY NAP (FT/SEC)
0.0000.0000.0000.0000.OCOO.0000.0000.0000.000
0.0000.0050.0050.0050.0050.0050.0050.0050.000
0.0000.OOSO.OOSO.00 SO.OOSO.OOSO.OOSO.OOSO.000
0.0000.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.000
0.0000.OOSO.OCSO.OOSO.OOSO.OOSO.OOSO.OOSO.000
0.0000.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.000
0.0000.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.OOSO.000
0.0000.OOSO.OOSO.00 SO.OOSO.OOSO.OOSO.DOS 0.000
0.0000.U050.0050.0050.0050.0050.0050.0050.000
0.0000.0000.0000.0000.UOOO.0000.0000.0000.000
NO. OF FINITE-DIFFERENCE CELLS IN AQUIFER * 56
AREA OF AQUIFER IN MODEL • O.*5360«+08 SO. FT.
NZCRIT
(MAX. NO. OF CELLS THAT CAN BE VOID OF
PARTICLES; IF EXCEEDED, PARTICLES ARE REGENERATED)
-------
MODEL OF SOLUTE TRANSPORT IN GROUND WATER
Selected output for tett problem S—Continued
NODE 1DENT1FICAT10N HAP
83
0
0
0
0
0
0
0
0
0
0
0
2
u
0
0
0
0
0
2
0
0
I
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
u
0
0
0
0
0
0
0
NO. OF NODE IDENT. COOES SPECIFIED * 2
THE FOLLOWING ASSIGNMENTS HAVE BEEN MADE:
CODE NO. LEAKANCE SOURCE CONC. RECHARGE
0.100e + U
0.100e*01
0.00
100.00
TICAI
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0
1
0
0
0
u
0
0
1
0
PERMEABILITY/TH1
.00 0.00 0.00 0.
.00 1.00 1.00 1.
.00 0.00 0.00 0.
.00 0.00 0.00 0.
.00 C.CC 0.00 0.
.00 0.00 0.00 0.
.00 0.00 0.00 0.
.00 0.00 0.00 0.
.00 1.00 1.00 1.
.00 0.00 0.00 0.
CKNESS
00 0.00
00 1.00
00 0.00
00 0.00
00 0.00
00 0.00
00 0.00
00 0.00
00 1.00
00 0.00
(FT/ (FT«SEC> )
0.00 0.00 0.00
1.00 1.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
1.00 1.00 0.00
0.00 0.00 0.00
WATER TABLE
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
100.
0.
0.
0.
0.
0.
0.
75.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-------
84
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Selected output for test problem 3—Continued
ITERATION PARAMETERS
0.2*67*00-01
O.A57299d-01
0.8*75390-01
.157080
.291125
.539560
1.00000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
o.coooco
0.000000
o.ooooco
o.oorrooo
0.000000
CONCENTRATION
NUMBER OF TIME STEPS
I IME< SECONDS)
CHEM.T1M£< SECONDS)
CHEM. TIME ( DAYS)
TIME< YEARS)
CHEM.T1M£( YEARS)
NO. MOVES C
0
0
Q
0
0
0
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
U. 00000
O.OOOOOe+00
O.OOOOOe+00
C.OOOOOe+00
O.OOOOOetOO
OMPLETEO
0
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
U
0
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Q
0
0
0
0
0
0
0
N • 1
NUMBER OF ITERATIONS * 20
-------
aeieetea output /or teit problem 3—Continued
HEAD DISTRIBUTION - ROU
NUMBER OF TIME STEPS * 1
TIHE(SECONDS) * 0.788944*08
TIME * 0.91313**03
TIME(TEARS) • 0.25000«*01
0.0000000 0.0000000
0.0000000 99.9999995
0.0000000 95.9387858
0.0000000 91.8816815
0.0000000 87.8530674
0.0000000 83.9382225
0.0000000 80.3627221
0.0000000 77.5265176
0.0000000 75.0000003
0.0000000 0.0000000
HEAD DISTRIBUTION - ROU
NUMBER OF TIME STEPS «
TIME(SECONOS) « 0
TIMECOATS) • 0
TIME(TEARS) • 0
000000
0 100 100 100 100 100
0 96 96 96 96 96
0 92 91 92 92 92
0 88 88 88 88 88
0 84 84 83 84 84
0 80 80 77 80 81
0 78 77 77 77 78
0 75 75 75 75 75
000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000033
99.9999995 99.9999995 99.9999995 99.9999995 99,9999995
95.9346978 95.9468712 95.9958792 96.0611455 96.1171357
91.8531641 91.8569301 91.9755221 92.1315893 92.2591335
87.7393101 87.6521342 87.9176617 88.2305223 88.4600393
83.5988909 83.0946482 83.8124811 84.4128118 84.774712?
79.6233998 77.3151005 79*8248158 80.8335448 81.2863911
77.2168501 76.7175099 77.3381095 77.8101323 78.0688953
75.0000003 75.0000002 75.0000003 75.0000003 75.0000034
0.0000000 0.0000000 0.0000000 0.0000000 0.0000033
1
.788944*08 »
.91313**03
.25000e*01
000
100 100 0
96 96 0
92 91 d
88 89 0
85 IS 0
81 81 0
78 78 0
75 75 0
000
0.0000000 0.0000000
99.9999995 0.0000000
96.1482887 0.0000000
92.3277521 0.0000000
88.5758019 0.0000000
84.9396259 0.0000000
81.4683757 0.0000000
78.1790838 0.0000000
75.0000004 0.0000000
0.0000000 0.0000000
i
O
M
f
o
axmos >•
H
»
VNSPORT IN G!
*v
O
55
O
S3
M
g.
-------
Selected output for test problem 3—Continued
oo
DRAWDOWN
0
0
0
0
U
0
0
0
0
0
0
0
-95
-91
-87
-83
-79
-77
0
0
0
0
-95
-91
-87
-83
-79
-76
0
C
0
0
-95
-91
-87
-82
-76
-76
0
0
0
0
-95
-91
-87
-83
-79
-76
0
0
0
0
-95
-91
-87
-83
-80
-77
0
0
0
0
-95
-91
-87
-84
-80
-77
0
0
U
0
-95
-91
-88
-84
-80
-77
0
0
0
0
0
0
0
0
0
0
0
0
CUMULATIVE MASS BALANCE
CUMULATIVE NET PUMPAGE « 0.78894e + li8
WATER RELEASE FROM STORAGE « O.OOOOOe+00
CUMULATIVE NET LEAKAGE ' 0.78895e»08
MASS BALANCE RESIDUAL * -767.00
ERROR (AS PERCENT) * -0.97219e-03
H
W
O
&
a
m
CO
RATE MASS BALANCE — (IN C.F.S.)
OIN « 2.7857
OOUT * -1.7857
ONET
X VELOCITIES
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
n
m 1 • Uw V
TPUM *
DELS *
O.OOU
0.935e-14
0.757e-07
0.528e-06
0.211e-05
0.628e-OS
0.137e-04
0.573e-05
0.708e-12
0.000
0.000
0.935e-14
0.757e-07
0.52de-06
0.211e-05
0.628e-05
0.137e-04
0.573«-05
0.708e-12
0.000
U
1.0000
0.00000
AT NODES
0.000
-0.924e-14
-0.749e-07
0.229e-06
0.186e-05
0.781e-05
0.282e-04
0.749e-05
0.925e-12
0.000
ON BOUNDARIES
0.000
-0.278e-13
-0.225e-06
-0.697e-07
0.161e-05
0.934*-05
0.427e-04
0.925e-05
0.1 14e-1 1
C.OOO
0.000
-0.6V9e-13
-0.566e-06
-0.113e-05
-0.165e-05
-0.198e-05
-0.1b6e-05
-0.112e-05
-0.139e-12
0.000
O.OCO
-0.112e-12
-0.908e-06
-0.220e-05
-0.492e-05
-0.133e-04
-0.465e-04
-0.115e-04
-0.142e-1 1
0.000
0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0.
0.
-0.
-0.
-0.
-0.
-0 .
-0.
-0.
-0.
U.
000
131e-12
106e-05
254e-05
536e-05
122e-04
326e-04
101e-04
125e-11
000
000
149e-12
121«-05
289e-05
579e-05
1 1 1e-04
187e-04
874e-05
108e-11
000
0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0.
0.
-0.
-0.
000
139e-12
112e-05
263e-05
502e-05
891e-05
135e-04
677e-05
835e-12
000
000
128e-12
104e-05
-0.236e-05
-0.
-0.
-0.
-0.
-0.
0.
42Se-OS
670e-OS
839e-OS
479e-05
592e-12
000
0.000
-0.996e-13
-0.807e-04
-0.182e-0>
-0.320e-35
-0.488«-35
-0.588e-35
-0.3*2e-35
-O.*22e-12
0.000
0.000
-0.712e-U
-0.577e-3S
-0.127e-3S
-0.214e-35
-0.305e-3>
-0.337e-35
-0.204e-35
-0.252e-ia
0.000
0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
000
712e-13
577e-06
127e-05
214e-05
J05«-05
337e-05
204e-05
252e-12
000
000
000
000
000
000
000
000
000
000
000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
RESOURCE
03
_,
z
to
H
o
>•
H
o
to
-------
Selected output for teat problem S—Continued
T VELOCITIES
AT NODES
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
X «
BD»
(MAX
0.000 0.000
0.752*-04 0.753e-04
0.752e-04 0.7S4e-04
0.749e-04 0.7S9e-04
0.736e-04 0.764C-04
0.694e-04 0.751e-04
0.594e-04 O.S91e-04
0.497e-04 0.42Bv-04
0.468e-04 0.411e-04
0.000 0.000
ON BOUNDARIES
0.000 0.000
0.752e-04 0.753e-04
0.751e-04 0.756e-U4
0.746e-04 0.762e-04
0.725«-04 0.767e-04
0.662e-04 U.736e-04
0.525e-04 0.446e-04
0.468e-04 0.411e-04
0.000 0.000
0.000 0.000
STABILITY CRITERIA M.O.C.
3.26e-C5 VHAY « 9.57e-05
4.65e-05 VMYBD= 1.07e-04
. INJ.) - 0.11955e«08
0.000
0.751e-04
0.754e-04
0.768e-04
0.811e-04
0.957e-04
0.590e-04
0.214e-04
0.318e-04
0.000
0.000
0.75U-04
0.757e-04
0.779e-04
0.844e-04
0.107e-03
0.111e-04
0.318e-04
0.000
O.OUO
0.000
0.742e-04
0.743e-04
0.748e-04
0.756e-04
0.749e-04
0. 599e-04
0.447e-0t
0.433e-04
0.000
0.000
0.742e-04
0.745e-04
0.751e-04
0.760e-04
0.738e-04
0.461e-04
0.433e-04
0.000
0.000
0.000
0.729«-04
0.729e-04
0.725e-04
0.715e-04
0.68Se-04
0.611e-04
O.S40«-04
O.S20e-04
0.000
0.000
0.729e-04
0.728«-04
0.722«-04
0.707e-04
0.663e-04
O.S60e-04
O.S20e-04
0.000
0.000
0.000
0.719e-3i
0.717e-3t
0.709*-34
0.693e-34
0.664e-3'<
0.621e-04
O.S82e-3'.
0.568e-0'«
0.000
0.000
0.719e-04
0.714e-3i
0.704e-0i
0.682e-3l
0.646e-3«
0.596e-34
O.S68e-34
0.000
0.000
0.000
0.713e-04
0.710e-04
0.701e-04
0.684e-04
0.6SBe-04
0.626e-04
O.S99e-04
0. 589e-04
0.000
0.000
0.713e-04
0.708e-04
0.695e-04
0.673e-04
0.643e-04
0.609e-04
O.S89e-04
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
iv (CELOIS) * 0.42045e»07
gg
o
o
f
o
•^
en
o
s
•-3
H
>
1^^
01
3
\J
H
^H
2!
0
o
o
<
^
H
w
90
TIHV « 4.20e»06
NTIHV =
18
T1H (N) • 0.788944+08
TIMEVELO « 0.41523e»07
TIMEOISP = 0.30143«+08
TIMV
4.15e+06
NTIMD
NflOV
NMOV *
19
19
THE LIMITING STABILITY CRITERION IS CELDIS
NO. OF PARTICLE MOVES REQUIRED TO COMPLETE THIS TIME STEP
19
-------
88
TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
Selected output for teat problem 3—Continued
CONCENTRATION
NunotN gr lint site's i
DELTA T 0.788944*08
T1ME( SECONDS) 0.78894d«08
CHEW. TIBE( SECONDS) 0.78894e+08
CHEM.TIME(OAYS) 0.91313e*03
TIME(YEARS) 0.2SOOOe+01
CHEN.TIHE(YEARS) 0.25000«+01
NO.
0
0
0
0
0
0
0
0
0
0
MOVES COMPLETED 19
0 U 0 0
0 2 98 100
0 4 96 100
0 7 92 99
0 9 89 96
1 10 81 89
1 8 56 73
0 2 20 3i
0 0 1 5
0000
0
98
96
93
88
80
46
19
3
0
000
200
400
700
900
10 1 0
8 1 0
300
000
000
CHEMICAL MASS BALANCE
MASS IN BOUNDARIES
MASS OUT BOUNDARIES
MASS PUMPED IN
MASS PUMPED OUT
INFLOW MINUS OUTFLOW
INITIAL MASS STORED
PRESENT MASS STORED
CHANGE MASS STORED
COMPARE RESIDUAL WITH
NET
MASS BALANCE RESIDUAL
ERROR (AS PERCENT)
0.946*2e»13
-0.13340e+OB
O.OOOOOe+03
-0.96281e+09
0.84881«+10
O.OOOOOe+00
0.84631e»10
0.84631e»10
FLUX AND MASS
0.24910e«08
0.29390e«00
-------
StleeUd output for test problem S—Continued
TEST PROBLEM NO. 3 (STEADY FLOW, 1 HE|_L» CONSTANT-HEAD BOUNDARIES)
TIME VERSUS HEAD AND CONCENTRATION AT SELECTED OBSERVATION POINTS*
PUMPING PERIOD NO. 1
o
o
W
r
STEADY-STATE SOLUTION
OBS.WELL NO. X
1 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1 7
18
19
HEAD (FT)
0.0
92.0
92.C
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92.0
92. 0
92.0
92.0
C3MC.MG/L)
3.0
0.0
0.2
1.2
2.9
15.5
33.0
53.1
64.6
72.9
79.8
35.4
89. 4
92.2
94.3
95.8
97.0
97.8
98.4
98.7
TIME (TEARS)
09
O
r
H
W
2!
09
•B
O
0.00
0.13
0.26
0.39
0.53
0.66
0.79
0.92
1 .05
1 .18
1.32
1.45
1 .58
1.71
1.84
1.97
2.11
2.24
2.37
2.50
H
5g
O
§
e
0
^
H
W
»
00
co
-------
Selected output for test problem 3—Continued
OBS.UELL NO.
2
o
o
*
2
a
I
I
«
i
o
i
2
3
4
5
6
7
B
9
10
11
12
13
14
15
16
1?
18
19
HEAD (FT)
D.O
79.8
79.8
79.8
79.8
79.8
79.8
79.8
79.8
79.8
79.8
79.6
79.8
79.8
79.8
79.8
79.8
79.8
79.8
79.8
COVC.(
H
W
JO
»
K
co
O
G
»
O
w
CO
NM
2!
M
co
H
i-^
s
>
Hj
s
s:
CO
-------
SECTION 3
PROGRAM UPDATES
-------
NOTE ON COMPUTER PROGRAM UPDATE
January 29, 1988
Reference t 'Computer model of two-dimensional solute transport and dispersion in
ground water." by L. F. Konikow and J. D. Bredehoeft (1978); U.S. Geological Survey
Techniques of Water-Resources Inv., Book 7, Chapter C2.
This update includes Modifications to iiprove operational aspects of the
code. Two additional input data checks are performed to verify zero thickness
on the grid boundaries and consistency between input thicknesses and
transnissivlties. The location of the cell with the Maxima velocity will be
printed on output if CELDIS is the liilting tiie step size criterion. A minor
error in MOVE related to velocities near boundaries has been corrected. The
INTEGER*2 specification statement has been changed to confon to ANSI Standard
Fortran 77. No changes in input foriats are required.
The modifications can be impleaented by deleting the following lines of
the codei
B3160
SC 85
C 86
D 35
SE 85
E 86
SE 671
SE 681
E1055R
E1060
E1072R
E1073R
E1074R
E1077R
E1078R
E1081R
E1090
E1100
E1120
E1125
E2451R
E2452R
E2461R
E2470
F 35
F 250
F 260
F 730
F 750
F 960
F 980
F1230
F1250
F1510
F1530
F2041R
F2051R
G1412R
SG1537R
SH 65
H 66
and by inserting the following statements in their proper sequential locations
(as indicated by the line numbers in coluins 73-80):
* REVISED JANUARY 1988
IF (THCK(IX.IY).GT.O.O) THEN
IF (IX.EQ.l.OR.IY.EQ.l.OR.IX.EQ.NX.OR.IY.EQ.NY)
1 WRITE (6,935) IX,IY
GO TO 430
END IF
IF (IX.NE.l) THEN
IF (TMRX(IX-1,IY,1).GT.O.O) WRITE (6,940) IX,IY
END IF
IF (IY.NE.1) THEN
IF (TMRX(IX,IY-1,2).GT.O.O) WRITE (6,950) IX,IY
END IF
935 FORMAT (1H ,5X.54H*** WARNING *** THCK.NE.0.0 ON BOUNDARY
IE IX -,I4,6H, IY -.14)
INTEGER PTID
* A 68A
B3161
B3162
B3163
B3164
B3165
B3182
B3183
B3184
B3185
B3186
B3187
AT NOD B4195
B4196
D 36
-------
MAXVXI-0
MAXVXJ-0
MAXVYI-0
MAXVYJ-0
IF (JCK.EO.O) THEN
IF (ABVX.GT.VMXBD) THEN
VMXBD-ABVX
MAXVXI-IX
MAXVXJ-IY
END IF
IF (ABVY.GT.VMYBD) THEN
VMYBD-ABVY
MAXVYI-IX
MAXVYJ-IY
END IF
END IF
WRITE (6,394) VMXBD.VMYBD
115 TDELXB-CELDIS*XDEL/VMXBD
ITCD-0
IF (TDELYB.LT.TDELXB) ITCD-1
TIMV-AMIN1(TDELXB,TDELYB)
IF (AMAX1(VMXBD,VMYBD).LE.1.0E-10) WRITE(6,570)
IF (ITCD.GT.O) THEN
MJ-MAXVYJ-H
WRITE (6,534) MAXVYI,MAXVYJ,MAXVYI,MJ
ELSE
MI-MAXVXI+1
WRITE (6,535) MAXVXI.MAXVXJ.MI.MAXVXJ
END IF
394 FORMAT (1HO,5X,46HMAXIMUM EFFECTIVE SOLUTE VELOCITIES. X-VEL - ,
1 1PE9.2.5X.8HY-VEL - .1PE9.2)
410 FORMAT (1H0.5X.35HMAXIMUM FLUID VELOCITIES. X-VEL - .1PE9.2.5X,
1 8HY-VEL - .1PE9.2)
,4X.52HMAX. Y-VEL. IS CONSTRAINT AND OCCURS BETWEEN NOD
AND (,I2,1H,,I2,1H))
535 FORMAT (1H .4X.52HMAX. X-VEL. IS CONSTRAINT AND OCCURS BETWEEN NOD
1ES (,I2,1H.,I2,7H) AND (.I2.1H.,I2,1H))
INTEGER PTID
CONST1-TIMV*DXINV/RF
CONST2-TIMV*DYINV/RF
IF (THCK(IXE+1,IVY).NE.O.O) VXNE-VXNW
IF (THCK(IVX.IYS-H).NE.O.O) VYSW-VYNW
IF (THCK(IVX-l.IVY).NE.O.O) VXNW-VXNE
IF (THCK(IXE.IYS-H).NE.O.O) VYSE-VYNE
IF (THCK(IVX.IVY-l).NE.O.O) VYNW-VYSW
IF (THCK(IXE-H.IYS).NE.O.O) VXSE-VXSW
IF (THCK(IXE.IVY-l).NE.O.O) VYNE-VYSE
IF (THCK(IVX-l.IYS).NE.O.O) VXSW-VXSE
290 DISTX-XVEL*CONST1
DISTY-YVEL*CONST2
220 CMSOUT-CMSOUT+RECH(JX,JY)*TVA2*(CNOLD(IX,IY)+C1)
E
E
E
E
E
E
E
E
E
E
E
E
E
534 FORMAT (1H
1ES (,I2,1H.,I2,7H)
286
287
288
289
SE 645
E 672
673
674
675
676
682
683
684
685
686
SE 687
E1079R
E1082R
Ellll
E1112
E1121
E1126
E2062
E2063
E2064
E2065
E2066
E2067
E2068
E2453R
E2454R
E2471
E2472
E2602
E2603
E2604
E2605
F
F
F
F
F
F
F
36
251R
261R
731
751
961
981
F1231
F1251
F1511
F1531
F2040
F2050
SG1538R
-------
NOTE ON COMPUTER PROGRAM UPDATE
May 15, 1987
Reference» 'Computer model of two-dimensional solute transport and dispersion in
ground water." by L. F. Konikow and J. D. Bredehoeft (1978); U.S. Geological Survey
Techniques of Water-Resources 7/iv., Book 7, Chapter C2.
The following modifications were made to improve model efficiency,
especially for one-dimensional problems. The way in which particles are
removed and replaced has been changed so that the total number of particles is
minimized. The program has also been modified to use only one row of particles
for one-dimensional problems. For example, if the user specifies 9 particles
(NPTPND) for a one-dimensional problem (NX or NY-3), then the program will use
3 particles aligned in the direction of flow. The final change is that the
computation of the exponential decay term has been moved outside of the DO loops
in MOVE and CNCON. No changes in input formats are required.
This update also notes that all REAL*8 statements should be changed to
the ANSI Standard DOUBLE PRECISION statement. These changes are not included in
the listing below, and are only required for compilers that do not accept
the REAL*8 statement.
The modifications can be Implemented by deleting the following lines of
the code:
D 220
D 460 - D 480
D1050
D2060
F 222
F 267R
F2415R
F2580 - F2620
F2640
F2680
F2690
SF2867R
SF3477
F3770
F3780
G 343R
G 345R
G 431R
G 472R
476R
489R
G1444R
SG1694E
SG1694F
G
G
SG1695C
SG1695D
SG1696E
SG1696F
SG1697C
SG1697D
and by inserting the following statements in their proper sequential locations
(as indicated by the line numbers in columns 73-80)«
• REVISED MAY 1987 BY D.J. COODE * A 67
IF((NX.E0.3.0R.NY.E0.3).AND.NPTPND.NE.l) WRITE(6,883) B 614A
883 FORMAT (1H0.5X,56H*«« ONE-DIMENSIONAL *•• WILL USE ONLY 1 ROU OF P B4013A
1ARTICLES/13X.35HUSE 2 PARTICLES FOR NPTPND - 4 OR 5/13X.35HUSE 3 P B4013B
2ARTICLES FOR NPTPND - 8 OR 9/13X.31HUSE 4 PARTICLES FOR NPTPND - 1 B4013C
36) B4013D
IONED-0 D 172
IF(NX.EQ.3.0R.NY.E0.3) IONED-1 D 173
IF (NPTPND.EO.5.AND.IONED.EQ.1) Fl-0.25 D 202
IF (NPTPND.EQ.8.AND.IONED.NE.1) F2-0.25 D 22^
IF (NPTPND.EQ.8.AND.IONED.E0.1) Fl-1.0/3.0 D 222
J.F(IONED.EQ.1.AND.T.T.EQ.1.AND.IS.EQ.2) CO TO 140 D 782
IF(IONED.E0.1.AND.IT.E0.2.AND.IS.EQ.l) CO TO 140 D 783
IF(IONED.EQ.1.AND.IS.EQ.2) PTIDdNDM D 834A
IF(IONED.EQ.1.AND.ITT.EQ.1.AND.ISS.E0.2) CO TO 138 D1019A
-1-
-------
IF(IONED.E0.1.AND.ITT.EQ.2.AND.ISS.E0.1) GO TO 138
IF(IONED.EQ.l) THEN
IF(rr.E0.1.AND.ISS.E0.2) PTIDdNDM
IFdT.EQ.2) THEM
IF(ISS.EO.l) PTID(IND)-13
IFdSS.EQ.2) PTIO(INDM6
END IF
END IF
IF ((NPTPND.E0.5.AND.IONED.NE.D.OR.NPTPND.EQ.9) GO TO 150
IF (NPTPND.EQ.8.ANO.IONED.EQ.1) GO TO ISO
IFdONED.EO.i) GO TO 290
KP-IND-1
DOUBLE PRECISION DCYFa.DCYT.DCfT2
IONED-0
IF(NX.E0.3.0R.NY.E0.3) IONED-1
IF (NPTPND.EQ.5.AND.IONED.EQ.1) Fl-0.25
IF (NPTPND.EQ.8.AND.IONED.NE.1) F2-0.25
IF (NPTPND.E0.8.AND.IONED.E0.1) F1-F2
DCYT-l.DO
DCYT2-1.DO
IF(DECAY.NE.O.O) THEN
DCYT-DEXP(-DaFa)
DGfT2-DEXP (-DCYFa*0. 5DO)
END IF
PART(3.IN)-PART(3.IN)«DCYT
360 CONTINUE
C GENERATE NEW TEMPORARY PARTICLE
398 SUMC(JX.JY)-SUMC(JX.JY)+CONC(JX.JY)»DCYT2
PART(3.IP)-CONC(JX.JY)«DCYT
c *••**••*•**••*••***•*•**•*••*•••*•*•*********•*•*•**•***********
INSERT TEMPORARY PARTICLES INTO LIMBO LOCATIONS
IF(NPTM.EQ.NP) GO TO 620
IN-NPTM
00 595 IL-1,500
IP-LIMBO (ID
IF(IP.EQ.O) GO TO 595
PART(l.IP)-PARTd.IN)
PART(1.IN)-0.0
PART(2.IP)-PART(2.IN)
PART(2.IN)-0.0
PART(3,IP)-PART(3.IN)
PART(3.IN}-0.0
PTID(IP)-PTIDdN)
PTID(IN)-0
LIMBO dL>*0
IN-IN-1
IF(IN.LE.NP) GO TO 596
595 CONTINUE
596 NPTM-IN
GO TO 620
DOUBLE PRECISION DCYFCT,DCYT.DCYT2
DCYT-1.00
DCYT2-1.DO
IF(DECAY.NE.O.O) THEN
DCYT-OEXP(-DCYFCT)
DCYT2-DEXP (-OCYFCT'O.500)
END IF
GO TO 70
CUCN-CNRECH (IX. IY) «DCYT2
CNREC-CNRECH(iX.IY)»DCYT2
CNREC2-CNRECH(IX.IY )*DCYT2
IF (NPCELL(IX.IY).LE.O) C1-CNOLD(IX,IY)«DCYT2
DELOa-CNOLD (IX, IY )-CNOLD (IX, IY )«DCYT
IF (FLU.GT.0.0) FLMIN-FLMIN+FLU*YT*CNOLD(1.JY)«DCYT
IF (FLU.LT.0.0) FLMOT-FLMOT+FLU«YT*CNOLD(1,JY)«DCYT
IF (FLU.GT.0.0) FLMIN-FLMIN+FLU*YT«CNOLD(NHX.JY)*DCYT
272 IF (FLU.LT.0.0) FLMOT-FLMOT+FLU*YT*CNOLD(NMX.JY)*DCYT
IF (FLU.GT.0.0) FLMIN-FLMIN+FLU«XT*CNOLD(JX,1)»DCYT
IF (FLU.LT.0.0) FLMOT-FLMOT+FLU«XT*CNOLD(JX.1)*DCYT
IF (FLU.GT.0.0) FLMIN-FLMIN-t-FLU*XT*CNOLD(JX.NMY)*DCYT
274 IF (aU.LT.0.0) FLMOT-FLMOT+FLU*XT*CNOLD(JX.NMY)*OCYT
D1019B
D1034A
D1034B
D1034C
D1034D
D1034E
D1034F
D1034G
D1051
D1052
D1132
D2061
F
F
F
F
F
F
F
F
F
F
33
211A
F 211B
F 217
222A
222B
268A
268B
268C
268D
268E
268F
F2416R
F2581
F2641
SF2868R
SF3478
F3762
F3763
F3764
F3765
F3766
F3767
F3768
F3769
F3771
F3772
F3773
F3774
F3775
F3776
F3777
F3778
F3779
F3781
F3782
F3783
F3784
F3785
G 42
346A
346B
346C
346D
G 346E
G 346F
G 347R
G 431A
G 472A
G 476A
G 489A
G1444A
SG1694G
SG1694H
SG1695E
SG1695F
SG1696G
SG1696H
SG1697E
SG1697F
G
G
G
G
-2-
-------
NOTE ON COMPUTER PROGRAM OPTION
MARCH 5, 1987
Reference» "Computer model of two-dimensional solute transport and dispersion in ground
water," by L. F. Konikow and J. D. Bredehoeft (1978); U,S. Geological Survey Techniques
of Water-Resources Inv., Book 7, Chapter C2.
The following modifications will convert the numerical solution technique
for the flow equation from the iterative Alternating Direction Implicit Procedure
in the original code to a Strongly Implicit Procedure. In those few situations
when iterative ADI has difficulty converging, SIP is usually successful and
relatively efficient.
To use the model with the SIP routine, the user should specify NITP - 10
in input card 2. No other changes in the input formats are needed.
To convert the program, the following lines of code should be deleted?
B 185 B3960-B3971 H 126
B 615 B4015
B2910-B2981 C 10-C1370
and the following lines Inserted in their proper sequential locations:
C * S.I.P. ROUTINE ADAPTED BY RICHARD HEALY — 1979 * A 53
C * S.I.P. - REVISED SEPTEMBER 1982 & FEB. 1987 * A 54
REAL *8HMAX B 63
COMMON /BALM/ TOTLQ.TOTLQI.TPIN.TPOUT.HMAX B 192
HMAX-1.0 B 453
IF (NITP.NE.10) WRITE (6,886) B 616
1RATION PARAMETERS) - .I4/13X,39HTOL (CONVERGENCE CRITERIA - SIP B3961
2) - .E9.2/13X.39HITMAX (MAX.NO.OF ITERATIONS - SIP) -,I4/13X,3 B3972
886 FORMAT (1H0.5X,38H*** WARNING *** NITP SHOULD EQUAL 10 ) B4016
SUBROUTINE ITERAT C 10
DOUBLE PRECISION DMIN1,DEXP,DLOG,DABS C 20
C C 30
C SOLUTION BY THE STRONGLY IMPLICIT PROCEDURE C 40
C_ ,_...._ _____.._ ^-r-^_ f Kfl
— ——™»» ^ ^y
C C 60
REAL *8TMRX,VPRM.HI,HR.HC.HK.WT.REC.RECH.TIM.AOPT.TITLE C 70
REAL *8DEL,ETA,V,XI,RHOP,TEMP,TEST3 C 80
REAL *8XDEL,YDEL,S,AREA,SUMT.RHO.PARAM,TEST.TOL,PINT,HMIN.PYR C 90
REAL *8B,G,W,A,C,E,F,DR,DC.TBAR,TMK,COEF,BLH,BRK,CHK,QL,BRH,HMAX C 100
REAL *8DXINV,DYINV,ARINV.PORINV C 110
COMMON /PRMJ/ NTIM,NPMP,NPNT.NITP.N,NX,NY,NP,NREC,INT,NNX.NNY,NUMO C 120
IBS,NMOV,IMOV,NPMAX,ITMAX,NZCRIT,IPRNT,NPTPND,NPNTMV,NPNTVL,NPNTD,N C 130
2PNCHV.NPDELC.ICHK C 140
COMMON /PRMC/ NODEID(40,40),NPCELL(20,20),NPOLD(20,20),LIMBO(500), C 150
-1-
-------
c
c
c
1IXOBS(5),IYOBS(5)
COMMON /HEDA/ THCK(40,40).PERM(40,40),TMUL(5,50),TMOBS(50).ANFCTR
COMMON /HEDB/ TMRX(40,40,2),VPRM(40,40),HI(40,40),HR(40,40),HC(40,
140),HK(40,40),UT(40,40),REC(40,40),RECH(40.40),TIM(100),AOPT(20),T
2ITLE(10),XDEL,YDEL,S.AREA.SUMT.RHO.PARAM,TEST.TOL.PINT.HMIN.PYR
COMMON /BALM/ TOTLQ.TOTLQI.TPIN.TPOUT.HMAX
COMMON /XINV/ DXINV.DYINV.ARINV.PORINV
DIMENSION DEL(40,40),ETA(40,40),V(40,40),XI(40,40),
1IORDER(21),RHOP(40),TEMP(40),TEST3(201)
DATA IORDER/1,2,3,4,5,1,2.3,4,5,11*!/
COMPUTE AND PRINT ITERATION PARAMETERS
PQIN-0.0
PQOUT-0.0
KOUNT—1
DO 1000 I-l.NX
DO 1000 J-l.NY
1000 HRd.J)-HK(I.J)
IF(INT.NE.l) GO TO 40
INITIALIZE ORDER OF ITERATION PARAMETERS
IN01-NX-1
JN01-NY-1
I2-IN01-1
J2-JN01-1
L2-NITP/2
PL2-L2-1
C
C
C
160
170
180
C 190
C
C
c
c
c
c
c
c
c
COMPUTE MAXIMUM PARAMETER FOR PROBLEM
DX-(1./NX)**2
DY-(1./NY)**2
W-1-AMIN1(2*DX/(1+ANFCTR*DX/DY),2*DY/(1+DY/(ANFCTR*DX)))
COMPUTE PARAMETERS IN GEOMETRIC SEQUENCE
PJ—1.
DO 20 I-1.L2
PJ-PJ+1
20 TEMP(I)-1.-(1.-W)**(PJ/PL2)
ORDER SEQUENCE OF PARAMETERS
DO 30 J-l.NITP
30 RHOP(J)-TEMP(IORDER(J))
WRITE(6,1002) HMAX,NITP,(RHOP(J),J-1,NITP)
1002 FORMAT(IX,6HBETA- ,F4.2,/,1X,I3,23H ITERATION PARAMETERS.,6(/1X,
16E15.6))
INITIALIZE DATA FOR A NEW ITERATION
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
-2-
-------
]
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
40 KOUNT-KOUNT+1
IF(KOUNT.LE.ITMAX) GO TO 50
WRITE (6, 160)
CALL OUTPT
WRITE (6 ,1003) (TEST3(I),I-1,KOUNT)
.003 FORMAT ( IX, 39HMAXIMUM HEAD CHANGE FOR EACH ITERATION:,
+20(/,1X,10(F12.5)))
STOP
50 IF(MOD(KOUNT,NITP))60,60,70
INITIALIZE DATA FOR A NEW ITERATION
60 NTH-0
70 NTH-NTH+1
W-RHOP(NTH)
TEST3(KOUNT+1)-0
TEST-0
DO 80 I-l.NX
DO 80 J-l.NY
DEL(I,J)-0
ETA(I,J)-0
V(I.JM)
80 XI(I,J)-0
BIGI-0
RHO-S/TIH(N)
CHOOSE SIP NORMAL OR REVERSE ALGORITHM
IF(MOD(KOUNT,2)) 100,230,100
ORDER EQUATIONS WITH ROW 1 FIRST- 3X3 EXAMPLE i
123
456
789
100 DO 210 J-2.JN01
DO 210 I-2.IN01
SKIP COMPUTATIONS IF NODE IS OUTSIDE AQUIFER BOUNDARY
IF(THCK(I,J).EQ.O.) GO TO 210
COMPUTE COEFFICIENTS
D-TMRX(I-1,J,1)/XDEL
F-TMRX(I,J,1)/XDEL
B-TMRX(I.J-1.2)/YDEL
H-TMRX(I.J,2)/YDEL
CH-DEL(I,J-1)*B/(1.+W*DELU.J-1))
GH-ETA (1-1 , J )*D/ (1 . +W*ETA (1-1 , J ) )
SIP 'NORMAL1 ALGORITHM
FOWARD SUBSTITUTE, COMPUTING INTERMEDIATE VECTOR V
C 690
C 700
C 710
C 720
C 730
C 740
C 750
• C 760
C 770
C 780
C 790
C 800
C 810
C 820
C 830
C 840
C 850
C 860
C 870
C 880
C 890
C 900
C 910
C 920
C 930
C 940
C 950
C 960
C 970
C 980
C 990
C1000
C1010
C1020
C1030
C1040
C1050
C1060
C1070
C1080
C1090
C1100
C1110
C1120
C1130
C1140
C1150
C1160
C1170
C1180
C1190
C1200
C1210
-3-
-------
C C1220
E~ B-D-F-H-RHO-VPRMU.J) C1230
BH-B-U*CH C1240
DH-D-H*GH C1250
EH-E+WMCH+GH) C1260
FH-F-W*CH C1270
HH-H-W*GH C1280
ALFA-BH C1290
BETA-DH . C1300
GAMA-EH-ALFA*ETA(I,J-l)-BETA*DEL(1-1,J) C1310
DEL(I,J)-FH/GAMA C1320
ETA(I,J)-HH/GAMA C1330
QL~VPRM(I,J)*WT(I,J) C1340
RES—D*HK (1-1. J )-F*HK (1+1, J )-H*HK (I, J-H )-B*HK (I, J-l)- Cl 350
1E*HK(I,J)-RHO*HR(I,J)+QL+RECH(I.J)+REC(I,J)*ARINV C1360
V(I,J)-(HMAX*RES-ALFA*V(I,J-l)-BETA*V(1-1,J))/GAMA Cl370
210 CONTINUE C1380
C C1390
C BACK SUBSTITUTE FOR VECTOR XI C1400
C C1410
DO 220 J-1.J2 C1420
J3-NY-J C1430
DO 220 1-1,12 C1440
I3-NX-I C1450
IF(THCK(I3,J3).EQ.O.) GO TO 220 C1460
XI(I3,J3)-V(I3fJ3)-DEL(I3,J3)*XI(I3-H,J3)- C1470
1ETA(I3.J3)*XI(I3,J3+1) C1480
C C1490
C COMPARE MAGNITUDE OF CHANGE WITH CLOSURE CRITERION C1500
C C1510
TCHK-DABS(XI(I3,J3)) C1520
IF(TCHK.GT.BIGI)BIGI-TCHK C1530
HK(I3,J3)-HK(I3,J3)+XI(I3,J3) C1540
220 CONTINUE C1550
221 IF(BIGI.GT.TOL)TEST-1 C1560
TEST3(KOUNT+1)-BIGI Cl570
IFCTEST.EQ.l.) GO TO 40 C1580
DO 130 IY-1.NY C1590
DO 130 IX-l.NX C1600
C CUMULATE PUMPAGE AND RECHARGE FOR MASS BALANCE C1610
IF (REC(IX.IY).GT.O.O) GO TO 32 C1620
PQIN-PQIN+REC(IX,IY) C1630
GO TO 34 C1640
32 PQOUT-PQOUT+REC(IX,IY) C1650
34 IF (RECH(IX.IY).GT.O.O) GO TO 36 C1660
PQIN-PQIN+RECH(IX,IY)*AREA C1670
GO TO 38 C1680
36 PQOUT-PQOUT+RECH(IX,IY)*AREA C1690
C COMPUTE LEAKAGE FOR MASS BALANCE C1700
38 IF (VPRM(IX.IY).EQ.O.O) GO TO 130 C1710
DELQ-VPRM(IX,IY)*AREA*(WT(IX,IY)-HK(IX,IY)) C1720
IF (DELO.GT.0.0) GO TO 125 C1730
TOTLQ-TOTLQ+DELQ*TIM(N) C1740
-4-
-------
-125
130
C
c
C
C
C
C
c
230
C
C
C
C
c
c
c
c
340
1030
C
C
GO TO 130
TOTLQI-TOTLQI+DELQ*TIM (N )
CONTINUE
TPIN-PQIN*TIM(N)+TPIN
TPOUT-PQOUT*TIM (N )+TPOUT
WRITE (6 ,140) N
KOUNT-KOUNT+1
WRITE(6,150) KOUNT, (TEST3(I),I-1,KOUNT)
RETURN
ORDER EQUATIONS WITH THE LAST ROW FIRST- 3X3 EXAMPLE.
789
456
123
DO 340 JJ-1.J2
J-NY-JJ
DO 340 I-2.IN01
SKIP COMPUTATIONS IF NODE IS OUTSIDE OF AQUIFER BOUNDARY
IF (THCK(I.J).EQ.O.) GO TO 340
COMPUTE COEFFICIENTS
D-TMRX(I-1,J,1)/XDEL
F-TMRX(I,J,1)/XDEL
B-TMRXU,J-1,2)/YDEL
H-TMRX(I,J,2)/YDEL
SIP 'REVERSE1 ALGORITHM
FOUARD SUBSTITUTE, COMPUTING INTERMEDIATE VECTOR V
E—B-D-F-H-RHO-VPRM (I , J )
CH-DEL(I.J+1)*H/(1.+V*DEL(I,J+1))
GH-ETA(I-1,J)*D/(1.+U*ETA(I-1,J))
BH-H-W-CH
DH-D-W*GH
EH-E+WMCH+GH)
FH-F-U*CH
HH-B-U*GH
ALFA-BH
BETA-DH
GAMA-EH-ALFA*ETA (I . J+l )-BETA*DEL (1-1 . J )
DEL(I,J)-FH/GAMA
ETA(I,J)-HH/GAMA
QL— VPRM(I,J)*WT(I,J)
RES— D*HK (1-1 , J )-F*HK (1+1 , J )-H*HK (I , J+l )-B*HK (I , J-l )-
1E*HK (I , J )-RHO*HR (I , J HQL+RECH (I , J )+REC (I , J ) *ARINV
V (I , J )- (HMAX*RES-ALFA*V (I , J+l )-BETA*V (1-1 , J ) )/GAMA
CONTINUE
FORMAT(1X,8F13.2)
BACK SUBSTITUTE FOR VECTOR XI
C1750
C1760
C1770
C1780
C1790
C1800
C1810
C1820
C1830
C1840
C1850
C1860
C1870
C1880
C1890
C1900
C1910
C1920
C1930
C1940
C1950
C1960
C1970
C1980
C1990
C2000
C2010
C2020
C2030
C2040
C2050
C2060
C2070
C2080
C2090
C2100
C2110
C2120
C2130
C2140
C2150
C2160
C2170
C2180
C2190
C2200
C2210
C2220
C2230
C2240
C2250
C2260
C2270
-5-
-------
DO 350 J-2.JN01 C2280
DO 350 13-1,12 C2290
I-NX-I3 C2300
IF(THCK(I.J).EQ.O.) GO TO 350 C2310
XIU,J)-V(I,J)-DEL(I.J)*XI(I-H,J)-ETA(I,J)*XI(I,J-1) C2320
C C2330
C COMPARE MAGNITUDE OF CHANGE WITH CLOSURE CRITERION C2340
C C2350
TCHK-DABS(XHI.J)) C2360
IF(TCHK.GT.BIGI) BIGI-TCHK C2370
HK(I,J)-HK(I,J)+XI(X.i) C2380
350 CONTINUE C2390
GO TO 221 " C2400
140 FORMAT(1HO//3X.4HN - ,114) C2410
150 FORMAT(IX,22HNUMBER OF ITERATIONS- ,I3,/,1X, C2420
139HMAXIMUM HEAD CHANGE FOR EACH ITERATION.,20(/,IX,10F12.5)) C2430
160 FORMAT(1H0.5X, 53H*** EXECUTION TERMINATED — MAX # ITERATIONS EXC C2440
1EEDED/26X.21HFINAL OUTPUT FOLLOWS:) C2450
C RETURN C2460
END C2470-
REAL *8HMAX H 34
COMMON /BALM/ TOTLQ.TOTLQI.TPIN.TPOUT.HMAX H 127
-6-
-------
NOTE ON COMPUTER PROGRAM UPDATE
MARCH 2. 1987
Reference i 'Computer model of two-dimensional solute transport and dispersion in
ground water," by L. F. Konikow and J. D. Bredehoeft (1978); U.S. Geological Survey
Techniques of Water-Resources Inv., Book 7, Chapter C2.
The following minor modifications were iade to perform all flow mass-
balance calculations in double precision (real*8), to place two time-step
parameters in a new common block, and to Improve the output formats. These
changes do not affect the accuracy of the solution, but may result in more
accurate calculation of the flow mass balance for some problems. The time-
step parameter change is required only for some FORTRAN compilers, and then
is needed only for transient flow problems with multiple pumping periods. No
changes in input formats are required.
The modifications can be Implemented by deleting the following lines of
the code»
A 420 B 860 B2980 B3970 D 440 F3570 11030 11040
and by inserting the following statements in their proper sequential locations
(as indicated by the line numbers in columns 73-80)>
* REVISED MARCH 1987 BY D.J. GOODE * A 64
REMN-1.0 A 338
IF (NPNT.GT.O) REMN-MOD(N.NPNT) . A 421
REAL *8TOTLQ,TOTLQI,TPIN,TPOUT B 62
COMMON /HEDD/ TINIT.TIMX B 157
WRITE (6,490) (TIM(K),K-l,NTIM) B 861
WRITE (6,460) (AOPT(IP),IP-1,NITP) B2981
2P) - .E9.2/13X.39HITMAX (MAX.NO.OF ITERATIONS - ADIP) - ,I4/13X,3 B3971
REAL *8TOTLd,TOTLOi,TPIN,TPOUT,PQIN,PQOUT,DELQ C 52
40 LIMBO(IN )-0 ' D 441
540 IFLAG-1 ' F3571
REAL *8TOTLQ,TOTLQI,TPIN,TPOUT,PQIN.PQOUT.DELQ,OOUT.QIN,QNET,DDRW H 32
REAL *8QSTR,TPUM,PUMP,TOTLQN.SRCS,SINKS,ERRMB.DENOM.PCTERR H 33
110 NTO-N 11031
IF (N.GT.50) NTO-MOD(N,50) 11041
-------
NOTE ON COMPUTER PROGRAM UPDATE
OCTOBER 20, 1986
Reference: "Computer model of two-dimensional solute transport and in ground water,"
by L. F. Konikow and J. D. Bredehoeft (1978). U.S. Ceol. Survey Techniques of
Water-Resources Inv., Book 7, Chapter C2.
Following are several modifications that will prevent zero-divide checks
that nay otherwise occur In certain cases. The nodifications can be
Implemented by deleting the following lines of the code:
E 412 E 491
and by inserting the following statements in their proper sequential locations
(as indicated by the line numbers in columns 73-80)t
PERHX-0.0 E 414
PERMD-PERN(IX.IY)+PERM(IX-1.IY) E 415
IF (PERMD.GT.0.0) PERMX-2.0*PERM(IX.IY)*PERM(IX-1.IY)/PERMD E 416
PERMY-0.0 E 494
PERMD-PERM2(IX.IY)+PERM2(IX.IY-1) E 495
IF (PERMD.GT.0.0) PERMY-2.*PERM2(IX,IY)*PERM2(IX.IY-1)/PERMD E 496
-------
NOTE ON COMPUTER PROGRAM UPDATE
JULY 2. 1986
Refer-encei 'Computer model of two-dimensional solute transport and dispersion in
ground water." by L. F. Konikow and J. D. Bredehoeft (1978). U.S. Ceol. Survey
Techniques of Water-Resources Inv., Book 7, Chapter C2.
The following modifications were made primarily to yield more efficient
and more accurate calculations of particle velocities, particularly in the
vicinity of permeability contrasts. No changes in input formats are required.
The modifications can be implemented by deleting the following lines of the
code>
SB 210 E 451 E 531 E 630
E 190 E 460 E 540 E 640
E 431 E 511 E 600 SF 170
E 441 E 521 E 610 SG 190
and by inserting the following statements in their proper sequential
locations (as Indicated by the-line numbers in columns 73-80):
C * REVISED JULY 1986 *
COMMON /CHMC/ SUMC(20,20),VXBDY(40,40),VYBDY(40,40),PERM2(40.40)
DK-0.0
PERM2(IX,IY)-0.0
C COMPUTE HARMONIC MEAN PERMEABILITY
DO 445 IX-2.NNX
DO 445 IY-2.NNY
IF (THCK(IX.IY).EQ.O.O) GO TO 445
PNODE-PERM(IX.IY)
PERM(IX,IY)-2.0*PNODE*PERM(IX+1,IY)/(PNODE+PERM(IX-H,IY))
PERM2(IX,IY)-2.0*PNODE*PERM(IX,IY+1)/(PNODE+PERM(IX,IY+1))
445 CONTINUE
COMMON /CHMC/ SUMC(20,20),VXBDY(40,40),VYBDY(40,40),PERM2(40,40)
PERMX-2.0*PERM(IX,IY)*PERM(IX-1,IY)/(PERM(IX.IYHPERM(IX-1,IY))
IF (THCK(IX-l.IY).NE.O.O) GO TO 13
PERMX-PERM(IX.IY)
DHX-HK(IX,IY)-HK(IX+1,IY)
13 IF (THCK(IX-H.IY).NE.O.O) GO TO 14
PERMX-PERM(IX-l.IY)
DHX-HK(IX-1,IY)-HK(IX,IY)
14 IF (THCK(IX-1,IY).EQ.O.O.AND.THCK(IX+1,IY).EQ.O.O) DHX-0.0
VX(IX,IY)-PERMX*GRDX*PORINV
PERMY-2.*PERM2(IX,IY)*PERM2(IX,IY-1)/(PERM2(IX,IY)+PERM2(IX,IY-1))
IF (THCKttX,IY-1).NE.0.0) GO TO 15
PERMY-PERM2(IX,IY)
DHY-(HK(IX,IY)-HK(IX,IY+D)
15 IF (THCKUX,IY+1).NE.0.0) GO TO 16
PERMY-PERM2(IX,IY-1)
DHY-(HK(IX,IY-1)-HK(IX,IY))
16 IF (THCKdX,IY-1).EQ.0.0.AND.THCKUX,IY+1).EQ.0.0) DHY-0.0
VY(IX,IY )-PERMY*GRDY*PORINV*ANFCTR
VXBDY(IX,IY )-PERM(IX,IY)*GRDX*PORINV
VYBDYUX, IY)-PERM2 (IX, IY)*GRDY*PORINV*ANFCTR
COMMON /CHMC/ SUMC(20,20),VXBDY(40,40),VYBDY(40,40),PERM2(40,40)
COMMON /CHMC/ SUMC(20,20),VXBDY(40,40),VYBDY(40,40),PERM2(40,40)
A 63
SB 211
B 297R
B 965
B3291
B3292
B3293
B3294
B3295
B3296
B3297
B3298
SE 191
412
423
424
425
426
427
428
452
461
491
503
504
505
506
507
508
509
541
611
641
SF 171
SG 191
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
-------
United States Department of the Interior
GEOLOGICAL SURVEY
RESTON, VA. 22092
In Reply Refer To: January 15, 1986
WGS-Mail Stop 431
Memorandum
To: Users of "Computer Model of Two-Dimensional Solute Transport and
Dispersion in Ground Water," by L. F. Konikow and J. D. Bredehoeft
(1978)
The attached updates to this model have been developed during the last two
years; their verification has just been completed. Overall, they serve to
improve the accuracy, efficiency, and usability of the model. Revisions can
be implemented by following the instructions in the updates. Otherwise,
copies of the updated computer program on tape are available from:
U.S. Geological Survey
WATSTORE Program Office
437 National Center
Reston, VA 22092
Leonard F. Konikow
Research Hydrologist
Attachments
-------
NOTE ON COMPUTER PROGRAM UPDATE
August 12, 1985
Reference: "Computer model of two-dimensional solute transport and dispersion in ground
water" by L. F. Konikow and J. D. Bredehoeft (1978): U.S. Geological Survey
Techniques of Water-Resources Investigations, Book 7, Chapter C2.
Following are several general modifications to the subject computer
program that are designed primarily to improve the readability of the output.
These minor changes will not affect the calculations. They also will allow
the user to specify NPTPND = 1; this will reduce significantly the computer
time required to solve a given problem, but may adversely affect the numerical
accuracy of the solution to the solute-transport equation. Hence, this option
is recommended only for prelininary or test runs in which high numerical
accuracy of the solution to the transport equation is not needed, such as when
the objective of the run is to check input data, boundary conditions, or
overall problem formulation.
The modifications can be implemented by deleting the following lines of
the code:
A 450
A 610
B 611
B1630
B2330
B2620
B4011
E2410
E2530
E2540
E2550
E2560
E2570
G 770
and by inserting the following statements in their proper sequential locations
(as indicated by the line numbers in columns 73-80):
IF (TDEL.EO.(PYR-TINT)) IPCK=1
IF (REMN.EQ.O.O.OR.N.EO.NTIM.OR.IPCK.E0.1) CALL OUTPT
120 IF (REMN.EO.O.O.OR.N.EO.NTIM.OR.MOO(N/50).EO.O.O».IPCK.EQ.1)
1 CALL CMMOT
1.AND.NPTPNO.NE.16.AND.NPTPND.NE.1) WRITE (6/880)
IF (NPTPNO.EQ.1) WRITE (6/882)
WRITE (6/755)
WRITE (6/755)
WRITE (6/755)
WRITE (6/755)
160 WRITE (6/840) ( VPRMUX/I Y) / IX»1/NX)
WRITE (6/755)
WRITE (6/755)
WRITE (6/755)
260 WRITE (6/840) (PERM(IX/IY)/IX=1/NX)
WRITE (6/755)
320 WRITE (6/840) (VPRM(IX/IY)/IX = 1/NX)
WRITE (6/755)
880 FORMAT (1HO/5X/47H*** WARNING *** NPTPND MUST = 1/4/5/8/9/ OR 16)
882 FORMAT (1HO/5X/53H*** CAUTION *** USE OF NPTPND=1 MAY CAUSE LOSS 0
1F ACCURACY)
IF (NPTPNO.E0.1) 60 TO 410
350 FORMAT (1H /1P10E12.3)
460 FORMAT (1MO/35X/14HXX COEFFICIENT/)
470 FORMAT (1MO/35X/14HYY COEFFICIENT/)
480 FORMAT (1HO/35X/14HXY COEFFICIENT/)
490 FORMAT (1MO/35X/14HYX COEFFICIENT/)
500 FORMAT (1M /1P10E11.2)
CNCNC(IX/IY)=CNCNC(IX/IY)+EQFCT1*(X1+X2+Y1»Y2+XX1-XX2+YY1-VY2)
336
406
451
611
612
612
614
61195
81347
3U35
B1515
B1631
B1945
B2075
B2315
B2331
B2615
32621
62655
B4011A
B4012A
B4012B
01115
E2411
E2531
E2541
E2551
E2561
E2571
G 771
-------
NOTE ON COMPUTER PROGRAM UPDATE
August 8, 1985
Reference; "Computer model of two-dimensional solute transport and dispersion in
ground water" by L. F. Konikow and J. D. Bredehoeft (1978): U.S. Geological Survey
Techniques of Water-Resources Investigations, Book 7, Chapter C2.
The following modifications will allow the user to solve the transport
equation within a smaller grid than is used to solve the flow equation. This
can yield a great savings in computer calculation time and storage
requirements for problems in which the hydraulic gradients within the area of
interest for transport are influenced by hydraulic stresses and (or) boundary
conditions outside of the area in which solute transport is occurring.
The approach is to define a primary finite-difference grid for the flow
model using the standard input data formats of the computer code. A smaller,
secondary subgrid for transport is then defined within the coordinates of the
primary grid. The revised input formats are structured so that implementation
of the changes will not necessitate the modification of any existing data
sets; that is, identical results will be obtained with the modified code as
with the unmodified program for problems which do not apply a transport
subgrid.
To utilize this new option, the user should specify "NX" as a negative
value in field 3 of data card 2. When the program reads such a negative
value, it will then reset NX = -AW and read a new data set, immediately
following data card 2, which contains the following four integer values in
free format (that is, values are separated by commas or spaces):
MX,MY The X" and y-coordinates within the primary grid of the
upper-left node of the transport subgrid, and
MMX,MMY The grid coordinates of the lower-right node of the
transport subgrid.
For example, if the primary grid is 20 by 20 (that is, NX = 20 and NY = 20),
and if you want the subgrid for transport to be 10 by 10, with the upper left
node of the subgrid corresponding to node (3,4) of the primary grid, then your
new data would specify MX « 3, MY = 4, MMX - 12, and MMY = 13.
Note that the "window" for the transport subgrid can overlap all or any
part of the primary grid, but can not extend beyond it. Also note that unless
the subgrid overlaps, the first or last row or column of the primary grid,
which are no-flow boundaries, then all nodes of the subgrid can be "active"
-------
nodes. Finally, the subgrid should be located so that there will not be a
significant amount of convective (advective) transport across the subgrid
boundary, or else the accuracy of the solution will be adversely affected.
The boundaries of the transport subgrid are assumed to represent a
constant concentration-gradient condition. Thus, the revised model has been
programmed to allow no dispersive flux across the outer boundary of the
subgrid and to set the concentration of any convective (advective) flux across
the boundary equal to the concentration at the node just inside the boundary,
regardless of whether the flux is into or out of the subgrid at that node.
The following instructions for implementing this option assume that all
"updates" released or dated prior to the date of this "update note" have
already been incorporated. The modifications can be implemented by deleting
the following lines in the code:
A 570 D 650 E1960 F3840 G1330
B 990 D 800 £1970 F4050 G1340
B1130 D 810 E2000 G 231 G1350
B1140 D1022 E2010 G 241 G1421
B1150 D1023 £2020 G 351 G1431
B1380 D1075 £2032 G 361 G1440
B1390 D1090 £2190 G 370 G1443R
B1400 D1170 £2200 G 381R G1445R
B2550 D1180 £2220 G 420 G1490
B3020 D1380 £2230 G 460 G1499R
B3030 D1390 £2250 G 474R G1520
B3040 £ 480 £2260 G 477R G1530
B3080 E 560 £2280 G 480 G1536R
B3092R E 670 E2290 G 595 G1560
B3420 E 680 F2420 G 851 G1585
B3500 £1350 F2430 G 861 G1600
B3550 £1360 F2500 G 870 H 140
B3840 £1510 F2866R G 900 H1070
B3850 £1530 F2875 G1010 H1190
D 511 £1650 F2885 G1020 I 350
D 521 £1670 F3530 G1061 I 360
D 530 E1710 F3580 G1071 I 380
D 600 E1720 F3635 G1080 I 540
D 610 E1740 F3662 G1160 I 550
D 620 E1760 F3664 G1280 I 580
D 630 £1810 F3666 G1300 11090
D 640 £1820 F3830 G1310
and inserting the following statements in their proper sequential locations,
as indicated by the line numbers in columns 73-80 (for identification
purposes, all inserts for this update are labeled with an "S" in column 74):
-------
c
t
* REV. JULY-DEC. 1985 TO ALLOW SECONDARY SUBGRID FOR TRANSPORT
COMMON /MEDC/ MXxMYxMMX/MMYxNMXxNMYxMCHK
IX=IXOBSCI)-MX+1
If (IXOBS(I).LT.MX.OR.IXOBS(I).GT.MMX) GO TO 110
IY=IYOBS(I)-MY+1
IF (IYOBS(I).LT.MY.OR.IYOBS(I).GT,MMY) GO TO 110
TMCN(IxJ)=CONC(lXxIY)
COMMON /MEDC/ MXxMYxMMXxMMYxNMXxNMYxMCHK
MCHK=0
NCA2=0
NMX-NX
NMY=NY
MMX=NX-1
MMY«NY-1
--- READ UPPER LEFT AXD LOWER RIGHT NOOAL COORDS. OF
TRANSPORT SUBGRID* IN FREE FORMAT/ IF NX.LT.O ---
IF (NX.GT.O) GO TO 5
NX=-NX
MCHK=1
READ (5**) MXxMYxMMXxMMY
NMX=MMX-MX+1
NMY = MMY-MY*1 •• :
CONTINUE
WRITE (6x755) '
IF (MCHK.GT.O) WRITE (6x775) NMXxNMYxMXxMYxMMXxMMY
WRITE (6x888)
00 75 !Y«1xNMY
DO 75 IX=1xNMX
CNRECM(lXxIY)«0.0
CONC(IX/IY)=0.0
CONINT(IX,IY)=0.0
SUMCCIX/.IY)=0.0
NPCELL(IX/IY)»0
CONTINUE
JX=IX-MX+1
JY=IY-MY*1
IF (JX.LT.1.0R.JY.LT.1.0R.JX.GT.NMX.OR.JY.GT.NMY) GO TO 105
IF (FCTR.LT.0.0) CNRECM( JXx JY)=CNREC
REC(IX,IY)«FCTR
WRITE (6x820) IX/I YxRECCIX/I Y) xCNREC
IF (MCHK.EO.O) GO TO 250
IF (IX.LT.MX.OR.IX.GT.MMX) GO TO 250
IF (IY.LT.MY.OR.IY.GT.MMY) GO TO 250
75
105
110
IF (MCHK.GT.O) NZCRIT*(NCA2+25)/50
IF (NZCRIT.EQ.O) NZCRIT=1
IF (MCHK.EQ.O) GO TO 265
AA02«NCA2*AREA
WRITE (6x633)
WRITE (6x635) NCAxAAQ
WRITE (6x634)
WRITE (6x630) NCA2xAAQ2xNZCRIT
GO TO 267
265 CONTINUE
267 CONTINUE
JX=IX-HX+1
SA
SA
SA
SA
SA
SA
SA
SA
SB
SB
So
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
SB
61
62
205
562
563
564
565
571
155
353
354
355
356
432
433
434
435
436
437
438A
438B
438C
438D
439A
4396
439H
545
565
617
SB1161
SB1162
SB1163
SB1164
SB1165
SB1166
SB1167
SB1168
SB1372
SB1373
SB1374
SB1382
SB1392
SB1402
SB2262
SB2263
S32264
SB2265
SB2301
SB2305
SB2332
SB2333
SB2334
SB2335
SB2336
SB2337
SB2338
SB2339
SB2345
SB2544
-------
JY=IY-MY+1 SB2545
IF (JX.LT.1.0R.jY.LT.1.0R.JX.GT.NHX.OR«JY.GT.NMY) 60 TO 285 SB2546
CNRECH(JX,JY)«FCTR2 SB2551
285 CONTINUE SB2555
C IF USING SMALLER SUBGRIO FOR TRANSPORT/ READ INITIAL SB3005
C CONCENTRATION ARRAY FOR SUBGRIO NODES ONLY—- SB3006
00 420 IY»1,NMY SB3021
JY»IY+MY-1 SB3025
IF (INPUT.E0.1) READ (5/660) (CONC(IX,IY),IX«1,NMX) SB3031
00 410 IX=1,NMX SB3041
JX=IX+MX-1 SB3045
390 IF (THCK(JX/JY).NE.O.O) CONC(IX,IY)*FCTR SB3081
CFCTR»CONINT(IX,IY)*THCK(JX,jr)*AREA S33093R
500 FORMAT (3H /25F5.1) SB3421
580 FORMAT (1M ,4013) SB3501
630 FORMAT (1HO/05X/05X/44HNO. OF FINITE-DIFFERENCE CELLS IN AQUIFER - SB3551
633 FORMAT (1HO,////2X,26HFLOW MODEL (PRIMARY GRID):/) SB3582
634 FORMAT (1HO,///2X,18HTRANSPORT SUBGRID:/) SB3583
635 FORMAT (1HO,05X,05X,44MNO. OF FINITE-DIFFERENCE CELLS IN AQUIFER * SB3564
1 ,I4//10X,28HAREA OF AQUIFER IN MODEL " ,G12.5,10H SQ. FT./) SB3585
755 FORMAT (1H ) SB3715
775 FORMAT C1HO,18X,31HSECONOARY SUBGRIO FOR TRANSPORT//16X,30HNMX ( SB3763
1NUMBER OF COLUMNS) * ,I4/16X,30NNMY (NUMBER OF ROWS) = /I SB3764
24//16X/38MCROSS-REF. TO PRIMARY GRID IX IY/46X/8H /18 SB3765
3X/28HFIRST NODE (UPPER LEFT) AT: /2I4/18X/28HLAST NODE (LOWER RICH SB3766
4T) AT: ,214) SB3767
2 POROSITY),8X,3H» ,F9.3/13X,39HBETA (LONGITUDINAL OISPERSIVITV SB3841
3) * ,F7.1/13X,31HDLTRAT (RATIO OP TRANSVERSE TO/21X,30HLONGITUDI SB3851
888 FORMAT (1H1) SB4017
COMMON /HEDC/ MX,MY,MMX,MMY,NMX,NMY,MCM£ SO 125
C TRACK PARTICLE LOCATIONS IN COORDINATES OF PRIMARY GRID SO 505
00 410 IX«1,NMX SO 512
JX»IX*MX-1 SD 515
DO 410 IY*1,NMY SO 522
JY=IY*MY-1 SO 525
IF (THCK(JX/JY).EQ.O.O) GO TO 410 . SO 531
IF (IX.EQ.1.0R.IX.EQ.NMX.OR.IY.EQ.1.0R.XY.EQ.NMY) TEST2«1.0 SO 595
IF (VPRM(JX,JY).GT.0.09) TEST2-1.0 SD 601
IF (RECUX,JY).NE.O.O) TEST2-1.0 SO 611
IF (THCK(JX+1sJV+1).EQ.O.O.OR.THCK(JX+1sJY-1>.EQ.O.O.OR.THCK(JX-1, SD 621
1JY+1).EQ.O.O.OR.THCK(JX-1,JY-1).EQ.O.O) TEST2=1.0 SD 631
IF ((THCK(JX/JY*1).EO.O.O.OR.TMCK(JX,JY-1).EQ.O.O.OR.TMCK(JX+1/JY) SO 641
1.EQ.O.O.OR.THCK(JX-1,JY).EQ.O.O).ANO.NPTPND.GT.5) TEST2=1.0 SO 651
PART(1,IND)sJX+F1*EVET SO 801
PART(2,IND)=JY*F1«EVES SD 811
PART(1,INO)=(JX+F1«EVET)+F2*EVET2 SD1022A
PART(2,INO)*(JY*F1*EVES)*F2»EVES2 S01023A
150 PART(1,IND)«JX SD1076
PART(2,INO)»-JY S01091
PART(1,INO)*JX+F2*EVET SD1171
PART(2,IND)«-JY SD1181
PARTC1,IND)=JX SD1381
PART(2,INO)ejY+F2*EVET SD1391
COMMON /HEOC/ MX,MY,MMX,MMY,NMX,NMY,MCMK. SE 145
IF (IX.GT.NMX.OR.IV.GT.NMV) GO TO 12 SE 315
12 JCK«0 SE 343
IF (IX.LT.(MX-1).OR.IY.LT.(MY-1).OR.IX.GT.(MMX+1).OR.IY.GT.(MMY*1) SE 344
1) JCK=1 SE 345
IF (A8VX.GT.VMAX.ANO.JCK.EQ.O) VMAX*ABVX SE 481
IF (ABVY.GT.VMAY.AND.JCK.EQ.O) VMAY-ABVY SE 561
-------
IF (A6VX.GT.VMXBO.ANO.JCK.EO.O) VMXBO«ABVX
IF (ABVY.GT.VMYBO.AND.JCK.EQ.O) VMYBD«ABVY
IF (JCK.GT.O) GO TO 20
DO 150 IX=2/MMX
00 150 IY»2/MMY
JX»IX-MX*1
JY»IY-MY+1
IF (JX.LT.1.0R.JY.LT.1) GO TO 150
IF ((IX-M).GT.MMX) GO TO 140
DISP(JX/JY/1)=(DALN*VXE2+OTRN*VYE2)/(VMGE2*XX2)
IF ((IY-1).LT.MY.OR.(IY+1).GT.MMY) GO TO 140
DISP(JX/JY/3)=(DALN-DTRN>*VXE*VYE/(VMGE2*XY2)
IF ((IV-M).GT.MMY) GO TO 150
DI$P(JX/JY/2)*(DALN*VY$2+DTRN*VXS2)/(VMGS2*YY2)
IF ((IX-1).LT.MX.OR.(IX+1).GT.MMX) GO TO 150
DISP(JX/JY/4)=(DAUN-DTRN)*VXS*VYS/(VMGS2*XY2)
00 160 IX«2/MMX
00 160 IV=2/MMY
JX=IX-MX+1
JY=IY-MY+1
IF (JX.LT.1.0R.JY.LT.1) GO TO 160
1>.EQ.O.O.OR.THCK(IX+1,IV-1).EQ.O.O> DISP( JX/ JY/3>=0.0
1).EQ.O.O.OR.THCK(IX-1/IY*1).EQ.O.O) DISP( JX/ JY/4)«0.0
00 170 IX=1/NMX
00 170 IY*1/NMY
00 190 IX=2/MMX
DO 190 IY=2/MMY
IF (JX.LT.1.0R.JY.LT.1) GO TO 190
DISP(JX,JY,1)«DISP(JX,JY,1>*BAVX
OISP(JX,JY,2)»DISP(JX*JY/2)*BAVY
DISP(JX/JY/3)=DISP(JX/JY/3)*BAVX
00 260 IY=1/NMY
260 WRITE (6x500) (OISPCIXx I Y,1 ) xIX'
DO 270 IY=1/NMY
270 WRITE (6/500) (DISPUX/I Y/2>/IX=1 ,NMX>
DO 280 IY=1/NMY
280 WRITE (6/500) (DISP(IX/IY/3)/IXc1 /NMX)
DO 290 IY=1/NMY
290 WRITE (6/500) (DISP(IX/I Y/4)/IX«1/NMX)
COMMON /HEOC/ MX/MY/MMX/MMY/NMX/NMY/MCHK
NLOC'O
JXsIX-MX+1
JY-IY-MY+1
JNX«INX-MX-»-1
JNY«INY-MY+1
IF (MCHK.EQ.O) GO TO 342
IF (JNX.LT.1.0R.JNX.GT.NMX.OR.JNV.LT.1.0R.JNY.GT.NMY) NLOC=1
IF (NLOC.GT.O) GO TO 345
342 CONTINUE
SUMC(JNX/JNY)aSUMC(JNX/JNY)-fPART(3/IN)
NPCELL(JNX/JNY)=NPCELL(JNX/JNY)+1
345 CONTINUE
IBD=0
IF (VPRM(IX/IY).LT.0.09) GO TO 348
348 IF (MCHK.EQ.O) GO TO 540
IF (JX.EQ.1.AND.VXBDY(IX-1/IY).GT.O.O.ANO.JNX.GT.JX) IBD*1
IF (JX.EQ.NMX.AND.VXBOY(IX/IY).LT.O.O.AND.JNX.LT.JX) IBD=1
SE 671
SE 681
SE 7C5
SE1351
SE1361
SE1375
SE1376
SE1377
SE1405
SE1511
SE1525
SE1531
SE1555
SE1651
SE1665
SE1671
SE1711
SE1721
SE1725
SE1726
SE1727
SE1741
SE1761
SE1811
SE1821
SE1961
SE1971
SE1973A
SE1973B
SE1973C
SE2001
SE2011
SE2021
SE2033
SE2191
SE2201
SE2221
SE2231
SE2251
SE2261
SE2281
SE2291
SF 125
SF 335
SF 415
SF 475
SF2395
SF2396
SF2397
SF2398
SF2405
SF2407
SF2421
SF2431
SF2445
SF2478
SF2501
SF2522
SF2523
SF2524
-------
IF CJY.EQ.1.ANO.VYBDYCIX,IY-1).GT.O.O.AND.JNY.GT.JY) 180=1 SF2525
IF (JY.EO.NMY.AND.VYBDY NPOLDUX/JY)=NPOLD(JX/JY)-1 SF2886
525 DLXsINX-IX SF3425
PARTC1,IP)=TEMPX-DtX SF3435
OLY=INY-IY SF3455
PART(2/IP)*TEMPV-Ol.Y SF3465
PART(2/IP)=-PART(2/IP> SF3475
PART(3*IP)*CONC(JX,JY>*EXP(-OCYFCT> SF3477
SUMCUX,JY)»SUMC SF3479
NPCELt(JX/JY)=NPCELl(JXsJY)+1 SF3481
GO TO 540 SF3483
PART(3*IP)=CONC(JX,JY> SF3531
550 IF (NLOC.GT.O) GO TO 565 SF3575
IF (VPRM(INX/INY).GT.0.09.AND.WT(INX/INY).LT.MK(INX,INY)) GO TO 56 SF3581
560 IF (NPOLD(JNX/JNY).LE.O) GO TO 590 SF3636
565 CONTINUE SF3638
IF (NLOC.GT.O) GO TO 56? SF3661
SUMC(JNX,JNY)=SUMC(JNX,JNY)-CONC(JNXxJNY) SF3663
NPCELL(JNXxJNY)aNPCELLUNX,JNY>-1 SF3665
NPOLD(JNX,JNY)*NPOLD SF4051
630 CONTINUE SF4053
COMMON /HEDC/ MX/MY*MMX^MMY*NMX/NMY/MCMK SG 135
00 10 IX»1xNMX SG 232
DO 10 IV*1/NMY SG 242
20 00 60 IX=1/NMX . SG 352
00 60 IY=1/NMY SG 362
JXsIx*HX-1 SG 366
JY=IY*MY-1 SG 367
IF (THCK(JXsJY).EQ.O.O) GO TO 60 SG 371
EQFCT1eRFFCT/THCK(JX,JY) . SG 382R
SLEAKc
-------
X1=DISP(IX/IY/1)*(CAVG(IX+1/IY)-C2)
If (ZX.LE.1) GO TO 42
X2=DISP(IX-1/IY/1)*(CAVG(IX-1/IY)-C2)
IF (IY.GE.NMY) GO TO 43
Y1*OISP(IX/IY/2)*(CAVG(IX/IY+1)-C2)
IF (IY.LE.1) GO TO 46
Y2=DISP(IX/IY-1/2)*(CAVG(IX/IY-1)-C2)
IF .GT.0.09) GO TO 90
00 100 IV*1sNMV
100 WRITE (6/330) (NPCELL ( IX,IY),IX«1 ,NMX)
110 DO 130 IX«1/NMX
00 130 IY«1/NMY
JX*IX+MX-1
JY=IY+MY-1
IF (THCK(JX/JY).EQ.O.O) GO TO 120
120 IF (CONC(IXsIY).GT.O.O) WRITE (6/310) JX/ JY/CONC
-------
FLW=VPRM(JX/JY>*(WT(JX/JY)-HK(JX/JY))
SUBGRIO BOUNDARIES
IF (MCHK.EQ.O) 60 TO 275
YT=YDEL*TIMV
XT=XOEL*TIMV
00 272 IY=MY/MMY
IX«MX
JY=IY-MY+1
FLW=TMRX(IX-1/IY/1)*
IF (FLU.GT.0.0) FLMIN»FLHIN+FLW*XT*CNOLO(JX,NMY)*EXP(-DCYFCT)
274 IF (FLW.LT.0.0) FLMOT«FLMOT+FLW«XT*CNOLDUX,NMY)*EXP(-OCYFCT)
275 CONTINUE
190 FORMAT (1HO,30I4)
300 FORMAT (3M ^2515)
COMMON /HEOC/ MX/MY,MMX/MMYxNMX,NMY/MCHK
DO 20 IY«1xNMY
00 10 IX=1,NMX
20 WRITE (6/240) (IC(IX)*IX*1sNMX)
00 40 IY = UNMY
DO 30 IX»1,NMX
40 WRITE (6/240) (1C(IX)/IX=1,NNX)
JX=IXOBS(J)
JY=IYOBS(J)
C1INT=0.0
IX»JX-MX*1
IY=JY-MY*1
IF (JX.LT.MX.OR.JY.LT.MV.OR.JX.GT.MMX.OR.JY.GT.MMY) GO TO 125
C1INT*CONINT(IXsIY>
GO TO 127
125 WRITE (6/435)
127 WRITE (6/440) MOZ/WT(JX,JY)/C1INT/
435 FORMAT (1M /3X/45H** NOTE ** THIS OBS. WELL IS LOCATED OUTSIDE/16
1X/24HOF THE TRANSPORT SUBGRIO)
SG1601
SG1692A
SG1692B
SG1692C
SG1692D
SG1694A
SG1694B
SG1694C
SG1694D
SG1694E
SG1694F
SG1695A
SG1695B
SG1695C
SG16950
SG1696A
SG1696B
SG1696C
SG1696D
SG1696E
SG1696F
SG1697A
SG1697B
SG1697C
SG16970
SG1696A
SH1071
SH1191
SI 125
351
361
381
541
551
581
SI1074
SI1076
SI1082
SI1083
SI1084
SI1085
SI1086
SI1087
SI1088
SI1091
SI1525
SI1526
SI
SI
SI
SI
SI
SI
-------
To optimize computer storage (or memory) requirements while using this
option, it may be desirable to redimension the arrays used by the flow model
to the size of the primary grid and the arrays used by the transport model to
the size of the subgrid. For example, if it were desired to use a primary
grid of (40,40) but keep the transport subgrid within the original dimensions
of (20,20), then the following changes would be required in the common and
dimension statements of the program:
COMMON /PRMC/ NODEID<40,40>,NPCELL(20,20),NPOLD(20,20),LIMBO<500), SA 145
COMMON /MEDA/ THCKUO,40) ,PERM(40,40) ,TMWL(5,50) ,TMOBS ( 50)/ANFCTR SA 170
COMMON /MED6/ TMRX(40,40,2),VPRM(40,40),HI(40,40),HR(4C,40),HC(40, SA 180
140),MK(40,40),WTC40,40),REC<40,40>,RECH(40,4C»,TIM(100>,AOPT(20>, SA 190
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5/50),VX(40,40),VY(40, SA 211
140),CONINT(20,20),CNRECH<20,20),POROS,SUMTCH,BETA,TIMV,STORM,STORM SA 220
COMMON /PRMC/ NOOEIO(40/40),NPCELLC20/20)/NPOLD(20/20)/LIMBO(500)/ SB 95
COMMON /MEOA/ THU(40/40)/PERM(40/40)/TMWLC5/50)/TMOBS(50)/ANFCTR SB 120
COMMON /HEOB/ TMRX(40/40/21/VPRM(40/40)/HI(40/40)/HR(40/40)/HC(40/ SB 130
140),HK(40,40),UT(40,40),REC(40,40),RECM<40,40),TIM(100),AOPT(20), SB 140
COMMON /CHMA/ PART(3/6400)/CONC(20/20)/TMCN(5/50)/VX(40/40)/VY(40/ SB 161
140)/CONINT(20/20),CNRECH(20/20)/POROS/SUNTCH/BETA,TIMV/STORM/STORM SB 170
COMMON /CHMC/ SUMC(20/20)/VXBDY(40/40)/VYBDY(40/40) SB 210
COMMON /PRMC/ NOOEIO(40/40)/NPCELL(20/20)/NPOLO(20/20)/LIMBO(500)/ SC 85
COMMON /HEDA/ THCKUO/40)/PERM(40/40)/TMWL(5/SO)/TMOBS(50)/ANFCTR SC 110
COMMON /HEOB/ TMRX(40/40/2)/VPRM(40/40)/HI(40/40)/HR(40,40)/HC(40/ SC 120
140)/HK(40/40),HT(40,40)/REC(40/40)/RECH(40/40)/TIM(100),AOPT(20)/ SC 130
DIMENSION H(40)/ 6(40), G(40) SC 171
COMMON /PRMC/ NODEIDUO,40),NPCELL(20,20)/NPOLD(20,20)/LIMBO(500), SO 65
COMMON /HEOA/ THCK(40/40)/PERM(40/40)/TMHL(5/50)/TMOBS(50)/ANFCTR SO 90
COMMON /HEDB/ TMRX(40,40,2),VPRM(40,40),Hl(40,40),HR(40,40),MC(40x SD 100
140),HK(40,40),HT(40,40),REC(40/40),RECH(40,40),TIM(100)/AOPT(20)/ SO 110
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5,50),VX(40,40),VY(40, SO 131
140>/CONINT(20,20),CN«ECH(20,20),POROS,SUMTCH,BETA,TIMV/STORM/STORM SO 140
COMMON /PRMC/ NOOEIDUO/40),NPCELL(20,20),NPOLD(20,20),LIMBO(500)/ SE 85
COMMON /HEOA/ TMCK(40,40),PERM(40,40),TMHL(5/50),TMOBS(50)/ANFCTR SE 110
COMMON /HEOB/ TMRX(40/40/2),VPRM(40,40),HI(40,40),MR(40,40),HC(40, SE 120
140),HK(40,40),WT(40,40),REC(40,40),RECH(40,40),TIM(100),AOPT(20), SE 130
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5,50),VX(40,40),VY(40, SE 161
140),CONINT(20,20)/CNRECH(20,20),POROS,SUMTCH,BETA,TIMV,STORM,STORM SE 170
COMMON /CHMC/ SUMC(20,20),VXBDY(40,40),VYBDY(40,40) SE 190
COMMON /PRMC/ NODEIO(40,40) ,NPCELK20,20) ,NPOLD(20/20)/LIMBO (500) , SF 65
COMMON /HEOA/ THCK(40,40),PERM(40,40),TMWL<5,50),TMOBS(50),ANFCTR SF 90
COMMON /HEDB/ TMRX(40,40,2),VPRM(40,40),HI(40,40),MR(40,40),HC(40, SF 100
140),HK(40,40),WT(40,40),REC(40,40),R£CH(40,40),TIM(100),AOPT(20), SF 110
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5,50),VX(40,40),VY(40, SF 141
140)/CONINT(20/20)/CNRECH(20/20)/POROS/SUMTCH/BETA,TIMV,STORM/STORM SF 150
COMMON /CHMC/ SUMC(20/20)/VXBDY(40,40),VY60Y(40,40) SF 170
COMMON /PRMC/ NODE 10(40,40),NPCELL(20,20),NPOLO(20,20),LIMBO(500), SG 75
COMMON /HEOA/ THCK(40,40),PERM(40,40),TMHL(5,50)/TMOBS(50),ANFCTR SG 100
COMMON /HEOB/ TMRX(40,40,2)/VPRM(40,40),HI(40,40),HR(40/40),HC(40, SG 110
140)/HK(40/40),WT(40,40),REC(40,40),RECM(40,40),TIM(100)/AOPT(20), SG 120
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5,SO),VX(40,40),VY(40/ SG 151
140),CONINT(20,20),CNRECM(20,20),POROS,SUMTCH,BETA,TIMV,STORM,STORM SG 160
COMMON /CHMC/ SUMC(20,20)/VXBOY(40/40),VY6DY(40,40) SG 190
COMMON /PRMC/ NOOEID(40,40),NPCELL(20,20),NPOLD(20,20),LIM80(500), SH 65
COMMON /HEDA/ THUUO,40) ,PERM (40,40) ,TMHL ( 5,50)/TMOBS (50) , ANFCTR SH 90
COMMON /HEDB/ TMRX(40,40,2),VPRM(40,40),HI(40,40),HR(40,40),HC(40, SH 100
140),HK(40,40),HT(40,40),REC(40,40),RECH(40,40),TIM(100),AOPT(20), SH 110
DIMENSION IM(40) ' SH 141
COMMON /PRMC/ NODEIO(40,40),NPCELL(20,20)/NPOLD(20,20),LIMBO(500)/ SI 65
COMMON /HEDA/ THCK(40,40),PERM(40,40),TM«L(5,50),TMOBS(50),ANFCTR SI 90
COMMON /HEOB/ TMRX(40,40,2)/VPRM(40/40)/HI(40,40>,MR(40,40),HC(40, SI 100
140),HK(40,40),WT(40,40),REC(40,40),RECH(40,40),TIM(100),AOPT(20), SI 110
COMMON /CHMA/ PART(3,6400),CONC(20,20),TMCN(5,50),VX(4C,40),VY(40, SI 131
140),CONINT(20,20),CNRECH(20,20),POROS,SUMTCH,BETA,TIMV,STORM,STORM SI 140
-------
NOTE ON COMPUTER PROGRAM UPDATE
August 2, 1985
Reference ; "Computer model of two-dimensional solute transport and dispersion in
ground water" by L. F. Konikow and J. D. Bredehoeft (1978): U.S. Geological Survey
Techniques of Water-Resources Investigations, Book 7. Chapter C2.
The following modifications to the subject computer code will allow the
model to simulate a first-order irreversible-rate reaction and (or)
equilibrium-controlled sorption-desorption for a linear isotherm.
An example of a first-order irreversible-rate reaction is radioactive
decay. The rate constant, x,_is defined as
X -./« 2/tM
where tj$ is the half -life of the solute. The decay is applied directly to
the tracer particles (rather than at the nodes of the finite-difference grid)
with the following exponential function:
k k-1
Cp = Cp exp(-XA/)
where Cp is the solute concentration of the tracer particle,
k is the index in the time dimension; and
A/ is the time increment.
This exponential formulation has no numerical stability restrictions. However,
if the half -life is much smaller than the time step (A/) for solving the
transport equation, then some numerical accuracy will be lost.
The equilibrium-controlled sorption-desorption is expressed in terms of a
retardation factor (RA, as:
where Kd is the distribution coefficient, L3/M;
Pb is the bulk density of the solid, M/L3; and
e is the porosity.
The revised input data formats will allow either one or both of these
types of reactions to be implemented by specifying a value of 1 for a new
variable, NREACT, in columns 69-72 of input card 2. If NREACT - 1, then
you must also insert a new card (or line) immediately following input card 3
that specifies values in the following order for DK (Kd), RHOB (Pb), and
THALF (tj$) (in seconds), using a free format (that is, the three values are
separated by spaces or commas, but blanks are not read as zeros). This
modification to the input data will not require any modifications to existing
data sets for nonreactive solutes (that is, identical results will be obtained
-------
with and without these program changes).
These modifications were evaluated by comparing the numerical solutions
with analytical solutions (van Genuchten and Alves, 1982) for various
combinations of parameters. As can be seen in figure l, the agreement is
excellent for all cases.
NO DECAY AND NO SORPTION
DECAY WITH NO SORPTION
0.1-
0.8-
0.7-
OJ-
0.4-
0.3
O.H
0 10 20 30 40 SO 10 70
DISTANCE (CM)
SORPTION WITH NO DECAY
90 no
- Analytical
Numerical
^S days
40 90 tO 70 80 tO tOO
DISTANCE (CM)
Analytical
• Numerical
ti/j= 4.5 days
« 20 jo «o so w TO
DISTANCE (CM)
DECAY WITH SORPTION
BO
to 100
20
10 40 SO tO 70
DISTANCE (CM)
BO tO
100
Figure 1.— Comparison of numerical and analytical solutions for transport
with reactions in one-dimensional, steady-state flow (Ax = 2 cm.
V = 25 cm/day, and
-------
This set of modifications also revises the structure of subroutine
CNCON. Previously, equation 40 was solved twice — using concentrations at
times A:-l and k* over 0.5 & each and summing the results. Now, following
the modifications of Tracy (1982), the concentrations at times k-1 and k* are
first averaged and equation 40 then solved once over A/. This will yield a
reduction in execution time on the order of 5 percent.
The program modifications can be implemented by deleting the following
statements:
A 60
B 430
B3100
B3690
E 710
E1080
E1830
E2360
E2460
F2040
G
G
F2050
F2865
G 200
220
320
G 330
G 340
G 380
G 400
G 410
G 430
G 440
G 470
475
620
650
660
670
680
690
G 700
G 710
G 720
G 730
G 740
G 750
G 760
.800
810
G
G
G1498
G1502
G1535
G1678
I 610
I 660
11360
11370
11380
G1470
and by inserting the following Fortran statements in the proper sequential
location:
C * REV. MAY-AUG. 1985 BY L. KONIKOW AND M. PERSON TO INCLUDE: *
C * DECAY AND EQUILIBRIUM SORPTION-DESORPTION REACTIONS *
C * *
COMMON /CHMR/ RF/DK/RHOB/THALF,DECAY/ADSORB,SORBI/DMASS1/CSTM2
SORBI=0
RMOB=0.0
DMASS1-0.0
DECAY=0.0
THALF=0.0
1PND/NCODES/NPNTMV/NPNTVL/NPNTD/NPOELC/NPNCHV/NREACT
READ REACTION TERMS IN FREE FORMAT
IF (NREACT.EQ.1) READ (5/*) DK/RHOS/THALF
RF=1.0+(DK*RHOB/POROS)
IF (THALF.GT.0.0) DECAY=ALOG(2.0)/THALF
WRITE (6/895) DK/RHOB/RF/THALF,DECAY
CFCTR2=DK*RHOB
CFCTR=CONINT(IX/IY)«THCK(IX/IY)*AREA
SORBI=SORBI+CFCTR*CFCTR2
410 STORMI=STORMI*CFCTR*POROS
740 FORMAT (1814)
895 FORMAT (1HO/23X/14HREACTION TERMS//13X/37HDK (DISTRIBUTION CO
1EFFICIENT) s /E12.5/13X/37HRHOB (BULK DENSITY OF SOLIDS) = /E
212.5/13X/37HRF (RETARDATION FACTOR) = /E12.5/13X/37HTMA
3LF (HALF LIFE OF DECAY/IN SEC)= /E12.5/13X/37MDECAY (DECAY CON
4STANTsLN 2/THALF)= ,E12.5)
COMMON /CHMR/ RF/DK./RHOB/THALF/DECAY/ADSORB/SORBI/DMASS1/CSTM2
TDIV=(POROS*THCK(IX/IY)*RF)/DABS(DIV)
WRITE (6/392)
IF (RF.LE.1.0) GO TO 115
WRITE (6/394)
VMAX«VMAX/RF
A 59R
A 60R'
A 69R
B 182R
B 295R
B 296R
B 396R.
B 397R
B 398R
B 399R
B 431R
B 454R
B 455R
B 532R
B 534R
B 635R
B3015R
B3092R
B3094R
B3096R
B3691R
B4121R
B4122R
B4123R
B4124R
B4125R
E 205R
E 711R
E1055R
E1071R
E1072R
-------
TIMV (CELOIS)
VMAY=VMAY/RF
VMXBD=VMXBD/RF
VMYBD=VMYBO/RF
WRITE (6x400) VMAX/VMAY
WRITE (6/410) VMXBD/VMYBD
115 TDELX=CELDIS*XDEL/VMAX
TDCO*(OISP(IX/IY/1)+OISP(lX/IY/2))/RF
310 FORMAT (1HO/19H TMV (MAX. INJ.) = /G12.5/20H
392 FORMAT (1MO/5X/16MFLUID VELOCITIES)
394 FORMAT (1MO/5X/27MEFFECTIVE SOLUTE VELOCITIES)
400 FORMAT (1H /8H VMAX = /1PE9.2t5X/7HVMAY = /1PE9.2)
COMMON /CHMR/ RF/DK/RHOB/THALF/DECAY/ADSORB/SORB I/OMASS1/CSTM2
IF (THALF.GT.0.0.AND.THALF.LT.TIMV) WRITE (6/685)
DCYFCT=TIMV*DECAY
DCY2=DCYFCT*0.5
290 DISTX=XVEL*CONST1/RF
DISTY=YVEL*CONST2/RF
DECAY PARTICLES
PART(3/IN)=PART(3/IN)«EXP(-DCYFCT)
398 SUMC(IX,IY)=SUMC(IX/IY)+CONC(lXxIY)*EXP(-DCY2)
685 FORMAT (1HO/5X/51H**« CAUTION *** DECAY HALF-LIFE IS LESS THAN TI
1MV/V23X/24HACCURACY MAY BE AFFECTED/23X/34H(REDUCE TIMV BY DECREAS
2ING CELOIS))
COMMON /CHMR/ RF/DK/RHOB/THALF/DECAY/AOSORB/SORBI/OMASSI/CSTMZ
DIMENSION CNCNC(20/20)/CNOLD(20/20)/CAVG(20/20)
CAVG(IX/IY)=CONC(IX/IY)
TVA2=TVA«0.5
TMCMK=TIMV»10.0
SRCDCY=0.0
RFPOR=RF*POROS
RFPORA=RFPOR*AREA
CONC. CHANGE DUE TO:
MIXING AT SOURCE CELLS...
...WITH DECAY OF RECHARGE DURING TIME INCREMENT
CONST=TIMV
DCYFCT=TIMV*DECAY
DCYHLF=DCYFCT*0.5
RFFCT=CONST/RF
GO TO 70
EQFCT1=RFFCT/THCK(IX/IY)
C1=CAVG(IX/IY)
C2 = C1
CLKCN=C1
IF (SLEAK.GE.0.0) GO TO 25
CLKCN=CNRECH(IX/IY)*EXP(-OCYHLF)
SRCOCY=SRCDCY*(CNRECH(IXxIY)-CLKCN)*SLEAR«TVA
25 CONTINUE
IF (RATE.GE.0.0) GO TO 27
CNREC=CNRECH(IX/IY)*EXP(-DCYHLF)
SRCDCY«SRCDCY+(CNRECH(IX/IY)-CNREO*RATE*TVA
27 IF (RECH(IX/IY).GE.O.O) GO TO 29
CNREC2=CNRECH(IX/IY)*EXP(-DCYHLF)
SRCDCY=SRCDCY+(CNRECH(IX/IY)-CNREC2)*RECH(IX/IV)*TVA
29 CONTINUE
IF (THALF.GT.TMCHK.OR.THALF.EQ.O.O) GO TO 37
IF (OIV.GE.0.0) GO TO 37
IF (CNOLD(IX/IY).LE.O.O.OR.CONC(IX/IY).LE.O.O) GO TO 37
E1074R
E1075R
E1076R
E1077R
E1078R
E1081R
E1831R
E2361R
E2451R
E2452R
E2461R
F 172R
F 205R
F 265R
F 267R
F2041R
F2051R
F24UR
F2415R
F2866R
F4174R
F4175R
F4176R
G 195R
G 201R
G 255R
G 295R
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
296R
297R
305R
306R
321R
322R
323R
341R
342R
343R
344R
345R
381R
4Q1R
403R
411R
425R
431R
432R
435R
471R
472R
473R
474R
A76R
477R
473R
482R
484R
486R
-------
37
220
C1=EXP((ALOG(CNOLD(IX,IY))+ALOG(CONC(IX/IY)))*0.5)
IF (NPCELLdX/IYKLE.O) C1=CNOLD(IX/I Y) *EXP (-OC YHLF)
CONTINUE
--- CONC. CHANGE DUE TO DISPERSION FOR TIMV ---
X1=DISP(IX,IY/1)**CCAVG(IX/IY+1)+CAVG(IX-1/IY-M)-CAVG(IX/IY-1)-C
AVG(IX-1/IY-1)>
YY1=DISP(IX/IY,4)*CCAVG(IX+1/IY)+CAVG(IX+1/IY+1)-CAVG(IX-1/IY)-CAV
G(IX-1/IY+1)>
YY2=DISP(IX,IY-1,4)*)
... AND DECAY ---
ADSORB=0.0
RFDCY=RFPOR*DECAY*TVA*0.50
C1=CONC
C1B=C1*THCK
DELDCY=CNOLD(IX,IY>-CNOLD(IX,IY)*(EXP<-DCYFCT))
DMASS1=DMASS1-DELDCY*THCK(IX/IY)*RFPORA
STORM=STORM+C1B*ARPOR
--- COMPUTE MASS ADSORBED ---
ADSORB = C1B*DMRHOB*AREA+AOSORB
CMSOUT=CMSOUT+RECCIX,IY)«TIMV*«1.0-HTFCT>*CNOLO(IX,IY)+WTFCT«C1)
CMSOUT=CMSOUT+RECM
FLMOT=FLMOT+FLW*TVA*((1.0-WTFCT)*CNOLD(IX/IY)+WTFCT*C1)
--- COMPUTE MASS LOST BY DECAY ---
CSTM2=CSTORM*ADSORB-SORBI
DMASS1=DMASS1*SRCDCY
COMMON /CHMR/ RF/DK/RH06/THALFxDECAY/ADSORB/S6RBI/OMASS1/CSTH2
50 RESID=SUMIO-CSTM2+DMASS1
IF (SUMIO.GT. (STORMI + SOR8D) GO TO 70
£RR3=-100.0*(RES1D>/(STORMI+SORBI-SUMIO)
WRITE (6*295) DMASS1
WRITE (6/296) ADSORB
WRITE (6/298) SOR6I
WRITE (6/332) CSTM2
IF (SUMIN.NE. 0.0. AND. SUMIO.GT. ( STORMI+SORBI ) ) GO TO 90
295 FORMAT (8X/25MMASS LOST BY DECAY = /1E12.5)
296 FORMAT (8X/25MMASS ADSORBED ON SOLIDS= /1E12.5)
298 FORMAT (8X/25HINITIAL MASS ADSORBED = /1E12.5)
310 FORMAT (8X/25MINITIAL MASS DISSOLVED = /1E12.5)
320 FORMAT (8X/25MPRESENT MASS DISSOLVED = /1E12.5)
330 FORMAT (8X/25MCMANGE MASS DISSOLVED = /1E12.5)
332 FORMAT (8X/25MCHANGE TOTL.MASS STORED= /1E12.5)
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
468R
489R
592R
621R
651R
661R
671R
681R
691R
701R
711R
721R
731R
741R
751R
761R
8A1R
935R
GU11R
GU12R
GU42R
GU43R
G1444R
G14A5R
GU71R
G1472R
G1473R
G1499R
G1536R
G1679R
G1715R
G1725R
G1726R
: 155R.
I 611R
I 637R
661R
751 R
752R
753R
795R
845R
I1341R
I1342R
I1343R
11361R
I1371R
I1381R
I13E2R
-------
REFERENCES
Tracy, J. V., 1982, Users guide and documentation for adsorption and decay
modifications to the USGS solute transport model: U.S. Nuclear
Regulatory Commission, Report NUREG/CR-2502, 138 p.
Van Genuchten, M. Th., and Alves, W. J., 1982, Analytical solutions of the
one-dimensional convective-dispersive solute transport equation: U.S.
Dept. of Agriculture, Technical Bulletin 1661, 151 p.
-------
NOTE ON COMPUTER PROGRAM UPDATE
July 31, 1985
Reference i "Computer model of two-dimensional solute transport and dispersion in
ground-water," by L. F. Konikow and J. D. Bredehoeft (1978): U.S. Geological Survey
Techniques of Water-Resources Investigations, Book 7, Chapter C2.
The solute-transport equations presented in the cited report include two
terms that should have canceled out during the derivation and expansion of the
basic governing equation. Although the corresponding changes to the code were
documented previously in the updates of August 26, 1981, the correct equations
are reproduced below for clarification. (The code changes reduce slightly the
cpu time.)
dC
dt
b dXj
dc
a*,.
W(C - C')
(14)
W(C - C')
(.b
(16)
W(C - C')
(27)
CiJ,k-l
(39)
AC:
0.5 At
±-{U>, "'1;
'7
dx.i
0.5 At
b
9 ,.n 9C(**) > t
, ^D/y fl > f
9.v. • 9x .-
wfc, » - r1 )
rT ( V- JL 4r *«• /
€
(40)
-------
BOTE 01 COMPUTER PROGRAM UPDATE
July 26, 1985
Reference: "Computer model of tvo-dlmenslonaJ to Jute transport Mod disper-
sion In ground vater" by 1. F. Konikov and J. D. Bredehoeft (1978): U.S.
Geological Survey Techniques of Vater-Resources Investigations, Book 7,
Chapter C2.
THE FOLLOWING MODIFICATIONS WILL CORRECT A PROGRAMMING ERROR IN THE
ROUTINE TO CALCULATE CHANGES IN CONCENTRATION CAUSED BY DISPERSION.
FOR MOST PROBLEMS/ THE DIFFERENCE IN THE RESULTS MILL BE NEGLIGIBLE.
HOWEVER/ IF THE PROBLEM BEING SOLVED IS ONE IN WHICH DISPERSIVE FLUXES
ARE VERY STRONG RELATIVE TO CONVECTIVE (ADVECTIVE) FLUXES/ THEN THE
ORIGINAL CODE COULD HAVE GENERATED NEGATIVE MASS-BALANCE ERRORS OF UP
TO SEVERAL PERCENT.
THE MODIFICATIONS CAN BE IMPLEMENTED BY DELETING: G1120
G1130
G1UO
AND INSERTING THE FOLLOWING STATEMENTS IN THEIR PROPER SEQUENTIAL
LOCATIONS (AS INDICATED BY THE LINE NUMBERS IN COLUMNS 73-60):
CNCPCTsQ.O G1084G
IF (CONC(IX/IY).GT.O.O) CNCPCT«CNCNC(IX/IY)/CONC(IX/IY> G10BSG
IF (CNCPCT.LT.0.0) SUMC(IX/IY)=CNCPCT G1125G
-------
NOTE ON COMPUTER PROGRAM UPDATE
June 10, 1985
Reference: "Computer model of ttro-dimenaional solute transport and diapei—
si on In ground vater" by L. F. Konikov and J. D. Bredehoeft (1978): U.S.
Geological Survey Techniques of Water-Resources Investigations, Book 7,
Chapter C2.
An additional program modification has been made since the previous update
of October 12, 1983. The following changes will allow the user to specify
16 particles per node. This option can lead to increased numerical accuracy
in some cases.
1. Delete the following Fortran statements from the source code:
A 210
B 160
B 600
B 610
B4010
D 130
D 155
D 160
D 380
D 510
D 520
D 832
D 840
D 880
D 900
D 920
D 940
0 950
D 970
D 980
D1000
D1010
D1020
D1030
D1040
E 160
F 140
F 175
F2905
G 150
G 230
G 240
G 350
G 360
G 850
G 860
G1060
G1070
G1420
G1430
I 130
2. Insert the following Fortran statements in the proper sequential
location: |. .,(
* REV. JUNE-AUG. 1984 BY W. SANFQRD TO ALLOW 16 PTS. PER NODE * A 59
COMMON /CHMA/ PART(3/6400),CONC(20/20),TMCN(5/50)/VX(20,20),VY(20/ A 211
COMMON /CHMA/ P ART (3/6400»COMC (20* 20) /TMCN (5/ 50) ,VX < 2C/20), V V (20, B 161
If (NPTPND.NE.4.AND.NPTPND.NE.5.AND.NPTPND.NE.S.AND.NPTPND.NE.9. B 601
1 .ANO.NPTPNO.NE.16) WRITE(6/880) B 611
880 FORMAT (1HO,5X,47H*»* WARNING *** NPTPNO MUST EQUAL 4*5/8/9,OR 16) B4011
COMMON /CHMA/ PART(3'6400)/CONC(20/20)/TMCN(5/50>/VX(20/20)/Vr(20s D 131
COMMON /CHMP/ PTID(6400) 0 156
DIMENSION RPT(16>/RNT(16)/RP(16)/RN(16)/IPT(16) 0 161
IF (NPTPND.EQ.16) F1=0.25 0 223
IF (NPTPNO.EO.16) F2=0.125 D 224
00 30 IA=1/16 0 381
RPT(IA)=0.0 D 401
RNT(IA)=0.0 0 402
DO 410 IX»2,NNX D 511
DO 410 IY=2/NNY 0 521
KR2=0 0 541
RR=KR+1 D 793
IF (NPTPNO.EG.16) CO TO 72 0 795
IPT(KR)=IND 0 833
GO TO 76 0 835
72 IF (TEST.LT.98.0.OR.TEST2.GT.0.0) GO TO 135 D 841
76 IF (TEST.LT.98.0.OR.TEST2.GT.0.0) GO TO 139 0 845
PARTC=CNODE+CONC(IXD/IYD)*F1 0 901
80 PARTC=2.0*C1*CONC(IXO/IYO)/(C1*CONC(IXO/IYO)) 0 921
100 RPT(KR)=CONC(IXD,IYD)-PARTC 0 941
-------
RNT(KR)=C1-PARTC
110 RPJUR)=0.0
RNT(KR)=0.0
120 RPT(KR)=C1-PARTC
RNT(KR)=CONC(IXO/IYO)-PARTC
130 IF (NPTPNO.E0.16) GO TO 135
PART(3/IND)=PARTC
RP(KR)=RPT(KR)
RNUR) = RNT(KR)
GO TO 139
135 00 138 ITT = 1,2
EVET2=(-1.0)*«ITT
00 138 ISS '= 1,2
EVES2=<-1.0)**ISS
PART(1,IND)=(IX+F1*EVET)+F2*EVET2
PART(2,IND)=(IY+F1*EVES)+F2*EVES2
PART(2,IND)=-PART(2,IND)
KR2=KR2+1
IF (TEST.LT.98.0.0R.TEST2-.GT.O.O)
PART(3,IND) = PARTC
RP(KR2) = RPT(KR)
RNUR2) - RNT(KR)
IPTUR2) = INO
GO TO 137
136 PART(3,IND) = C1
137 PTIO/CONC<20/20>,TMCN<5,50>'VX<20/20>/VY(20/
PART (3* 6400) *CONC( 20/20) 'TMCN(5s50>'VX(20/20>/VY(20/
PTIDC6400)
16) F1=0.25
IF (NPTPND.EQ. 16) F2=0.125
IF (NPTPNO.EC.16) GO TO 400
GO TO (401, 411/421/431/441,451,461/471, 481), ITEM
GO TO (482/4 83/4 84 / 485 / 486/487, 488/489/490/491,4 92/493, 494/49 5 /
496, 497), ITEM
GO TO 441
GO TO 530
PART(1,IP)=IX-F1-F2
PART(2/IP)=IY-F1-F2
PTIO(IP)=1
GO TO 530
PART(1/IP)=IX-F1-F2
PART(2/IP)=IY-F1*F2
PTID(IP)=2
GO TO 530
PART(2/IP)=IY-F1-F2
(>TJD(IP)=3
0 951
D 971
0 981
D10C1
01011
D1012
01013
D1014
D1015
01016
01017
01018
01019
01021
01022
01023
01024
D1C25
01026
D1027
D1028
01029
01031
01032
01033
01034
D1035
01036
01037
01036
01039
01045
E 161
F 141
F 176
F 223
F 224
F29C1
F2906
F2921
F2922
F2924
F3266
F3267
F3268
F32t9
F3271
F3272
F3273
F3274
F3275
F3276
F3277
F3278
-------
485
486
AS?
488
GO TO 530
PARTC1/IP)=IX-F1+F2
PARTC2/1P)=IY-F14F2
PTID(IP>=4
GO TO 530
PART(1/1P)=IX-F1-F2
490
491
492
493
PTID(IP>=5
GO TO 530
PAKT(1/1P)
PART<2,IP)
PTID(IP)=6
GO TO 530
PA?T(1/IP)
PART(2/IP)
PTIOCP)=7
GO TO 530
PARTU/IP)
PART(2/IP>
PTID(IP>=8
GO TO 530
PART(1/IP)
PART(2/IP>
PTIO(IP)=9
GO TO 530
PART(1/IP)
PART(2/IP)
PTID(IP>=1
GO TO 530
PART<1/IP)
495
496
497
=IX-M-F2
=IY+F1+F2
=IX-F1+F2
=IY+F1-F2
=IX-F1+F2
=IY+F1+F2
=IX+F1-F2
=IY-F1-F2
=IX+F1-F2
=IY-F1+F2
0
=IX+F1+F2
PT10(IP)=1
GO TO 530
PART(1/IP)
PART(2/IP)
PTID(IP)=1
GO TO 530
PART(1rIP)
PART(2/IP)
PTID(IP>=1
GO TO 530
PART(1,IP>
PART(2/IP>
PTIO(IP>=1
GO TO 530
PART(1/IP)
PART(2/IP)
PTID(IP)=1
GO TO 530
PART (1,IP)
1
=1X*F1*F2
=IY-F1*F2
2
=lX-»-F1-F2
=IY+F1-F2
3
=IX+F1-F2
*IY+F1+F2
4
=IX+r1*F2
=IY+F1-F2
5
=IX*F1**2
PTIDCIP)=16
GO TO 530
COMMON /CUM A/
PART(3/64GO)/CCNC(2C'/2C)/TMCN(5/50)/VX(2C<20)/VY(2G/
F32S1
F3282
F32£3
F3284
F3285
F3286
F3267
F3283
F3289
F329.1
F3292
F32.93
F3294
F3295
F3296
F3297
F329S
F3299
F3301
F33C2
F3305
F33C4
F3305
F3306
F3307
F3308
F33C9
F3311
F3312
F3313
F33U
F3315
F3316
F3317
F3318
F3319
F3321
P3322
F3323
F3324
F3325
F332C
P3327
F332;
F332?
F3331
F3332
F3323
F3334
F3335
F 5 3 3 6
F3337
G 151
-------
DO 10 IX=2/NNX G 231
DO 10 IY=2/NNY G 241
20 DO 60 IX=2/NNX G 351
DO 60 IY=2/NNY G 361
70 DO 90 IX-2/NNX G 851
DC 90 IY=2/NNY . G 861
110 DO 130 IX=2/NNX G1061
DO 130 IY=2/NNY G1071
00 270 IX=2/NNX G1421
DO 270 IY = 2/NNY GU31
COMMON /CMMA/ PART(3/6400)/CONC<20/20)/TMCN(5/50)/VX(20/20)/VY(20* I 131
-------
NOTE ON COMPUTER PROGRAM UPDATE
October 12, 1983
Reference; "Computer model of two-dimensional solute transport and dispersion
in ground-water," by L. F. Konikow and J. D. Bredehoeft (1978): U.S.
Geological Survey Techniques of Water-Resources Investigations, Book 7,
Chapter C2.
Several additional program modifications have been made since the previous
update of August 26, 1981. These can be implemented as follows:
1. The following changes assure that all time-step and flow calculations
are perfomed entirely in double precision. These changes will only make
a difference on certain computers.
a) Delete the following Fortran statements from the source code:
A 115
B 55
b) Insert the following Fortran statements in the proper sequential
location:
REAL *8TMSUM/ANTIM/TDEL A 116
REAL *8TMSUM/ANTIM/TDEL B 56
REAL *80XINV/OYINV/ARINV/PORINV 3 57
REAL *80XINV/DYINV/ARINV/PORINV C 45
REAL *80XINV/OYINV/ARINV/PORINV E 35
REAL *80XINV/DYINV/ARINV/PORINV F 33
REAL *80XINV/DYINV/ARINV/PORINV G 35
2. The following format changes are made to provide more convenient
printouts for most situations.
a) Delete:
B1630 B2620 B3600
B2330 B3440
b) Insert:
160 WRITE (6x840) (VPRM(IX/IY),1X = 1/NX) B1631
260 WRITE (6/540) (PERMCIX,IY)/IX = 1/NX) 52331
320 WRITE (6/840) (VPRM(IX/IY)/IX=1/NX) 326?1
-------
3. The following changes will assure that all output routines are called
at the end of the last time step of a pumping period.
a) Delete:
A 450
A 610
b) Insert:
IPC.ISQ
IF (TOEL.EO.(PyR-TlNT)) IPCK=1
IF (REMN.EQ.O.O.OR.N.EG.NTXM.C8.IPCK.EQ.1) CALL OuTPT
120 IF
IF (NPNCHV.EQ.O)
SNOFILE(7)
155 CONTINUE
GO TO 155
A 702
A 703
A 704
A 705
5. The following changes were made primarily to improve the interpolated
estimates of velocities at tracer particles located in wells adjacent to no-
flow boundaries and to assure a more consistent and uniform regeneration
of particles at fluid sources.
a) Delete:
420
430
440
450
500
510
520
530
F 780
F 800
F1010
F1030
F1070
F1280
F1300
F1340
F1560
F1580
F1620
F1660
F1840
F1860
F1880
F1890
F1920
F1930
F1940
F1950
F1960
F1980
F1990
F2715
F2725
F2735
F2745
F2755
F2765
F2775
F2785
F2795
F2805
F2815
F2825
F2835
F3390
F3395
F3410
F3420
F3430
F3440
F3450
F3460
-------
b) Insert:
* REVISED OCTOBER 1983
DHXsHK(lX-1/lY)-HK(IX+1/IY)
IF
-------
5b) Inserts (continued)
1275
1277
1273
1279
1280
1282
1283
1 284
1235
1287
1283
1239
1290
GO TO 1277
GO TO 1278
GO TO 1279
IF CTHCK(IVX,IVY).EQ.O.O>
IF CTHdUlXE/IYS>.EQ.O.O>
IF (THCIUIXE/IVY>.EQ.O.O>
GO TO 1290
VXNW*VXSW
IF (THCK
IF (THCK(IVX/IVY).EQ.O.O)
IF
GO TO 1290
VXSE*VXNE
IF (THCIUIVX/IVYKGT.O.C) GO TO 1284
VYNHSVYNE
VXSWsVXNW
VYSWSVYSE
F1744A
GO TO 1282
GO TO 1283
GO TO 1284
,EQ
.EQ
,EQ
,0)
,0)
,0)
GO
GO
GO
TO
TO
TO
•GT.0.0) GO TO 1289
GO TO 1290
IF (THCIUIVX/IYS),
IF (THCIUIXE/IVY>,
IF (THCHCIXE/IYS)
GO TO 1290
VXSU-VXNW
IF (THCK(IXE/IVY)
VYNE«VYNW
VYSEsVYSW
VXSE=VXNE
CONTINUE
CELYQsCELDYH*2.0
VYWsVYNW»(1.0-CELYO)*VYSW*CELYO
VYEsVYNE-(1.0-CELYD)*VYSE*CELYO
1287
1288
1289
F1744C
F17440
F1744E
F1744F
F1744G
F1744H
F1744I
F1744J
F1746A
F17468
F1746C
F17460
F1740E
F1746F
F1746G
F1746M
F1746I
F1746J
F1743A
F17488
F1748C
F17480
F1743E
F1748F
F1743G
F1748H
F1748I
F1749A
F1921
F1931
F1951
-------
Reference:
NOTE ON COMPUTER PROGRAM UPDATE
August 26, 1981
"Computer model of two-dimensional solute transport and
dispersion in ground water," by L. F. Konikow and J. D.
Bredehoeft (1978): U.S. Geological Survey Techniques of
Water-Resources Investigations, Book 7, Chapter C2.
Several additional program modifications have been made since the previous
updates of March 26 and December 4, 1980. One improvement included in
these changes is a correction to allow for variable-length pumping periods and
(or) changing pumping rates during simulations involving transient flow and
the use of data set 10. All of the changes since March 26, 1980 can be
implemented as follows:
1. Delete the following Fortran statements from the source code:
A 140 B 880 E2050 G 530 H 125
A 380 B3790 F 60 G 540 H 436
A 470 C 80 F 180 G 550 H 438
A 620 C 145 F4080 G 560 H 715
B 90 C1200 G 70 G 570 H 720
B 185 D 60 G 490 G 580 H 725
B 460 E 80 G 500 G 590 H 735
B 640 E 270 G 510 G 600 I 60
B 700 E 720 G 520 H 60 11160 i
11530
2. Insert the following Fortran statements in the proper sequential
location:
C * REVISED DECEMBER 1980 * A 56
C * REVISED AUGUST 1981 * A 57
REAL *3TMSUM/A,MT1M ' A 115
2PNCHV/NPDELC/1CHK A 141
TMSUMsQ.O A 265
IF (INT.GT.1) TMSUMsTMSUM+PYR A 325
TINT=SUMT-TMSUM A 381
IF (S.EQ.O.O.ANO.ICHK.EQ.O.AND.(N.GT.1.0R.INT.GT.1) ) GO TO 101 A 435
101 CALL MOVE A 471
IF (SUMT.GE.(PYrt+TMSUM)) GO TO 140 A 621
REAL *8TMSUM/ANTIM a 55
2PNCHV/NPDELC/ICHK B 91
COMMON /BALM/ TOTLQ/TOTLQI/TPIN/TPOUT S 186
TPINsQ.O B 317
TPOUT=0.0 B 318
ICHKsQ B 395
IF (NITP.LE.O) WRITE (6/385) B 615
IF (ZCHK.LE.O) WRITE (6/1110) INT B 695
IF (ICHK.LE.O) GO TO 20 B 7U'i
PYRsPINT*S6400.0*365.25 B aJ5
IF (NPNTMV.EU.O) NPNTMV=999 B 8j
IF (TINIT.GT.PYR) WRITE (6/475) B 3i
50 ANTIM=NTIM B 882
00 55 Ksl/NTIM B 884
55 TIM«)»PYR/ANTIM B 886
IF (INT.GT.1.AND.ICHK.LE.O) RETURN B1345
-------
NOTE ON COMPUTER PROGRAM UPDATE
March 26, 1980
Reference; "Computer model of tuo-dimensional solute transport and
dispersion in ground-water," by L. F. Konikow and J. D. Bredehoeft
(1978): U.S. Geological Survey Techniques of Voter-Resources Inuesti-
gotions, Book 7t Chapter C2.
Several additional program modifications have been made since the
previous update of May 16, 1979. These can be implemented as follows:
1. Delete the following Fortran statements from the source
code:
E1980
E1990
E2030
F 480
2. Insert the following Fortran statements in the proper
sequential location:
IF (THC<( IX,IY).EQ.O.O> GO TO 199 E1972
3AVX32.0*THC«IX,IY>*THCK(IX+1/IY)/(THCK(IX,IY)+THCK E1976
OISP(IX,IY,4>»DISP
-------
IS LONGER TH
IF (NX.GT.3.AND.NY.GT.3) 60 TO 185
HMX-PIES/XNS
HMY»PIES/YNS
HMIN*DMIN1(HMIN/HMX/HMY)
185 CONTINUE
475 FORMAT (1 HO/5X/65H*** WARNING *** INITIAL TIME STEP
1AN PUMPING PERIOO/25X/34H***ADJUST EITHER TINIT OR
2 « /I6/13X/39HPINT (PUMPING PERIOD IN YEARS) a/F11.3/13X/39
885 FORMAT (1HO/5X/38H*** WARNING *** NITP MUST BE POSITIVE)
1110 FORMAT (1H1/5X/25HSTART PUMPING PERIOD NO. /I2//2X/23HNO PARAMETER
1S REDEFINED/)
2PNCHV/NPOELC/ICHK
COMMON /BALM/ TOTLQ/TOTLQI/TPIN/TPOUT
PQIN»0.0
PQOUTaQ.O
; CUMULATE PUMPAGE AND RECHARGE FOR MASS BALANCE
IF (REC(IX/IY).GT.O.O) GO TO 32
PQINaPQIN+RECUX/IY)
GO TO 34
32 PQOUTsPQOUT+RECUX/IY)
34 IF (R£CH(IX/IY).GT.O.O) GO TO 36
PQINsPQIN + RECHUX/IY)*AREA
GO TO 38
36 PQOUTapQOUT+RECH(lX/IY)*AREA
- 38 IF (VPRM(IX/IY).EQ.O.O) GO TO 130
TPINsPQIN*TIM(N)+TPlN
TPOUT«PQOUT*TIM(N)+TPOUT
2PNCHV/NPDELC/ICHK
2PNCHV/NPDELC/ICHK
TMV»TIM(N)*1.0E5
MAXX'O
MAXYaQ
IF (TDIV.GE.TMV) GO TO 20
TMV»TOIV _ _ _
MAXXaJX
MAXYaiy
IF (AMAX1(VHAX,VM.AY/VMX8D/VMYBD).LE.1.0E-10) WRITE(6/570)
200 IF (NMOV.EQ.1) GO TO 235
IF (LIM) 210/220/230
WRITE (6/560) MAXX/tlAXY
GO TO 240
235 WRITE (6/580)
560 FORMAT (1H /15X/35HHAX. INJECTION OCCURS AT CELL IX a ,13,7H IY a
570 FORMAT (1 HO/5X/47H*** WARNING •*• DECREASE CRITERIA IN c 230-260)
530 FORMAT (1HQ,10X/63H*TIME INCREMENT FOR SOLUTE TRANSPORT EQUALS TIM
1E STEP FOR FLOW*)
2PNCHV/NPDELC/ICHK
IF (HOO(IMOV/50).E3.0) I?RNT=1
IF (M00( IMOV/NPNTMV).EQ.O) IPRNT*-1
650 IF (IPRNT.NE.O) CALL CHMOT
2PNCHV/NPOELC/ICH<
CMREC2=C1
IF (RECH(IX/.IY) .LT.0.3) CP4REC 2« CNRECH (I X , I Y }
DELCsEQFCT2«(C1«OIV-aATE*CNR£C-SLcAiC«CLICC.-J-RECH(IX,IY)*C.NREC2)
COMMON /BALM/ TJTLU/TOTL«H *TP IN,TPOUT
TPUMapQlN*PuOUT
.PUHPafP IN + TPOJT
2PNCHV/NPDELC/ICHK
IF (S.Ea.Q.O.AND.N.LT.NTIM.AND.INT.GT.C) GO TO 100
150 IPRNTsQ
RETURN
440 FORMAT CH /5dX/!2/6x/F7.1/8X/F7.1/8X/F7.3)
81912
B1913
81914
81915
81916
83384
83385
33791
84015
84532
84533
C 81
C 146
C 192
C 193
C1181
C1182
C1183
C1184
C1185
C1186
C1187
C1188
C1189
C1201
C1232
C1233
61
81
275
284
285
722
724
725
726
£1125
E2052
E2054
E2102
£2104
£2106
E2635
£2636
E2637
£2633
£2639
F 61
F4J65
F4082
F4QS5
G 71
ti 455
G 475
G 595
H 61
H 126
H 71 6
H 721
I 61
I 905
11155
11165
1*531
-------
Table 1 -- List of Fortran statements to be deleted from original
source deck (line identification numbers in columns 73-80)
A 150
fi 100
B 190
B3900
C 90
C 150
D 70
D 350
D 870
D1080
E 90
F 70
F 220
F 360
F2710
- A 160
- B 110
- C 100
- D 80
- D 360
- E 100
- F 80
- F 240
- F 390
- F3380
F3400
F3470 - F3500
F3540
F3630 - F3640
F3740
G 80 - G 90
G 640
G1100
G1500
G1540
G1590
G1630
G1660
G1680
H 70 - H 80
H 130
H 490
H 570
H 730
H 870
H 890
H 920
H1060
H1080
H1130
I 70
I 620
I 800
- H 580
- H 820
- H 900
- H 930
- HL110
- I 80
- I 640
Table 2 -- (follows) -- Listing of new or replacement Fortran state-
ments to be inserted into program at sequential location
indicated by line identification number in columns 73-80.
For example, statement A 55 should be inserted between
lines A 50 and A 60.
-------
NOTE ON OCMPUTER PROGRAM UPDATE
May 16, 1979
Reference: "Computer model of tuo-dunensional solute transport and
dispersion in ground water," by L. F. Konikow and J. D. Bredehoeft
(1978): U.S. Geological Survey Techniques of Water-Resources Inves-
tigations, Book 7t Chapter C2.
A number of refinements and modifications have been made to the
computer program that is documented in the above report since it was
published. These changes improve the accuracy of the numerical solu-
tion for many problems, but slightly increase the execution time and
core storage requirements. The degree of improvement in accuracy is
problem dependent. For some problems the changes will have no sig-
nificant effect on the numerical solution, but for other problems
the improved accuracy will more than offset the increased cost.
Thus, in general it is recommended that these changes be incor-
porated into the program.
Most of the program changes affect the treatment of tracer
particles at nodes that represent fluid sources and sinks. Other
changes improve the methods for calculating the mass balance errors
for the fluid and for the solute. The program changes will be
invisible to the model user in the sense that the input data require-
ments and formats are not affected.
Implementation of these changes will require the deletion of
146 statements from the original program listing (Attachment I in
the report), and the insertion of 179 new statements. The state-
ments to be deleted are listed sequentially in Table 1 of this
update note. The new statements to be inserted are listed sequen-
tially in Table 2. All statements have unique identification numbers
in columns 73-80; the sequential order of these line identification
numbers must be maintained in making the program changes.
-------
IF (NPOLDUX/IY) .GT.Q) NPOLD
-------
Table 2
» REVISED APRIL 1979 *
COMMON /PRMC/ NODE I0(20/20)/NPCELL(20/20)/NPOLO(20/20)/LIMBO(500)/
1 IX03S(5),IYJBS(5)
INTEGER OVERriD
COMMON /PRMC/ NOOE10(20,20),NPCELL(20,20),NPOLO(20,20),LIMdO(500),
1 !XOJS(5),IYOiS(5)
COMMON /dALM/ TOTLQ,TOTLiJI
TOTLQI=0.0
520 FORMAT (1H ,7X,2I4,3X,F9.4,3X,F8.2)
COMMON /PRKC/ NODE 10(20,20),NPCELL(20,20),NPOLO(20,20),LIMBO(500),
1 IX03S(5),IY08S(5)
COMMON /3ALM/ TQTLQ,TOTLQI
IF (OELQ.GT.0.0) GO TO 125
GO TO 130
125 TOTLai"TOTLQI+DELD*TIH(N)
INTEGER *2 PTIO
COMMON /PRKC/ NOOE10(20,20),NPCELL(20,20),NPOLO(20,20),LIM80(500),
1lXOdS(5),IY03S(5)
COMMON /CHMP/ PTIO(3200)
10 00 20 IN*1,NPMAX
PTIO(IN)*0
00 20 I0s1,3
NPOLO(IX,IY)sNPTPNO
150
PTID(INO)=KR
PART(1,IND)sIX
PTIO(INO).*S
IF (EVET.LT
IF (EVET.GT
IF (EVET.LT.O)
IF (EVET.GT.O)
COMMON /PRMC/
O)
O)
PriD(INO)=6
PTIO(INO)=8
PTIO(INO)s7
PTIO(I NO)=9
NOOEI0(20/20)/NPCELL(20/20)/NPOLD(20/20)/LIMBO(500)/
390
1 IX03S(5) /I YOBS( 5)
INTEGER *2 PTIO
COMMON /PRMC/ NODEID(20/20)/NPCELL
1 IX03S(5) /IY08S(5;
COMMON /CHMP/ PTIO(3200)
F1«0.30
F2«1. 0/3.0
IF (NPTPNO.EQ.4) FlaQ.25
IF (NPTPNO.EQ.9) F1*F2
IF (NPTPNO.Ea.8) F2aQ.25
IF (KFLAG.EQ.O) GO TO 398
IF (THCK (IX+1,IY).EQ. 0.0. AND. (VPRM
1).LT.O.O.OR.THCK(IX,IY-1 ) . EQ. 0. 0) .
2C(IX/IY-H).LT.O.O.OR.THCK(1X^IY-H)
IF (THCK(IX-1/IY) .EQ. 0.0. AND. (VPRM
1).LT.O.O.OR.THCK(IX/IY-1) . EQ. 0. 0) .
2C(lX«IY*1).lT.O.O.OR.THCKCIXsIY+1>
IF (THCK (IX, I Y- 1 ). EQ. 0.0. AND. (VPRM
1 ) ,LT.O.O.OR.THCK(IX-1/IY).EQ.O.O).
2C(IX+1,IY>.LT.O.O.OR.THCK(IX+1,IY)
IF (THCK(IX,IY+1).EQ.O.O.AND.(VPRM
1 ) .LT.O.O.Oft.THCK(ZX-1«ZY) . EQ. 0. 0) .
(20/20)/NPOLD(20/20)/LIMBO(500)/
(IX/IY-1)
AND. ( VPRM
.EQ.O.O) )
( I X , I T-1 )
AND. ( VPRM
.EQ.O.O)>
(IX-1,IY)
ANO.(VPRM
.EQ.O.O))
(IX-1,IY)
ANO. ( VPRM
.GE. 0.09
( IX, I Y+1
GO TO 5
.GE.0.09
( IX/ I Y +1
GO TO 5
. GE.0.09
-------
FCT2»NPCELL(IX/IY)
IF (FCT2.GT.0.0) WTFCT3FCT1/FCT2
FLMOTsFLMOT+FLW*TVA*((1.0-WTFCT)*CNOLD(IX/If)+WTFCT *CONC ( IX/I Y»
265 NPOLO(IX/IY)*NPCELL(IX/IY)
fy,PCELL(IX/IY)*0
COMMON /PRMC/ NODE I 0(20/20)/NPCELL(20/20)/NPOLD(20/20)/LIMBO(500)/
1IX03S(5)/IY08S(5)
COMMON /3ALM/ TOTLQ/TOTLGI
PQINsO.O
P30UTsO.O
TPIN-0.0
TPOUTaQ.O
IF (REC(IX/IY).GT.0.0) GO TO 32
PQINapQIN + RECUX/IY)
GO TO 34
32 PQOUTapQQUT+REC(IX/IY)
34 IF (RECH(IX/IY).GT.0.0) GO TO 36
PQINapQlN+RECH(IX/IY)*AREA-
GO TO 38
36 PQOUTsPQOUT+RECH(IX/IY)*AREA
33 IF (VPRMUX/IY) .EQ.0.0) GO TO 60
TPUMaTPUM+PQIN+PQOUT
TPINSPQIN*SUMT
TPOUTapQQUT*SUMT
TOTLQNaTOTLQ*TOTLQI
SRCS*QSTR-TPIN+TOTLQI
SINSINKS)*O.S
IF (DENOM.EJ.0.0) GO TO 100
PCTERR=EfiRM8*100.0/DENOM
WRITE (6/211) TPIN
TPOUT
TOTLQI
TOTLQ
TOTLQN
PCTERR
130
201
202
203
204
210
211
212
240
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
WRITE
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
COMMON
(6/212)
(6/202)
(6/203)
(6/260)
(6/280)
(6/201)
(6/202)
(6/203)
(6/204)
(6/211)
(6/212)
QIN
QOUT
QNET
PQIN
PQOUT
(1HO/10F12.7)
(1HO/2X/33HRATE MASS BALANCE — (IN C.F.S.)
(4X/29HLEA
-------
SECTION 4
BIBLIOGRAPHY
-------
SELECTED BIBLIOGRAPHY ON SOLUTE-TRANSPORT
PROCESSES IN GROUND WATER
Leonard F. Konlkow
U. S. Geological Survey
Reston, VA 22092
revised: January 1988
-------
CONTENTS
Topic Page
General 3
Theory and Development of Solute-Transport Equation 5
Macrodlsperslon and Stochastic Approaches 6
Diffusion and Dispersion 9
Accounting for Reactions 12
Flow of Immiscible Fluids and Multiphase Transport 15
Transport in Fractures 17
Analytical Solutions 18
Numerical Methods and Models 20
Parameter Determination and Tracers 24
Analysis of Field Problems 27
Aquifer Reclamation and Management Aspects 30
Freshwater-Saltwater Relationships 31
-------
-------
Bear, Jacob, 1979, Hydraulics of groundwater: McGraw-Hill, New York,
567 p.
Bear, J., and Verruijt, A., 1987, Modeling groundwater flow and pollution:
D. Reidel Publishing Company, Dordrecht, Holland, 414 p.
Bird, R. B., Stewart, V. E., and Lightfoot, E. N., 1966, Transport
phenomenal John Wiley and Sons, New York, 780 p.
Domenlco, P. A., 1977, Transport phenomena in chemical rate processes
In sediments: Ann. Rev. Earth Planet. Sci., v. 5, p. 287-317.
Freeze, R. A., and Cherry, J. A., 1979, Groundwatert Prentice-Hall, Inc.,
Englewood Cliffs, N.J., 604 p.
Glllham, R. U., and Cherry, J. A., 1982, Contaiinant migration In
saturated unconsolidated geologic deposits! Geological Society of
America, Special Paper 189, p. 31-61.
Greenkorn, R. A., 1983, Flow phenomena in porous medlai Marcel Dekker,
Inc., New York, 550 p.
Grlsak, G. E., and Jackson, R. E., 1978, An appraisal of the hydro-
geological processes involved in shallow subsurface radioactive
waste management in Canadian terrain: Inland Waters Directorate,
Ottawa, Canada, Scientific Series No. 84, 194 p.
IAHR-ISSS, 1972, Fundamentals of transport phenomena in porous media:
Proc. Second Symposium, Univ. of Guelph, Ontario, Aug. 7-11,
1972, 797 p.
National Research Council, 1984, Groundwater contamination: Studies in
Geophysics, National Academy Press, Washington, D. C., 179 p.
Nelson, R. W., 1978, Evaluating the environmental consequences of
groundwater contamination, 1. An overview of contaminant arrival
distributions as general evaluation requirements: Water Resources
Research, v. 14, no. 3, p. 409-415. [Also see parts 2-4, same
issue, p. 416-450.]
Rellly, T. E., Franke, 0. L., Buxton, H. T., and Bennett, G. D., 1987, A
conceptual framework for ground-water solute-transport studies with
emphasis on physical mechanisms of solute Movement: U.S. Geol. Survey
Water-Resources Inv. Report 87-4191, 44 p.
Schwartz, F. W., 1975, On radioactive waste management: An analysis
of the parameters controlling subsurface contaminant transport:
Jour. Hyd., v. 27, p. 51-71.
-------
General, continued
Vrba, J., and Romijn, E.. [eds.l, 1986, Impact of agricultural activities
on ground watert International Assoc. of Hydrogeolegists, International
Contributions to Hydrogeology, v. 5, 332 p.
Yaron, B., Dagan, G., and Goldshiid, J., eds., 1984, Pollutants in porous
•edia — The unsaturated zone between soil surface and groundwateri
Ecological Studies 47, Springer-Verlag, Berlin, Heidelberg, New York,
Tokyo, 296 p.
-------
THEORY AND DEVELOPMENT OF SOLUTE-TRANSPORT EQUATION
Bachnat, Y., and Bear. J., 1964. The general equations of hydrodynamic
dispersion in homogeneous, isotroplc, porous tediums: Jour.
Geophys. Research, v. 69, no. 12, p. 2561-2567.
Biake, T. R., and Garg, S. K.. 1976, On the species transport equation
for flow in porous Media» Water Resources Research, v. 12, no. 4.
p. 748-750.
Bredehoeft, J. D., and Pinder, G. F., 1973, Mass transport in flowing
ground watert Water Resources Research, v. 9, no. 1, p. 194-209.
Dagan, Gedeon, 1987, Theory of solute transport by groundwaten Ann. Rev.
Fluid Mech., v. 19, p. 183-215.
Domenico, P. A., and Palciauskas, V. V., 1979, The volume-averaged
•ass-transport equation for chemical diagenetic Modelst Jour.
Hydrology, v. 43, p. 427-438.
Gray, W. G., 1982, Derivation of vertically averaged equations describing
multiphase flow in porous mediai Water Resources Research, v. 18,
no. 6, p. 1705-1712.
Gray, W. G., and O'Neill, K., 1977, Comment on "On the species transport
equation for flow In porous media" by Thomas R. Blake and Sabodh K.
Gargi Water Resources Research, v. 13, no. 3, p. 695-696.
Hatton, T. A., and Llghtfoot, E. N., 1984, Dispersion of trace solutes in
flowing groundwaten Water Resources Research, v. 20, no. 9, p. 1253-
1259.
Konikow, L. F., and Grove, D. B., 1977, Derivation of equations describing
solute transport in ground water* U.S. Geol. Survey Water-Resources
Inv. 77-19, 30 p.
Parker, J. C., and Genuchten, M. Th. van, 1984, Flux-averaged and volume-
averaged concentrations in continuum approaches to solute transport!
Water Resources Research, v. 20. no. 7, p. 866-872. [Also see Comment
by G. Dagan and E. Bresler, and Reply by authors* Water Resources
Research, v. 21, no. 8, p. 1299-1302.]
Sposito, G., and Barry, D. A., 1987, On the Dagan model of solute transport
in groundwatert Foundational aspectsi Water Resources Research, v. 23,
no. 10. p. 1867-1875.
Whitaker, S., 1967, Diffusion and dispersion in porous media« Am.
Inst. Chen. Eng. Jour., v. 13, p. 420-427.
-------
HACRODISPERSION AND STOCHASTIC APPROACHES
Black, T. C., and Freyberg, D. L., 1987, Stochastic modeling of
vertically averaged concentration uncertainty In a perfectly stratified
aquifer> Water Resources Research, v. 23, no. 6, p. 997-1004.
Bresler, E., and Dagan, G., 1981, Convective and pore scale dispersive
solute transport in unsaturated heterogeneous fieldst Water Resources
Research, v. 17, no. 6. p. 1683-1693.
Gala, M. A., and Greenkorn. R. A., 1986, Velocity effects on dispersion in
porous Media with a single heterogeneity! Water Resources Research,
v. 22, no. 6, p. 919-926.
Chu, Shu-Yuan, and Sposito, G.. 1980, A derivation of the macroscopic
solute transport equation for honogeneous, saturated, porous media:
Water Resources Research, v. 16, no. 3, p. 542-546.
Dagan, Gedeon, 1986, Statistical theory of grounduater flow and
transport* Pore to laboratory, laboratory to formation, and formation to
regional scalet Water Resources Research, v. 22, no. 9, p. 120S-134S.
Davis, A. D., 1986, Deterministic modeling of a dispersion in heterogeneous
permeable medlat Ground Water, v. 24, no. 5, p. 609-615.
Gelhar, L. W., 1986, Stochastic subsurface hydrology from theory to
applications! Water Resources Research, v. 22, no. 9, p. 135S-145S.
Gelhar, L. W., and Axness, C. L.. 1983. Three-dimensional stochastic
analysis of macrodispersion in aquiferst Water Resources Research, v.
19, no. 1, p. 161-180. [Also, see Comment by Cushman and Reply by
authors in v. 19, no. 6, p. 1641-1644.]
Gelhar, L. W., Gutjahr, A. L., and Naff, R. L., 1979, Stochastic analysis
of macrodispersion in a stratified aquifer: Water Resources Research,
v. 15. no. 6, p. 1387-1397.
Gillban, R. W.. Sudicky, E. A., Cherry, J. A., and Frind, E. 0., 1984,
An advection-diffusion concept for solute transport in heterogeneous
unconso11dated geological deposltst Water Resources Research,
v. 20, no. 3, p. 369-378. [Also, see Comment by Guven, Holz, and
Melville and Reply by Sudicky and Gillham, v. 22, no. 1, p. 89-94, Jan.
1986.]
Gupta, V. K., and Bhattacharya, R. N., 1986, Solute dispersion in multi-
dimensional periodic saturated porous media: Water Resources Research,
v. 22, no. 2, p. 156-164.
Guven, 0., Holz, F. J., and Melville, J. G., 1984, An analysis of dispersion
in a stratified aquifer: Water Resources Research, v. 20, no. 10, p.
1337-1354.
-------
Macrodisperslon and Stochastic Approaches, continued
Giiven.O., and Molz, F. J., 1986, Deterministic and stochastic analyses of
dispersion in an unbounded stratified porous Medium* Water Resources
Research, v. 22, no. 11, p. 1565-1574.
Matheron, G., and De Marsily, G., 1980, Is transport in porous media
always diffusive? A counterexamples Water Resources Research,
v. 16, no. 5, p. 901-917.
Hercado, A., 1984, A note on micro and macrodispersions Ground Water, v. 22,
no. 6, p. 790-791.
Neuman, S. P., Winter, C. L., and Newman, C. M., 1987, Stochastic theory of
field-scale Fickian dispersion in anlsotropic porous media: Water
Resources Research, v. 23, no. 3. p. 453-466.
Pickens, J. F., and Grisak, G. E., 1981, Scale-dependent dispersion in a
stratified granular aquifer* Water Resources Research, v. 17, no. 4,
p. 1191-1211.
Pickens, J. F., and Grisak, G. E., 1981, Modeling of scale-dependent
dispersion in hydrogeologic systems* Water Resources Research,
v. 17, no. 6, p. 1701-1711.
Rao, P. V., Rortier, K. M., and Rao, P. S. C., 1981, A stochastic
approach for describing convective-dispersive solute'transport In
saturated porous mediat Water Resources Research, v. 17, no. 4,
p. 963-968.
Refsgaard, A., 1986, Laboratory experiments on solute transport in
non-homogeneous porous media* Nordic Hydrology, v. 17. no. 4/5, p.
305-314.
Schwartz, F. W., 1977, Macroscopic dispersion in porous media* The
controlling factors* Water Resources Research, v. 13, no. 4,
p. 743-752.
Silliman, S. E., and Simpson, E. S., 1987, Laboratory evidence of the
scale effect In dispersion of solutes in porous media* Water Resources
Research, v. 23, no. 8, p. 1667-1673.
Smith, L., and Schwartz, F. W., 1980, Mass transport, 1. A stochastic
analysis of macroscopic dispersion* Water Resources Research,
v. 16, no. 2, p. 303-313.
Smith, L., and Schwartz, F. W., 1981, Mass transport, 2. Analysis of
uncertainty in prediction* Water Resources Research, v. 17, no. 2,
p. 351-369.
-------
Macrodlspersion and Stochastic Approaches, continued
Sposito, G., Jury, U. A., and Gupta, V. K., 1986, Fundamental problems in
the stochastic convection-dispersion model of solute transport in
aquifers and field soils: Water Resources Research, v. 22, no. 1,
p. 77-88.
Tang, D. H., and Finder, G. F., 1979, Analysis of mass transport with
uncertain physical parameterst Water Resources Research, v. 15,
no. 5, p. 1147-1155.
Tang, D. H., Schwartz. F. U., and Smith, L., 1982, Stochastic modeling
of mass transport in a random velocity field: Water Resources
Research, v. 18, no. 2, p. 231-244. [Also see Commentary by Dagan
and Reply by authors in v. 19, no. 4, p. 1049-1054.]
Ufflnk, G. J. H., 1983, A random walk method for the simulation of
macrodispersion in a stratified aquifer: Relation of Groundwater
Quantity and Quality (Proceedings of the Hamburg Symposium), IAHS Publ
no. 146. p. 103-114.
8
-------
DIFFUSION AND DISPERSION
Bachmat, Y., 1967, On the similitude of dispersion phenomena In
homogeneous and Isotropic porous mediumi Water Resources Research,
v. 3, no. 4, p. 1079-1083.
Bachmat, Y., and Bear, J., 1983, The dispersive flux in transport
phenomena in porous medlai Adv. Water Resources, v. 6, p. 169-174.
Baker, L. E., 1977, Effects of dispersion and dead-end pore volume in
•Iscible floodingi Soc. Petrol. Eng. Jour., v. 7, no. 3, p. 219-227.
Banks, R. B., and Jerasate, S., 1962, Dispersion in unsteady porous
•edia flow. ASCE, Jour. Hyd. Div., v. 88, no. HY3, p. 1-21.
Bear, Jacob, 1961, On the tensor form of dispersion in porous media:
Jour. Geophys. Research, v. 66, no. 4, p. 1185-1198.
Biggar, J. W., and Nielsen, D. R., 1960, Diffusion effects in miscible
displacement occurring in saturated and unsaturated porous materials:
Jour. Geophys. Research, v. 65, no. 9, p. 2887-2896.
Blackuell, R. J., 1962, Laboratory studies of miscroscopic dispersion
phenomenal Soc. Petrol. Eng. Jour., v. 2, no. 1, p. 1-8.
Brenner, H., 1961, The diffusion model of longitudinal mixing in
beds of finite length. Numerical values: Chemical Engineering
Science, v. 17, p. 229-243.
Bresler, E., and Dagan, G., 1979, Solute dispersion in unsaturated
heterogeneous soil at field scale: II. Applications: Soil Sci.
Soc. Am. Jour., v. 43, p. 467-472.
Coats, K. H., and Smith, B. D., 1964, Dead-end pore volume and
dispersion in porous media: Soc. Petrol. Eng. Jour., v. 4, no. 1,
p. 73-84. [Also see discussions in v. 4, no. 3, p. 282-284.]
Dagan, G., and Bresler, E., 1979, Solute dispersion in unsaturated
heterogeneous soil at field scale: I. Theorys Soil Scl. Soc.
Am. Jour., v. 43, p. 461-467.
de Josselin de Jong, G., 1958, Longitudinal and transverse diffusion
in granular deposits: Am. Geophys. Union Trans., v. 39, no. 1,
p. 67-74.
Feenstra, S., Cherry, J. A., Sudicky, E. A., and Haq, Z., 1984, Matrix
diffusion effects on contaminant migration from an injection well in
fractured sandstone: Ground Water, v. 22, no. 3, p. 307-316 [also, see
Discussion by G. R. Walter and Reply by authors, v. 22, no. 6, p.
786-787].
-------
Diffusion and Dispersion, continued
Fried, J. J., and Combarnous, M. A., 1971, Dispersion in porous media, in
Advances in hydrosciencet New York, Academic Press, v. 7. p. 170-282.
Goltz, H. N., and Roberts, P. V., 1986, Three-dimensional solutions for solute
transport in an infinite medium with mobile and immobile zonest Water
Resources Research, v. 22, no. 7, p. 1139-1148.
Green, T., 1984, Scales for double-diffusive fingering in porous media: Water
Resources Research, v. 20, no. 9, p. 1225-1229.
Harleman, D. R. F., Helhor, P. F., and Ruier, R. R., Jr.. 1963,
Dispersion-permeability correlation in porous mediat ASCE, Jour.
Hyd. Div., v. 89, no. HY2, p. 67-85.
Harleman, D. R. F., and Rumer, R. R., Jr., 1963, Longitudinal and
lateral dispersion in an isotroplc porous mediums Fluid Mechanics
Jour., v. 16, pt. 3, p. 385-394.
Hoopes, J. A., and Harleman, D. R. F., 1967, Wastewater recharge and
dispersion in porous media» ASCE, Jour. Hyd. Div.. v. 93,
no. HY5, p. 51-71.
Hunt, B. W., 1973, Dispersion in nonuniform seepage» ASCE, Jour. Hyd.
Div., v. 99, no. HY2, p. 293-299.
Ogata, A., 1961, Transverse diffusion in saturated isotroplc granular
media« U.S. Geol. Survey Prof. Paper 411-B, 8 p.
1964a, The spread of a dye stream in an isotropic granular medium>
U.S. Geol. Survey Prof. Paper 411-G, 11 p.
1964b, Mathematics of dispersion with linear adsorption isotherm:
U.S. Geol. Survey Prof. Paper 411-H, 9 p.
1970, Theory of dispersion in a granular medium: U.S. Geol.
Survey Prof. Paper 411-1, 34 p.
Perkins, T. K., and Johnson, 0. C., 1963, A review of diffusion and
dispersion in porous media: Soc. Petrol. Eng. Jour., v. 3,
no. 1, p. 70-84.
Pozzi, A. L., and Blackwell, R. J., 1963, Design of laboratory models
for study of miscible displacement: Soc. Petrol. Eng. Jour.,
v. 3, no. 1, p. 28-40.
Saffman, P. G., 1959, A theory of dispersion in a porous medium: Jour.
Fluid Mech., v. 6, p. 321-349.
1960, Dispersion due to molecular diffusion and macroscopic
mixing in flow through a network of capillaries: Jour. Fluid Mech.,
v. 7, p. 194-208.
10
-------
Diffusion and Dispersion, continued
Scheidegger, A. E., 1961, General theory of dispersion In porous media:
Jour. Geophys. Research, v. 66, no. 10, p. 3273-3278.
SI 11 loan, S. E., Konikow, L. F., and Voss, C. I., 1987, Laboratory
Investigation of longitudinal dispersion In anlsotroplc porous media»
Water Resources Research, v. 23. no. 11, p. 2145-2151.
Simpson, E. S., 1962, Transverse dispersion In liquid flow through
porous ledla» U.S. Geol. Survey Prof. Paper 411-C, p. C1-C30.
Skibitzke, H. E., 1964, Extending Darcy's concept of ground-water notion:
U.S. Geol. Survey Prof. Paper 411-F, 6 p.
Skibitzke, H. E., and Robinson, G. H., 1963, Dispersion of ground water
flowing through heterogeneous Materialsi U.S. Geol. Survey Prof.
Paper 386-B, 3 p.
Smith, I. M., Farraday, R. V., and O'Connor, B. A., 1973, Raylelgh-Ritz
and Galerkin-finite elements for diffusion-convection problems:
Water Resources Research, v. 9, no. 3, p. 593-606.
Taylor, Geoffrey, 1953, Dispersion of soluble Batter in solvent flowing
slowly through a tube: Royal Soc. London Proc.. Ser. A, v. 219,
p. 187-203.
Warren, J. E., and Sklba, F. F., 1964, Macroscopic dispersions Soc.
Petrol. Eng. Jour., v. 4, no. 3, p. 215-230.
11
-------
ACCOUNTING FOR REACTIONS
Amundsen, N. R., 1950, Mathematics of adsorption in beds, lit Jour.
Phys. Coiloid Chen., v. 54, p. 812-820.
Bahr, J. H., and Rubin, J., 1987, Direct conparlson of kinetic and iocai
equilibrium formulations for solute transport affected by surface
reactions: Water Resources Research, v. 23, no. 3, p. 438-452.
Banks, R. B., and All, I., 1964, Dispersion and adsorption in porous
media flowi ASCE Jour. Hyd. Dlv., v. 90, no. HY5, p. 13-31.
Borden, R. C., and Bedlent, P. B., 1986, Transport of dissolved hydrocarbons
influenced by oxygen-1 lilted bI©degradation — 1. Theoretical develop-
ment! Water Resources Research, v. 22, no. 13, p. 1973-1982. [Also
see Part 2. Field application, same issue, p. 1983-1990.]
Cameron, D. R., and Klute. A., 1977, Convective-dispersive solute
transport with a combined equilibrium and kinetic adsorption model<
Water Resources Research, v. 13, no. 1, p. 183-188.
Cederberg, G. A., Street, R. L., and Leckle, J. 0., 1985, A groundwater mass
transport and equilibrium chemistry model for multlcomponent systems:
Water Resources Research, v. 21, no. 8, p. 1095-1104.
Charbeneau, R. J., 1981, Grounduater contaminant transport with adsorption
• and ion exchange chemistry: Method of characteristics for the case
without dispersiom Water Resources Research, v. 17. no. 3, p. 705-
713.
Dria, M. A., Bryant, S. L., Schechter, R. S.. and Lake, L. V., 1987,
Interacting precipitation/dissolution waves: The movement of inorganic
contaminants in groundwateri Water Resources Research, v. 23, no. 11,
p. 2076-2090.
Fenske, P. R., 1979, Time-dependent sorption on geological materials:
Jour. Hydrology, v. 43, p. 415-425.
Grove, D. B., and Stollenwerk, K. G., 1985, Modeling the rate-controlled
sorption of hexavalent chromium! Water Resources Research, v. 21,
no. 11, p. 1703-1709.
Grove, D. B., and Stollenwerk, K. G., 1987, Chemical reactions simulated
by ground-water-quality modelsi Water Resources Bulletin, v. 23, no. 4,
p. 601-615.
Gupta, S. P., and Greenkorn. R. A., 1973. Dispersion during flow in
porous media with bilinear adsorption! Water Resources Research,
v. 9, no. 5, p. 1357-1368.
12
-------
Accounting for Reactions, continued
Gupta, S. P., 1974, Determination of dispersion and nonlinear adsorption
parameters for flow in porous media« Water Resources Research,
v. 10, no. 4, p. 839-846.
Hlgglns, G. H., 1972, Sorption in flow through porous media: In
Fundamentals of transport phenomena in porous mediat Elsevier
Publishing Co., p. 384-392.
Jennings, A. A., 1987, Critical chemical reaction rates for
multicomponent grounduater contamination models« Water Resources
Research, v. 23, no. 9, p. 1775-1784.
Jennings, A. A., Kirkner, D. J., and Theis, T. L., 1982, Multicomponent
equilibrium chemistry in~groundwater quality modelss Water Resources
Research, v. 18, no. 4, p. 1089-1096.
Lai, S. H., and Jurinak, J. J., 1972, Cation adsorption In one-dimensional
flow through sol 1st A numerical solutions Water Resources
Research, v. 8, no. 1, p. 99-107.
Lapldus, L., and Amundson, N. R., 1952, Mathematics of adsorption in
beds, VIi Jour. Phys. Chem., v. 56, p. 984-988.
HI Her, C. W., and Benson, L. V., 1983, Simulation of solute transport
in a chemically reactive heterogeneous systems Model development
and applications Water Resources Research, v. 19, no. 2, p. 381-391.
Palclauskas, V. V., and Domenlco, P. A., 1976, Solution chemistry, mass
transfer, and the approach to chemical equilibrium in porous
carbonate rocks and sediments. Geological Society of America
Bull., v. 87, p. 207-214.
Reardon, E. J., 1981, Kd's - Can they be used to describe reversible ion
sorption reactions in contaminant migration? Ground Water, v. 19,
no. 3, p. 279-286.
Rubin, Jacob, 1983, Transport of reacting solutes in porous media:
Relation between mathematical nature of problem formulation
and chemical nature of reactions: Water Resources Research,
v. 19, no. 5, 1231-1252.
Rubin, Jacob, and James, R. V., 1973, Dispersion-affected transport of
reacting solutes in saturated porous media: Galerkin method applied
to equilibrium-controlled exchange in unidirectional steady water
flows Water Resources Research, v. 9, no. 5, p. 1332-1356.
Satter, A., Shum, Y. M., Adams, W. T., and Davis, L. A., 1980, Chemical
transport in porous media with dispersion and rate-controlled
adsorption: Soc. Petrol. Eng. Jour., p. 129-138.
13
-------
Accounting for Reactions, continued
Valocchi, A. J., 1984, Describing the transport of ion-exchanging con-
tan inants using an effective Kd approachi Water Resources
Research, v. 20, no. 4, p. 499-503.
Valocchi, A. J., 1985. Validity of the local equilibrium assumption for
•odeling sorbing solute transport through homogeneous soils: Water
Resources Research, v. 21, no. 6, p. 808-820.
Valocchi, A. J., 1986, Effect of radial flow on deviations from local
equilibrium during sorblng solute transport through homogeneous
sol 1st Water Resources Research, v. 22, no. 12, p. 1693-1701.
Valocchi, A. J., Street, R. U., and Roberts, P. V., 1981, Transport of
ion-exchanging solutes in grounduateri Chromatographic theory
and field simulation! Water Resources Research, v. 17, no. 5,
p. 1517-1527.
Willis, C., and Rubin, J., 1987, Transport of reacting solutes subject to a
moving dissolution boundaryt Numerical methods and solutions: Water
Resources Research, v. 23, no. 8, p. 1561-1574.
14
-------
FLOW OF IMMISCIBLE FLUIDS AND MULTIPHASE TRANSPORT
Abriola, L. M.( and Finder, G. F., 1985, A multiphase approach to the
•odeling of porous media contanination by organic compounds, 1.
Equation development! Water Resources Research, v. 21, no. 1,
p. 11-18 [Also see Part 2, Numerical Simulation: same issue,
p. 19-26.]
Allen, H. B., Ill, 1985, Numerical modelling of multiphase flow in porous
mediai Adv. Water Resources, v. 8, p. 162-187.
Baehr, A. L., 1987, Selective transport of hydrocarbons in the
unsaturated zone due to aqueous and vapor phase partitioning: Water
Resources Research, v. 23, no. 10, p. 1926-1938.
Baehr, A. L., -and Corapcioglu, M. Y., 1987, A compositional multiphase model
for groundwater contamination by petroleum products, 2. Numerical
solution: Water Resources Research, v. 23, no. 1, p. 201-213. [Also see
Part 1. Theoretical considerations, same issue, p. 191-200.]
Crittenden, J. C., Hutzler, N. J., and Geyer, D. G., 1986, Transport of
organic compounds with saturated groundwater flow: model development
and parameter sensitivity: Water Resources Research, v. 22, no. 3,
p. 271-284.
Cushman, J. H., 1984, On unifying the concepts of scale, Instrumentation,
and stochastlcs in the development of multiphase transport theory:
Water Resources Research, v. 20, no. 11, p. 1668-1676.
Eckberg, D. K., and Sunada, D. K., 1984, Nonsteady three-phase immiscible
fluid distribution in porous media: Water Resources Research, v. 20,
no. 12, p. 1891-1897.
Faust, C. R., 1985, Transport of immiscible fluids within and below the
unsaturated zone: A numerical model: Water Resources Research, v. 21,
no. 4, p. 587-596.
Gupta, S. P., and Greenkorn, R. A., 1974, An experimental study of
immiscible displacement with an unfavorable mobility ratio in porous
media* Water Resources Research, v. 10, no. 2, p. 371-374.
Hubbert, M. K., 1953, Entrapment of petroleum under hydrodynamic
conditionsi Bull. American Assoc. Petroleum Geol., v. 137, no. 8,
p. 1954-2026.
Kuppusamy, T., Sheng, J., Parker, J. C., and Lenhard, R. J., 1987,
Finite-element analysis of multiphase Immiscible flow through soils:
Water Resources Research, v. 23, no. 4. p. 625-631.
Letkeman, J. P., and Ridings, R. L., 1970, A numerical coning model:
Soc. Petrol. Eng. Jour., v. 10, no. 4, p. 418-424.
15
-------
Flow of Immiscible Fluids and Multiphase Transport, continued
Liu, P. L-F., Cheng, A. H-D., Liggett, J. A., and Lee, J. H., 1981,
Boundary integral equation solutions to Moving interface between
two fluids in porous mediai Water Resources Research, v. 17, no. 5,
p. 1445-1452.
Osborne, H., and Sykes, J., 1986, Numerical nodeling of immiscible organic
transport at the Hyde Park Landfillt Water Resources Research, v. 22,
no. 1, p. 25-33.
Pinder, G. F., and Abriola, L. H., 1986, On the simulation of nonaqueous phase
organic compounds in the subsurfacet Water Resources Research, v. 22,
no. 9, p. 109S-119S.
Sudicky, E. A., and Frlnd, E. 0., 1982, Contaminant transport in frac-
tured porous mediat Analytical solutions for a system of parallel
fracturesi Water Resources Research, v. 18, no. 6, p. 1634-1642.
Varnon, J. E., and Greenkorn, R. A., 1970, Nonuniqueness of steady
state fingering solutions in porous media> Water Resources Research,
v. 6, no. 5, p. 1411-1414.
16
-------
TRANSPORT IN FRACTURES
Bibby, R., 1981, Mass transport of solutes in dual-porosity media:
Water Resources Research, v. 17, no. 4, p. 1075-1081.
Grisak, G. E., and Pickens, J. F., 1980, Solute transport through fractured
media, 1. The effect of matrix diffusion! Uater Resources Research,
v. 16, no. 4, p. 719-730.
Neretnieks, I., 1983, A note on fracture flow dispersion mechanisms in
the groundi Water Resources Research, v. 19, no. 2, p. 364-370.
Novakowski, K. S., Evans, G. V., Lever, D. A., and Raven, K. G., 1985, A
field example of measuring hydrodynamic dispersion in a single
fracture» Water Resources Research, v. 21, no. 8, p. 1165-1174.
Schwartz, F. W., Smith, L., and Crowe, A. S., 1983, A stochastic analysis
of macroscopic dispersion in fractured media« Water Resources Research,
v. 19, no. 5, p. 1253-1265.
Smith, L., and Schwartz, F. W., 1984, An analysis of the influence of
fracture geometry on mass transport in fractured media: Water
Resources Research, v. 20, no. 9, p. 1241-1252.
Tang, D. H., Frlnd, E. 0., and Sudlcky, E. A., 1981, Contaminant transport
in fractured porous mediai Analytical solution for a single fracture»
Water Resources Research, v. 17, no. 3, p. 555-564.
17
-------
ANALYTICAL SOLUTIONS
Al-Nlami, A. N. S., and Rushton, K. R., 1979, Dispersion in stratified
porous mediat Analytical solutions! Water Resources Research,
v. 15, no. 5, p. 1044-1048.
Eldor, H., and Oagan, G., 1972, Solutions of hydrodynamic dispersion
in porous mediat Water Resources Research, v. 8, no. 5,
p. 1316-1331.
Goltz, M. N., and Roberts, P. V., 1987, Using the method of moments to
analyze three-dimensional diffusion-limited solute transport from
temporal and spatial perspectives! Water Resources Research, v. 23, no.
8, p. 1575-1585.
Gureghian, A. B., and Jansen, G., 1985, One-dimensional analytical solutions
for the migration of a three-member radionucllde decay chain in a
multilayered geologic medium* Water Resources Research, v. 21, no. 5,
p. 733-742.
Holly, D. E., and Fenske, P. R., 1968, Transport of dissolved chemical
contaminants in ground-water systemsi in Nevada Test Site,
Geological Society of America Memoir 110, p. 171-183.
Hsieh, P. A., 1986, A new formula for the analytical solution of the radial
dispersion problemi Water Resources Research, v. 22, no. 11,
p. 1597-1605.
Huyakorn, P. S., Ungs, M. J., Mulkey, L. A., and Sudicky, E. A., 1987, A
three-dimensional analytical method for predicting leachate migration!
Ground Water, v. 25, no. 5, p. 588-598.
Lenau, C. W., 1972, Dispersion from recharge welli ASCE, Eng. Hech.
Div. Proc. Pap., v. 98, no. EM 2, p. 331-344.
1973, Contamination of discharge well from recharge welli ASCE,
Hyd. Div. Proc. Pap. no. 9958, v. 99, no. HY8, p. 1247-1263.
Lindstrom, F. T., 1976, Pulsed dispersion of trace chemical concentrations
in a saturated sorbing porous medlumi Water Resources Research,
v. 12. no. 2, p. 229-238.
Marino, M. A., 1974, Models of dispersion in a granular medium! Jour.
Hydrology, v. 23, p. 313-318.
1974, Distribution of contaminants in porous media flowi Water
Resources Research, v. 10, no. 5, p. 1013-1018.
L978, Flow against dispersion in nonadsorbing porous media!
Jour. Hydrology, v. 37, p. 149-158.
18
-------
Analytical Solutions, continued
1978, Flow against dispersion In adsorbing porous media: Jour.
Hydrology, v. 38, p. 197-205.
Moench, A. F., and Ogata, A., 1981, A numerical inversion of the Laplace
transform solution to radial dispersion in a porous medium: Water
Resources Research, v. 17, no. 1, p. 250-252.
Ogata, A., 1976, Two-dimensional steady-state dispersion in a saturated
porous tediumi U.S. Geol. Survey Jour, of Research, v. 4, no. 3,
p. 277-284.
Ogata, A., and Banks, R. B., 1961, A solution of the differential equation
of longitudinal dispersion in porous media: U.S. Geol. Survey
Prof. Paper 411-A, p. A1-A7.
Parlange, J. Y., and Starr, J. L., 1977, Comment on "Analytical
solution of the equation for transport of reactive solutes through
soils" by H. M. Selim and R. S. Hansel1< Uater Resources Research,
v. 13, no. 3, p. 701.
Selim, H. H., and Hansel 1, R. S., 1976, Analytical solution of the
equation of transport of reactive solutes through soils: Uater
Resources Research, v. 12, no. 3, p. 528-532.
Shamir, U. Y., and Harleman, D. R. F., 1967, Dispersion in layered
porous media: ASCE, Jour. Hyd. Div., v. 93, no. HY5, p. 237-260.
Sudicky, E. A., and Frind, E. 0., 1984, Contaminant transport in fractured
porous mediat analytical solution for a two-member decay chain
in a single fracture: Uater Resources Research, v. 20, no. 7, p. 1021-
1029.
van Genuchten, H. Th., and Alves, W. J., 1982, Analytical solutions
of the one-dimensional convective-dlspersive solute transport
equations U.S. Department of Agriculture, Technical Bull. No.
1661, 151 p.
Tang, D. H., and Babu, D. K., 1979, Analytical solution of a velocity
dependent dispersion problem: Uater Resources Research, v. 15,
no. 6, p. 1471-1478.
19
-------
NUMERICAL METHODS AND MODELS
Ah1strom, S. V., and Baca, R. G., 1974, Transport model user's manual:
Battelle Pacific Northwest Laboratories rept. BNUL-1716, 25 p.
Burnett, R. D., and Frind, E. 0., 1987, Simulation of contaminant
transport in three dimensions, 2, Dimensionality effects: Water
Resources Research, v. 23, no. 4, p. 695-705.
Cheng, R. T., and Hodge, D. S., 1976, Finite-element method in modeling
geologic transport processes! Mathematical Geology, v. 8, no. 1,
p. 43-56.
Chatwal, S. S., Cox, R. L., Green, D. U., and Ghandi, B., 1973,
Experimental and mathematical modeling of liquid-liquid miscible
displacement in porous mediat Water Resources Research, v. 9,
no. 5, p. 1369-1377.
Domenico, P. A., and Robbins, G. A., 1984, A dispersion scale effect in
model calibrations and field tracer experiments! Jour. Hydrology,
v. 70, p. 123-132.
Frind, E. 0., and Hatanga, G. B., 1985, The dual formulation of flow for
contaminant transport modeling, 1. Review of theory and accuracy
aspectsi Water Resources Research, v. 21, no. 2, p. 159-169.
Garder, A. 0., Peaceman, D. W., and Pozzi, A. L., Jr., 1964, Numerical
calculation of multidimensional miscible displacement by the method
of characteristics! Soc. Petrol. Eng. Jour., v. 4, no. 1, p. 26-36.
Gray, W. G., and Pinder, G. F., 1976, An analysis of the numerical solution
of the transport equation: Water Resources Research, v. 12, no. 3,
p. 547-555.
Grove, D. B., 1977, The use of Galerkin finite-element methods to solve
mass-transport equations: U.S. Geol. Survey Water-Resources Inv. 77-49,
55 p.
Grove, D. B., and Stollenwerk, K. G., 1984, Computer model of one-dimensional
equilibrium controlled sorptlon processes: U.S. Geol. Survey Water-
Resources Inv. 84-4059, 58 p.
Guymon, G. L., Scott, V. H., and Herrman, L. R., 1970, A general
numerical solution of the two-dimensional diffusion-convection
equation by the finite-element method! Water Resources Research,
v. 6, no. 6, p. 1611-1617.
Huyakorn, P.S., Andersen. P. F., Mercer, J. W., and White, H. 0., Jr., 1987,
Saltwater intrusion in aquifers: Development and testing of a
three-dimensional finite element model: Water Resources Research, v. 2,
no. 2, p. 293-312.
20
-------
Numerical Methods and Models, continued
Huyakorn, P. S., Jones, B. G., and Andersen, P. P., 1986, Finite element
algorithms for simulating three-dimensional groundwater flow flow and
solute transport in multilayer systems* Water Resources Research, v. 22,
no. 3, p. 361-374.
Huyakorn, P. S., Lester, B. H., and Mercer, J. W., 1983, An efficient finite
element technique for modeling transport In fractured porous media,
1. Single species transport! Water Resources Research, v. 19,
no. 3, p. 841-854.
INTERA Environmental Consultants, Inc., 1979, Revision of the documentation
for a model for calculating effects of liquid waste disposal in deep
saline aquiferst U.S. Geol. Survey Water-Resources Inv. 79-96, 73 p.
INTERCOM? Resource Development and Engineering Inc., 1976, A model for
calculating effects of liquid waste disposal in deep saline aquifers:
U.S. Geol. Survey Water-Resources Inv. 76-61.
Javandel, I., Doughty, C., and Tsang, C. P., 1984, Groundwater transport:
Handbook of mathematical models: American Geophysical Union, Water
Resources Monograph 10, 228 p.
Khaleel, R., and Reddell, D. L., 1986, MX solutions of convective-
dispersion problems: Ground Water, v. 24, no. 6, p. 798-807.
Konlkow, L. P., and Bredehoeft, J. D., 1978, Computer model of two
dimensional solute transport and dispersion in ground water: U.S.
Geol. Survey Techniques of Water-Resources Inv., Book 7. Chap. C2,
90 p.
Lantz, R. B.. 1970, Rigorous calculation of miscible displacement using
immiscible reservoir simulators: Soc. Petrol. Eng. Jour., v. 10,
no. 2, p. 192-203.
Mercer, J. W., Larson, S. P., and Paust, C. R., 1980, Finite-difference
model to simulate the areal flow of saltwater and freshwater
separated by an interface: U.S. Geol. Survey Open-File Report
80-407, 88 p.
Nalluswami, M., Longenbaugh, R. A., and Sunada, D. K., 1972, Finite
element method for the hydrodynamic dispersion equation with
•ixed partial derivatives: Water Resources Research, v. 8, no. 3,
p. 1247-1250.
Naymik, T. G., 1987, Mathematical modeling of solute transport in the
subsurface: Critical Reviews in Environmental Control, v. 17, no. 3, p.
229-251.
21
-------
Numerical Methods and Models, continued
Peaceman, D. U., and Rachford, H. H., Jr., 1962, Numerical calculation of
multidimensional nisclble displacement: Soc. Petrol. Eng. Jour., v. 2,
no. 4, p. 327-339.
Plckens, J. F., Gillhan, R. W., and Cameron, D. R., 1979, Finite-element
analysis of the transport of water and solutes in tile-drained soils:
Jour. Hydrology, v. 40, no. 2, p. 243-264.
Pickens, J. F., and Lennox, U. C., 1976, Numerical simulation of waste
movement in steady groundwater flow systems« Water Resources
Research, v. 12, no. 2, p. 171-180.
Pinder, G. F., and Cooper, H. H., Jr., 1970, A numerical technique
for calculating the transient position of the saltwater front: Water
Resources Research, v. 6, no. 3, p. 875-882.
Pinder, G. F., and Shapiro, A., 1979, A new collocation method for the
solution of the convection-dominated transport equation: Water
Resources Research, v. 15, no. 5, p. 1177-1182.
Price, H. S., Cavendish, J. C., and Varga, R. S., 1968, Numerical methods
of higher-order accuracy for diffusion-convection equations: Soc.
Petrol. Eng. Jour., v. 8, p. 293-303.
Prickett, T. A., Nayilk, T. G., and Lonnquist, C. G., 1981. A "Random-
Walk" solute transport model for selected groundwater quality
evaluations: Illinois State Water Survey, Bull. 65, 103 p.
Reeves, H., and Cranwell, R. M., 1981, User's manual for the Sandia
waste-isolation flow and transport model (SWIFT) Release 4.81:
Sandia National Lab., NUREG/CR-2324, U.S. Nuclear Regulatory
Commission, 145 p.
Reeves, H.. Ward, D. S., Davis, P. A., and Bonano, E. J., 1986, SWIFT II
self-teaching curriculum: Illustrative problems for the Sandia
waste-isolation flow and transport model for fractured media: Sandia
National Laboratories, NUREG/CR-3925, U.S. "Nuclear Regulatory Commission,
96 p.
Reddell, 0. L., and Sunada, D. K., 1970, Numerical simulation of dispersion
in groundwater aquifers: Colorado State Univ. Hydrology Paper 41,
79 p.
Settarl, A., Price, H. S., and Dupont, T., 1977, Development and appli-
cation of variational methods for simulation of misclble displace-
ment in porous media: Soc. Petrol. Eng. Jour., v. 17, no. 3, p. 228-246.
Segol, G., Pinder G. F., and Grey, W. G., 1975, A Galerkin-finite element
technique for calculating the transient position of the saltwater
front: Water Resources Research, v. 11, no. 2, p. 343-347.
22
-------
Numerical Methods and Models, continued
Shamir, U. Y., and Harleman, D. R. F., 1967, Numerical solutions for
dispersion in porous mediai Water Resources Research, v. 3, no. 2,
p. 557-581.
Tagamets, T., and Sternberg, Y. M., 1974, A predictor-corrector method
for solving the convection-dispersion equation for adsorption in
porous mediai Water Resources Research, v. 10, no. 5, p. 1003-1011.
van Genuchten, M. T., Finder, G. F., and Frind, E. 0., 1977, Simulation of
two-dimensional contaminant transport with Isoparametric hermitian
finite elements! Water Resources Research, v. 13, no. 2, p. 451-458.
Voss, C. I.. 1984. SUTRA — Saturated Unsaturated Transport—
A finite-element simulation model for saturated-unsaturated
fluid-density-dependent ground-water flow with energy transport
or chemically-reactive single-species solute transport! U.S. Geol.
Survey Water-Resources Invest. Report 84-4369.
23
-------
PARAMETER DETERMINATION AND TRACERS
Davis, S. N., Thompson, G. H., Bentley, H. U., and Stiles, G.,
1980, Ground-water tracers - A short reviews Ground Water,
v. 18, no. 1, p. 14-23.
Caspar, £., and Oncescu, H., 1972, Radioactive tracers In hydrology:
Elsevler Publishing Co., New York, 342 p.
Grove, 0. B., and Beeten, U. A., 1971, Porosity and dispersion constant
calculations for a fractured carbonate aquifer using the two-well
tracer Methods Water Resources Research, v. 7, no. 1, p. 128-134.
Grove, D. B., Beeten, W. A., and Sower, F. B., 1970, Fluid travel time
between a recharging and discharging well pair in an aquifer having
a uniform regional flow fields Water Resources Research, v. 6,
no. 5, p. 1404-1410.
Gupta, S. P., and Greenkorn, R. A., 1974, Determination of dispersion
and nonlinear adsorption parameters for flow in porous medias Water
Resources Research, v. 10, no. 4, p. 839-846.
Guvanasen, V., and Guvanasen, V. H., 1987, An approximate seminalytical
solution for tracer injection tests in a confined aquifer with a radially
converging flow field and finite volume of tracer and chase fluid: Water
Resources Research, v. 23, no. 8, p. 1607-1619.
Guven. 0., Falta, R. W., Holz, F. J., and Melville, J. G., 1985, Analysis
and interpretation of single-well tracer tests in stratified aquifers:
Water Resources Research, v. 21, no. 5, p. 676-684.
Hoehn, E., and Santschi, P. H., 1987, Interpretation of tracer displacement
during infiltration of river water to groundwatert Water Resources
Research, v. 23, no. 4, p. 633-640.
Huyakorn, P. S., Andersen, P. F., Molz, F. J., Guven, 0., and Melville, J. G.,
1986, Simulations of two-well tracer tests in stratified aquifers at the
Chalk River and the Mobile sites: Water Resources Research, v. 22, no.
7, p. 1016-1030.
Knopman, D. W., and Voss, C. I., 1987, Behavior of sensitivities in the
one-dimensional advection-dispersion equations Implications for parameter
estimation and sampling designs Water Resources Research, v. 23, no. 2,
p. 253-272.
Kreft, A., and Zuber, A., 1979, Determination of aquifer parameters by a
two-well pulsed method using radioactive tracers—Commentss Jour.
Hydrology, v. 41, no. 2, p. 171-176.
24
-------
Parameter Detemination and Tracers, continued
Mackay, D. M., Freyberg, D. L., Roberts, P. V., and Cherry, J. A., 1986,
A natural gradient experiment on solute transport In a sand aquifer —
1. Approach and overview of plume movement: Water Resources Research,
v. 22, no. 13, p. 2017-2029. [Also see Parts 2-5, same Issue.]
Holz, F. J., Giiven, 0., Melville, J. G., Crocker, R. D., and Hatteson, K. T.,
1986, Performance, analysis, and simulation of a two-well tracer test at
the Mobile sltei Water Resources Research, v. 22, no. 7, p. 1031-1037.
Molz, F. J., Melville, J. G., Gliven, 0., Crocker, R. D., and Matteson, K.
T., 1985, Design and performance of single-well tracer tests at the
Mobile sitei Water Resources Research, v. 21, no. 10, p. 1497-1502.
Murty, V. V. N., and Scott, Vr H., 1977. Determination of transport model
parameters In groundwater aquifersi Water Resources Research, v. 13, no.
6, p. 941-947.
Naymik, T. G., and Sievers, M. E., 1985, Characterization of dye tracer
plumes: In situ field experiments! Ground Water, v. 23, no. 6,
p. 746-752.
Ogata, Akio, 1963, Effect of the injection scheme on the spread of
tracers In ground-water reservoirs: U.S. Geol. Survey Prof. Paper 475-B,
p. B199-B202.
Pickens, J. F., Jackson, R. E., Inch, K. J., and Merritt, W. F., 1981,
Measurement of distribution coefficients using a radial injection
dual-tracer test: Water Resources Research, v. 17, no. 3, p. 529- 544.
Rainwater, K. A.. Wise, W. R., and Charbeneau, R. J., 1987, Parameter
estimation through groundwater tracer tests> Water Resources Research,
v. 23, no. 10, p. 1901-1910.
Sauty, J. P., 1980. An analysis of hydrodispersive transfer in aquifers:
Water Resources Research, v. 16, no. 1, p. 145-158.
Schwarzenbach, R. P., and Westall, J., 1981. Transport of nonpolar
organic compounds from surface water to groundwater. Laboratory sorption
studies* Environmental Science & Technology, v. 15, no. 11,
p. 1360-1367.
Smart, P. L.. and Laidlaw, I. M. S., 1977, An evaluation of some
fluorescent dyes for water tracing: Water Resources Research, v. 13, no.
1. p. 15-33.
Strecker. E. W., and Chu, Wen-sen, 1986, Parameter identification of a
ground-water contaminant transport model: Ground Water, v. 24,
no. 1, p. 56-62.
25
-------
Parameter Detent Ination and Tracers, continued
Sudicky, E. A., Gillhan, R. V., and Frind, E. 0., 1985, Experimental
investigation of soiute transport in stratified porous media—1. The
nonreactive cases Water Resources Research, v. 21, no. 7, p. 1035-
1041.
Umarl, A., Uiliis, R., and Liu, P. L. F., 1979, Identification of aquifer
dispersivitles in two-dimensional transient groundwater contaminant
transports An optimization approachi Water Resources Research, v. 15,
no. 4, p. 815-831.
Wagner, B. J., and Corelick, S. H., 1986, A statistical methodology for
estimating transport parameterss Theory and applications to one-
dimensional advective-disperslve systemss Water Resources Research,
v. 22. no. 8, p. 1303-1315.
Webster, D. S., Proctor, J. F., and Marine, I. W., 1970, Two-well
tracer test in fractured crystalline rock: U.S. Geol. Survey Water
Supply Paper 1544-1, 22 p.
Wiebenga, W. A., Ellis, W. R., Seatonberry, B. W., and Andrew, J. T. G.,
1967, Radioisotopes as groundwater tracerst Jour. Geophys. Research, v.
72, no. 16, p. 4081-4091.
Wood, W. W., 1981, A geochemical method of determining dispersivity in
regional ground-water systemst Jour. Hydrology, v. 54, p. 209-224.
Wood, W. W., and Ehrlich, G. G., 1978, Use of Baker's yeast to trace
mlcrobial movements in ground waters Ground Water, v. 16, no. 6,
p. 398-403.
26
-------
ANALYSIS OF FIELD PROBLEMS
Barcelona, M. J., and Naynik, T. G., 1984, Dynamics of a fertilizer
contaminant plume in grounduaters Reprinted from Environmental Science
& Technology, v. 18, p. 257.
Bennett, G. D., Mundorff, M. J., and Hussaln, S. A., 1968, Electric
analog studies of brine coning beneath fresh-water wells in the Punjab
Region, West Pakistani U.S. Geol. Survey Water-Supply Paper 1068-J, 31
P-
Boomer, P. M., and Schechter, R. S., 1979, Mathematical modeling of
in-situ uranium leaching: Soc. Petrol. Eng. Jour., p. 393-400.
Brown, D. L., and Silvey, W. D., 1977, Artificial recharge to a fresh
water-sensitive brackish-water sand aquifer, Norfolk, Virginia: U.S.
Geol. Survey Prof. Paper 939, 53 p.
Freeberg, K. M., Bedient, P. B., Connor, J. A., 1987, Modeling of TCE
contamination and recovery in a shallow sand aquifers Ground Water,
v. 25, no. 1, p. 70-80.
Goltz, M. N., and Roberts, P. V., 1986, Interpreting organic solute
transport data from a field experiment using physical nonequillbrium
•odelsi Journal of Contaminant Hydrology, v. 1. no. 1/2, p. 77-93.
Grove, D. B., and Wood, W. W., 1979, Prediction and field verification of
subsurface-water quality changes during artificial recharge, Lubbock,
Texasi Ground Water, v. 17, no. 3, p. 250-257.
Helweg, 0. J., and Labadie, J. W., 1977, Linked models for managing river
basin salt balance: Water Resources Research, v. 13, no. 2, p. 329-336.
Jackson, R. E.. and Inch, K. J., 1980, Hydrogeochemical processes
affecting the migration of radlonuclldes in a fluvial sand aquifer at the
Chalk River Nuclear Laboratories: Environment Canada, Inland Waters
Directorate, NHRI Paper No. 7, 58 p.
Jackson, R. E., and others, 1985, Contaminant hydrogeology of toxic organic
chemicals at a disposal site, Gloucester, Ontario: 1. Chemical
concepts and site assessment: Environment Canada, Inland Waters
Directorate, NHRI Paper No. 23, 114 p.
Kipp, K. L., Jr., Stollenwerk, K. G., and Grove, D. B., 1986, Groundwater
transport of strontium 90 in a glacial outwash environment: Water
Resources Research, v. 22, no. 4, p. 519-530.
Konikow, L. F., 1977, Modeling chloride movement in the alluvial aquifer
at the Rocky Mountain Arsenal, Colorado: U.S. Geol. Survey Water Supply
Paper 2044, 43 p.
27
-------
Analysis of Field Probleis, continued
Konikow, L. F., and Bredehoeft, J. D., 1974, Modeling flow and chemical
quality changes in an irrigated stream-aquifer system: Water Resources
Research, v. 10, no. 3. p. 546-562.
Konikow, L. F., and Person, H. A., 1985, Assessment of long-term salinity
changes in an irrigated stream-aquifer system: Water Resources Research,
v. 21. no. 11, p. 1611-1624.
LeBlanc, D. R., 1984, Sewage plume in a sand and gravel aquifer, Cape Cod,
Massachusettsi U.S. Geol. Survey Water-Supply Paper 2218, 28 p.
Lewis, B. D., and Goldstein. F. J.. 1982, Evaluation of a predictive
ground-water solute-transport model at the Idaho National Engineering
Laboratory, Idahot U.S. Geol. Survey Water-Resources Investigations
82-25. 71 p.
MacFarlane, D. S., Cherry, J. A., Egboka, B. C. E., Sudicky, E. A., Dance, J.
T., Nicholson, R. V., Greenhouse, J. P., and others, 1983, Migration of
contaminants in groundwater at a landfill: A case study (in 7 parts: 1.
Groundwater flow and plume delineation^ 2. Groundwater monitoring
devices* 3. Tritium as an indicator of dispersion and recharge; 4. A
natural-gradient dispersion test) 5. Cation migration in the dispersion
testi 6. Hydrogeochemistryt and 7. DC, VLF, and Inductive resistivity
surveys): Jour. Hydrology, v. 63, p. 1-197.
Mattraw, H. C., Jr., and Franks, B. J. [eds.], 1986, Movement and fate of
creosote waste in ground water, Pensacola, Florida: U.S. Geological
Survey Toxic Waste-Ground-Water Contamination Program: U.S. Geological
Survey Water-Supply Paper 2285, 63 p.
Mercado, A., 1976, Nitrate and chloride pollution of aquifers: A regional
study with the aid of a single-cell model: Water Resources Research, v.
12, no. 4, p. 731-747.
Mundorff, M. J., Carrigan. P. H.. Jr., Steele, T. 0., and Randall, A. D.,
1976, Hydrologlc evaluation of salinity control and reclamation projects
in the Indus Plain, Pakistan—A Summary: U.S. Geol. Survey Water-Supply
Paper 1608-0, 59 p.
Pankow, J. F., Johnson, R. L., Hewetson, J. P., and Cherry, J. A., 1986,
An evaluation of contaminant migration patterns at two waste disposal
sites on fractured porous media in terms of the equivalent porous
medium (EPM) model: Journal of Contaminant Hydrology, v. 1, no. 1/2,
p. 65-76.
Pinder, G. F., 1973, A Galerkin-finite element simulation of ground-water
contamination on Long Island, New York: Water Resources Research, v. 9,
no. 6, p. 1657-1669.
28
-------
Analysis of Field Problems, continued
Robertson, J. B., 1974, Digital nodeling of radioactive and chemical waste
transport in the Snake River Plain aquifer at the National Reactor
Testing Station, Idaho* U.S. Geol. Survey Open-File Rept. IDO-22054, 41
P-
1977, Numerical modeling of subsurface radioactive solute transport from
waste-seepage ponds at the Idaho National Engineering Laboratory! U.S.
Geol. Survey Open-File Rept. 76-717, 68 p.
Robson, S. G., 1974, Feasibility of digital water-quality modeling illustrated
by application at Barstow, California! U.S. Geol. Survey Water-Resources
Inv. 46-73, 66 p.
Robson, S. G., and Saulnier, G. J., Jr., 1980, Hydrogeochemistry and simulated
solute transport, Plceance Basin, Northwestern Colorado: U.S. Geol.
Survey Open-File Rept. 80-72, 89 p.
Segol, G., and Finder, G. F., 1976, Transient simulation of saltwater
Intrusion in southeastern Florida: Water Resources Research, v. 12, no.
1, p. 65-70.
Souza, W. R., and Voss, C. I., 1987, Analysis of an anlsotropic coastal
aquifer system using variable-density flow and solute transport
simulation: Journal of Hydrology, v. 92, p. 17-41.
Thurman, E. M., Barber, L. B., Jr., and LeBlanc, D. R., 1986, Movement and
fate of detergents in groundwatert A field studyt Journal of
Contaminant Hydrology, v. 1, no. 1/2, p. 143-161.
Valocchi, A. J., Roberts, P. V., Parks, G. A., and Street, R. L., 1981,
Simulation of the transport of ion-exchanging solutes using laboratory
determined chemical parameter values: Ground Water, v. 19, no. 6, p.
600-607.
29
-------
AQUIFER RECLAMATION AND MANAGEMENT ASPECTS
Andersen, P. F., Faust, C. R., and Mercer, J. W., 1984, Analysis of conceptual
designs for remedial measures at Liparl Landfill, New Jersey:
Ground Water, v. 22, no. 2, p. 176-190.
Gorelick, S. M., Evans, B., and Reason, I., 1983, Identifying sources of
grounduater pollution: An optimization approach: Water Resources
Research, v. 19, no. 3, p. 779-790.
CorelIck, S. M., Reason, I., and Cottle, R. W., 1979, Management model of
groundwater system with a transient pollutant source» Water Resources
Research, v. 15, no. 5, p. 1243-1249.
Corelick, S. M., Voss, C. I., and others, 1984, Aquifer reclamation design:
The use of contaminant transport simulation combined with nonlinear
programming: Water Resources Research, v. 20, no. 4, p. 415-427.
Javandel, I., and Tsang, Chin-Fu, 1986, Capture-zone type curves: A tool
for aquifer cleanup: Ground Water, v. 24, no. 5, p. 616-625.
Kaunas, J. R., and Halines, Y. Y., 1985, Risk management of groundwater
contamination in a multiobjective framework: Water Resources Research,
v. 21, no. 11, p. 1721-1730.
Massmann, J., and Freeze, R. A., 1987, Groundwater contamination from waste
management sites: The Interaction between risk-based engineering design
and regulatory policy, 1, Methodology: Water Resources Research, v. 23,
no. 2, p. 351-367. [Also see Part 2, Results: same issue, p. 368-380.)
Herritt, M. L., 1986, Recovering fresh water stored in saline limestone
aquifers: Ground Water, v. 24, no. 4, p. 516-529.
Sharefkin, M., Shechter, M., and Kneese, A., 1984, Impacts, costs, and
techniques for mitigation of contaminated groundwater: A review: Water
Resources Research, v. 20, no. 12. p. 1771-1783. [Also see
Comment by R. S. Main, v. 22, no. 3, p. 429-430.]
Wagner, B. J., and Corelick, S. M., 1987, Optimal groundwater quality
management under parameter uncertainty: Water Resources Research, v. 23,
no. 7, p. 1162-1174.
Ward, D. S., Buss, D. R., Mercer, J. W., and Hughes, S. S., 1987, Evaluation
of a groundwater corrective action at the Chem-Dyne hazardous waste site
using a telescopic mesh refinement modeling approach: Water Resources
Research, v. 23, no. 4, p. 603-617.
Willis, R., 1979, A planning model for the management of groundwater quality:
Water Resources Research, v. 15, no. 6, p. 1305-1312.
30
-------
SECTION 5
PERSPECTIVE ON MODELING
-------
Proceedings of the NATO Advanced Research Workshop on
Advances in Analytical and Numerical Groundwaler Flow and Quality Modelling
Lisbon. Portugal
June 2-6.1987
Library of Congress Cataloging in Publication Data
NATO Advanced Workshop on Advances in Analytical and Numerical Groundwater Flow and
Quality Modelling (1987: Lisbon, Portugal)
Groundwater flow and quality modelling / edited by E. Custodio, A. Gurgui. J. P. Lobo
Ferreira.
p. cm. — (NATO ASI series. Series C, Mathematical and physical sciences; vol. 224)
"Proceedings of the NATO Advanced Research Workshop on Advances in Analytical and
Numerical Groundwater Flow and Quality Modelling, Lisbon, Portugal, June 2-6,1987"—T.p.
verso.
"Published in cooperation with NATO Scientific Affairs Division."
Includes index.
ISBN 90-277-2655-8
1. Groundwater flow—Mathematical models—Congresses. 2. Water, Underground
—Quality—Mathematical models—Congresses. I. Custodio, Emilio. II. Gurgui. A.
(Antonio). 1953- . III. Ferreira. J. P. Lobo (Joao Paulo Lobo). 1952-
IV. North Atlantic Treaty Organization. Scientific Affairs Division. V. Title. VI. Series:
NATO ASI series. Series C, Mathematical and physical sciences; no. 224.
TC176.N386 1987
628.ru — dc19 87-30968
CIP
Groundwater Flow and
Quality Modelling
edited by
E. Custodio
Polytechnic University of Catalonia (ETSICCP/DIT) and
International Course on Groundwater. Barcelona. Spain
A. Gurgui
Polytechnic University of Catalonia (ETSIIB/DHT) and
International Course on Groundwater. Barcelona. Spain
and
J. P. Lobo Ferreira
Civil Engineering National Laboratory.
Lisbon. Portugal
Published by D. Reidel Publishing Company
P O. Box 17.3300 AA Dordrecht. Holland
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers.
101 Philip Drive. Norwell. MA 02061. U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group.
PO Box 322.3300 AH Dordrecht. Holland
D. Reidel Publishing Company is a member of the Kluwer Academic Publishers Group
All Rights Reserved
* 1988 by D. Reidel Publishing Company, Dordrecht. Holland.
No part ol the material protected by this copyright notice may be reproduced or utilized
in any lorm or by any means, electronic or mechanical, including photocopying, recording
or by any information storage and retrieval system, without written permission (rom the
copyright owner.
Printed in The Netherlands
D. Reidel Publishing Company
Dordrecht / Boston / Lancaster / Tokyo
Published in cooperalion wilh NATO Scientific Aflairs Division
-------
PRESENT LIMITATIONS AND PERSPECTIVES ON MODELING
POLLUTION PROBLEMS IN AQUIFERS
Leonard F. Konikow
U.S. Geological Survey
431 National Center
12201 Sunrise Valley Drive
Reston, VA 22092 U.S.A.
ABSTRACT. In recent years there has been an explosive increase in the
DSC of deterministic, distributcd-parameter, ground-water simulation models
for analyzing contaminant transport in ground-water systems. Predictive
errors arising strictly from inaccuracies in the equation-solving algorithm
• are usually much smaller than the predictive errors associated with or
produced by: (1) theoretical misconceptions or overidealizations about the
system that are incorporated into the model, (2) uncertainty and error in
the specification of system properties, boundary conditions, and initial
conditions, and (3) uncertainty in future stresses. The next major level of
improvement in ground-water simulation models will not arise from
improved numerical procedures; rather, a greater investment must be made
towards obtaining more accurate descriptions of aquifer properties and
their variability. It is especially critical for transport models that
variability in the permeability and porosity fields be defined as accurately
and precisely as possible. The tradeoff between accuracy and cost will
always be a difficult one to resolve, but will always have to be made for
both model development and data collection.
I. INTRODUCTION
<.
i In recent years there has been an explosive increase in the use of
; deterministic, distributed-parameter, ground-water simulation models for
1 analyzing contaminant transport in ground-water systems and for predicting
i lystem responses to changes in stresses. Because many people who are
" using ground-water models or relying on their results are not fully aware
°f the assumptions and idealizations that have been incorporated into them,
'here is a danger that some may infer that the accuracy of such a
Prediction is somehow coincident with the numerical accuracy of the
Wathematical solution to the governing equations. This assumption is
obviously invalid; the numerical errors arising strictly from inaccuracies in
'he equation-solving algorithm are usually much smaller than the predictive
-------
644
conditions, and initial conditions, and (3) uncertainty in future stresses.
This false sense of accuracy and unjustified confidence may arise from the
quantitative nature of numerical simulation, and the uninitiated may tend
to confuse quantitativeness and precision with reliability and accuracy.
The purpose of this paper is to review some of the practical
limitations on modeling complex ground-water pollution problems.
Theoretical shortcomings and data constraints are summarized and
contrasted, and a case history is presented in which the predictive accuracy
of a solute-transport model is analyzed.
2. GROUND-WATER FLOW
A general form of the equation describing the transient flow of a
slightly compressible fluid in a nonhomogeneous anisotropic aquifer may be
derived by combining Darcy's Law with the continuity equation (for
detailed derivations see Bear, 1979; or Freeze and Cherry, 1979). A
general ground-water flow equation may be written in Cartesian tensor
notation as
a ai- 3h
- S,— + W* (1)
where K-,: is the hydraulic conductivity tensor, LT~'; Ss is the specific
storage, L"1; h is the hydraulic head, L; W* = W*(x,y,z,t) is the volume
flux per unit volume (positive sign for outflow and negative for inflow),
T"'; x; are the Cartesian coordinates. L; and t is time, T. The
summation convention of Cartesian tensor analysis is implied in equation I.
That is, each term is summed over the range of its subscripts.
The dependent variable in eq. 1 is the hydraulic head. However, in
cases where fluid properties, such as density or viscosity, vary significantly
in time or space because of changes in pressure, temperature, or chemical
composition, the fluid is nonhomogeneous, and the relations among water
levels, heads, pressures, and fluid velocities are less straightforward.
Calculations of flow rates and directions then require pressure, density,
and elevation data, instead of just head measurements. Davies (1987) shows
that using the concept of equivalent freshwater head as a basis for
analyzing and modeling areal ground-water flow in a variable-density
system can lead to significant errors in predicted flow directions and
velocity magnitudes.
In some ground-water studies it can be reasonably assumed that
ground-water flow is two-dimensional. This allows the three-dimensional
flow equation to be reduced to the case of two-dimensional areal or
cross-sectional flow, for which several additional simplifications are
possible. The advantages of reducing the dimensionality of the equations
include less stringent data requirements and simpler, more efficient
645
mathematical or numerical solutions. The disadvantage is the risk of
' losing meaningful details of the system and inducing compensating errors
during the model calibration procedure. If there are minor components of
flow into or out of the plane of the two-dimensional model, they may
have a much greater impact on the solute concentration field than on the
. head distribution.
Because contaminant transport in ground water is strongly dependent
oo ground-water flow, it is often feasible to use a ground-water flow
model to analyze directions of flow and transport, as well as travel times.
An illustrative example is the analysis at the Love Canal area, Niagara
Falls, New York, described by Mercer and others (1983). Faced with
inadequate and uncertain data describing the system, they used Monte
Carlo simulation and uncertainty analysis to estimate a range of travel
• times (and their associated probabilities) from the contaminant source area
to the Niagara River.
3. SOLUTE TRANSPORT IN GROUND WATER
The purpose of a model that simulates solute transport in ground
water is to compute the concentration of a dissolved chemical species in an
aquifer at any specified place and time. Because convective transport and
hydrodynamic dispersion depend on the velocity of ground-water flow, the
mathematical simulation model must solve at least two simultaneous partial
differential equations. One is the equation of flow, from which
ground-water velocities are obtained, and the second is the solute-transport
equation, describing the chemical concentration in ground water.
The theory behind the equation describing solute transport has been
well documented in the literature (see, for example. Bear, 1979). Changes
in chemical concentration occur within a dynamic ground-water system
primarily due to four distinct processes: (1) convective (or advective)
transport, in which dissolved chemicals are moving with the flowing
ground water; (2) hydrodynamic dispersion, in which molecular and ionic
diffusion and small-scale variations in the velocity of flow through the
Porous media cause the paths of dissolved molecules and ions to diverge or
spread from the average direction of ground-water flow; (3) fluid sources,
where water of one composition is introduced into and mixed with water
°f a different composition; and (4) reactions, in which some amount of a
Particular dissolved chemical species may be added to or removed from the
ground water due to chemical, biological and physical reactions in the
*ater or between the water and the solid aquifer materials. There are
"gnificant practical problems in quantifying the role of each of these four
Processes in the field.
A generalized form of the solute-transport equation is presented by
e (1976), in which terms are incorporated to represent chemical
factions and solute concentrations both in the pore fluid and on the solid
'"'face, as follows:
-------
646
where CHEM equals
(2)
— for linear equilibrium controlled ion-exchange reactions,
33t
for s chemical rate-controlled reactions, or
k-, R"
-\(eC + pbC) for decay, and where C is concentration of the solute,
ML"3; Vj is the seepage velocity in the direction x;, LT"1; DJJ is the
coefficient of hydrodynamic dispersion (a second-order tensor), L T"1; C
is concentration of the solute in the source or sink fluid, ML" ; pj, is bulk
density of the solid, ML"3; « is the effective porosity; C is concentration
of the species adsorbed on the solid (mass of solute/mass of sediment); R^
is the rate of production of the solute in reaction k, ML"3T" ; and X is
the decay constant (equal to In 2/half life), T"'.
In the conventional formulation of equation 2, the dispersion
coefficient itself is a function both of the intrinsic properties of the
aquifer (such as heterogeneities in hydraulic conductivity) and of the fluid
flow. This relationship was expressed by Scheidegger (1961) as:
' °ijmn
(3)
where ajjmn is the dispersivity or characteristic length of the porous
medium (a fourth-order tensor), L; Vm and Vn are the components of the
flow velocity of the fluid in the m and n directions, respectively, LT" ;
and IVl is the magnitude of the velocity vector, LT1. Both Scheidegger
(1961) and Bear (1979) show that the dispersivity of an isotropic porous
medium can be defined by two constants. These are the longitudinal
dispersivity of the medium, OL, and the transverse dispersivity of the
medium, «]-. Most applications of transport models to ground-water
contamination problems that have been documented to date have been
based on this conventional formulation.
647
The consideration of solute transport in a porous medium that is
gnisotropic would require the estimation of more than two parameters. For
example, Moranville and others (1977) and Greenkorn (1983) indicate that
for the case of transversely isotropic media, the dispersion tensor can be
characterized by six scalar invariants. In practice, it is rare that field
values for even the two constants o^ and otj can be defined uniquely.
Thus, it appears impractical to be able to measure or define as many as
5jx dispersivity constants in the field. So, although anisotropy in hydraulic
conductivity (a second-order tensor) is recognized and accounted for in
ground-water flow simulation, it is commonly assumed out of convenience
that the same system is isotropic with respect to dispersion.
The error that can be introduced by neglecting material anisotropy is
illustrated in field data where o-r has been shown to be sensitive to
direction. An example is the study of a contaminant plume at Barstow,
California (Robson, 1974; 1978). Robson applied two-dimensional
solute-transport models in both area! and cross-sectional planes. To achieve
a best fit to the field data, he had to reduce the value of ctj in the
cross-sectional model by a factor of 100 from the value of 60 ft used in
the area) model (OL - 200 ft in both planes). As flow is predominantly
horizontal in this study area, Robson (1978) explains the change in
dispersivity values as follows: 'In the areal-oriented model DL and D-r
ire essentially measures of mixing along aquifer bedding planes, as is DL
in the profile model, whereas Of in the profile model is primarily a
measure of mixing across bedding planes.*
If single values of ct^ or crj- are used in predicting solute transport
when the flow direction is not always parallel to one of the principal
directions of anisotropy, then dispersive fluxes will be either overestimated
or underestimated for various parts of the flow system (depending on
whether the values of at and a-f are characteristic of dispersive transport
in the horizontal or vertical direction). This can lead to significant errors
in predicted concentrations.
There are many aspects of solute transport and dispersion in
anisotropic porous media that are still poorly understood. Fattah and
Hoopes (1985) state "the tensor nature of the dispersion coefficient in
inisotropic porous media . . . has not been established." Celhar and Axness
0983) and Neuman and others (1987) present general three-dimensional
stochastic analyses of macrodispersion (or field-scale dispersion) in
anisotropic media. Gelhar and .Axness conclude that the macrodispersivity
coefficient (A;:) is a second-rank symmetric tensor; because the
off-diagonal terms are nonzero, there is an offset between the mean flow
direction and the principal axis associated with the largest principal value
of AJJ when the flow is not parallel to the principal axes of the hydraulic
conductivity tensor. On the other hand, Neuman and others conclude that
"large Peclet numbers, the dispersivity tensor reduces to a single
Principal component parallel to the mean velocity, regardless of the
orientation of the velocity vector; at small and intermediate Peclet numbers
'"ere is an offset toward the axis of highest spatial correlation, a direction
• Opposite from that inferred by Gelhar and Axness.
-------
648
The seepage velocity is obviously a critical parameter to define for a
field problem involving solute transport, as it directly influences both
convective transport and the dispersive flux. An expression for the
average seepage velocity of ground water can be derived from Darcy's law
and can be written in Cartesian tensor notation as:
V:
3h
(4)
The velocity distribution can be computed on the basis of observed or
calculated hydraulic gradients. But the relation between velocity and
dispersion is at least partly dependent on the relationship between the scale
of observations of concentration and the scale of definition of velocity. In
general, for a field problem at a scale that incorporates local and regional
aquifer heterogeneities, the smaller or finer the scale at which the velocity
is defined, the smaller will be the apparent magnitude of the dispersion
coefficient.
Although OL is generally deemed to be an intrinsic property of the
aquifer, it is found in practice to be dependent on and proportional to the
scale of the measurement. Celhar (1986) shows that most reported values
of
-------
650
Well documented and efficient multiphase models applicable to
contamination of ground water by immiscible organic chemicals are not yet
generally available. One of the very few documented field applications is
Osborne and Sykes (1986). Jn summary, regardless of how accurately »e
can solve the commonly accepted governing equation, cq. 2, that equation
itself is not necessarily a definitive and sufficient description of the
processes controlling contaminant transport at the scale of most field
problems. Hence, any predictions arising from the solution of that equation
should be appropriately qualified.
4. NUMERICAL METHODS
Analytical solutions are available to solve the solute-transport
equation (see, for example. Bear, 1979; Javandel and others, 1984; and van
Genuchten and Alves, 1982). However, obtaining the exact analytical
solution to the partial differential equation requires that the properties and
boundaries of the flow system be highly and perhaps unrealistically
idealized. For simulating most field problems, the mathematical benefits
of obtaining an exact analytical solution are probably outweighed by the
errors introduced by the simplifying approximations of the complex field
environment that are required to apply the analytical approach.
The solute-transport equation is in general more difficult to solve
numerically than the ground-water flow equation, largely because certain
mathematical properties of the transport equation vary depending upon
which terms in the equation are dominant in a particular situation. When
solute transport is dominated by conveclive transport, as is common in
many field problems, then cq. 2 approximates a hyperbolic type of
equation (simitar to equations describing the propagation of a wave or of
a shock front). But if a system is dominated by dispersive fluxes, such as
might occur where fluid velocities are relatively low and aquifer
dispersivities are relatively high, then eq. 2 becomes more parabolic in
nature (similar to the ground-water flow equation). The numerical methods
that work best for parabolic partial differential equations are not best for
solving hyperbolic equations, and vice versa. Thus, no one numerical
method or simulation model will be ideal for the entire spectrum of
ground-water transport problems likely to be encountered in the field.
Further compounding this difficulty is the fact that the ground-water flow
velocity within a given multidimensional flow field will normally vary
greatly, from near zero in low permeability zones or near stagnation
points, to several feet or meters per day in high permeability areas or near
stress points. Thus, for a given single ground-water system, the
mathematical characteristic of the transport process may vary between
hyperbolic and parabolic, so that no one model may even be best over the
entire domain of a single problem.
Three types of numerical methods are commonly used to solve the
solute-transport equation: finite-difference methods, finite-element methods,
and the method of characteristics. Each has some advantages,
disadvantages, and special limitations for applications to field problems. A
651
comprehensive review of solute-transport models is presented by Anderson
(|979). The model survey of van der Heijde and others (1985) reviews a
total of 84 numerical, mass-transport models. Hamilton and others (1985)
compare the application of three different transport models to a single
field problem; they conclude that the Peclet number is a critical criterion
lo evaluate.
The method of characteristics was originally developed to solve
hyperbolic equations. If solute transport is dominated by convective
• transport, as is common in many field problems, then equation 2 may
closely approximate a hyperbolic equation and be highly compatible with
the method of characteristics. Documented models based on variants of
,' this approach include Konikow and Bredehoeft (1978) and Prickett and
:j others (1981). Finite-difference and finite-element methods can accurately
> and efficiently solve the transport equation, particularly when dispersive
transport is large compared to convective transport. However, problems of
numerical dispersion and oscillations may induce significant errors for
. some problems. Examples of recently documented three-dimensional,
transient, finite-difference models that simultaneously solves the fluid
pressure, energy-transport, and solute-transport equations for
.. nonhomogeneous miscible fluids include Kipp (1987) and Reeves and others
'. (1986). A two-dimensional finite-element transport model is documented by
Voss (1984).
I
Because none of the standard numerical methods are ideal for a wide
range of transport problems, there is currently much research on mixed or
adaptive methods that aim to minimize numerical errors and combine the
best features of alternative standard numerical approaches. Examples
include Carrera and Mellon! (1987), Ewing, Russell, and Wheeler (1983).
Fujinawa (1986), and Neuman (1984).
5. MODEL DESIGN AND CALIBRATION
In the development of a deterministic ground-water model for a
specific area and purpose, we must select an appropriate level of
complexity (or, rather, simplicity). We are inclined to believe that finer
resolution in a model will yield greater accuracy. However, there also
exists the practical constraint that even when appropriate data are
*vailable, a finely discretized three-dimensional numerical transport model
""ay be too large or too expensive to run on available computers. The
Election of the appropriate model and appropriate level of complexity will
remain subjective and dependent on the judgement and experience of the
•nalysts, the objectives of the study, and level of prior information on the
*ystem of interest. The trade-off between accuracy and cost will always be
* difficult one to resolve, but will always have to be made. In any case,
Managers and other users of model results must be made aware that these
•'ade-offs and judgements have been made and may affect the reliability
or the model.
In general, it is more difficult to calibrate solute-transport model of
-------
652
an aquifer than it is to calibrate a ground-water flow model. Fewer
parameters need to be defined to compute the head distribution with a
flow model than are required to compute concentration changes with a
solute-transport model. Because the ground-water seepage velocity is
determined from the head distribution, and because both convectivc
transport and hydrodynamic dispersion are functions of the seepage
velocity, a model of ground-water flow in an aquifer is often calibrated
before a solute-transport model is developed. In fact, in a field
environment perhaps the single most important key to understanding a
solute-transport problem is the development of an accurate definition (or
model) of the flow system. This is particularly relevant to transport in
fractured rocks, where simulation is commonly based on porous-media
concepts. Although the potential field can often be simulated, the required
velocity field may be greatly in error.
Major questions in the application of a ground-water model concern
the model's ability to represent the processes that are controlling responses
in the system of interest and the reliability of the predictions. First and
foremost, it must be demonstrated that the model accurately solves the
governing equations (this is rarely a problem for the solution to the flow
equation, but may sometimes be significant for the solute-transport
equation). Some errors may be introduced by inappropriate approximations
inherent in the assumed governing equations because of inadequacies of the
conceptual model. However, in most model applications to field problems.
the dominant cause of errors in model output is the presence of errors or
uncertainty in the input data, which reflect our inability to accurately and
quantitatively describe the aquifer properties, stresses, and boundaries.
Concerning both concepts and parameters, Watson's (1969) cautioning
statement is relevant: 'Just because we do or must describe the world in a
given way does not mean that the world is really that way.*
To demonstrate that a deterministic ground-water simulation model is
realistic, it is usual to compare field observations of aquifer responses
(such as changes in water levels or potcntiometric heads for ground-water
flow problems and concentration for transport problems) to corresponding
values obtained from the model. The objective of this calibration
procedure is to minimize differences between the observed data and
computed values. Usually, the model is considered calibrated when it
reproduces historical data within some acceptable level of accuracy.
Although a poor match provides evidence of errors in the concepts (or
hypotheses) underlying the simulation model, a good match in itself does
not prove the validity or adequacy of the model.
Matalas and Maddock (1976) argue that model calibration is
synonymous with parameter estimation. The calibration of a deterministic
ground-water model is often accomplished through a trial-and-error
adjustment of the model's input data (aquifer properties, sources and sinks,
and boundary and initial conditions) to modify the model's output. Because
a large number of interrelated factors affect the output, this may become
a highly subjective procedure. Advances in parameter identification
procedures, such as described by Cooley (1982). Knopman and Voss (1987),
653
pleuman (1980), Umari and others (1979), Wagner and Gorelick (1986), and
yen (1986), help to eliminate some of the subjectivity inherent in model
calibration. However, the hydrologic experience and judgement of the
giodcler continues to be a major factor in calibrating a model both
,ccurately and efficiently. The modeler should be familiar with the
specific field area being studied to know that both the data base and the
guinerical model adequately represent prevailing field conditions. The
modeler must also recognize that the uncertainty in the specification of
sources, sinks, and boundary and initial conditions should be evaluated
during the calibration procedure in the same manner as the uncertainty in
aquifer properties. Failure to recognize the uncertainty inherent both in
the input data and in the calibration data may lead to Tine-tuning" of the
model through artificially precise parameter adjustments strictly to improve
the match between observed and calculated variables. This may only serve
to falsely increase the confidence in the model without producing an
equivalent (or any) increase in its predictive accuracy.
Figure I illustrates in a general manner the role of models in
providing input to the analysis of ground-water contamination problems.
The value of the modeling approach is its capability to integrate
site-specific data with equations describing the relevant processes as a basts
for predicting changes or responses in ground-water quality. A major
difference between evaluating existing contaminated sites and new or
planned sites is that for the former, if the contaminant source can be
reasonably well defined, the history of contamination itself can, in effect,
serve as a surrogate long-term tracer test that provides critical information
on velocity and dispersion at a regional scale. However, it is common
when a contamination problem is recognized, that the locations, timing, and
strengths of the contaminant sources are for the most part unknown. At
new sites, historical data are commonly not available to provide a basis
for model calibration and to serve as a control on the accuracy of
predictions. As indicated in Fig. 1, there should be allowances for feedback
from the stage of interpreting model output both to the data collection
and analysis phase and to the conceptualization and mathematical
definition of the relevant governing processes.
6. EXAMPLE OF MODEL APPLICATION TO FIELD PROBLEM
The Idaho National Engineering Laboratory (INEL) is located on 890
X). mi. of semiarid land in the eastern Snake River Plain of southeast
(
-------
654
655
referred (or additional details.
As described in those two reports, the eastern Snake River Plain is a
large structural and topographic basin about 200 miles long and 50 to 70
miles wide. It is underlain by 2,000 to 10,000 feel of thin basaltic lava
flows, rhyolite deposits, and interbedded alluvial and lacustrine sediments.
These formations contain a vast amount of ground water and comprise the
major aquifer in Idaho, which is known as the Snake River Plain aquifer.
Ground-water flow is generally to the southwest at relatively high
velocities (5 to 20 feet per day, or 1.5 to 6 meters per day), according to
the reports on this area. The principal water-bearing zones occur in the
basalts, the permeability fabric of which is highly heterogeneous,
anisotropic, and complicated by secondary permeability features, such as
fractures, cavities, and lava tubes.
Because of the concern about the ground-water contamination
resulting from the waste discharge, in 1973 Robertson developed a digital
solute-transport model to simulate the underlying aquifer system to help
analyze ground-water flow and contaminant transport at the site. The
numerical model was based on the method of characteristics. He first
calibrated a flow model for a 2,600 sq. mi. (6,600 sq. km.) area, and then
calibrated the transport model for a smaller part of that area in which
contamination was of concern. The calibration of the transport model was
based on a 20-year history of contamination, as documented by samples
from about 45 wells near and downgradient from the known point sources
of contamination. These data showed that chloride and tritium had spread
over a 15 sq. mi. (39 sq. km.) area and migrated as far as 5 mi. (8 km.)
downgradient from discharge points. The distribution of waste chloride
observed in November 1972 is shown in fig. 2. Robertson notes that the
degree of observed lateral dispersion in the plumes is particularly large.
Robertson used the calibrated transport model to predict future
concentrations of chloride, tritium, and strontium-90 for the years I9SO
and 2000 under a variety of alternative possible future stresses. The
scenario that came closest to what actually occurred for the chlorides
included assumptions that disposal continues at 1973 rates and the Big Lost
River recharges the aquifer in odd numbered years. The projections
indicated that by 1980 the leading edges of both the chloride (see fig. 3)
and the tritium plumes would be at or near the INF.L southern boundary.
Lewis and Goldstein (1982) report that eight wells were drilled
during the summer of 1980 near the southern boundary to help fill data
gaps and to monitor contaminants in ground water flowing across the
INEL boundary. They also used the data from the eight wells to help
evaluate the accuracy of Robertson's predictive model. The distribution of
waste chloride observed in October 1980 is shown in figure 4. A
comparison of fig. 4 with fig. 2 indicates that the leading edge of the
chloride plume had advanced 2M to 3 miles (4 to 5 km) during that 8 year
period, and that the highest concentrations increased from around 85 mg/L
to around 100 mg/L.
A comparison of figs. 3 and 4 indicate that although the observed
and predicted plumes show general agreement in the direction, extent, and
magnitude of contamination, there exist some apparently significant
differences in detail. The observed plume is broader and exhibits more
lateral spreading than was predicted, and has not spread as far south and
as close to the INEL boundary as was predicted. Also, the predicted
secondary plume north of the Big Lost River, emanating from the Test
Reactor Area, was essentially not detected in the field at that time.
In view of these differences between the predicted and observed
concentrations it is reasonable to ask why the errors occurred, whether the
errors are significant in relation to the overall problem, and whether the
model predictions had any value. Lewis and Goldstein (1982) present a
number of factors which they felt contributed to the discrepancy. These
reasons can be summarized as: (1) less dilution from recharge during
1977-80 because of below-normal river flow; (2) chloride disposal rates at
the ICPP facility were increased during the several years preceding 1980;
(3) the model grid may have been too coarse; (4) the model calibration
• selected inaccurate hydraulic and transport parameters; (5) vertical
components of flow and transport may be significant in the aquifer but
can not be evaluated with the two-dimensional areal model; (6) there may
be too few wells to accurately map the actual plumes, and some existing
wells may not be constructed properly to yield representative measurements;
and (7) the numerical method introduces some errors (however. Grove's
• 1977 analysis of this same system used finite-difference and finite-element
methods, and comparisons of numerical results offer no basis for
concluding that the numerical solution algorithm used by Robertson was in
itself a significant source of the predictive errors).
Although these factors can be expanded upon, and additional factors
added, it is extremely difficult to assess the contribution of any single
factor to the total error. One approach that would help would be to
recalibrate the earlier model using the now extended historical record and
use it to test some of these hypotheses. Other factors could only be tested
if new models are developed that incorporate additional or more complex
concepts, such as density differences and three-dimensienal flow. Such a
recalibration and model revision should lead to a model that has greater
predictive power and reliability. Whether the errors in this case were
significant in relation to the overall problem can be best (or perhaps, only)
answered by those who sponsored the model study in light of (1) what
they expected, (2) what actions were taken or not taken because of these
Predictions, and (3) what predictive alternatives were available. It is clear,
however, that the model predictions represented one hypothesis of future
- contaminant spreading that could be tested in the field, and indeed the
-'•. 1980 test drilling was designed to a large extent to test that very
.' Prediction. The process of collecting data is most efficient when guided
: by an objective of hypothesis testing. So perhaps for the INEL site, a
•'.". major value of the model so far has been to help optimize the data
1 collection and monitoring process; that is, the predictive model offers a
. means to help decide how frequently and where water samples should be
•? collected to track the plume.
-------
656
7. CONCLUSIONS
To make the most reliable prediction for a given ground-water
problem, all relevant information should be considered and evaluated in
order to arrive at the best estimate of the future behavior of the system
Deterministic simulation models can help one accomplish this quantitatively
by providing a format- to integrate and synthesize all of that available
information in a manner consistent with theories describing the governing
processes. Our present understanding of the many processes affecting
ground water is sufficiently adequate to allow us, in theory, to forecast
the behavior of a ground-water system. In practice we are severely
limited by the inadequacy of data available to describe aquifer properties
and historical stresses and responses and by an inability to predict future
stresses. Overall, extreme caution is required in making, presenting, and
accepting predictions of future ground-water behavior. Because the
confidence in estimates of future stresses decreases with predictive time,
and because historically observed system behavior may not reflect the
relative dominance or strengths of different governing processes under a
new set of stresses, forecasts will have greater uncertainty with increasing
predictive time.
The theoretical elegance and power of the purely deterministic
approach must be tempered by the practical compromises imposed by
considering the complex real world of the heterogeneous geological media
that contain the ground-water resources of the world. This compromise
comes in the form of melding, in one way or another, statistical and
deterministic approaches. These ways may range from a straightforward
sensitivity analysis using a deterministic model 10 development and solution
of stochastic differential equations that directly incorporate the variance in
aquifer parameters.
An advantage of deterministic models is that they represent processes
and thus have cause and effect relationships built into them. But
careful attention must be paid to the accuracy with which future "causes"
(stresses) can be predicted (or estimated), because that can be the major
source of error in the predictions of future "effects" (system responses).
This asset of representing processes provides the basis for predicting or
extrapolating responses beyond the range of previously observed stresses
and responses. However, concepts inherent in a given model (for example,
two-dimensional flow and vertically averaged parameter values, or assumed
geometry and boundary conditions) may be adequate over the observed
range of stresses, but prove to be oversimplified or invalid approximations
under a new and previously inexperienced type or magnitude of stresses. It
should be recognized that when model parameters have been adjusted to
obtain a 'best fit" to historical data, a bias may be induced towards
extrapolating existing trends when predicting future conditions.
Between the two general types of ground-water problems -- flow and
transport — the latter is clearly the more difficult to handle and predict.
Flow problems can often be simplified through the principle of
superposition, so that changes in head resulting from changes in stress can
657
•' be computed directly. The flow problem is merely a subset of the transport
problem, in which the flow must be described in terms of actual heads
' |pd hydraulic gradients, not just their changes. Also, the conventional
jolute-transport equation provides a less definitive description of the
processes and factors affecting solute concentration than does the flow
equation for hydraulic head; the former is more difficult and costly to
so|ve accurately. Because the response times for propagation of fluid
• pressure changes is much shorter than for the migration of solutes, the
spatial scale for variance in concentration is much smaller than the scale
for variance in head. Thus, the response times for transport phenomena
ire proportionately greater, and it is more difficult to calibrate and
evaluate transport models with field data than it is for flow models.
The next major level of improvement in ground-water simulation
T models will probably not arise from improved numerical procedures; rather,
a greater investment must be made in obtaining more accurate descriptions
of aquifer properties and their variability. Better definitions are needed of
-. the geometry, boundary conditions, heterogeneities of the system being
< analyzed, and field data to calibrate and verify models. It is especially
'
-------
658
Dagan, G., 1987, Theory or solute transport by groundwater: Ann, Rev
Fluid Mech., v. 19, p. 183-215.
Davies, P. B., 1987, Modeling area), variable-density, ground-water f\0
using equivalent freshwater head - analysis of potentially *
significant errors: ill Proc. Solving Ground Water Problems with
Models, v. 2, Natl. Water Well Assoc., Dublin, OH, p. 888-903.
Davis, A. D., 1986, Deterministic modeling of dispersion in heterogeneous
permeable media: Ground Water, v, 24, no. 5, p. 609-615.
Domenico, P. A., and Robbins, G. S., 1984, A dispersion scale effect in
model calibrations and field tracer experiments: Jour. Hydrology
v. 70, p. 123-132.
Ewing, R. E., Russell, T. F., and Wheeler, M. F., 1983, Simulation of
rniscible displacement using mixed methods and a modified
method of characteristics: SPE 12241, Proc. 7th SPE Symp. On
Reservoir Simulation, p. 71-81.
Fattah, Q. N., and Hoopes, J. A., 1985, Dispersion in anisotropic,
homogeneous, porous media: Jour, of Hyd. Eng., ASCE, v. 111 no'
5, p. 810-827.
Faust, C. R.. 1985, Transport of immiscible fluids within and below the
unsaturated zone: A numerical model: Water Resources Research
v. 21, no. 4, p. 587-596.
Freeze, R. A., and Cherry, J. A., 1979, Groundwater: Prentice-Hall, Inc.
Englewood Cliffs, NJ, 604 p.
Ftjinawa, K... 1986, A 'characteristic' finite element scheme for
convective-dispersive transport with non-equilibrium reaction: Int.
Jour. Numer. Methods Eng., v. 23, p. 1161-1178.
Glrabcdian, S. P., and LeBlanc, D. R., 1987, Results of spatial moments
analysis for a natural-gradient tracer test in sand and gravel, Cape
Cod, Mass.: [abs.J Eos, v. 68, no. 16, p. 322-323.
Gtlhar, L. W., 1986, Stochastic subsurface hydrology from theory to
applications: Water Resources Research, v. 22, no. 9, p. I35S-145S.
Gelhar, L. W., Gutjahr, A. L., and Naff, R. L., 1979, Stochastic analysis of
macrodispersion in a stratified aquifer: Water Resources Research, v.
IS, no. 6, p. 1387-1397.
Gelhar, L. W., and Axness, C. L., 1983, Three-dimensional stochastic
analysis of macrodispersion in aquifers: Water Resources Research.
v. 19, no. I, p. 161-180.
Grcenkorn, R. A., 1983, Flow phenomena in porous media: Marcel Dekker,
659
Inc., New York, 550 p.
Grove. D. B., 1976, Ion exchange reactions important in groundwater
quality models: in^ Advances in Groundwater Hydrology, American
Water Res. Assoc., p. 144-152.
Grove, D. B., 1977, The use of Galerkin finite-element methods to solve
mass-transport equations: U.S. Geol. Survey Water Resources Inv.
77-49, 55 p.
Hamilton, D. A.. Wiggert, D. C., and Wright, S. J., 1985, Field comparison
of three mass transport models: Jour. Hydraulic Eng., ASCE, v. Ill,
no. I. p. 1-11.
> Javandel, I., Doughty, D., and Tsang, C-F., 1984, Groundwater transport:
•2*. Handbook of mathematical models: Am. Geophys. Union, Water Res.
V ' Monograph 10, 228 p.
i: Kipp. K- L- Jr- l987. HST3D: A computer code for simulation of heat
and solute transport in three-dimensional ground-water flow systems:
U.S. Geol. Survey Water-Res. Inv. Report 86-4095, 517 p.
Knopman, D. S, and Voss, C. I., 1987, Behavior of sensitivities in the one-
dimensional advection-dispersion equation: Implications for parameter
estimation and sampling design: Water Resources Research, v. 23, no.
2, p. 253-272.
Konikow, L. F., 1981, Role of numerical simulation in analysis of ground-
water quality problems: Science of the Total Environment, v. 21,
p. 299-312.
Konikow, L. F., and Bredehoeft, J. D., 1978, Computer model of
two-dimensional solute transport and dispersion in ground water:
U.S. Geol. Survey Techniques of Water-Resources Inv., Book 7, Chap.
C2, 90 p.
Lewis, B. D., and Goldstein, F. J., 1982, Evaluation of a predictive
ground-water solute-transport model at the Idaho National
Engineering Laboratory, Idaho: U.S. Geol. Survey Water-Resources
Investigation 82-25, 71 p.
•{, Lewis, F. M., Voss, C. I., and Rubin, J, 1987, Solute transport with
j£ equilibrium aqueous complexation and either sorption or ion
Jg exchange: simulation methodology and applications: Jour. Hydrology,
f v. 90, p. 81-115.
ly, D. M, Ball, W. P., and Durant, M. G., 1986, Variability of aquifer
sorption properties in a field experiment on groundwater transport
of organic solutes: methods and preliminary results: Jour.
Contaminant Hyd, v. 1, p. 119-132.
-------
660
Mackay, D. M-, Freyberg, D. L., Roberts, P. V., and Cherry, J. A., 1986, 4
natural gradient experiment on solute transport in a sand aquifer: I
Approach and overview or plume movement: Water Resources Res
v. 22. no. 13. p. 2017-2029.
Matalas, N. C., and Maddock, T, III, 1976, Hydrologic semantics: Water
Resources Research, v. 12, no. I, p. 123.
Matheron, G., and De Marsily. G., 1980, Is transport in porous media
always diffusive? A counterexample: Water Resources Research, v
16, no. 5, p. 901-917.
Mercer, J. W.. Silka, L. R., and Faust, C. R., 1983, Modeling ground-water
flow at Love Canal, New York: Jour. Env. Eng., ASCE, v. 109, no.
4, p. 924-942.
Moll, F. J., Giiven, O., Melville, J. G., and Keely, J. F., 1987, Performance
and analysis of aquifer tracer tests with implications for contaminant
transport modeling -- a project summary: Ground Water, v. 25, no. 3,
p. 337-341.
Moranville, ML B., Kessler, D. P., and Grcenkorn, R. A., 1977, Directional
dispersion coefficients in anisotropic porous media: Ind. Eng. Chem..
Fundam., v. 16, no. 3, p. 327-332.
Neuman, S. P., 1980, A statistical approach to the inverse problem of
aquifer hydrology, 3, Improved solution method and added
perspective: Water Resources Research, v. 16, no. 2, p. 331-346.
Neuman, S. P., 1982, Statistical characterization of aquifer heterogeneities:
an overview: iii Narasimhan, T. N., ed.. Recent trends in
hydrogeology, Geol. Soc. Am. Spec. Paper 189, p. 81-102.
Neuman, S. P., 1984, Adaptive Eulerian-Lagrangian finite-element method
for advection-dispersion: Int. Jour. Numer. Methods Eng., v. 20, p.
321-337.
Neuman, S. P., Winter, C. L., and Newman, C. M, 1987, Stochastic theory
of field-scale Fickian dispersion in anisotropic porous media: Water
Resources Research, v. 23, no. 3, p. 453-466.
Osborne, M., and Sykes, J., 1986, Numerical modeling of immiscible organic
transport at the Hyde Park Landfill: Water Resources Research, v.
22, no. I, p. 25-33.
Finder, G. F., and Abriola, L. M., 1986, On the simulation of nonaqueous
phase organic compounds in the subsurface: Water Resources
Research, v. 22. no. 9. p. 109S-119S.
Prickett, T. A., Naymik, T. G., and Lonnquist, C. G., 1981, A
"Random-Walk" solute transport model for selected groundwater quality
661
evaluations: Illinois State Water Survey, Bull. 65, 103 p.
Reeves. M., Ward, D. S., Johns, N. D., and Cranwell, R. M., 1986, Theory
and implementation for SWIFT II, the Sandia waste-isolation flow
and transport model for fractured media, release 4.84: Sandia Natl.
Labs., NUREG/CR-3328, SAND83-1159, Albuquerque, NM, 189 p.
gobertson, J. B., 1974, Digital modeling of radioactive and chemical waste
transport in the Snake River Plain aquifer at the National Reactor
Testing Station, Idaho: U.S. Geol. Survey Open-File Report IDO-220S4,
41 p.
Robson, S. G., 1974, Feasibility of digital water-quality modeling illustrated
by application at Barstow, California: U.S. Geological Survey
Water-Resources Investigations 46-73, 66 p.
Robson, S. G., 1978, Application of digital profile modeling techniques to
ground-water solute transport at Barstow, California: U.S. Geological
Survey Water-Supply Paper 2050, 28 p.
Rubin, J., 1983, Transport of reacting solutes in porous media: Relation
between mathematical nature of problem formulation and chemical
nature of reactions: Water Resources Research, v. 19, no. 5, p.
1231-1252.
Scheidegger, A. E., 1961, General theory of dispersion in porous media:
Jour. Geophys. Research, v. 66, no. 10, p. 3273-3278.
Smith, L., and Schwartz, F. W., 1980, Mass transport, 1, A stochastic
analysis of macroscopic dispersion: Water Resources Research, v. 16,
no. 2, p. 303-313.
Umari, A., Willis, R., and Liu, P. L.-F., 1979, Identification of aquifer
dispersivities in two-dimensional transient groundwater contaminant
transport: an optimization approach: Water Resources Research, v.
15, no. 4, p. 815-831.
v»n Genuchten, M. T., and Alves, W. J., 1982, Analytical solutions of the
one- dimensional convective-dispersive solute-transport equation: U.S.
Dept. Agriculture, Tech. Bull. 1661, 151 p.
v»» der Heijde, P. K. M., Bachmat, Y., Bredehoeft, J. D., Andrews, B.,
Holtz, D., and Sebastian, S., 1985, Groundwater management: The use
of numerical models: Am. Geophys. Union, Water Resources
Monograph 5, 2nd ed., 180 p.
V<|W, C. I., 1984, SUTRA -- Saturated Unsaturated Transport ~ A
finite-element simulation model for saturated-unsaturated
fluid-density-dependent ground-water flow with energy transport or
chemically-reactive single-species solute transport: U.S. Geol. Survey
Water-Resources Invest. Report 84-4369, 409 p.
-------
662
Wagner, B. J., and Gorelick, S. M, 1986. A statistical methodology for
estimating transport parameters: Theory and applications to
one-dimensional advective-dispersive systems: Water Resources
Research, v. 22, no. 8, p. 1303-13IS.
663
Watson, R. A., 1969, Explanation and prediction in geology
Geology, v. 77, p. 488-494.
Jour, of
Yeh, W. W-G., 1986, Review of parameter identification procedures in
groundwater hydrology: The inverse problem: Water Resources
Research, v. 22, no. 1, p. 95-108.
— — — —
V^. fflfl
we *
-jMtooaRpPu
»*A«ACA.MC
aoujwcco
CTCNRND
CfiTONflNC
|
XXlSOfG
NTfWMmr
t
JL
. —
CUJBRKIDNf
KMtuanet
ramspom
CONCOTW.M:
OCOVdVMG
nfSC%.O«A*
PROCESSES
—
XXLS
<«c »
Figure 1. Schematic overview of the role of simulation models in
evaluating ground-water contamination problems (from Konikow, 1981).
F'8ure 2. Map of ICPP-TRA vicinity showing observed distribution of
chloride in the Snake River Plain aquifer water in 1972 (from
K°bertson, 1974).
-------
664
Figure 3. Model-projected distribution of waste chloride in the Snake
River Plain aquifer for 1980. ICPP-TRA vicinity, assuming disposal
continues at 1973 rates and the Big Lost River recharges the aquifer in
odd numbered years (from Robertson. 1974).
Figure 4. Distribution of waste chloride in the Snake River Plain aquifer-
ICPP-TRA vicinity, October 1980 (from Lewis and Goldstein, 1982).
-------
SECTION 6
CASE HISTORY
-------
Modeling Chloride Movement
in the Alluvial Aquifer at
the Rocky Mountain Arsenal,
Colorado
By LEONARD F. KONIKOW
GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2044
-------
UNITED STATES DEPARTMENT OF THE INTERIOR
JAMES G. WATT, Secretary
GEOLOGICAL SURVEY
Dallas L. Peck, Director
First printing 1977
Second printing 1983
CONTENTS
Pa*
Abstract 1
Introduction 1
Selection of study area 2
Procedure of investigation 4
Acknowledgment* 4
Simulation model 4
Background •. 4
Flow equation 6
Transport equation 6
Dispersion coefficient 7
Numerical methods ..., 7
Boundary conditions 9
Description of study area 10
History of contamination 10
Contamination pattern 12
Hydrogeology 12
Application of simulation model 16
Finite-difference grid 15
Data requirements 15
Aquifer properties 15
Aquifer stresses 18
Calibration of flow model .' 20
Calibration of solute-transport model 23
Predictive capability 32
Application to water-management problems 36
Summary and conclusions 40
References cited 42
ILLUSTRATIONS
For (ale by the Distribution Branch, U.S. Geological Survey,
604 South Pickett Street, Alexandria, VA 22304
FIOURB 1-4. Maps showing:
1. Location of study area 3
2. Major hydrologic features 11
3. Observed chloride concentration, 1966 13
4. General water-table configuration in the alluvial aquifer
in and adjacent to the Rocky Mountain Arsenal,
1966-71 14
5. Finite-difference grid used to model the study area 16
6. Graph showing change in standard error of estimate for suc-
cessive simulation tests 19
m
-------
IV
CONTENTS
P»ge
FIGURE 7. Graph showing relation between the assumed rate of net
recharge in irrigated areas and the mean difference of ob-
served and computed water levels 20
8-18. Maps showing:
8. Computed chloride concentration, 1966 26
9. Observed chloride concentration, January 1961 26
10. Computed chloride concentration at the start of 1961 .. 27
11. Observed chloride concentration, January-May 1969 .. 28
12. Computed chloride concentration at the start of 1969 .. 29
13. Observed chloride concentration, May 1972 30
14. Computed chloride concentration at the start of 1972 .. 31
15. Chloride concentration predicted for 1980, assuming that
pond C is filled with fresh water during 1972-80 32
16. Chloride concentration predicted for 1980, assuming that
recharge from pond C is minimal during 1961-80 ... 34
17. Computed drawdown caused by maintaining two con-
stant-head sinks along the northern boundary of the
Rocky Mountain Arsenal 36
18. Chloride concentration predicted for 1980, assuming that
artificial recharge from Pond C is coupled with
drainage through two hydraulic sinks 38
19. Generalized cross section from vicinity of source of artificial
recharge through hydraulic sink (represented as a well) ... 39
TABLES
TABU 1. Summary of main data requirements for numerical model
2. Generalized history of disposal pond operations at the Rocky
Mountain Arsenal, 1943-72
3. Elements of hydrologic budget computed by ground-water flow
model
17
21
23
CONTENTS
CONVERSION FACTORS
English units used in this report may be converted to metric unit* by the following
conversion factors:
namatrt
English unite
Feet (ft) ............................................
Feet per year (ft/yr) --------------------
Feet per day (ft/d) ..........................
Feet per second per foot (tft/sl/ft)
Square feet (ft1)
Feet squared per day (ft'/d)
Cubic feet per second (ft»/s)
Multiply by
4.047 x 10~3
.3048
.3048
.3048
1.0
.0929
.0929
2.832 x 10-*
Cubic feet per second per mile 1.760 x 10~*
(IftVsl/mi).
Miles (mi) 1.609
Square miles (mi1) 2.690
IboMofa
Metric unite
Square kilometers (km1).
Meters (m).
Meters per year (m/yt).
Meters per day (m/d).
Meters per second per meter
Um/B]/m).
Square meters (m1).
Meters squared per day
(m'/d).
Cubic meters per second
(mVs).
Cubic meters per second per
kilometer ((mVs]/km).
Kilometers (km).
Square kilometers (km1).
-------
MODELING CHLORIDE MOVEMENT IN THE
ALLUVIAL AQUIFER AT THE ROCKY
MOUNTAIN ARSENAL, COLORADO
By LEONARD F. KONIKOW
ABSTRACT
A solute-transport model that can be used to predict the movement of dissolved
chemicals in flowing ground water was applied to a problem of ground-water con-
tamination at the Rocky Mountain Arsenal, near Denver, Colo. The model couples a
finite-difference solution to the ground-water flow equation with the method-of-charac-
teristics solution to the solute-transport equation.
From 1943 to 1956 liquid industrial wastes containing high chloride concentrations
were disposed into unlined ponds at the Arsenal. Wastes seeped out of the unlined dis-
posal ponds and spread for many square miles in the underlying shallow alluvial
aquifer. Since 1956 disposal has been into an asphalt-lined reservoir, which contributed
to a decline in ground-water contamination by 1972. The simulation model quan-
titatively integrated the effects of the major factors that controlled changes in chloride
concentrations and accurately reproduced the 30-year history, of chloride ground-water
contamination.
Analysis of the simulation results indicates that the geologic framework of the area
markedly restricted the transport and dispersion of dissolved chemicals in the
alluvium. Dilution, from irrigation recharge and seepage from unlined canals, was an
important factor in reducing the level of chloride concentrations downgradient from
the Arsenal. Similarly, recharge of uncontaminated water from the unlined ponds since
1966 has helped to dilute and flush the contaminated ground water.
INTRODUCTION
The contamination of a ground-water resource is a serious problem
that can have long-term economic and physical consequences and
might not be easily remedied. Although the prevention of ground-
water contamination provides the most satisfactory result (Wood,
1972), the capability to predict the movement of dissolved chemicals
in flowing ground water is also needed in order to (1) plan and design
projects to minimize ground-water contamination, (2) estimate spatial
and temporal variations of chemical concentrations, (3) estimate the
traveltime of a contaminant from its source to a ground-water sink (a
discharge point, such as a stream, spring, or well), (4) help design an
effective and efficient monitoring system, and (5) help evaluate the
-------
2 ROCKY MOUNTAIN ARSENAL. COLORADO
physical and economic feasibility of alternative reclamation plans for
removing contaminants from an aquifer and (or) preventing the con-
taminants from spreading.
Reliable predictions of contaminant movement can be made only if
we understand the processes controlling convective transport, hy-
drodynamic dispersion, and chemical reactions that affect the dis-
solved chemicals in ground water, and if these processes can be ac-
curately represented in a systematic model. For a model to be usable
in a variety of hydrogeologic situations, the modeling technique must
be accurate, functional, and transferable. Because aquifers generally
have heterogeneous properties and complex boundary conditions,
quantitative predictions would appear to require the use of a deter-
ministic, distributed parameter, digital simulation model.
This study is part of the US. Geological Survey's Subsurface Waste
Program, the objective of which is to appraise the impact of waste dis-
posal on the Nation's water resources. The main objective of this study
was to demonstrate the applicability of the method-of-characteristics
model to a problem of conservative (nonreacting) contaminant move-
ment through an alluvial aquifer. By studying a field problem in which
the effects of reactions are negligible, the effects of other processes
that affect solute transport may be isolated and described more ac-
curately. This study should serve as a basis for investigating more
complex systems whose chemical reactions are significant and in-
teract with the other processes. The purposes of this report are (1) to
briefly describe the general simulation model and (2) to demonstrate
its application to a complex field problem.
Because convective transport and hydrodynamic dispersion depend
on the velocity of ground-water flow, the mathematical simulation
model must solve two simultaneous partial differential equations. One
is the equation of flow, from' which ground-water velocities are ob-
tained, and the second is the solute-transport equation, describing the
chemical concentration in the ground water. Three general classes of
numerical methods have been used to solve these partial differential
equations: finite-difference methods, finite-element methods, and the
method of characteristics. Each method has some advantages, disad-
vantages, and special limitations for application to field problems.
SELECTION OF STUDY AREA
The field area selected for this study is in and adjacent to the Rocky
Mountain Arsenal, near Denver, Colo. (See fig. 1.) A 30-year history of
ground-water contamination in this area is related to the disposal of
liquid industrial wastes into ponds (Petri, 1961; Walker, 1961; Walton,
1961). The Rocky Mountain Arsenal area is well suited for this study
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQt|
_ ADAMS CO
ARAPAHOE CO
10 KILOMETERS
PlOUHB 1.—Location of study area.
because (l) the geology and hydrology of the area are well known, (2)
adequate, though limited, water-quality data are available to calibrate
the mathematical model, and (3) the history of liquid waste-disposal
operations at the Arsenal can be approximately reconstructed.
Furthermore, the waste water has a very high chloride concentration,
which can serve as a conservative tracer.
-------
ROCKY MOUNTAIN ARSENAL. COLORADO
PROCEDURE OF INVESTIGATION
This investigation was conducted in three distinct phases. During
the first phase, all available data were collected, interpreted, and
analyzed to produce accurate, comprehensive, and quantitative
descriptions for the alluvial aquifer of its (1) geologic properties and
boundaries, (2) hydraulic properties, boundaries, and stresses, and (3)
chemical sources arid distributions over space and time. Many of the
geologic and hydraulic interpretations were presented by Konikow
(1975). Most chemical data are presented in this report.
During the second phase of the investigation, a steady-state flow
model was developed to estimate recharge rates to the aquifer and to
compute ground-water flow velocities. In the third phase of the in-
vestigation, the solute-transport model was calibrated to reproduce
the observed history of ground-water contamination at the Rocky
Mountain Arsenal. Much of the output from the flow model was used
as input to the solute-transport model.
ACKNOWLEDGMENTS
John D. Bredehoeft, U.S. Geological Survey, and George F. Finder,
formerly with the Survey and now at Princeton University, jointly
developed the original version of the solute-transport model used in
this study. J.D. Bredehoeft was also instrumental both in the further
development of this model and in the selection of the area for this
study. Their work is gratefully acknowledged. Many data were sup-
plied by the Rocky Mountain Arsenal, the U.S. Army Corps of
Engineers, and the* Colorado Department of Health, and their assist-
ance also is appreciated.
SIMULATION MODEL
BACKGROUND
The purpose of the simulation model is to compute the concentra-
tion of a dissolved chemical species in an aquifer at any specified place
and time. Changes in chemical concentration occur within a dynamic
ground-water system primarily due to four distinct processes:
1. Convective transport, in which dissolved chemicals are moving with
the flowing ground water.
2. Hydrodynamic dispersion, in which molecular and ionic diffusion
and small-scale variations in the velocity of flow through the
porous media cause the paths of dissolved molecules and ions to
diverge or spread from the average direction of ground-water
now.
3. Mixingjor dilution), in which water of one composition is introduced
r of a different composition.
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
4. Reactions, in which some amount of a particular dissolved chemical
species may be added to or removed from the ground water due to
chemical and physical reactions in the water or between the
water and the solid aquifer materials.
The model presented in this report assumes that no reactions occur
that affect the concentration of the species of interest and that the
density and viscosity of the water are constant and independent of the
concentration. Robertson (1974) expanded the model to include the
effects of radioactive decay and ion exchange with a linear adsorption
isotherm.
The modeling technique used in this study couples an implicit finite-
difference procedure to solve the flow equation and the method of
characteristics to solve the solute-transport equation. The ap-
plicability of this (or any other) type of model to complex field
problems can only be demonstrated by first testing it for a variety of
field conditions in which observed records of contaminant movement
can be compared with concentration changes computed by the model.
In this manner, the accuracy, limitations, and efficiency of the method
can be shown for a wide range of problems. Also, calibrating the model
in an area for which historical data are available will provide insight
into the use of the model in areas where few or no data are available.
FLOW EQUATION
By following the derivation of Finder and Bredehoeft (1968), the
equation describing the transient two-dimensional flow of a
homogeneous compressible fluid through a nonhomogeneous an-
isotropic aquifer may be written in cartesian tensor notation as:
where
TJ: is the transmisflivity tensor, l?IT\
h is the hydraulic head, L;
S is the storage coefficient, L°;
t is the time, 7;
W is the volume flux per unit area, LIT; and
x, y are cartesian coordinates.
If we only consider fluxes of (1) direct withdrawal or recharge, such as
well pumpage, well injection, or evapotranspiration, and (2) steady
leakage into or out of the aquifer through a confining layer,
streambed, or lake bed, then W(xy,0 may be expressed as:
t - h),
(2)
-------
6
ROCKY MOUNTAIN ARSENAL, COLORADO
where
Q is the rate of withdrawal (positive sign) or recharge (negative
sign), LIT;
Kg is the vertical hydraulic conductivity of the confining layer,
streambed, or lake bed, LIT;
m is the thickness of the confining layer, streambed, or lake bed,
L; and
Ha is the hydraulic head in the source bed, stream, or lake, L.
Lohman (1972) showed that an expression for the average seepage
velocity of ground water can be derived from Darcy's Law. This ex-
pression can be written in cartesian tensor notation as:
lh (3)
where
Vjf is the seepage velocity in the direction of *,-, LIT;
Ky is the hydraulic conductivity tensor, LIT; and
n is the effective porosity of the aquifer, L°.
TRANSPORT EQUATION
The equation used to describe the two-dimensional transport and
dispersion of a given dissolved chemical species in flowing ground
water was derived by Reddell and Sunada (1970), Bear (1972), and
Bredehoeft and Finder (1973) and may be written as:
8C
d* "
where
C
8C.
'**
nb
i'j-1,2, (4)
is the concentration of the dissolved chemical species, Mil?;
Dy is the dispersion tensor, I?IT;
b is the saturated thickness of the aquifer, L;
C' is the concentration of the dissolved chemical in a source or
sink fluid, MIL?; and
Rfr is the rate of production of the chemical species in reaction k
of s different reactions, M/L3T.
The first term on the right side of equation 4 represents the change
in concentration due to hydrodynamic dispersion and is assumed to be
proportional to the concentration gradient. The second term describes
the effects of convective transport, and the third term represents a
fluid source or sink. The fourth term, which describes chemical reac-
MODEUNG CHLORIDE MOVEMENT, ALLUVIAL AQ
tions, must be written explicitly for all reactions affecting the chemi-
cal species of interest. This term may be eliminated from equation 4
for the case of a conservative (nonreactive) species.
DISPERSION COEFFICIENT
The dispersion coefficient may be related to the velocity of ground-
water flow and to the nature of the aquifer using Scheidegger's (1961)
equation:
vv
(5)
where
a(jmn w tne dispersivity of the aquifer, L;
Vm and Vn are components of velocity in the m and n directions,
LIT; and
| vl is the magnitude of the velocity, LIT.
Scheidegger (1961) further showed that, for an isotropic aquifer, the
dispersivity tensor can be defined in terms of two constants. These are
the longitudinal and transverse dispersivities of the aquifer (a t and a2,
respectively). These are related to tv j longitudinal and transverse dis-
persion coefficients by
and
(6)
UP-a, | V|. (7)
After expanding equation 5, substituting Scheidegger's identities,
and eliminating terms with coefficients that equal zero, the compo-
nents of the dispersion coefficient for two-dimensional flow in an
isotropic aquifer may be stated explicitly as:
(8)
(9)
(10)
NUMERICAL METHODS
Because aquifers have variable properties and complex boundary
conditions, exact solutions to the partial differential equations of flow
-------
8
ROCKY MOUNTAIN ARSENAL, COLORADO
(eq 1) and solute transport (eq 4) cannot be obtained directly.
Therefore, an approximate numerical method must be employed.
Finder and Bredehoeft (1968) showed that if the coordinate axes
are aligned with the principal directions of the transmissivity tensor,
equation 1 may be approximated by the following implicit finite-
difference equation:
F
L
(Ajc)2
[
f
L
(A,y)2
A*
where
i , j , k are indices in the x, y, and time dimensions, respectively;
Ax, Ay, At are increments in the x, y, and time dimensions, respec-
tively; and
?u> is the volumetric rate of withdrawal or recharge at the
(iJ)node,Ls/T.
The numerical solution of the finite-difference equation requires
that the area of interest be subdivided into small rectangular cells,
which constitute a finite-difference grid. The finite-difference equa-
tion is solved numerically, using an iterative alternating-direction im-
plicit procedure described by Finder (1970) and Prickett and Lonn-
quist (1971).
After the head distribution has been computed for a given time step,
the velojto of ground-water flow is computed at each node, using an
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
9
explicit finite-difference form of equation 3. For example, the velocity
in the x direction at node (i,j) would be computed as:
(12)
2Ax
A similar expression is used to compute the velocity in the y direction.
The method of characteristics presented by Carder, Peaceman,
and Pozzi (1964) is used to solve the solute-transport equation (eq 4).
The development and application of this technique in ground-water
problems has been presented by Finder and Cooper (1970), Reddell
and Sunada (1970), Bredehoeft and Finder (1973), Konikow and
Bredehoeft (1974), Robertson (1974), and Robson (1974). The
method actually solves a system of ordinary differential equations
that is equivalent to the partial differential equation (eq 4) that
describes solute transport.
The numerical solution is achieved by introducing a set of moving
points that can be traced with reference to the stationary coordinates
of the finite-difference grid. Each point has a concentration associated
with it and is moved through the flow field in proportion to the flow
velocity at its location. The moving points simulate convective
transport because the concentration at each node of the finite-
difference grid changes as different points enter and leave its area of
influence. Then, the additional change in concentration due to disper-
sion and to fluid sources is computed by solving an explicit finite-
difference equation. In this study, four points were initially distributed
in each cell of the grid.
BOUNDARY CONDITIONS
Several different types of boundary conditions can be represented in
the simulation model. These include:
1. No-flow boundary By specifying a transmissivity equal to zero at a
given node, no flow can occur across the boundary of that cell of
the finite-difference grid. The numerical method used in this
model also requires that the outer rows and columns of the finite-
difference grid have zero transmissivities.
2. Constant-head boundary: Where the head in the aquifer will not
change with time, a constant-head condition is maintained by
specifying a very high value of leakance (1.0 [ft/sl/ft or [m/s]/m),
which is the ratio of the vertical hydraulic conductivity to the
thickness of the confining layer, streambed, or lake bed. The rate
of leakage is then a function of the difference between the head
-------
10
ROCKY MOUNTAIN ARSENAL, COLORADO
of the aquifer and the head in the source bed, stream, or lake and
is computed implicitly by the model.
3. Constant flux: A constant rate of withdrawal or recharge may be
specified for any node in the model.
At any boundary that acts as a source of water to the aquifer, the
chemical concentration of the source must also be defined.
DESCRIPTION OF STUDY AREA
HISTORY OF CONTAMINATION
The Rocky Mountain Arsenal has been operating since 1942, pri-
marily manufacturing and processing chemical warfare products and
pesticides. These operations have produced liquid wastes that contain
complex organic and inorganic chemicals, including a charac-
teristically high chloride concentration that apparently ranged up to
about 5,000 mg/1 (milligrams per liter).
The liquid wastes were disposed into several unlined ponds (fig. 2),
resulting in the contamination of the underlying alluvial aquifer. On
the basis of available records, it is assumed that contamination first
occurred at the beginning of 1943. From 1943 to 1956 the primary dis-
posal was into pond A. Alternate and overflow discharges were col-
lected in ponds B, C, D, and E.
Much of the area north of the Arsenal is irrigated, both with surface
water diverted from one of the irrigation canals, which are also
unlined, and with ground water pumped from irrigation wells.
Damage to crops irrigated with shallow ground water was observed in
1951, 1952, and 1953 (Walton, 1961). Severe crop damage was
reported during 1954, a year when the annual precipitation was about
one-half the normal amount, and ground-water use was heavier than
normal (Petri, 1961).
Several investigations have been conducted since 1954 to determine
both the cause of the problem and how to prevent further damages.
Petri and Smith (1956) showed that an area of contaminated ground
water of several square miles existed north and northwest of the dis-
posal ponds. These data clearly indicated that the liquid wastes seeped
out of the unlined disposal ponds, infiltrated the underlying alluvial
aquifer, and migrated downgradient toward the South Platte River. To
prevent additional contaminants from entering the aquifer, a 100-
acre (0.405 km2) evaporation pond (Reservoir F) was constructed in
1956, with an asphalt lining to hold all subsequent liquid wastes
(Engineering News-Record, Nov. 22,1956).
In 1973 and 1974 there were new (and controversial) claims of crop
and livestock damages allegedly caused by ground water that was con-
taminated at the Arsenal (The Denver Post, Jan. 22, 1973; May 12,
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQ
11
1O4-5O'
39-50' -
L ROCKY MOUNTAIN AKSENALl BOUNDARY
O l 2 MILES
h
0 1 2 KILOMETERS
EXPLANATION
Irrigated «r««
Irrigation w*ll
Unlimd rnarvolr
Lln«d rcnrvolr
FIGURE 2.— Major hydrologic features. Letters indicate disposal-pond designation*
assigned by the VS. Army.
1974; May 23, 1974). Recent data collected by the Colorado Depart-
ment of Health (Shukle, 1975) have shown that DIMP
(Diisopropylmethylphosphonate), a nerve-gas byproduct about which
relatively little is known, has been detected at a concentration of 0.57
ppb (parts per billion) in a well located approximately 8 miles (12.9
km) downgradient from the disposal ponds and 1 mile (1.6 km) upgra-
dient from 2 municipal water-supply wells of the City of Brighton. A
DIMP concentration of 48 ppm (parts per million), which is nearly
-------
12
ROCKY MOUNTAIN ARSENAL, COLORADO
100,000 times higher, was measured in a ground-water sample col-
lected near the disposal ponds. Other contaminants detected in wells
or springs in the area include DCPD (Dicyclopentadiene), endrin,
aldrin, and dieldrin.
CONTAMINATION PATTERN
Since 1955 more than 100 observation wells and test holes have
been constructed to monitor changes in water quality and water levels
in the alluvial aquifer. The areal extent of contamination has been
mapped on the basis of chloride concentrations in wells, which ranged
from normal background concentrations of about 40 to 150 mg/1 to
about 5,000 mg/1 in contaminated ground water near pond A.
Data collected during 1955-56 indicate that one main plume of con-
taminated water extended beyond the northwestern boundary of the
Arsenal and that a small secondary plume extended beyond the north-
ern boundary. (See fig. 3.) However, the velocity distribution computed
from the water-table map available at that time (Petri and Smith,
1956) could not, in detail, account for the observed pattern of spread-
ing from the sources of contamination. Because contaminant
transport depends upon flow, the prediction of concentration changes
requires the availability of accurate, comprehensive, and quantitative
descriptions for the aquifer of its hydraulic properties, boundaries,
and stresses.
HYDROGEOLOGY
The records of about 200 observation wells, test holes, irrigation
wells, and domestic wells were compiled, analyzed, and sometimes
reinterpreted to describe the hydrogeologic characteristics of the
alluvial aquifer in and adjacent to the Rocky Mountain Arsenal.
Konikow (1975) presented four maps that show the configuration of
the bedrock surface, generalized water-table configuration, saturated
thickness of alluvium, and transmissivity of the aquifer. These maps
show that the alluvium forms a complex, nonuniform, sloping, discon-
tinuous, and heterogeneous aquifer system.
A map showing the general water-table configuration for 1955-71
is presented in figure 4. The assumptions and limitations of figure 4
were discussed in more detail by Konikow (1975). Perhaps the
greatest change from previously available maps is the definition of
areas in which the alluvium either is absent or is unsaturated most of
the time. These areas form internal barriers that significantly affect
ground-water flow patterns within the aquifer. The contamination
patten shown in figure 3 clearly indicates that the migration of dis-
solved^Wpride in this aquifer was also significantly constrained by
the acaHB' boundaries.
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
13
104'5O'
39-50' h-
L ROCKY MOUNTAIN ARSENALl BOUNDARY BaBB |
0 1 2 MILES
I 1—H '
0 1 2 KILOMETERS
EXPLANATION
• Data point (Sept. 1955-March 1966)
—300 - Line of equal chloride concentration (in milligram* per liter).
Interval variable
LA.-.;«! Area in which alluvium I* absent or unaaturated
FIGURE 3.— Observed chloride concentration, 1956.
The general direction of ground-water movement is from regions of
higher water-table altitudes to those of lower water-table altitudes
and is approximately perpendicular to the water-table contours.
Deviations from the general flow pattern inferred from water-table
contours may occur in some areas because of local variations in
aquifer properties, recharge, or discharge. The nonorthogonality at
places between water-table contours and aquifer boundaries indicates
that the approximate limit of the saturated alluvium does not consist-
ently represent a no-flow boundary, but that, at son^Hfoces, there
-------
14
ROCKY MOUNTAIN ARSENAL, COLORADO
1CW50'
0 1 2 KILOMETERS
EXPLANATION
,00— WATER-TABLE CONTOUR - Shows approximate altitude of
water table, 1955-71. Contour interval 10 feet 13 meters).
Datum is mean sea level
Area in which alluvium ii absent or unsaturated
FlOURB 4.— General water-table configuration in the alluvial aquifer in and adjacent
to the Rocky Mountain Arsenal, 1955-71.
may be significant flow across this line. Such a condition can readily
occur in areas where the bedrock possesses significant porosity and
hydraulic conductivity, or where recharge from irrigation, unlined
canals, or other sources is concentrated. Because the hydraulic con-
ductivity of the bedrock underlying the alluvium is generally much
lower than that of the alluvium, ground-water flow through the
bedrock was assumed to be negligible for the purposes of this in-
vestigation.
MODELING CHLORIDE MOVEMENT, ALLUVIAL A
15
The position of the boundary that separates the alluvial aquifer
from the areas in which the alluvium is either absent or unsaturated
may actually change with time as the water table rises or falls in
response to changes in recharge and discharge, although the bound-
ary was assumed to remain stationary for the model study. The effect
of the changing boundary was most evident in the vicinity of pond A.
A map of the water-table configuration during the period when pond A
was full (Konikow, 1976) shows that during this time, there was
ground-water flow from pond A to the east and northeast into the
alluvial channel underlying the valley of First Creek, in addition to the
northwestward flow indicated in figure 4.
APPLICATION OF SIMULATION MODEL
FINITE-DIFFERENCE GRID
The limits of the modeled area were selected to include the entire
area having chloride concentrations over 200 mg/1 and the areas
downgradient to which the contaminants would likely spread, and to
closely coincide with natural boundaries and divides in the ground-
water flow system. The model includes an area of approximately 34
mi2 (88 km2).
The modeled area was subdivided into a finite-difference grid of
uniformly spaced squares. (See fig. 5.) The grid contains 25 columns
(i) and 38 rows 0)- Because of the irregular boundaries and discon-
tinuities of the alluvial aquifer, only 516 of the total 950 nodes in the
grid were actually used to compute heads (or water-table altitudes) in
the aquifer. Each cell of the grid is 1,000 feet (305 m) on each side. By
convention, nodes are located at the centers of the cells of the grid. All
aquifer properties and stresses must be defined at all nodes of the grid.
DATA REQUIREMENTS
Many factors influence the flow of ground water and its dissolved
chemicals through the alluvial aquifer near the Rocky Mountain Ar-
senal. To compute changes in chloride concentration, all parameters
and coefficients incorporated into equations 1 and 4 must be defined.
Thus, many input data are required for the model, and the accuracy of
these data will affect the reliability of the computed results. The main
input data requirements for modeling chloride movement in this
alluvial aquifer are summarized in table 1.
AQUIFER PROPERTIES
The transmissivity of an aquifer reflects the rate at which ground
water will flow through the aquifer under a unit hydraulic gradient
(Lohman and others, 1972). Konikow (1975) showed that the
-------
16
ROCKY MOUNTAIN ARSENAL, COLORADO
104-50-
39-55'
39-50-
[ ROCKY MOUNTAIN ARSENM.IBOUNPARY __i \ I
n 1 2 MILES
0 1 2 KILOMETERS
EXPLANATION
Zero-tran»mi«ivitv cell
Conitant-head call
A Ditposal-pond call. Letter correspond* to designation in figura 2
I Irrigation-racharga call
L Canal-leakage cell
Boundary ot araas in which alluvium it absent or unsaturated
FIGURE 6.— finite-difference grid used to model the study area.
transmissivity of the alluvial aquifer in this study area ranges from 0
to over 20,000 fWd (over 1,800 nWd), and that the saturated thickness
is gene^fe less than 60 feet (18 m). The highest transmissivities,
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
17
TABLE 1. — Summary of main data requirement* for numerical
model
Aquifer pnpertiei
Aquifer i
Transmissivity
Storage coefficient
Saturated thickness
Effective porosity
Diaperaivity
Boundaries
Initial chloride
concentration
Ground-water withdrawals
Irrigation recharge1
Canal leakage1
Disposal-pond leakage1
{Quantity ind qnOHy mutt ba Mined.-
greatest saturated thicknesses, and lowest hydraulic gradients
generally occur near the South Platte River in the northwestern part
of the modeled area. The finite-difference grid was superimposed on
the maps of transmissivity and saturated thickness presented by
Konikow (1975), and corresponding values were determined for each
node of the grid.
The storage coefficient of the aquifer is an approximate measure of
the relation between changes in the amount of water stored in the
aquifer and changes in head. Because no changes in head with time
occur in steady-state flow, a value for this parameter is needed only
for an analysis of transient (time-dependent) flow, which was not con-
sidered in this study.
Values of effective porosity and dispersivity of the aquifer must be
known to solve the solute-transport equation. Because no field data
are available to describe these parameters in this study area, values
were selected by using a trial-and-error adjustment within a range of
values determined for similar aquifers in other areas.
No-flow and constant-head boundaries used in this model are indi-
cated in figure 5. Constant-head boundaries were specified where it
was believed that either underflow into or out of the modeled area or
recharge was sufficient to maintain a nearly constant water-table
altitude at that point in the aquifer. Altitudes assigned to the con-
stant-head cells were determined by superimposing the finite-
difference grid (fig. 5) on the water-table map (fig. 4).
No data were available to describe the chloride concentrations in
the aquifer when the Arsenal began its operations. Because more re-
cent measurements indicated that the normal background concentra-
tion may be as low as 40 mg/1, an initial chloride concentration of 40
mg/1 was assumed to have existed uniformly throughout the aquifer in
1942.
-------
18
ROCKY MOUNTAIN ARSENAL, COLORADO
AQUIFER STRESSES
No direct measurements of long-term aquifer stresses were availa-
ble. Hence, these factors were estimated, primarily using a mass-
balance analysis of the observed flow field.
The areas that had probably been irrigated during most of the
period from 1943 to 1972 were mapped from aerial photographs.
These irrigated areas are shown in figure 2. In the model, irrigation
was assumed to occur at 111 nodes of the finite-difference grid, which
represents an area of 1.11x10" ft2 (1.03X107 m2).
The net rate of recharge from irrigation and precipitation on irrig-
ated areas was estimated through a trial-and-error analysis, in which
the simulation model was used to compute the water-table configura-
tion for various assumed recharge rates. Initial estimates of net
recharge were used in a preliminary calibration of the model.
Transmissivity values and boundary conditions in the model were ad-
justed between successive simulations with an objective of minimizing
the differences between observed and computed water-table altitudes
in the irrigated area. The standard error of estimate (or scatter) is a
statistical measure similar to the standard deviation (Croxton, 1953,
p. 119). It is used here to indicate the extent of deviations between
computed and observed heads. Figure 6 shows that the standard error
of estimate generally decreased as successive simulation tests were
made. After about seven tests, additional adjustments produced only
small improvements in the fit between the observed and computed
water tables.
A final estimate of the net recharge rate in irrigated areas was
made using the set of parameters developed for the final test of figure
6. Figure 7 shows that the mean of the differences between observed
and computed heads at all nodes in the irrigated area is minimized
(equal to zero) when a net recharge rate of approximately 1.54 ft/yr
(0.47 m/yr) is assumed. Also, irrigation recharge was assumed to have
a chloride concentration of 100 mg/1.
The recharge rate due to leakage from unlined canals was similarly
estimated to be approximately 2.37 ft/yr (0.72 m/yr), which is
equivalent to 0.40 [ftVsl/mi (0.0070 [mVsl/km). The standard error of
estimate in this case was about 1.3 feet (0.40 m). Canal leakage was
assumed to have a chloride concentration of 40 mg/1.
Changes in the chemical concentration of ground water in irrigated
areas are partly caused by the mixing (or dilution) of ground water
having one concentration with recharged water having a different
concentration. Because the magnitude of this change is a function of
the gross recharge, rather than of the net recharge, an estimate of the
gross recharge must be made. Hurr, Schneider, and Minges (1975)
presented data indicating that the average rate of application of ir-
rigation water in the South Platte River valley is about 4.2 ft/yr (1.3
MODELING CHLORIDE MOVEMENT, ALLUVIAL A)
19
10 11 12 13 14 15 1e
SIMULATION TEST NUMBER
FIGURE 6.—Change in standard error of estimate for succedvenmulationtecU.
m/yr). Hurr, Schneider, and Minges (1975) also stated that 45 to 50
percent of the applied irrigation water IB recharged to the aquifer.
Thus, the gross recharge to the aquifer in irrigated parts of the study
area was assumed to equal 1.9 ft/yr (0.58 m/yr).
In the study area irrigation water is derived both from surface
water, diverted through canals and ditches, and from ground water,
pumped from irrigation wells. The difference between the gross
recharge and the net recharge, 0.35 ft/yr (0.11 m/yr), was assumed to
equal the total ground-water withdrawal rate through wells.
It was estimated from data presented by Schneider (1962) and Me-
Conaghy, Chase, Boettcher, and Major (1964) that 62 irrigation wells
operated in the study area during 1955-71, the period represented by
the water-table map (fig. 4). Only a small number of wells were drilled
after 1965 (Hurr and others, 1975, p. 5), so the estimate based on data
up to 1964 is probably an accurate approximation. By multiplying the
total ground-water withdrawal rate by the irrigated area and then
dividing by the number of irrigation wells, the average sustained
pumping rate per well is computed to be 0.02 ft3/s (5.7xlO~4 ms/s).
-------
20
ROCKY MOUNTAIN ARSENAL, COLORADO
O.4O
NET RECHARGE. IN METERS PER YEAR
0.4S
0.56
1.4
1.B 1.6 1.7
NET RECHARGE. IN FEET PER YEAR
1.8
1.9
0.0 2
FIGURE 7.— Relation between the assumed rate of net recharge in irrigated areas and
the mean difference of observed and computed water levels.
Leakage from the unlined disposal ponds at the Arsenal represents
both a significant source of recharge to the aquifer and the primary
source of ground-water contamination in the area. Because no records
were available to describe the variations in discharge of liquid wastes
to the 6 unlined ponds, the general history of their operation was
reconstructed primarily from an analysis of aerial photographs, which
were available in 20 sets with varying degrees of coverage during
1948-71. The summary in table 2 shows that four characteristic sub-
periods were identified during which the leakage rates and concentra-
tions were assumed to remain constant for modeling purposes.
CALIBRATION OF FLOW MODEL
The flow model computes the head distribution (water-table
altitudes) in the aquifer on the basis of the specified aquifer proper-
ties, boundaries, and hydraulic stresses. Because the ground-water
seepage velocity is determined from the head distribution, and
because both convective transport and hydrodynamic dispersion are
functions of the seepage velocity, an accurate model of ground-water
flow is a prerequisite to developing an adequate and reliable solute-
transport model. In general, the flow model was calibrated by compar-
ing observed water-table altitudes with corresponding computations
of the model.
Insufficient field data were available to accurately calibrate a tran-
sient-flo^kdel. However, the use of the disposal ponds varied over
MODELING CHLORIDE MOVEMENT. ALLUVIAL AQUIFER
21
TABLE 2. — Generalized history of disposal pond operations at the Rocky Mountain
Arsenal, 1943- 72
IN.A. out applicable)
Y«n
1943-66
1967-60
1961-67
1968-72
A**nf»
A — Full
BAB — Full
C — 1/2 Full
A — Empty
B.D.E — Empty
C — Full
A — Empty
BAE — 1/3 Full
C — 1/3 Full
A — Empty
B.D.E — Empty
C — Full
Compnud
fcnkM.
0.16
.18
.64
.0
.0
1.08
.0
.06
.36
.0
.0
1.08
AMvnrad chloride
eonecntntioD
4,000
3,000
3,000
N.A.
N.A.
1,000
N.A.
600
500
N.A.
N.A.
160
time and induced the only significant transient changes noted in the
area. Several water-level measurements in observation wells at the
Arsenal showed that the water table fluctuated locally by up to 20 feet
(6 m), mainly in response to filling and emptying of the unlined ponds.
Therefore, the hydraulic history of the aquifer was approximated by
simulating four separate steady-flow periods, based on the generalized
history of disposal pond operations shown in table 2.
The first period simulated was 1968-72, when it was assumed that
pond C was full and that all other unlined ponds were empty. Con-
stant-head boundary conditions were applied at the 5 nodes corre-
sponding with pond C, and the rate of leakage from pond C was com-
puted implicitly by the model to be about 1.08 fWs (0.031 ms/s). A com-
parison of the heads computed for 1968—72 with the observed water-
table configuration for 1955-71 shows good agreement in most of the
modeled area. The computed heads were within 2.5 feet (0.75 m) of the
observed heads at more than 84 percent of the nodes. The greatest
residuals (difference between the observed and computed heads at a
node) were between 7.5 and 9.5 feet (2.3 and 2.9 m). Residuals in this
range only occurred at less than than 1.5 percent of the nodes, and
only at nodes near the disposal ponds, where the greatest variations in
observed water-table altitudes had been measured. It must be
emphasized that the general water-table configuration presented in
figure 4 represents a composite of water-level measurements made
during 1955-71 and is not necessarily an accurate representation of
the water-table configuration at any specific time durij^^Bat period.
-------
22
ROCKY MOUNTAIN ARSENAL, COLORADO
The observed water-table configuration indicates that a source of
recharge to the alluvial aquifer occurs in an area located approx-
imately one-half mile (0.80 km) northeast of the center of pond C,
which corresponds to the node at (»- 10,> = 25). This recharge might
represent leakage from an unlined canal (Sand Creek Lateral) or the
concentrated discharge of seepage through the unsaturated alluvium
to the east and south. The model analysis indicated that an average
flux of about 0.10 ftVs (0.0028 mVs) would be required to maintain the
observed hydraulic gradient in this area. This average flux was thus
assumed to have existed at this node from 1943-72. Because this
recharge would probably be uncontaminated, it was assumed to have a
chloride concentration of 80 mg/1.
Similarly, the water-table map presented by Konikow (1975) indi-
cates that significant recharge may occur in or near the industrial
area located south of pond A and north of the fresh water reservoirs.
Thus, constant-head boundary conditions were applied to the three
nodes located at (i = 5,j = 32-34). The model computed that a com-
bined total of about 0.09 ftVs (0.003 m3/s) of recharge would occur
there during 1968-72. The source of this recharge could be infiltrated
surface runoff from paved areas in the industrial complex. Because
the chloride concentration of some ground-water samples taken in
this area were slightly above normal background levels, it was
assumed that any recharge from this area would have a chloride con-
centration of 200 mg/1.
The second period simulated was 1943-56, when pond C was
assumed to leak at 50 percent of the rate computed for 1968-72. All
other unlined ponds were assumed to be full during 1943-56 and were
represented as constant-head boundaries in the model. Except for the
changes at the disposal ponds, all other parameters and boundary con-
ditions in the model were identical with the 1968-72 simulation. The
head distribution for 1957-60 was assumed to be the same as during
1968-72 because of the apparent similar use of the disposal ponds.
Therefore, the 1957-60 period did not require a separate flow simula-
tion.
The third period simulated was 1961-67, when ponds B, C, D, and E
were all assumed to leak at one-third of the rates computed for the
periods when each was full. As in the second simulation period, all
other parameters and boundary conditions in the model were assumed
to be unchanged.
The flow model calculated a mass balance for each simulation run to
check the numerical accuracy of the solution. As part of these calcula-
tions, the net flux contributed by each separate hydrologic component
of the model was also computed and itemized to form a hydrologic
budget for the aquifer in the modeled area. The hydrologic budget is
valuable because it provides a measure of the relative importance of
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQBHER
23
each element to the total budget. The hydrologic budgets for the final
calibrations of the four steady-state flow models are presented in table
3. The date in table 3 indicate that the major sources of ground-water
inflow are (1) infiltration from irrigated fields, (2) underflow through
the aquifer into the study area, (3) seepage losses from the unlined ir-
rigation canals, and (4) infiltration from the unlined disposal ponds.
The major ground-water outflow occurs as (1) seepage into the South
Platte River, (2) withdrawals from irrigation wells, and (3) underflow
through the aquifer out of the study area. The computed total flux
through the aquifer in the study area averages about 14 ft3/s (0.40
nWs). However, most of this is flowing through the part of the aquifer
north and west of the Arsenal boundary that receives most of the
recharge and has the highest transmissivity.
TABLE 3. — Elementf of hydrologic budget computed by ground-water flow model
Computed flux1 OMM
1943-M
1967-60
1961-67
1868-78
Well discharge
Irrigation recharge
Canal leakage
Pond A
Pond B .
Pond C
Pond D
Pond E
Industrial area
Underflow across:
Southwest boundary
Southeast boundary
Northeast boundary
South Platte River
First Creek
Sand Creek Lateral
Total flux:
Recharge
Discharge
-1.264
6.648
1.606
165
022
642
108
060
076
.019
4.713
096
-.487
-12.361
-.041
100
14.133
-14.133
-1.264
6.648
1.606
.0
.0
1.083
.0
.0
.081
.094
4.473
.089
-.496
-12.290
-.122
.097
14.171
-14.171
-1.264
6.648
1.606
.0
.007
.361
.036
.017
.086
.147
4.822
.109
-.478
-12.214
.014
.100
13.953
-13.963
-1.264
6.648
1.606
.0
.0
1.083
.0
.0
.081
.094
4.473
.089
-.498
-12.290
-.122
.097
14.171
-14.171
'A ixwttY. nlu. in Ou* UN. fawlata* nduri* to th. xprffo in UM nodiM «••; • taftttn nh»
chart* fan tin aquifer.
CALIBRATION OF SOLUTE-TRANSPORT MODEL
The solute-transport model applied to the Rocky Mountain Arsenal
area was designed to compute changes in the chloride concentration
in the alluvial aquifer during 1943-72. Heads and fluxes computed by
the flow model were used as input to the transport model. A different
velocity field was computed for each steady-state flow period outlined
in table 2.
-------
24
ROCKY MOUNTAIN ARSENAL, COLORADO
The solute-transport model was calibrated mainly on the basis of
the chloride concentration pattern that was observed in 1956 (fig. 3).
Field measurements of the effective porosity and dispersivity of the
aquifer were not available, so a range of realistic values were tested in
a sensitivity analysis. The computed concentrations were most sensi-
tive to variations in the value of effective porosity and least sensitive
to the transverse dispersivity. A comparison of observed and com-
puted chloride concentration patterns indicated that an effective
porosity of 30 percent and longitudinal and transverse dispersivities of
100 feet (30 m) were best.
After appropriate concentrations were assigned to all sources, and
an initial background concentration of 40 mg/1 was assigned to all
nodes in the aquifer to represent conditions at the end of 1942, the
transport model was run for a 14-year simulation period (1943-56).
The model computed a chloride concentration pattern (fig. 8) that
agreed closely with the observed pattern (fig. 3). The small difference
in the directions of the axes of the main plumes between the observed
and computed data is probably due mainly to errors in the computed
flow field, rather than to errors in the transport model.
Since 1956, all disposal has been into the asphalt-lined Reservoir F,
thereby eliminating the major source of contamination. However, that
alone could not eliminate the contamination problem because large
volumes of contaminants were already present in the aquifer. In
January 1961 sufficient data were again available to contour the pat-
tern of contamination (fig. 9). Although this is more than 4 years after
the source of contamination had been apparently eliminated, only
minor changes can be observed in the overall contamination pattern.
These changes include a small downgradient spreading of dissolved
contaminants and a significant decrease in chloride concentrations
near the center of the contaminated zone. At this time the downgra-
dient spreading was most noticeable near the northeastern limit of
the contaminated zone, where a third distinct plume had formed. Dur-
ing 1957-72 water in the unlined disposal ponds was derived pri-
marily from local surface runoff and canal diversions, which had
relatively low chloride concentrations. Thus, much of the observed im-
provement in water quality near the center of the contaminated zone
from 1957 to 1961 was probably the result of dilution by recharge from
the former disposal ponds and from the Sand Creek Lateral.
The solute-transport model was next used to simulate the period
1957-60, using the chloride concentrations computed for the end of
1956 as initial conditions. The chloride concentrations thus computed
for the end of 1960 (or the start of 1961) are illustrated in figure 10,
which can be compared with the observed pattern for January, 1961
(fig. 9)^jy; computed concentrations show the same general changes
from jthat occurred in the observed chloride pattern. However,
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER 25
104*50'
39'5O' -
104-55'
KOCKY MOUNTAIN AKSEN All BOUND
0 l 2 MILES
I r—H '
1 2 KILOMETERS
EXPLANATION
- MO - Line of equal chloride concentration (in milligram t per liter).
Interval variable
LiSi'^fciJJ Area in which alluvium is absent or untaturated
FIGURE 8.— Computed chloride concentration, 1966.
the model results indicated a more direct discharge toward the South
Platte River than was observed, and the model did not indicate any
spreading to the northeast to form a third plume. Some of this ob-
served spreading may have been caused by transient changes in the
flow field that could not be reproduced with the steady-state flow
model.
Available data suggest that recharge of the aquifer was relatively
low from 1961 to about 1968. Nevertheless, data collected in early
1969, the next time for which field data were available, d^adicate the
occurrence of a further significant decrease in the ovei^^pze of the
-------
26
ROCKY MOUNTAIN ARSENAL, COLORADO
39-50' -
L ROCKY MOUNTAIN
ARSENALI BOUNDARY
..J
i
2 MILES
0 I 2 KILOMETERS
EXPLANATION
Data point (Jan. 1961)
~~~ Lin* of equal chloride concentration (in milligrams par litar).
Interval variable
I Area in'which alluvium i* absent or uniaturated
? Position of contour uncertain
FIGURE 9.— Observed chloride concentration, January 1961.
affected area. (See fig. 11.) Apparently, as the contaminated water
continued to migrate downgradient, its chloride concentration was
diminished by dispersion and dilution. Also, the concentrations
decreased even more near the former disposal ponds. Chloride con-
centrations greater than 1,000 mg/1 were now limited to only a few iso-
lated areas.
The observed data from 1961 and 1969 also indicate that some con-
taminants were present in the aquifer near the freshwater reservoirs,
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQ
27
104*50-
39'SO' -
| ROCKY MOUNTAIN AKSENAll BOUND,
0 I 2 MILES
_l
0 1 2 KILOMETERS
EXPLANATION
Line of equal chloride concentration (In milligrams par liter).
Interval variable
Area In which alluvium It absent or unsaturated
FIGURE 10.— Computed chloride concentration at the §Urt of 1961.
adjacent to the industrial area. It is unlikely that these contaminants
were derived from the disposal ponds and, thus, were not predicted by
the model. The chloride concentration pattern computed for the end of
1968 (or start of 1969), using the chloride concentrations computed
for the end of 1960 as initial conditions, is presented in figure 12. For
the most part, the solute-transport model has also reproduced this
period of record, from 1961 to 1969, fairly well.
From about 1968 or 1969 through 1974, pond C was apparently
again maintained full most of the time by diverting water from the
freshwater reservoirs to the south. Available data showed that by
-------
28
ROCKY MOUNTAIN ARSENAL, COLORADO
1O4-5CV
39'50' -
[ ROCKY MOUNTAIN ARS
MOUNTAIN AgSENAll BOUNDARY
0 I 2 MILES
0 1 2 KILOMETERS
EXPLANATION
• Data point (Jan.-May 1969)
300 Lin* of equal chloride concentration (in milligramt per liter).
Interval variable
Liv.ijiiJtiJ Ar*8 in wnich elluvium '• abtent or untaturated
T Petition of contour uncertain
FIGURE 11.— Observed chloride concentration, January-May 1969.
1972 the areal extent of contamination, as indicated by chloride con-
centration, had significantly diminished (fig. 13), and concentrations
above 1,000 mg/1 were now limited to just two small parts of the main
zone of contamination. Because both are areas of relatively low hy-
draulic conductivity, it appears that low flow velocities have retarded
the movement of the contaminated ground water out of or through
areas. Chloride concentrations were almost at normal back-
in the middle of the affected area. This largely reflected
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
29
1W50'
39.50- -
ROCKY MOUNTAIN AR.SEMAL.I BOUN
0 1 2 KILOMETERS
EXPLANATION
Line of equal chloride concentration (in milligramt per liter).
Interval variable
Area in which alluvium it absent or untaturated
FIGURE 12.—Computed chloride concentration at the ftart of 1969.
the infiltration of fresh water from pond C, which had the effect of
diluting and flushing the contaminated ground water.
The pattern of contamination computed for the start of 1972, by
using the chloride concentrations computed for the end of 1968 as ini-
tial conditions, is presented in figure 14. The computed pattern agrees
fairly well with the observed pattern (fig. 15), although the former
shows somewhat longer plumes. After a 30-year simulation, the model
has identified (1) the two areas where high chloride concentrations
were still present, (2) the reduction in size and strentfhpf the main
-------
30
ROCKY MOUNTAIN ARSENAL, COLORADO
104'50'
39-50' -
[ ROCKY MOUNTAIN ARSENALl BOUNDARY
2 MILES
1
0 1 2 KILOMETERS
EXPLANATION
Data point (May 19721
o Lin* of equal chloride concentration (in milligrams per liter).
Interval variable
• I Area in which alluvium it absent or unsaturated
-•••-**
1 Position of contour uncertain
FIGURE 13.— Observed chloride concentration, May 1972.
plume, and (3) the significant reduction in chloride concentration in
the middle of the contaminated zone.
The simulation model computes the velocity of ground-water flow at
each node of the model, but these data could not be independently
verified with field data. The computed velocities ranged from less than
1.0 ft/d (0.3 m/d) to over 20 ft/d (6.1 m/d). Because the computed
velocity varies greatly within the modeled area, depending on the
transmissivity and hydraulic gradient, one value of velocity cannot be
MODELING CHLORIDE MOVEMENT, ALLUVIAL AP,
31
1O4-50'
39-5O' -
104
ROCKY MOUNTAIN AUSENAll BOUND
O 1 2 MILES
h
..J
0 1 2 KILOMETERS
EXPLANATION
Line of equal chloride concentration (In milligrams per liter).
Interval variable
Area In which alluvium Is absent or unsaturated
FIOUHE 14.—Computed chloride concentration at thecUrt of 1972.
used to estimate the average time of travel of dissolved chemicals be-
tween two points on a flow line. For problems where this type of infor-
mation is desired, the computer program could be easily modified to
provide these data.
Mass balance calculations were performed during the calibration
procedure to check the numerical accuracy of the model simulations.
Errors in the mass balance were always less than 1 percent for the
flow model, but averaged about 14 percent for the solute-transport
simulations. The latter is somewhat higher than desirable and indi-
-------
32
ROCKY MOUNTAIN ARSENAL. COLORADO
39.50- _
[ [tOCKY MOUNTAIN ARSENAtlBOU
J
2 MILES
0 1 2 KILOMETERS
EXPLANATION
aoo Lin* of equal chloride concentration (|n milligrams per liter).
Interval variable
EgO|| Area In which alluvium ii absent or umatureted
FiOUBl 16.—Chloride concentration predicted for 1980, aiauming that pond C U filled
with fresh water during 1972-80.
cates the need for further refinements in the numerical procedure
used to solve the transport equation.
PREDICTIVE CAPABILITY
Once a model has been adequately calibrated, it can be used to pre-
dict or analyze the effects of either future or past changes in stresses
or boundary conditions. The Rocky Mountain Arsenal model, which
was calibrated over a 30-year historical period, appeared to be reliable
enough to be used for limited predictive purposes. The predictive
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
33
capability of this model can help to (1) isolate the effects of past
measures, (2) evaluate the causes of present and recurring problems,
and (3) predict future concentrations under a variety of assumptions.
Several simulation tests were made, both to demonstrate the potential
uses of this type of model and to better understand the nature of the
ground-water contamination problem at the Arsenal.
Because of the relative importance of leakage from pond C (table 3),
a simulation test was made to evaluate its possible effect on future
chloride concentrations in the aquifer. One simulation run was made
to predict the chloride concentration in 1980 if pond C were kept full of
fresh water during 1972-80. These results (fig. 15) indicate that if the
artificial recharge due to leakage from pond C were to continue, then
in 1980 there would remain only one area of significant contamina-
tion, which would be confined entirely within the Arsenal boundaries.
There would also still be one small area north of the Arsenal that
would contain chloride concentrations between 200 and 500 mg/1.
The importance of the effects of artificial recharge from pond C can
be illustrated by computing what the chloride concentration would be
in 1980 if pond C were not kept full, and then comparing this pattern
with the one in figure 15. Therefore, the chloride concentrations in
1980 were recomputed after assuming that the minimal recharge rate
from pond C that was estimated for 1961-67 (table 3) had continued
during 1968-80. These results are presented in figure 16 and indicate
that if the artificial recharge from pond C would not occur during
1961-80, then in 1980, which is about 25 years after the sources of
ground-water contamination were supposedly eliminated, there would
still be two relatively large areas of contaminated ground water re-
maining.
A comparison of the results presented in figure 16 with those shown
in figure 15 indicates that the effects of artificial recharge from pond
C had significantly increased the rate of water-quality recovery in the
aquifer. In addition to the effects of dilution, the recharge created a
mound on the water table, which increased the hydraulic gradients,
and consequently, the flow velocities. In effect, it "pushed" or
"flushed" the contaminated ground water out of the area faster than
would have occurred naturally. The apparent difference in the mass of
chlorides present in the aquifer between figures 15 and 16 is caused by
two factors. First, in figure 15 a greater percentage of the total
chloride is contained in areas having a concentration less than 200
mg/1. Second, during the simulation period upon which figure 15 is
based, a greater mass of chlorides has discharged from the aquifer in
the modeled area, mostly to the South Platte River and as ground-
water underflow across the model boundaries.
By comparing figures 15 and 16, it can also be inferred that it would
probably take at least many decades for this contaminated aquifer to
-------
34
ROCKY MOUNTAIN ARSENAL, COLORADO
104-501
39.50- -
[ ROCKY MOUNTAIN ARSENALl BOUND
0 l 2 MILES
J
I
0 I 2 KILOMETERS
EXPLANATION
900 Lin* of equal ctilorid* concentration (in milligrami per liter).
Interval variaole
^^^^1 Area in which •lluvlum it abMnt or untaturated
Fwtmi 16.— Chloride concentration predicted for 1980, assuming that recharge from
pond C is piinimul during 1961-80.
naturally recover its original water-quality characteristics. But it can
also be inferred that appropriate water-management policies can help
to reduce this restoration time to the order of years, rather than
decades.
More than one-half of the total ground-water flux through the
modeled area is derived from recharge from irrigation applications
and canal leakage. (See table 3.) A simulation test was designed to
demonstrate that these sources of recharge have an important effect
on the chemical concentrations in the aquifer. A simulation run was
MODELING CHLORIDE MOVEMENT, ALLUVIAL Ar.
made for 1943-56, assuming zero dilution from these recharge
sources. The chloride concentrations computed for 1956 under this
assumption were then compared with the computed pattern shown in
figure 8. If there were no dilution from recharge, in 1956 the area con-
taminated with chloride concentrations greater than 1,000 mg/1 would
have been slightly larger than the area within the 500 mg/1 isochlor
shown in figure 8, and the higher concentrations would have spread to
the north much earlier. Therefore, dilution from irrigation recharge
and seepage from unlined canals were both important factors in
reducing the level of chloride concentrations downgradient from the
Arsenal.
APPLICATION TO WATER-MANAGEMENT PROBLEMS
Changes in water use or water management in an area can signifi-
cantly affect both the flow and chemical quality of ground water.
Because a wide variety of alternative decisions or policies are possible
regarding water planning, management, and quality control, it is
difficult to determine the optimum set of alternatives that will mini-
mize detrimental effects and maximize beneficial effects. Thus, an ac-
curate solute-transport model can be a valuable planning tool because
it can help to analyze the relative sensitivity of the aquifer system to
different management alternatives and demonstrate the impact of
specific practices on the chemical quality of ground water.
To demonstrate this use of the model, a hypothetical change in
ground-water management at the Rocky Mountain Arsenal was
simulated. This illustrative example evaluates a proposal (Konikow,
1974) to maintain hydraulic sinks along those parts of the northern
boundary of the Arsenal under which the plumes of contaminated
ground water were moving. Construction of the hydraulic sinks could
physically involve either drilling a line of wells for pumping or ex-
cavating a trench or ditch below the water table for drainage. The
main purpose of the hydraulic sink would be to intercept and remove
contaminated ground water from the aquifer before it migrates
downgradient from the Arsenal. This proposal is evaluated here only
to demonstrate the general value of the model and is intended neither
to endorse this particular plan nor to suggest that any changes in
water management should necessarily be implemented at the Rocky
Mountain Arsenal.
The hydraulic sinks could greatly modify the heads and flow
velocities in their vicinities. Therefore, these hydraulic changes would
have to be computed before the effects on solute transport could be
predicted. For this example problem a simplified scheme was used to
generate hydraulic sinks in the flow model that was calibrated for the
period 1968-72. Two sinks, A and B, were represented by imposing
-------
36
ROCKY MOUNTAIN ARSENAL, COLORADO
39-5O- -
ROCKY MOUNTAIN ARSENALJBOUNDARY
O 1 2 MILES
O 1 2 KILOMETERS
EXPLANATION
Line of conitant water-level decline, in feet. Interval variable
Area in which alluvium is absent or unsaturated
Hydraulic sink
Constant-head altitude at A-5.085 ft
Constant-head altitude at B-5.124 ft
FIGURE 17.— Computed drawdown caused by maintaining two constant-head rinks
along the northern boundary of the Rocky Mountain Arsenal.
constant-head boundary conditions at appropriate nodes in the finite-
difference grid of the model. Sink A was along the northwestern
boundary and was simulated as a constant head of 5,085 feet (1,550 m)
at nh (i = 5-9, j - 17). Sink B was along the northern boundary
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
37
and was simulated as a constant head of 6,124 feet (1,562 m) at nodes
(14,19), (16,20), and (16,21).
The effect of these two constant-head sinks on steady-state ground-
water flow is illustrated in figure 17, which depicts the computed
drawdown (water-level decline) relative to the heads computed for
1968-72. The water-level declines extend a greater distance to the
south and southeast of the sinks than to the north and northwest
because of the much lower availability of recharge to the south and
southeast. The model computed that the discharge of sink A would be
about 0.98 ft'/s (0.028 mVs), whereas discharge of sink B would be
about 0.15 ftVs (0.0042 mVs). The greater computed discharge of sink
A reflects its location in an area of higher transmissivity and its closer
proximity to the outer constant-head boundary of the model. The ex-
tent and magnitude of drawdown shown in figure 17 indicates that hy-
draulic gradients, and resulting flow velocities and solute transport,
would be significantly affected if the hydraulic sinks were actually
present. i
The two hydraulic sinks were assumed to have begun operating in
1968, and pond C was assumed to have remained full after 1968. The
chloride concentration pattern then computed for 1980 is shown in
figure 18, which represents the combined effects of artificial recharge
from pond C and artificial drainage to the two hydraulic sinks. This
pattern can be compared with the one shown in figure 15, which just
represents the effect of artificial recharge from pond C. The most
noticeable difference is that figure 18 shows the persistence of higher
chloride concentrations in larger areas downgradient (north) of the
hydraulic sinks.
Although it may seem anomalous to produce less water-quality im-
provement with a source-sink combination than with a source alone,
this occurrence is not unreasonable and can be explained with the aid
of a schematic cross-section through the source of artificial recharge
and the hydraulic sink. (See fig. 19.) Figure 19 shows both the original
water table with recharge from the unlined pond and the new steady-
state water-table position and directions of flow that were established
after pumping began. The change in hydraulic gradients caused by the
sink indicates that the velocity of ground-water flow would increase
on the upgradient side of the sink. On the downgradient side of the
sink, there would be a reversal of the hydraulic gradient within a
small area near the sink. However, just beyond the area of reversal is
an area where the new gradients would be much less than before,
creating a zone of near stagnation in the aquifer. Because of ex-
tremely low flow velocities in this zone, any contaminants that were
present in this area at the time the sink was constructed would re-
main in the area much longer than if no sink had b^& constructed.
-------
38
ROCKY MOUNTAIN ARSENAL, COLORADO
104'StV
39'50' -
ROCKY MOUNTAIN ARStNALJ BOUNDARY
I 2 MILES
.J
'0
I-
0 I 2 KILOMETERS
EXPLANATION
Lino of equal chloride concentration (In milligrams per liter).
Interval variable
Area In which alluvium it absent or unsaturated
Hydraulic link
FIGURE 18.— Chloride concentration predicted for 1980, assuming that artificial
recharge from pond C ia coupled with drainage through two hydraulic sinks.
The construction of the hydraulic sinks would slightly increase the
rate of water-quality improvement between 1968 and 1980 in the area
between the source and the sinks. In fact, the results of the simulation
run using sinks indicate that the chloride concentrations in the area
between the source and the sinks would virtually reach an equilibrium
pattern after about 10 years.
Comparison of figures 15 and 18 indicate that water management
using a source-sink combination as postulated here would produce less
MODELING CHLORIDE MOVEMENT. ALLUVIAL AQUIFER
39
SOUTH
6200-
6050
164O
O 1 KILOMETER
EXPLANATION
Saturated alluvium
Bedrock
Original water level
Water level after pumping
•*- Direction of flow after pumping
FIGURE 19.— Generalized cross-section from vicinity of source of artificial recharge
through hydraulic sink (represented aa a well).
desirable results overall than would a simple artificial recharge source
alone. The primary reason for this appears to be that the sinks were
placed near the middle of the contaminant plume. In the study area
this type of scheme would be most effective if the hydraulic sinks were
located at or just beyond the maximum extent of the plume. Similarly,
if an artificial recharge source is to be used for flushing and dilution, it
should be placed just upgradient of the contaminated zone, if possible.
In general, designs would depend on the circumstances of each specific
problem and should be evaluated individually.
At the Rocky Mountain Arsenal, the hydraulic sinks would provide
a secondary benefit that is not apparent in the map of chloride con-
centration. Drainage due to the hydraulic sinks would produce water-
table declines that might prevent soil salinity problems caused by high
water tables in contaminated areas. This same effect would also
reduce possible discharge of contaminated ground water to springs or
streams, such as First Creek.
Removing pollutants from a contaminated aquifer may seem to be
an almost impossible task. While this may be true for some or even
most contaminated aquifers, others may be highly amenable to one or
more plans for artificial reclamation that could significantly acceler-
ate the rate of water-quality improvement in the aquifer. The
feasibility of any such reclamation plan would be strongly dependent
on the hydraulic properties of the aquifer and on the type and source
of contamination. An accurate model of the aquifer is a prerequisite
for reliably predicting changes in concentration and thereby estimat-
ing the benefits that might be derived from a given plan.
-------
40
ROCKY MOUNTAIN ARSENAL, COLORADO
SUMMARY AND CONCLUSIONS
The movement of dissolved chemicals in flowing ground water can be
simulated with a computer model that couples a finite-difference solu-
tion to the ground-water flow equation with the method-of-charac-
teristics solution to the solute-transport equation. The usefulness of the
model was illustrated by its application to a problem of ground-water
contamination in the Rocky Mountain Arsenal area, Colo., where the
model integrated the effects of several factors that controlled changes
in chloride concentrations and successfully reproduced the record of
chloride contamination observed during a 30-year period.
The method of characteristics offers one workable solution tech-
nique to the solute-transport equation. Although every ground-water
contamination problem is in many ways unique, the processes con-
trolling solute transport are the same. Thus, this method-of-charac-
teristics model is generally applicable to a wide variety of ground-
water contamination problems.
The predictive accuracy of the model is most limited by the ade-
quacy of the input data. The results of applying the model to the
ground-water contamination problem at the Rocky Mountain Arsenal
indicate that where adequate hydrogeologtc data are available, the
model can be used to predict the rates and directions of spreading of
conservative (nonreactive) contaminants from known or projected
sources.
The predictive capability of the model can be helpful in designing a
monitoring network. By indicating the most probable and least proba-
ble areas of future contamination and the rate of spreading, optimal
locations and sampling frequencies for observation wells can be deter-
mined. The model can also indicate areas where contaminated ground
water might seep into surface water.
In some cases of aquifer contamination it may be both physically
and economically feasible to institute a reclamation, program to im-
prove or control the quality of ground water. Because a large variety of
water-management plans can be proposed for any one problem, an ac-
curate model of flow and solute transport in the aquifer could be an in-
valuable tool for planning an efficient and effective program.
Conclusions of this study that pertain specifically to the Arsenal can
be summarized as follows:
1. Ground water in the alluvial aquifer in and adjacent to the Rocky
Mountain Arsenal flows predominantly to the north and north-
west. The alluvium generally has the greatest transmissivity,
saturated thickness, and rate of recharge in the area between the
South Platte River and the north and northwest boundaries of
the^pcky Mountain Arsenal. Within the boundaries of the Ar-
s^^pbhe main source of ground-water recharge since 1943 has
amHrentlv been infiltration from the unlined disooRal oonda.
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
41
2. The pattern of chloride contamination was principally controlled by
the rates and directions of ground-water flow. Thus, variations in
the hydraulic conductivity (or transmissivity) and boundary con-
ditions of the aquifer directly influence solute transport. The ob-
served contamination pattern clearly indicates that the spread-
ing of contaminants was significantly restricted or constrained
by the areas in which the aquifer is either absent or unsaturated.
Model analyses support the hypothesis that dilution, both from ir-
rigation recharge and from seepage from unlined canals, was an
important factor in reducing the level of chloride concentrations
in the contaminated ground water that flowed past the bound-
aries of the Arsenal.
3. Most of the contaminants that seeped into the aquifer were proba-
bly derived from the overflow ponds (ponds B, C, D, and E).
Because the original primary disposal pond (pond A) was located
in an area where the aquifer had a relatively low hydraulic con-
ductivity, only small quantities of contaminated ground water
could seep through the aquifer downgradient from pond A.
4. In 1972, approximately 16 years after the main sources of ground-
water contamination had been eliminated, a large area of the
alluvial aquifer still contained chloride concentrations that were
significantly above normal background levels. But the magnitude
and extent of contamination, as measured by the chloride con-
centration, had significantly diminished in comparison with ob-
servations during 1956 and 1961. By 1980 high chloride con-
centrations (that is, greater than 200 mg/1) will probably occur in
only two comparatively small areas. One is north of the Arsenal,
near First Creek, and the other is near and downgradient from
the site of pond A.
6. The diluting and flushing effects of freshwater recharge from pond
C contributed to a significant reduction in the concentrations and
total quantity of chlorides present in the aquifer.
6. If the Rocky Mountain Arsenal or a similar industrial plant were
first beginning operations today, this model could be used with
reliable aquifer descriptions to predict the magnitude and extent
of ground-water contamination that could be expected to result
from the disposal of nonreactive liquid industrial wastes into
unlined ponds. Perhaps more importantly, the model could have
been used either to determine where the disposal ponds should
have been located to minimize the extent of contamination or to
demonstrate, in the first place, that this particular method was
inappropriate for liquid waste disposal in this particular environ-
ment and that an alternative method was nee
7. The stringent date requirements for applying the
mnAol r»ftinf«»H mit rfofiHf>nrtf>R in Hntj» extfltinor at the start of this"
-------
42
ROCKY MOUNTAIN ARSENAL, COLORADO
investigation. The subsequent analysis and reinterpretation of
existing hydrogeologic data led to a revised conceptual model that
accounted for the effects on ground-water flow and solute
transport of the areas in which the alluvium either is absent or is
unsaturated most of the time.
8. The model for chloride movement cannot predict the behavior of
nonconservative (reactive) chemical species. But any comprehen-
sive study or management plan of ground-water quality at the
Arsenal would need to include any such reacting species with ap-
propriate modifications to the model.
REFERENCES CITED
Bear, Jacob, 1972, Dynamics of fluids in porous media: Am. Hsevier Publishing Co.,
New York, 764 p.
Bredehoeft, J. D., and Finder, G. F., 1973, Mass transport in flowing groundwater:
Water Resources Research, v. 9, no. 1, p. 194-210.
Croxton, F. E., 1953, Elementary statistics with applications in medicine and the
biological sciences: New York, Dover Publishers, Inc., 376 p.
Engineering News-Record, 1956, Asphaltic membrane is used to leakproof a lake: v.
157, no. 21, p. 40-41.
Carder, A. O., Peaceman, D. W., and Pozzi, A. L., Jr., 1964, Numerical calculation of
multidimensional miscible displacement by the method of characteristics: Soc.
Petrol. Eng. Jour., v. 4, no. 1, p. 26-36.
Hurr, R. T., Schneider, P. A.. Jr., and Minges, D. R.. 1975, Hydrology of the South Platte
River valley, northeastern Colorado: Colorado Water Conserv. Board Water-
Resources Circ. 28, 24 p.
Konikow, L. F., 1974, Reclamation of a contaminated aquifer [abs.J, in Abstracts with
programs: Geol.Soc. America, v. 6. no. 7, p. 830-831.
1975, Hydrogeologic maps of the alluvial aquifer in and adjacent to the Rocky
Mountain Arsenal, Colorado: U.S. Geol. Survey Open-File Rept. 74-342.
. 1976, Modeling solute transport in ground water, in Internal. Conf. on Environ-
mental Sensing and Assessment: Las Vegas, Nev., art. 20-3.
Konikow, L. F., and Bredehoeft, J. D., 1974, Modeling flow and chemical quality
changes in an irrigated stream-aquifer system: Water Resources Research, v. 10,
no. 3, p. 546-562.
Lohman, S. W., 1972, Ground-water hydraulics: VS. Geol. Survey Prof. Paper 708,70 p.
Lohman, S. W., and others, 1972, Definitions of selected ground-water terms—Revisions
and conceptual refinements: U.S. Geol. Survey Water-Supply Paper 1988,21 p.
McConaghy, J. A., Chase, G. H., Boettcher, A. J., and Major, T. J., 1964, Hydrogeologic
data of the Denver Basin, Colorado: Colorado Water Conserv. Board Basic-Data
Rept. 15, 224 p.
Petri, L. R., 1961, The movement of saline ground water in the vicinity of Derby, Col-
orado: in Ground Water Contamination Symposium: Robert A. Taft Sanitary Eng.
Center Tech. Rept. W61-5, p. 119-121.
Petri, L. R., and Smith, R. O., 1956, Investigation of the quality of ground water in the
vicinity of Derby, Colorado: VS. Geol. Survey open-file report, 77 p.
Pinder, G. P., 1970, A digital model for aquifer evaluation: VS. Geol. Survey Tech-
niques Water-Resource Inv., book 7, chap. Cl, 18 p.
Pinder, G. F., and Bredehoeft, J. D., 1968, Application of the digital computer for
aquifer evaluation: Water Resources Research, v. 4, no. 5, p. 1069-1093.
MODELING CHLORIDE MOVEMENT, ALLUVIAL AQUIFER
43
Pinder, G. F., and Cooper, H. H., Jr., 1970, A numerical technique for calculating the
transient position of the saltwater front: Water Resources Research, v. 6, no. 3, p.
876-882.
Prickett, T. A., and Lonnquist, C. G., 1971, Selected digital computer techniques for
groundwater resource evaluation: Illinois State Water Survey Bull. 65, 62 p.
Reddell, D. L., and Sunada, D. K., 1970, Numerical simulation of dispersion in ground-
water aquifers: Colorado State Univ. Hydrology Paper 41, 79 p.
Robertson, J. B., 1974, Digital modeling of radioactive and chemical waste transport in
the Snake River Plain aquifer at the National Reactor Testing Station, Idaho: VS.
Geol. Survey Open-File Rept. IDO-22054, 41 p.
Robson, S. G., 1974, Feasibility of digital water-quality modeling illustrated by applica-
tion at Barstow, California: VS. Geol. Survey Water-Resources Inv. 46-73, 66 p.
Scheidegger, A. E., 1961, General theory of dispersion in porous media: Jour. Geophys.
Res., v. 66. no. 10, p. 3273-3278.
Schneider, P. A., Jr., 1962, Records of logs and selected wells and teat holes, and chemi-
cal analyses of ground water in the South Platte River basin in western Adams and
southwestern Weld Counties, Colorado: Colorado Water Conserv. Board Basic-Data
Rept. 9, 84 p.
Shukle, R. J., 1975, 1974-76 groundwater study of the Rocky Mountain Arsenal and
some surrounding area: Colo. Dent, of Health, Denver, Colo., 20 p.
Walker, T. R., 1961, Ground-water contamination in the Rocky Mountain Arsenal area,
Denver, Colorado: Geol. Soc. America Bull., v. 72, p. 489-494.
Walton, Graham, 1961, Public health aspects of the contamination of ground water in
the vicinity of Derby, Colorado: in Ground Water Contamination Symposium:
Robert A. Taft Sanitary Eng. Center Tech. Rept. W61-5, p. 121-125.
Wood, L. A., 1972, Groundwater degradation — Causes and cures: Proc. 14th Water
Quality Conf., Urbana, Dl., p. 19-26.
-------
• • ' *•' \ '»« " f .' i — -.'.,•..' i,"* •* "v.'VJ -i*1^'-". -^-V."v^. ,-^'i . *!.-..• -"-^v''-^i^"ri^jy^v/.j^sftt^i.5";'?\c'*"^'.''"T»-' j-'s't .^ii>i5i' 0.-"J'":'"ij*\,i %'. i •"-'
.... -;.•'. v' .> Ji" . . ;• _ •.*.••' • V|S«?t - : *> •_;- ••*". • : *•?" .- •- .-v- «jf* . *- Jf^V-**24'*-* «;v '-t,V**'5,"4. VN-.-;^--.* - •• .^v?S'5ji?."i^rJ ;*,•,-** •*> "i;,-.: i-» - ' • »
STUDIES IN HlbPHYSICS 1 S??^:?;;
;v.--fe-";-
.'••."• # V" •v^v-;.- "- ,*w*:-. "•*' • * •- •>. - ,• • •' '. - . • - 'f'-*" v- -••.- • .-. '
'^'^•^•^i^^
' ''' ' •••••••-•-•
•-•
,. :v-,:.:.^- .-.
^ ' " . ^V ™ - _^ .^-. ^_ _^^ — ,^ — _^ _— .^^ — ^ .^ — _^ — " > • • • . -J'*" • ' • • •. ' '-^ . r- ^ • "*.
Geophysks Study Com
.; :-.;W.:,J
-------
Groundwater Contamination
and Aquifer Reclamation at the
Rocky Mountain Arsenal,
Colorado
6
l.KONARD I-. KONIKOW
U.S. Geological Survry
DOl'CLAS \V. THOMPSON
I'.S. Army Corfi.v of Eiifii
ABSTRACT
pin
Croimdvvatcr contamination .it tin- Kix-ky Mountain Arsenal. Colorado. is related In the dispos.il ol lu
industrial wastes and (u industrial leaks and spills thai lia\r occurred during llir 10-vr lnslnr\ nl opri.ilioi,
of the Arsenal. From 1913 to 195ft llic liquid wastes were discharged into milmrcl ponclv which leMilled MI
contamination of part of the underlying alluvial aquifer. Since l!)5(i. disposal lias liren accomplished l>\
discharge into an .ispli.ilt-lincd reservoir. which significantly reduced the volume ol contaminants ciitcrim:
the aquifer. In the mid-1970s toxie organic elieinieals were deleeted outside ol the Arsenal in llie alliivi.il
U(|iiilei The Colorado Department of Health issued three orders, \\lijeh ealli-d for ilia h.ilt to nn.intlioi i/< i!
dischariii's. (2) cleanup, and (3) uionndwaler nioiiitiiriim Snlisei|iiently a management eomniitmeiil ».<••
made to mitigate tile prolilem. A pilot tJmiimlu.ilcr containnienl and trealinc'nt system was ninslriM h oiindaiy. (2i Irealiim the ».iler with an uctiv.iteil . .n!"n,
priKrss, and (3) injecting the treated water on the dowiitfradient side of the harrier tliiiiuiih several reili.iiX'
wells. Because ol the success ol the pilot operation, it is IMMIIK expanded at present to intercept most ol lln
contaminated underflow crossing the entire north iKiimdary. llow<'ver. homnlary interception alone eannoi
achii'M ai|iiiler restoratiiin at the Arsenal. It is anticipated that the overall final program will also li;i\e to
include elements of source containment and isolation, source elimination, process modification to reduce tin
volume of wastes generated, and development of alternative waste-disposal procedures th.il are nonpolliilinu
A variety ol alternatives have IHVM proposed and are currently hcinu evaluated to determine the most leasllili
for implementation. The research plannini;. and design studies that are neeessarx to achieve the reclamation
goal at (lie Arsenal illustrate that an ellcclive a<|iiifei restoration program is dillicnlt to drsiun and c\|X'iivi\<
to iniplemenl.
l\'TR()ntK'TIO\ I'iisi-s xvlicrc a Sfrious H'-omulxvater contamination priililein i'X-
ists. (lie single most iiii|Xiilant rcinedi.il aclinn tliul can lit' taken
The I'ontaniination of a grovnulwatei resiMirif is u serious pro!)- is to eliminate the source of contamination Hut even then.
lem that cat) have loiin-terin cconoinn and physical ciinse- coiitaininatits already in the a<|iiiln xvill continue to miuial.
(piences Ix'causc in most cases the problem is neither easily and spread unless some action is taken to innnoliih/c. ueu-
nor cjnickly remedied. Wood (1972) concluded, "The most sal- trali/e, or IXMIIOVC them. Hence, there is often a need In clean
isfaclory cure lor grouiulwaler pollution i. preventiini.' In many up or restore eontaminatc'd aquifers.
93
-------
94
l.r.ONUM) K KONIkOVA 1111(1 IMU CI.AS \\ THOMPSON
Tin' "rcstorabilit) nl a contaminated ai|HJlcr is dependent
on thehydrogcologicandgeochcmical properties ol the allccled
aquifer and on tin* chemical aiul physical properties ol the
contaminant. Restoration ol a contaminated aqnitcr is neither
technically nor economically IcasiMc in many cases. Factors
frequently hindering restoration include (I) tlie slow diffusive
nature ol gronndwatcr How. (2) (lie dillicnlty of defining scc-
ondary permeability effects. (.'}) tlie generally low oxygen eon-
tent and lack of biologic reactivity in grouudvvatcr. (4) (lie re-
tention ol some chemicals in the aquilcr because they tend to
he siirlx'd hy minerals in the rocks making up the aquifer. (5)
the lack ol transfcrability ol some restoration techniques from
one site to another, and Ifi) the lack ol knowledge almut the
source ol the contamination.
Effective aquifer restoration programs, il technically feasihle.
are Ixilli dillicnlt to design and expensive' to iniplement. Never-
theless. in res|)onse to pulilic or governmental demands for
positive action in clearly documented cases where gronudwatcr
contamination threatens pnl>lic health, aqniler cleanup pro-
"rams are being re<|uired anil instituted more frequently. Some
programs are being financed and operated hy the federal gov-
ernment. Examples include the Kocky Mountain Arsenal. Col-
orado, where irrigation and domestic water-supply wells in
adjacent areas have Keen contaminated from industrial wastes
stored at tin- Arsenal, and also \Vurtsmith Air Force Base.
Michigan, where toxic organic solvents used in aircraft main-
tenance have entered and spread through the underlying aqui-
fer. Other programs may he implemented I >ccanse of violations
of federal regulations. Kor example, a recent Justice Depart-
ment suit was filed in North Carolina under the imminent
ha/urd provision of the Resource Conservation and Hccovcry
Act. the suit asks that the defendants". . . permanently restore
the aqniler to a condition commensurate with sale human use"
\Hazartluns \\'ttntc .Yens 2(2'. Jan. 21. 19SO. p. 12). As an
example of an aquifer restoration program being initiated he-
cause of state regulations, a chemical company in northern
Michigan has come to an agreement with the state of Michigan
to remove the contaminants from the soil and gronndwater at
their former dump site; the projected cost is $12 million to S15
million (The Wall Stn-el Journal. Sept. 25, UWI. p. 48).
General management options lor restoring water quality in
aquifers currently available include the following: (1) eliminate
the source ol contamination but allow restoration to proceed
only through natural Hushing, dilution, and gcochcmical or
biological reactions; (2) accelerate removal ol contaminants
through withdrawal wells, drains, or trenches: (3) accelerate
Hushing with artificial recharge; (4) install "impermeable" bar-
riers to contain a contaminated area; (5) induce in situ chemical
or biologic reactions that would neutralise or immohili/.e (he
contaminant; and ((i) excavate .mil remove the contaminated
part of the aquifer. The selection of the best approach for a
paiticular situation requires the ability to predict changes in
How ant) chemical concentration in the aquiler lor each possible
management alternative. This iu turn requires both adequate
field data to describe the aquifer systems and the development
ol accurate simulation models to define the grouudwater How
system, pollutant-transport mechanisms, and nature and rate
ol chemical or biological reactions.
COLORADO
—i
5 10 MUSS
10 KILOMETERS
KKil'hT* () I IjK-.ition ol sliuly area
This chapter locuscs on the groundwatcr contamination
problem at the Kocky Mountain Arsenal, which is located near
Denver, Colorado (sec Figure (>. 1). This area is well suited for
serving as a case study to illustrate data requirements, inves-
tigative approaches, anil management options related to the
reclamation of contaminated aquifers because (I) the 40-yr his-
tory ol groundvvatcr contamination is relatively well docu-
mented in the scientific and engineering literature; (2) the
geology and hydrology of the area are fairly well known; (.'})
adequate, though limited, water-quality data are available to
calibrate numerical simulation models; (4) the locations and
strengths ol contaminant sources can be approximately recon-
structed; (5) a management commitment has been made to
aquifer reclamation; ant) (ft) construction, operation, and eval-
uation ol a pilot reclamation system at the Arsenal have been
completed.
DF.SCHII'TION OF SITDY AUK A
History of Contamination
The Hockv Mountain Arsenal has been operating since 1942.
primarily manufacturing and processing chemical warfare prod-
-------
Coiitiiiiiiiiution ami Aquifer Rtrlinnatiun
lifts and pesticides. These operations have produced liquid
wastes that contain coniplev organic and inorganic chemicals,
including a characteristically high chloride concentration that
apparently ranged up to about 5(XK) mg/L.
The liquid wastes were discharged to several iinlined ponds
(Figure 6.2). resulting in the contamination ol the underlying
alluvial aquifer. On the basis of available records, it is assumed
that contamination first occurred at the beginning of 19-43.
From 1943 to 1956 the primary disposal was into pond A.
Alternate and overflow discharges were collected in ponds B,
C. D. and E.
Much of the area north of the Arsenal is irrigated. Imth with
surface water diverted from one of the irrigation canals, which
are also iinlined. and with gromulwatcr pumped from irrigation
well:.. Some damage to crops irrigated with shallow ground-
water was observed in 1951. 1952, and 1953 (Walton. 1961).
Severe crop damage was reported during 195-4, a vear when
the annual precipitation, was about one hall the normal amount
and groundwater use was heavier than normal (Fetri, 1%1).
Several investigations have been conducted since 195-4 to
determine Itoth the cause of the problem and how to prevent
further damage. Petri and Smith (1956) showed that an area ol
contaminated gronndwater of several square miles existed north
and northwest of the disposal ponds. These data clearly indicate
IW50-
r~
i
I J
0
t-
0
—mm .1,
- _ *
• Irrigation
1 '"*•«., ,««-,... v
1
1 KIM'KV MIM'NTAIN AJ^SKNAI. HIH'MiABV
1 1 HatS
1 t «ILO*IC1Cn
EXPLANATION
!••>' ^^» unllrwd rMCrvoir
«Mll ^^ Lined rlMrvoir
J
J
KKil'Ht* 6.2 Major Imlrulogic features: Inters iiuiicati' dis|x>s.il-|XHnl
ilrsimutions assigned In lli<- I'.S. Army iKimikovv. 19771.
that the lii|iiid wastes seeped out ol (lie iinlined disposal ponds.
infiltrated the underlying alluvial aquilcr. and migrated down-
gradient toward the South I'latle Hiver. To prevent addition,il
contaminants from entering the aqniler. a KKI-acre (0.045-knr'1
eva|xiration pond (reservoir F) was constructed with an asphalt
lining in 1956 to hold all subsequent liquid wastes. Although
the liner eventually tailed, even if the lining were to have
remained totally impervious, this new disposal pond in itself
would not eliminate the contamination problem because large
amounts ol contaminants were alrcadv present in and slow|\
migrating through (lie aquifer.
From about 196S or 1969 through about 197-1. pond (.' was
maintained lull most ol the time by diverting water trom (lie
freshwater reservoirs to the south. This resulted in the inlil-
tration ol about I ft'/sec (0.03 in'/sce) ol freshwater into the
alluvial aquifer. This artificial recharge bad the effect of diluting
and Hushing the contaminated groundwater away from pond
(.' (aster than would have occurred otherwise. By 1972 tin1 are.il
extent and magnitude ol contamination, as indicated bv chlo-
ride concentration, had significantly diminished, (.'hloride con-
centrations were then above 1000 mg'L in only two relatively
small parts of the contaminated area and were almost at normal
background levels in the middle ol the aflectcd area limme-
diately downgradient from pond C).
In 1973 and 197-4 there were new claims oi crop and livestock
damages allegedly caused by groundwater that was contami-
nated at the Arsenal. Data collected by the Colorado Depart-
ment of Health (Shukle. 1975) show that dnsnpropylinethvl-
phosphonate(DIMP). a nerve-gas by-product, has been detected
at a concentration of 0.57 part per billion (ppb) in a well located
approximately 8 mi (12.9 km) downgradient from the disposal
ponds and I mi (1.6 km) upgradient trom two municipal water-
supply wells of the city of Brighton. A DIMP concentration of
48 parts per million (ppin). which is nearly lOO.(XK) times higher.
was measured in a groundwater sample collected near the dis-
|H>sal ponds. Other contaminants detected in wells or springs
in the area include dicyclopcntadicnc (IX.'PI)I, cndrin. aldriu.
dieldrin. and several organo-sullur compounds.
The detection of these chemicals, which were manufactured
or used at the Arsenal, in areas o(T the Arsenal property led
the Colorado Department of Health to issue cease and desist,
cleanup, and monitoring orders in April 1975 to the Rocky
Mountain Arsenal and Shell Chemical Company, which was
leasing industrial facilities on the site. The Cease and Desist
Order called for a halt to unaiithori/.cd discharges of contam-
inants into surface water and groundwater just north of the
Arsenal. The cleanup order applied to all sources of DIM P and
DCPD located at the facilities. The third order called for a
groundwater monitoring program, the results of which would
be rc|x>rtcd to the State Health Department on a regular basis.
Consequently, a program that included groundwater monitor-
ing and studies to determine a means to intercept contaminants
flowing across the north boundary ol the Arsenal was estab-
lished by the U.S. Army.
As a result of continued monitoring, additional contaminants
have been identified in the groundw.ilcr at the Arsenal. The
most widespread of those found are Nemagon (dibromochlo-
ropropanc) and various industrial solvents. Nemagon contain-
-------
9fi
I.K.ONAHI) K. kONIKOXX tliul DOl'CI.AS XV. THOMPSON
in.ilinii li.is been identified as probably resulting from Arsenal-
relaled activities, xvhcrcas the industrial solvents identified arc
not unique to Arsenal activities. F.xtrcmely low concentrations
of Xcir.agon (< 2 ppb) have been found in wells located im-
mediately.,west of the Arsenal Ixmndary. Otlier organic con-
taminants associated with pesticide manufacturing have been
found in wells located in a centrally located manufacturing plant
area known as the South Plants area. These contaminants prob-
ably entered the aquifer from accidental spills and leaks and
appear to be migrating from this area very slowly.
Hxdrogeology
The records ol several hundred observation wells, test holes,
irrigation wells, and domestic wells were compiled and anal-
y/cd to describe the hydrogeologic characteristics of the alluvial
aquitcr in and adjacent to the llocky Mountain Arsenal. Kon-
ikoxv (1975) presented lour maps that show the configuration
ol bedrock surlace. generalized water-table confirmation, sat-
urated thickness of alluvium, and transmissivity ol the aquifer.
These maps show that the alluvium forms a complex, sloping.
discontinuous, and heterogeneous aquifer system. -~
A map showing the general water-table configuration for
1955-1971 is presented in Figure (i.3. The assumptions and
limitations of Figure (i.'} are discussed in more detail by kon-
ikow (1975). The areas in which the alluvium either is absent
or is unsaturated most ol the time form internal barriers (hat
significantly affect groundwater flow patterns within the aquifer
and. hence, significantly influence solute trans|x>rt.
The general direction of groundwater movement is from
regions of higher water-table altitudes to those ol lower water-
table altitudes and is approximately perpendicular to the
water-table contours. Deviations from the general flow pattern
inferred from water-table contours may occur in some areas
because of local variations in aquifer properties, recharge, or
discharge. The nonorthogonality at places between water-table
contours and aquifer lM>nndaries indicates that the approximate
limit of the saturated alluvium does not consistently represent
a no-llow boundary but that, at some places, there may In-
significant flow across this line. Such a condition can readily
occur in areas where the bedrock |x>sscsscs significant porosity
and hydraulic conductivity or where recharge from irrigation,
unlined canals, or other sources is concentrated. Recatisc the
hydraulic conductivity ol the bedrock underlying the alluvium
is generally much lower than that of the alluvium, groundwater
lloxv and contaminant transport through the bedrock are as-
sumed to be secondary considerations compared with llow and
transport i" the alluvial aquifer. Croundwatcr withdrawals in
the area are predominantly from wells tapping the alluvial
aquifer.
Contamination Pattern
Since 1955 several hundred observation wells and lest holes
have been constructed to monitor changes in water qualilv and
xvaler levels in the alluvial aquifer. The areal extent of contam-
ination has been mapped on the basis ol concentration ol chlo-
ride. 131 NIP. and other inorganic and organic compounds in
EXPLANATION
nix>— WATER-TABLE CONTOUR - Showt aporo»tmata almuda o<
watar tabla. 1955-71. Contour interval 10 faat 13 matan).
Datum it maan aaa lava)
Ar*« in which alluvium it ftbMnt or unt*turar«d
HOIHI. (i..°) (tt'iieral watrr-talilccniiliunralion in llie alluvial aquifer
ill and adjacent to the Hooky Mountain Arsenal. 1055-1971 ikonikou.
1977)
wells. Chloride concentrations ranged from normal background
concentrations of about 40 to 150 ing/I, to about 5(XH) mg/L in
contaminated groundwater near pond A. Chloride data col-
lected during 1955-19.% indicate that one main plume ol con-
taminated water extended beyond the northwestern Ixnmdary
of thi' Arsenal and that a small secondary plume extended
beyond the northern Ixnmdary (see Figure (>.-!). The contam-
ination pattern shown in Figure (>.4 clearly indicates that the
migration of contaminants in (his aquilcr is also signilieantK
constrained by the aquifer l>ouiularics.
Because chloride generally behaves as a conservative (that
is, nonreactive) solute in groundwater. it is often assumed that
chlorides can IK- used to indicate the maximum extent ol con-
tamination from a source that contains chloride. But this as-
sumption is not always reasonable because chloride is also a
common natural constituent in gromidwater. At the Kocky
Mountain Arsenal the extent of contamination as indicated by
chloride concentration reflects a dilution ratio of about 3.1:1
from the contaminant source to the definable downgradient
limit of contamination. However, the extent ol contamination
as indicated by some of the organic coui|X>unds. such as DIM P
(sec Itobsou, I9SI), is much greater because they have a zero
background concentration and can be delected to trace con-
-------
('.ontdinintition intd Aifiiijt'i'
&*. 7-
--' erf'
•i i t •iLOxiim
EXPLANATION
• O«l point (S«pt 19S5-M»cti 19561
300 Lin* o* aqual cMond* conc«nlr«iion {in milhgrami p«r lil«rl.
(n,«t..l v«n«bl«
K \\ Af«» in which alluviuni it abMnl or unialurat«d
KKil'HK (i.-t Olisi'iAed ililoridc iinifrntratiiin in H)">i> (ki>nikc adsorlxxl. Oilier diHercnces among
shapes and locations of plumes of different contaminants arise
liecause they entered the aquifer at significantly different times
and (or) locations within the Arsenal. For example, the Ncni-
agon plume occurs west of the chloride plume because the
source of the Ncmagon was not from the disposal ponds hul
apparently from a spill that occurred west of the ponds.
Contaminants have also liccn delected in several shallow
bedrock wells in or near the Arsenal. However, at present there
are inadequate data to define the areal extent, depth of pen-
etration, or'rate of 'spreading of contaminants in the bedrock.
APPLICATION OF SIMl'LATION MODF.LS
The reliable assessment ol hazards or risks arising from ground-
water contamination problems and the design of efficient and
elleclive techniques to mitigate them require the capability to
predict the Ix'li.ivior of chemical contaminants in (lowing
grouudwater. Reliable and (|iiautitativc predictions of contam-
inant movement can only be made il the processes controlling
convcctive tr.ins|x>il, hydrodxnainic dispersion; and cliemical.
physical, anil biological reactions thai affect solute concentra-
tions in the ground arc nuderstiHKl. 'fhese prm-esses. in turn.
must be expressed in precise mathematical equations having
defined parameters. The theorx and developnienl ol the equa-
tions describing Krouudwatcr flow and solute liansport lia\e
been well documented in the literature. Perhaps the most
important technical advancement iiT the anal)sis of pomid-
walcr contamination problems during the past ID yr has been
the development ol deterministic numerical simulation nuxlek
that efficiently solve the noverninU flow and transport equations
for the properties and boundaries ol a specific field situation
Although many of the processes that ailed waste movement
are individually well understood, their complex interactions in
a heterogeneous environment may not be understood well
enough for the net outcome to be reliably predicted. Thus, the
analysis of pomidwater contamination problems ean be erealK
aided by the application of deterministic numerical simulation
models that solve the equations describing groundwater llou
and solute trans|X)rt.
Tin1 solute-transport model described by konikow and Hrc-
dehoelt (I97S) was used to simulate the movement of chloride
through the alluvial aquifer at the Arsenal in an ellurl lo re-
produce the 30-yr (19-13-1972) history of contamination, lo help
test hy|M)llieses concerning governing processes and parame-
ters to develop an improved conceptual model of the problem.
to aid in setting priorities lor the collection of additional data.
and lo evaluate |Missible management alternatives (Konikow.
1977). The model included an area of approximately 3-4 mi-' (SS
km-'). The stringent data requirements for applying the' solnte-
transport model pointed out deficiencies in the data base avail-
able at the start of the slud\. Specifically, it was found dial the
velocity distribution determined from the water-table config-
uration mapped in 1956 (see Pctri and Smith. 195ft) was in part
inconsistent with the observed pattern of contaminant spread-
ing. The subsequent quantitative analysis and reinterpret.ition
of available hydrogeologic data, based partK on feedback from
the numerical simulation model, led to a revised conceptual
model of the aquifer properties and bonnduries that incorpo-
rated the strong influence of the internal harriers within the
alluvial aquifer
The solute-transport model ol konikow (1977) was calibrated
mainly on the basis of (he chloride concentration pattern that
was observed in 195fi (Figure 6.4). Computed chloride patterns
agreed closely with observed patterns, which during the 30-yr
history were available only for 19.%. I9KI. l%9, and 1972.
The calibrated model was then used to analyze the ellccts of
future and past changes in stresses and boundary conditions.
For example, comparative analyses illustrated that it would
probably take at least many decades for this contaminated aqui-
fer to recover naturally its original water-quality characteristics.
But it was also inferred that appropriate water-management
policies for aquifer reclamation can help to reduce this resto-
ration time to the order of years, rather than decades, for the
relatively mobile contaminants, konikow (197-4) also noted that
(lie simulation results showed that a reclamation scheme using
a network of interceptor wells would aid in containing and
removing the contaminated grouudwaler.
-------
i.i.oNvui) K kOMKovv• antl i)or<;i..\s vv THOMPSON
Hobsou (19M) developed and calibrated a solute-transport
model lor 1)1 Ml1 to help evaluate (1) (lie mechanisms mid pa-
rameters controlling 131MF migration, (2) future DIMF con-
centrations in nearby municipal water supply wells, and (3) the
effectiveness of various gronndwatcr harrier configurations de-
signed to halt otl-Arsenal movement of contaminated ground-
water. Tin- model included an area of ahont 90 mi- (230 kin-)
and assumed that DIMF is conservative. Using the calibrated
model. Rohsnn was ahle to reconstruct the historical movement
of .DIMF in the aquifer lietween 1952 and 1975. to estimate
DIMF concentrations in the1 South Flatte River resulting from
discharge of contaminated groundwatcr. and to predict future
DIMF concentrations under a variety of assumed mana.uenient
alternatives.
To evaluate more fully the range of engineering approaches
or alternatives that would he feasible for construction along the
north honndary of the Arsenal, Warner (1979) modeled a smaller
part of the aquifer (2.5 mr or ft. 4 kmj) in that area in much
finer detail. He predicted the impact on DIMF concentration
of implementing a variety of interception schemes that incor-
porated variants of a basic plan that included elements of
groundvvater withdrawal, a barrier, ami reinjection of treated
water. Among other findings. Warner (1979) showed that a
proper!) operated hydraulic harrier, consisting of a line of
pumping wells, would he just as effective as a bentonite barrier
in stopping the movement of DIM F-contaminatcd gronndwatcr
across the northern boundary of the Arsenal.
It is recogni/.ed that oilier organic contaminants of concern
may hi- sorbed or altered by chemical and biological reactions
as they move through the aquifer. The movement of a solute
that is sorbed will be retarded relative to the movement of a
conservative solute. This is beneficial in the sense that in a
given time a contaminant that is sorbed will not migrate as far
as a conservative contaminant. However, the soiption process
could pose a significant obstacle to aquifer reclamation Ix-cansc
even after the contaminant source- has been eliminated, the
sorbed organics could later desorb and continue to migrate
through the aquifer, perhaps still (losing a ha/urcl alter all con-
servative contaminants have been llu.shcd out of the aquifer.
Sorption processes can and have been incorporated into solute-
transport mtxlels (see C.rove. 197(il. and this allows a more
realistic evaluation to be made of their behavior and response
to mi|X>se(l aquifer reclamation stresses. Although this then
presents no great conceptual difficulty, in practice- it is quite
difficult to determine the coefficients that describe the rates of
reactions and exchange capacity of the aquifer material for each
individual contaminant.
An overall systems-management model is currently in final
development under the sponsorship of the U.S. Army. This
computer model is expected to provide a valuable management
and decision-making tool to aid in evaluating aquifer recla-
mation alternatives at the Rocky Mountain Arsenal. The model
will be composed of numerous modules, including (1) ground-
vvater flow. (2) solute transport. (3) groundvvatcr interception
and control. (4) surface-water control. (5) groundvvater and sur-
face-water treatment, (h'l cost estimation, and (7) re|xirl and
graphics output. The model will be evaluated and verified using
the Kockv Mountain Arsenal as a test case because of the abun-
dance of historical data there. After verification, selected al-
ternatives for contamination control and elimination at the Ar-
senal will lie modeled with a goal of predicting long-term system
responses and costs. If successful, this model will be applied
to Installation Restoration programs under way at other loca-
tions.
AOUIFKR KKSTORATION FKOCRAM
Response to Cease and Desist Orders
As a result of the (Vase and Desist Orders, an Installation
Restoration program was established at the Rocky Mountain
Arsenal under the direction of the Frogram Manager for Chem-
ical Demilitari/ation and Installation Restoration. Aberdeen
Froving ('.round. Maryland This office was later rcorgani/ed
into the U.S. Army Toxic and Ha/ardons Materials' Agency
(USATHAMA), which currently directs the Installation Res-
toration program at the Arsenal. The- main objective of this
program is to limit the migration of contaminants from the
Arsenal to the degree required by applicable federal and state
regulations. The program is primarily concerned with contam-
ination problems resulting from historical activities on the Ar-
senal as opposed to ongoing operations.
The installation Restoration program consists ol three major
parts or subprograms that include regional groundwater mon-
itoring, contaminant migration control, and elimination ol con-
taminant sources. This program had been nig.mi/.cd to allow a
phased approach in developing and implementing contaminant
control systems, thereby accelerating the reduction of potential
environmental hazards. More than $25 million has been ex-
pended to date in the Installation Restoration program, ex-
cluding the costs associated with construction of the control
systems.
A comprehensive groundvvater monitoring program was de-
veloped based on historical contaminant distribution infor-
mation and initiated late in 1975. It included sample collection
from Ixilh oil-site and adjacent off-site wells. This monitoring
program has been continually updated since that time to in-
clude additional wells and analytical parameters as required.
Currently, it involves the collection and analysis ol samples
from 91) to KM) wells on a quarterly basis. The information
generated from the monitoring program is used to define the
distribution and track the migration of known contaminants.
identify new contaminants, develop design criteria for contam-
ination control and treatment systems, and evaluate the op-
eration of existing systems.
The subprogram concerning contaminant migration control
at the Arsenal boundaries was initiated in late 1975 with the
goal of rapidly eliminating the migration of contaminants off
the Arsenal's grounds. Boundary control was the only viable1
option because of the already wide distribution of contami-
nants, the long travel times associated with contaminant mi-
gration from the sources to the boundaries, and the lack of
precise definition of all source areas. Filot and lull-scale Ixxmd-
ary control systems have been implemented at the northern
Arsenal boundary, and plans have been developed to expand
-------
C.iniliiinindtinn tinil A^III/CC Kcclaination
99
the treatment system along llic northwestern Arsenal bound-
ary. Those systems will lie discussed in more detail later in
this chapter.
Planning lor the control and elimination of contaminant sources
evolved several years later as additional data became available
on specific source areas. The goal is to control or eliminate the
contaminant sources on the Arsenal grounds and thereby elim-
inate the need lor boundary control in the future. Studies have
been undertaken to aid further identification and definition of
contaminant sources, to develop feasible source control and
elimination alternatives, and to develop control and treatment
systems. A summary of the strategy and progress of this sub-
program is given at the end of this chapter.
Contaminant Migration Control at Arsenal Boundaries
Hccansc the contamination that resulted in the issuance of the
< lease and Desist Order was detected in surface water and
groundwater immediately north of the Arsenal, the primary
locus of the Installation Ucstoration program during 197(i and
1977 was the northern Arsenal boundary. A dike was con-
structed to stop the miration oil the Arsenal of contaminated
surface water. Studies were initiated to determine a feasible
alternative for stopping the flow of contaminated groundwater
oil the Arsenal without significantly altering the normal ground-
watcr flow pattern in the area. The concept selected involved
interception of the grouudwatcr a short distance south of the
northern Arsenal boundary, treatment of the water to remove
the contaminants, and reinjcction of the treated water at the
boundary.
Two method!) were proposed for intercepting the flow of
groundwater. The first method involved the use of a hydraulic
barrier, one or two lines of closely spaced pumping wells that
would provide for dewatcring of the aquifer along or between
the lines. The permeability in the area is sufficiently high lor
this concept to have worked, but the gradient is shallow and
concern was expressed over the potential lor excessive recy-
cling of water from the reinjection wells back to the withdrawal
wells. As a result of this concern and to provide an additional
safety factor, a second method was selected that involved the
use of a slurry cntoll wall to lorm an impermeable barrier
between, the withdrawal and reinjection wells.
Treatment Process
l«ite in 1975 a lalx>ratorv study was initiated to evaluate various
methods for removing organic compounds from representative
groundvvrtter samples from the area. Treatment processes in-
vestigated include granular activated-carbon adsorption, pow-
dered activated-carbon adsorption, chemical oxidation using
ultraviolet (I'V) light and ozone, and an ionic exchange resins.
Key chemical parameters for analysis included Dl M P and D( 'PI).
Extensive lalxiratory studies were conducted using standard
isotherm tests for evaluating the carbons and resins and using
hatch reactor tests for evaluating the I'V/ozone process. The
anionic exchange resins were dropped from further consider-
ation because of low cllicicncy and high cost. A vries ol licit!
studies was initiated on the carbon adsorption and I'V/o/one
oxidation processes to permit further evaluation.
Powdered activated-carbon adsorption tests incorporating a
polymeric coagulant were conducted usjnu a standard Arinv
Krdlator water-treatment unit (chemical addition, mixing, up-
llowclarilicationHSwcder. 1977). fGranular activated-carbon ad-
sorption tests were conducted usinj; a dynamic -flow, multi-
column system (Sweder, 1977). l'V/o/onc oxidation tests were
conducted using a continuous-flow, mechanically mixed reactor
(Hunts et ill.. I97K). Granular activatcd-carlxm was found to
be more efficient (110 mg ol carbon/I, of water) in removing
the contaminants than was the powdered activated-carbon (20 ft (305 in). Ik-cause little operational information
was available on groundwater contamination control systems
similar to the one proposed, the Army decided to install a
limited pilot containment system in the area of high-contam-
inant concentrations and evaluate the possibility of extending
the treatment system across the entire affected part of the
northern )>oundary.
The North Honndary Pilot System AMPS) was constructed
and placed in operation in July I97S It included the following
live subsystems: a barrier, dewatering wells, reinjection wells.
treatment plant, and monitoring wells. A schematic diagram
of the system is provided in Kigure h'.5.
The barrier was constructed by filling a 3-ft-wide, 1500-lt-
long trench, averaging 25 ft in depth, with a mixture of soil
and bentouite clay. The barrier was anchored approximately 2
ft into the bedrock all along the alignment.
The dewatering wells were installed south (npgradient) of
the barrier approximately 225 ft apart on a straight line parallel
to the barrier. There were six S-inch-diametcr wells placed
within 30-inch-diameter gravel-packed holes. Kach well was
screened throughout the entire saturated portion of tlir alluvi.il
aquifer. A submersible pump and flow control system were
installed at each well site. Water from the wells was pumped
through an underground manifold to a single sump at the treat-
ment plant.
-------
KM)
LEONAIUJ K. KONIKOW IIH(I l)()l;CI.AS \V THOMPSON
The injection wells were installed north ulowngradicnt) of
the harrier, approximately HX) It apart on a straight line be-
tween the harrier and the northern Arsenal honndary. There
were twelve 18-inch-dianioter wells, which were installed in
36-inch-diameter gravel-packed holes. The recharge wells were
screened to a point al>ove the water tahle. Treated water was
continuously injected into the recharge wells l»y gravity flow
through an underground manifold system. Sensors and (low
control valves were installed in the wells to prevent overflow
or surface discharge in the event that a well experienced an
excessively high huildup of hydraulic head hecause of clogging
of well screens or other factors.
The treatment plant subsystem was designed to treat 10.(XX)
gallons of water per hour. It consisted of two mixed-media
pressure filters, each 4 It in diameter, and two adsorl>er vessels
IIH columns), eaeh 10 fl in diameter and II It high, designed
to contain .lUiil 20.(MM) Hi ('I I (HI kg) of granular activated e.n
lion Water Irom the collection sump -was pumped through the
filters in parallel to remove suspended material, then through
the carbon adsorbers, and finally to the injection wells. Only
one carbon a'dsorber was in operation at any one time. \Vhen
the 1)1 NIP concentration approached 50 pph. the carbon was
replaced. During 1978-1981. replacement was required ap-
proximate!) once every 9 mouths. The exhausted carbon was
transported offsite (or regeneration by a commercial vendor.
Carbon usage rates ranged trom 1(X) to 150 mg of carbon/I, of
water. The treatment system was designed to be largely au-
tomatic and simple to operate by incorporating automatic back-
washing of the filters and sensors for control of pumps and
valves.
Ten monitoring wells were installed both upgradicnt and
downgradient ot the pilot containment system. They were cased
with small-diameter PYC pipe and screened in the alluvial
PILOT TREATMENT
PLANT
KK.l'HK (v.'i S> lie-main Typical gas rliroiiiutograpliv7iiia.ss spcctromvtry scan ol
north boundary pilot treatment system iitllnrnt.
aquifer. Water levels and chemical qualitv wen1 monitored
periodically to provide information on the ctlcctivencss ol the
operation of the system.
The cost of the barrier and the wells as constructed in 197S
was $450,(XX). The facility for housing the treatment system
cost approximately $4(MXX). The treatment equipment was ob-
tained under a lease/service contract agreement with a com-
mercial vendor with an initial cost of approximately SKX).(XX)
and a yearly fee ranging from S 1:15.000 to SI50.000.
The NBPS operated successfully for a period of approxi-
mately 3 yr. For example, during fiscal year 1979, downtime
was less than I |XTecnt ot operating time. The granular acti-
vated carbon cflcctivcly removed the organic contaminants from
the groundwater, generally to a level of less than 10 pph. as
illustrated by a comparison ol typical gas chroinatography/mass
spectrometry analyses of the influent (Figure (i.(i) and effluent
(Figure 6.7) of the treatment system. The flow of groundwater
downgradient from the NHPS was essentially unchanged
(D'Appolonia Consulting Engineers. Inc.. 1979). Preliminary.
data indicate that the concentration of orgauics in the ground-
water downgradieut from the pilot system has diminished sig-
nificantly.
Expanded Containment System
As a result of the successful operation of the pilot containment
system, construction of the expanded containment system was
begun in early 1981. The expanded system consists ol a (i8(X)-
ft barrier ranging from 25 to 50 ft deep, 54 withdrawal wells.
and 38 reinjection (or recharge) wells. The expanded barrier
effectively intercepts all the contaminated groundwater flowing
across the northern Arsenal boundary in the alluvial aquifer.
The expanded treatment system is designed to treat 3ft.IKK)
gallons (!3(i.(XX) I.) of water per hour. The adsorlx-rs used in
the pilot operation have been replaced with three pnlsed-bed
adsorbers designed to contain 30.(XX) II) (H.ofX) kg) ol earlxin
-------
Contamination mid Aytiijer Reclamation
101
If
JV.A.
5 J
I 1
1 2 3 « ', 6 7 « » 10 II I? 13 14 16 16
RETENTON TME
FKil'HK (i.7 Typical gas clmiinatograpliy/mass s|K'clronielry scan of
noitli Ixiiindaiy pilot treatment svslein cllliient.
ruch. Tlit1 new adsorbers should he much more efficient than
the old ones because the anticipated carbon usage rate is only
25 to 30 nig of carlwn/L of water. The mixed-media filters have
been replaced with cartridge filters, which are easier to main-
tain. The whole system is highly automated and will require
only intermittent monitoring by a single operator. The esti-
mated cost for the expanded system is approximately $6 million.
The expanded system became operational in 1983.
Other Contaminant Migration Control Systems
Concepts have Ix-en developed for two additional Ixiundury
contaminant migration control systems located along the north-
western Arsenal boundary (Figure b'.8). One system will lie
located at the southern end of that Ixmndary and the other
midway along that Ixnmdary. Both systems have been devel-
oped primarily to control (he migration of low concentrations
of Nemagon across the boundary. Both systems will br similar
in si/e to the NBPS and will incorporate granular activatcd-
carlxm treatment of the gronndwater. The system to be located
on the southern end of the boundary (Irondalc System) was
constructed under the direction of Shell Chemical Company
and incorporates a hydraulic barrier for interception of the
groundwater, along with the injection wells. It became oper-
ational in 19H3. The other system, to be constructed by the
Army, will incorporate a slurry cutoff wall, withdrawal wells.
and reinjeclion wells, similar to the pilot system. It is scheduled
to l>e operational in 1985.
Planning for Control and Elimination of Contaminant
Sources
Contaminant migration control at the boundaries of the Hocky
Mountain Arsenal was initiated to stop or severely limit the
migration ol contaminants of) the Arsenal grounds as soon as
possible. Owing to the si/.e ol the Arsenal and the extent of
the source areas, the boundary control systems could IK- re-
quired to operate for an indefinite' period of time. The only
way to limit this requirement and the associated cost is to
control or eliminate the contaminant sources. Therefore a stud)'
was initiated in 1980 to identity and assess existing and inno-
vative control or elimination alternatives that are capable of
bringing the Arsenal into compliance with all applicable federal
and state environmental laws and-rcgulations. Another stud)
objective was to develop preliminary cost data and technical
data for use in a subsequent detailed evaluation and comparison
of alternatives. A study team made up of 12 government and
independent scientists and engineers was established to con-
duct and manage the study. A review ol historical operations.
past study reports, and data from ongoing studies was made t<«
identify, where (xissible, potential sources of contaminant mi-
gration problems.
The next phase of the study involved the development .-a!
control strategies. Guidelines and criteria for developmental)
the strategies were required because of the complexity of and
relationships between the contaminant sources and migration
characteristics. In addition, some degree ol commonality ol
structure or organi/ation among the strategies was needed to
enable a comparison and ranking ol the alternatives to IK- de-
veloped As a result, a hierarchical approach and structure lor
generation and classification of control strategies were devel-
oped incorporating five levels of detail ranging from cowept
to unit operation (Kocky Mountain Arsenal Contamination Con-
trol Study Team, unpublished report, August 1981). Each team
member individually developed a number of strategies using
the hierarchical approach and determined the problem defi-
nition and technical data-base deficiencies associated with *-ach
scheme. The schemes were then submitted to the group as a
whole lor integration and evaluation.
Screening criteria were developed to aid in evaluating and
comparing the alternative schemes. The goal was to pitwlmv
EXPLANATION
«Dtwit*lnQ Ml!
ffl LKKM) TrMtnwil
NORTHWEST BOUNDARY
SYSTEM (PraooMdl
IRONDALf SYSTEM
(9w« Ownc« Co
KKJUHK (> H Ideation ol existing anil pro|x>s
-------
102
I.KONAHI) K KONIKOU and Dot c:i.\S \V. TIIOMI'sUN
a set of criteria that could IK- applied at the various hierarchical
levels, thereby enabling a general screening of the .schemes
rather than a detailed evaluation ol'each one. The major criteria
selected li>r use are as follows:
1. Availability of technology,
2. Amount of additional data required,
3. Cost and time needed to fill data gaps,
4. Life cycle costs—capital and O&M,
5. Compatibility between systems,
6. Degree of risk—environmental and technological,
7. Compliance with regulatory requirements.
The individual schemes developed by the study team mem-
bers were integrated, evaluated, and screened by the study-
group as a whole. This work resulted in the presentation of 14
alternative schemes that were recommended for detailed eval-
uation by the Contamination Control Study Team. The schemes
incorporate various aspects of the technologies listed in Table
6.1. The schemes address only the known contaminant sources
at the Arsenal and therefore may have to IK- expanded if ad-
ditional sources are identified in the future.
In addition to the development of the alternative schemes,
the study team identified a number of data gaps concerning
both problem definition and technology development that must
be filled before final selection of a control or elimination al-
ternative can be made. Studies have been included in the
overall Installation Restoration program to fill these data gaps.
They include additional hydrogeologic definition of certain areas
on the Arsenal, surface-water hydrology definition, technology
development for water treatment, and technology development
tor disposal of contaminated soil and residue. As the data from
these additional studies become available, the study team will
further evaluate and revise the alternatives as required with
the goal of selecting one alternative for implementation.
The implementation of the selected alternative will l>e con-
ducted using a phased approach. As soon as a particular part
TABLE B.I Contaminant Source Control and t'liminatiou
Technologies
C.roimdwatt'r Intercept inn
Hydraulic harrier
Slum trench
Drvvalrrint; trench I I'rcncli ilr.iin)
Water Treatment
Adsorption (carlx>n and resin)
Chemical addition/coagulation/prccipitation
Filtration
Membrane separation
Chemical oxidation
Activated iludue
Volatile stripping
Ion exchange
Contaminated Soil and Residue Treatment
Incineration ~
fixation/stabilization
In situ forced leaching
l-'vc.ivatum and dis|»>sal
of the alternative is defined and design criteria are developed.
construction will IK- initiated. For example, the elimination of
Basin F will probably In- one of the first major actions initiated
Ix-cause it is known to leak and because the extent and nature
of the contamination associated with this area of the Arsenal
have been better defined than elsewhere. Tin- control and
elimination of known contaminant sources at the Kocky Moun-
tain Arsenal are currently expected to involve a 5-yr construc-
tion program that is scheduled to start in 19S5. A final cost
estimate for the construction program has not been developed,
but preliminary estimates range from $50 million to SHX) mil-
lion.
SUMMARY AND CONCLUSIONS
Removing pollutants from a contaminated aquifer may seem
to be an almost impossible task. While this may be true for
some contaminated aquifers, others may be amenable to one
or more plans for artificial reclamation that could significantly
accelerate the rate of water-quality improvement in the aquifer.
The feasibility of any such reclamation plan would be strongly
dependent on the hydraulic and chemical properties of the
aquifer, on the type and source of contamination, and on the
duration and area! extent of contamination. Because a variety
of reclamation plans can be proposed lor any one problem, an
accurate model ol How and contaminant transport in the aquifer
is an invaluable tool for planning an efficient and effective
program.
The control and elimination of contaminant migration and
contaminant sources at the Rocky Mountain Arsenal represent
a large, complex, and costly undertaking (over S25 million has
been spent in the Installation Restoration program). An exten-
sive well-monitoring program has been required to define the
extent of the conta'mination and the relationships between the
sources and contaminant migration patterns. Control of con-
taminant migration at the Arsenal Itoundarics has proved fea-
sible using a system involving groundwater interception.
treatment, and rcinjection. The system was operated success-
fully without adversely affecting the How and distribution of
groundwater dowugradieut from the treatment system, and it
has resulted in a significant decrease in the concentration of
organic contaminants in groundwater downgradient from tin-
pilot system.
Although Unindary-control systems can be used successfully
to stop or restrict the migration of contaminants off the Arsenal's
grounds, they cannot solve the problem of continued contam-
inant migration from the source areas to the environment. The
overall solution thus involves the control or elimination of the
contamination at the sources. A program has been successfully
initiated at the Rocky Mountain Arsenal to develop and assess
source control and elimination strategies. Through additional
data collection and feasibility studies, a single strategy will be
selected and implemented using a phased construction ap-
proach. The ultimate goal of these activities is to bring the
Arsenal into compliance with all applicable federal and state
environmental laws and regulations.
The great difficulty and expense involve d in mitigating
-------
('iintainiitatiini tiiul Aquifer Kirltinnitiiin
Uronndwatcr contamination prolilcms do not lessen (lie need
In do so; they do illustrate (lie long-term hcuclits ol planning
and designing waste-disposal activities to prevent or nn'niini/.e
future contamination liauirds.
ACKNOWLEDGMENTS
The Installation Restoration -program at the Rocky Mountain
Arsenal (RMA) is being funded and directed In the U.S. Army
Toxic and Hazardous Materials Agency. Aberdeen Proving
(Ground. Maryland, in cooperation with the Rocky Mountain
Arsenal. Denver, Colorado Tlic authors wish to thank the
personnel from these organizations lor their support. Special
thanks are extended to Carl lx>\cn. ("hid. Process Develop-
ment and Evaluation Division. RMA. and Donald Mailer, Ru-
lu'l.iiid I lager. Inc., Tucson. Ari/.ona. lor providingoperational
and cost data on the RMA contaminant control svslenis.
REFERENCES
Buhls. R. K.. 1'. <;. Malonr. anil I). U. 'Ilininpsim (197S). Evaluation
of ullraxiolct/ozoiie treatment of Hockx Mountain Arsenal gromul-
xx-aler. C.S. Army Eniiinivr Watei-u-uij\ t'.v»criiiii'iil Station. Tech-
nical Report V-76-/, 7S pp.
DAppolonia Consultmn Engineers. Inc. (1979). Evaluation of north
houndary pilot ciintahniifiit system. KMA. Denver. Colorado. I'roj-
eel Number RM79-3S9. Wl pp.
drove, D. B. (I97(i'. Ion exchange reactions in Kroumlwatcr quality
miKli.'K. in Ailranrex in GnHiiiihrntrr Hijtlnilnnij. Am. Water !<<•-
sour. Assot'.. pp. 144-152.
Konikoxv. L. F. (197-1). licflamatioii ol a ct)ntaminati'(l ai|iiilfr. (•<•(*/.
Stir. Am. Almtr. Profiraiii.\ 6. S30-H31.
konikovv, L. K. (1975). llydrotieologic maps ol'tlie alluvial aquifer in
103
and adjaei'iit to the Kix-ky Monnluin Aiscnal. <.'olniad'i. I'.S. C.cnl
Sun . t)iM'>i-Hlc Ki-fi. 7/-W2
Konikow, L. F. (1977). Modeling clilornlc nuni-iiicnl in tlir allnxi.il
ai|iiiliT at llic Kix'kx Mountuin Arsenal. (!olni.«ln. C..S (.in/ Sun
\\uti-i -Siii>iil 2(H-I. 4.) pp.
Konikou. I,. K.. ami J. I), llreclrliiicll |I97S). Coinputor miMlel ol IVMI-
ilimc'iisional solute trans|x»l and dis|MTsion in ground w.ilci, C.S
(•I'til. SUIT. '/i>c/iNJf/iurrr\ lin .. Huvk ~. (°/n//i
C2. 9t) pp.
Hetri. I.. U (ISKil). II if tiioxcmciit ol -..ilinc uroniul water in I lie viiiinU
ol Derhy, Ooloradn. in (•nmiir/ \\utfi f'tintiimiiwtiini .Si/mjxi.viiiin.
HoU-rt A. Taft Sanitarx KIIK. Center Teili Hep Whl-5. pp. II')-
121
I'ctn. I.. K.. and K. (). Smitli (l'JV)i. Imestication ol the i|U,ilit\ <>l
)!roiin(l watri in tlie vicinity of l)i-rl>\. (.'olor.nlo. C.S. (ii'iil. Sun .
O/trii-fi/r HI'II.. 77 pp.
Kolison. S. ('. |I9SI). (loinpiiler simulation ol moxvmetit ol 1)1 Ml'-
contaminated Kroiimlualcr near tlic HiK'kx Mountain AISCIM!. (.Hl-
orad(K 'I. F. /immir and (.*. (). Hi^s. fd** . in />r('ifirr//>i/f/f/ nml
C.iininiltKili i Ciinliiiiiiiiinil 7Vuii.v/inr(. Anifiicui S\iiim. Holier! A lalt Sanitary Kim (it-liter Tecli.
Rep W6I-5. pp. 121-125.
Warner. ]. W. (1979). Digital-transport model stiulx of diJMipropyl-
mi'thylphosphoiiate (DIMP) croinul-xx'ater cuiitainiuation at the Koiky
Mountain Arsenal. Colorado. C.S. (.'<•«/. Siirr. ();«'ii-/;i/i- HCJJ. '•)-
676. 39 pp.
U'ood. L. A. (1972). (>roundwater degradation — i-auso and cures, in
Prucvetlinns l-ltli Water Quality Coiif.. I'rli.in.i. III., pp. 19-25.
-------
SECTION 7
SELECTED SLIDES
-------
£-W
- ' J If •
C -
o
3.
q. ^ - ^ A - -
r.
. (V ^ V
: ^ " °*i}
3-0
-------
-------
at
il
dt
l
•^^•^
b
*
d*
*-(}>&.*£
V/ N H-
r' /x
^c\
-------
I (
LfiTTI CE-
&*.)!>
-------
I
-------
FOR. MO-C-
f r to/umm X 6 rows)
>• x
IX =/
t
AX
,.,_A
Jo \jvt> fifty
-------
or
-f
or
N
TINTT
\
M
i \TQ/U
FOHFIJDW
il
/i
H
>*•
!i
.
f wi+k 3
SUMTCH -*
-------
Q
~ 1ST W-'-
= w,
w = w
ntt
-eb
-------
WELL
node,J
L/
INFLOW = QBc,=zf(Hs -hi)
Schematic: representation of constant-head boundary condition
< F :i. om Vas?;;, .1.984 f )
-------
(\ffre
-------
00
c
RELATIVE SORBED CONCENTRATION
»- o
M- >-•
a B>
m oa
—^t» M
MS
?i?
1TSC *
1 3 M.
"t M, 0
2 »°°
" oc:
-» 2U
T-S
3 «• »-
£=?
9-03
•/* B M
to M
•* «,
O
M
3)
m
m
g
CO
CO
O
m
o
o
O
z
o
m
O
Z
-------
f
or
-------
/ftt
- AC
-------
REACTION TERMS:
INPUT DATA INSTRUCTIONS
1. SET NREACT = 1 IN COL. 72 ON INPUT CARD 2.
2. SPECIFY VALUES FOR DK, RHOB. AND THALF IN FREE
FORMAT ON NEW LINE IMMEDIATELY FOLLOWING
DATA CARD 3.
-------
b
co
lt/%
-
-------
\*
USE OF
MX
HMX
I
I
7
/C
A7
s«A
6 7
AT/Vvyv
VV^A4l^-/
Primary
Primary
A/X ^
-------
USE OF SECONDARY SUBGRID FOR TRANSPORT:
INPUT DATA INSTRUCTIONS
1. SPECIFY NX AS A NEGATIVE VALUE IN FIELD 3 OF
DATA CARD 2.
2. SPECIFY THE UPPER LEFT AND LOWER RIGHT CORNERS
OF THE SUBGRID (MX, MY, MMX. MMY) IN FREE FORMAT
IN A NEW DATA CARD IMMEDIATELY FOLLOWING DATA
CARD 2.
-------
SECTION 8
CLASS PROBLEM
-------
-------
(M .
tO '
CO -
O i
(0 c '
u "•
Z e
0^" ik
7 -
-------
: SAMPLE PROBLEM TOR lCTTnV.ilT.iUH JJP 2-3UHEHSIOK&L SOLDTE-TRANSPORT MODEL BASED
, on METHOD OF CflMBm^MjifTgyTCS i
This exercise is designed to illustrate the application of the model to a
realistic problem, using a variety of boundary conditions. The boundaries,
properties, and stresses are approximations of the long-term contamination
problem at the Rocky Mountain Arsenal, Colorado, U.S.A. (Reference: Konikow,
1977, -Modeling chloride aoveaent in. the alluvial aquifer at the Rocky Mountain
Arsenal, Colorado: U.S. €eol. Survey Water-Supply Paper 2044, 43 p.). To
minimize computational costs for the class exercise, the problem has been
simplified to use a relatively coarse -grid and uniform aquifer properties.
!The class will be divided into groups .of two. The basic data file is designed
to simulate the .problem for a 2(Hyear period using NPTPND - 9, CELDIS =
0.50, € = 0.20, and «L =MDO ft. Each group will run several variants of the
basic problem that requires a modification of the basic data file, as
follows:
- i. JfPTPNJ* = J.
2. NPTPND - 4
'3. ''NPTPND'-* 5
-4, tfPTPND - 8
as a nrrngfranfr-hcad condition*
6. Longitudinal dispersivity = 0.0 feet
7. IrangitudiTial dispersivtty - 20.0 feet
^«. Twngitxtatnal flispersivity -"--500; Q -feet
9. Transverse dispersivity = 0.0 feet
10. Transverse dispersivity = 100.0 feet
11. CELDIS" 0.25
J2
13. Porosity = 0.30
It. 'Use fi x 3 sulngrifl .for
16. — 10 years
_!&. 1^ = J^D-^nd ^ =— LO
19. 10 years of contaainati«n followed by 10 years of flushing with
• (same Q, C' =
lal 4"ff^T
The results of all runs wlH be compared and discussed in class so that all
participants can see tl» Tesults of runs Trade by other groups. Each group
"will ~plt>t "tare uuuuuiiliatipn -veiBnB tine for observation well 3 for their runs.
ComparisCTW yill •« i i^nrtygtg t^ sensitivity of precision, accuracy, and
efficiency of ±fte srrtTrt-jrm-*T> -pByj^jpns of the selected parameters.
-------
CLASS PROBLEM — Input data for base conditions
ROCKY HT ARSENAL -- APPROXIMATE SOLUTION
1 1 10 132000 1 7 1 100 4
1
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
0
0
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
0
0
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
0
0
0
0
0
0
0
0
0
0
0
20. .001 0.20 100. 0.0 0.0 0.02000.2000. 0.3 0.5 1.0
6 e
0310 0.2
0510 0.2
0710 0.2
0605 -1.0 1000.
1 0.01
0
0
0
0
0
0
0
0
0
0
1 40.0
0
0
0
0
0
0
0
0
0 0.0
1 1.0
0011111100
0000000000
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0111111110
1 0.1
1 1.0
10.0
250 250 250 250 250 250
20 25 30 35 40 45 50 55
0 10.0
-------
<*r
ritdi
"1
-i
j
/•'••.
C too-
I
^
h—
¥»t>
:.::
o 100
— r
IX)
/to
-.-:/':-
-y:-~
/••;:'••
::j
•-.
7 f f
/O
// Av
-JT": :r:;T
•--y—-
-------
v7~-iHe or Ob*-
JDOO
^
C too
o 300-
0~
I
I
t (0 //
»3
J-t»ii
ll
ff /; TO
-------
JflOO
0/AHe^i
;
'pi
(00
<
*
0 30CK
/IC
2- 5
f L 7 V Ct
J b ' * 7
fl or- y~'"lt ('
n if /; 10
-------
PARTICLE PATHS
j mis
10
20
(note: map is mirror image; east & west are reversed from original map and grid)
-------
CLASS PROBLEM — / = 20 years
Contours of concentrations of nodes
Contours of concentrations of particles
-------
SECTION 9
CLASS PROBLEM - RESULTS
-------
MOC
-
JD00
>*'ii
Yw
I .....
-DtitripfcOv^
fktttk resu.lrs :
'sttoAitiin^'
i *t
3
o
/to
rrj:
j i •
ih^
-::J
'".'I'
:rE,u-i'
':SL
i::-:|.
in
O.I1.
OJd^70
•for conjT.-( i
7 f f M /i IT- &
-I
..
Or-
/;
-------
>ni(MI M > M 10 I MH
>1H IOIM««»OIM»>
-------
- • . . .
v. T~iH-e xr Ob*-
nofa. t>,
-------
•fhttcJL-"retijTS. : Vary
If If ZO
-------
-------
ccr Obs- frW/ 3 ^o
-------
imow to * » 10 » •*«
1IH IOINAMOH»HIM»iOGtlJWVm *C«MtID
AMOTCmiHIMOGtlJWVttf ACCIXtID S
v± Tine, or Obi- \J*II 3 ftiofo. 4,
: t :::::::: : ::::::: :::::: : • s :;::•::: :: ::::::::
• HsISImSSiSSSSEiS! SI •• •!••••• •••••• • I • -• .-^ t • • •• ••••'!• *
: SfUiiiMhissiiM^ " » »•»:: "•"•"• • • - •• i::: ! : •::::
• •l*li*!«l!*l»"i*!""" •• *• ••••••• •••••• • • • •• •{• • • i •• I!!!!!! I
• •••••••••••••••••••B •• •• ••••••• •••••• • • • •'. ••• • • • •• SISSSSI S
• •••••{••••••••IiiaiB •• •• •••!••• •••••• • • • '.* ••• • • • •• ••••••• •
• '. ••••••••••§•••••••••[••••
- • ••••••••••••••••••••••••i
• • •••••••••••••••••••••••••
• t •••••••••••••••••••••••••
• • •••••••••••••••••••••••••
• • ••••••••••^•••••{••••••!
• • ••••••••i«iiuiii|iiaiiii
b
f
/'
/JT
-------
miOM *> • ja to i MCH
MM IOIMAnOWIHIIMtftOG«miVt*iifl91i**iI«]i
• • ••••. ••••••••••••••••••••
•• • ••••^•••••••••••{••••••l
SS • •••••i.MiMiill"**"Il"3
S! "5"1*5*v•!•••••••ilit""li"
•• • ••••••^••••••••iiiliMii
•• ••••••••> •••••••••••••••••
• ::::::::ri::;i:::::::i:>:
: :::i:::.:r::!i::::!]:::::
• ••••••••••.•••••••••••••••
• ••••••••••»•••••••••••••••
• ••••••••••• •••••••••{••••i
* •••••BBB|iii•••••••••••!••
• •••••••itiik*••••••!•!••••
• • •••••••••••• <••••••••••••• •
• • ••»•••••••••>•!!•••••*•••• •
1 • • f ••••••••••••!«•••••••••••• •
• • •• • • ••••••••••••• •••••••••••• •
i. noves con'ierta •
3 .1 n « A
0
0
0
0
0
0
0
0
0
0
0
0
10
10
10
10
10
12
12
t2
19
10
13
0
10
Id
10
to
It
It
17
11
11
11
10
3
10
10
14
112
III
411
0
0
21
142
2>
0
10
11
20
It
21
It
III
m
S10
21
0
20090
10
10
It
17
11
tt
41
22*
ItO
111
21
l«»92
19
to
t>
21
»l
0
0
t9)
111
101
11
to
10
11
12
IM
921
>10
201
tt
10
10
10
10
11
tr
21
It
2t
It
to
to
0
9
0
0
0
0
0
0
0
0
0
•• • ••••• t «••
•i • ••••• •. ••
•f
A/
10
/y
t j
-------
CLASS PROBLEM — Input data for Run 5
(*indicates lines modified or inserted in comparison to base conditions)
SOCKY MT i»SEN4L -- flPPROXIMSTE SOLUTION — CONSTANT-HEAD SOURCE
1 1 13 132000 1
20. .001 3.20 100. 0.0
0
6 5
3 5
6 8
3 3
V 5
310 0.2
0510 0.2
0710 0.2
1
0.31
3 1 . 1 .
0 1 . 1 . 1
•3 1 . 1 . '
Q 1 . 1 .
0 1 . 1 .
0 1. 1 .
C 1. 1.
0 1. 1.
0 1. 1.
3 1. 1.
C 1. 1.
. 1. 1 .
1 . 1 .
. 1. 1.
1 . 1 .
. 1. 1 .
. 1. 1 .
1. 1.
1. 1 .
. 1. 1 .
. 1. 1 .
. 1. 1 .
7 5 100 3 9
0.0 0.02000.2000.
2100
0.3 0.5 1.0
1 40.0
0 1
0 1
0 1
0 1
3 1
0 1
0 1
0 1
0 1
0 1
0 1
1 1
1 1
1 1
1 1
1 1
1 1
1 0
1 0
1 1
1 1
1 1
11110
11113
111110
111110
11110
10110
10113
11110
11110
11110
111110
0 0.0
1 1.0
0011111 IOC
0000020000
0111111110
0.1
0.1
1 .0
10.0
1030.
250 250 250 250 250 250
2*7
20 25 30 35 40 45 50 55
0 10.0
-------
CLASS PROBLEM ~ Input data for Run 14
^indicates lines modified or inserted in comparison to base conditions)
ROCKY MT ARSE
1 1 -10
3/3/3/11
20. .001 C.
o 3
3 5
6 a
8 8
9 5
0310 0.2
0510 0.2
0710 0.2
0605 -1.0
1 0.01
n 1 . 1 .
1
0
1
0 1
0 1
0 1.
0 1
0 1
0 1.
0 1.
0 1
0 1.
0 1
40.0
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0.0
1.0
1 .
1 .
1.
1 .
1 .
1.
1 .
1 .
1 .
1 .
1
1
1
1
1
1
0
0
1
1
1
NAL — APPRCXIMAT
132000 1 7
20 100. 0.0 0.0
1000.
1 . 1 1 - i -
1 . 1
1 . 1
1. 1
1 . 1
1 . 1
0 1
0 1
1 . 1
1. 1
1 . 1
1 1
1 1
1 1
1
1
1
1
1
1
1
1
. 1 .
. 1 .
. 1.
. 1 .
. 1 .
. 1.
. 1 .
. 1 .
. 1.
1 .
1 1
1 1
1 1
1 1
1 1
0 1
0 1
1 1
1 1
1 1
1 1
1 . 1
1
1. 1
1 1
0 1
0
1. 1
1
1. 1
1 .
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
5100 4 9 1 1 0 0 0 0
0.02000.2000. 0.3 0.5 1.0
0011111100
0000000000
0111111110
1 0.1
1 1.0
10.0
250 250 250 250 250 250
20 25 30 35 40 45 50 55
0 10.0
-------
CLASS PROBLEM — Input data for Run 18
('indicates lines modified or inserted in comparison to base conditions)
ROCKY «T ARSEM4L — APPROXIMATE SOLUTION •* RETARDATION AND DECAY •*
1 1 10 132COO 1 7 5103 49 12 00001
20. .001 0.20 100. 3.0 0.0 O.C2003.2000. 0.3 0.5 1.0
0.1030CEOO 2.00000500 3.15576E03
t> 3
3 5
4 S
3 6
9 5
031C 0.:
0510 0.2
0710 0.2
06C5 -1.0 1000.
1 0.01
0
C
0
0
0
0
0
0
0
0
0
0
o
3
D
j
0
0
0
0
c
0
1 . 1 . 1.
1 . 1 . 1.
1 . 1 . 1.
1 . 1 . 1.
1 . 1 . 1 .
1 . 1 . 1.
1. 1. 0
1 . 1 . 0
1 . 1 . 1 .
1 . 1 . 1 .
1 . 1. 1.
1. 1. 1.
1. 1. 1.
1. 1 . 1.
1. 1 . 1.
1 . 1 . 1 .
1. 1. 0
1. 1. 0
1. 1 . 1.
1 . 1. 1.
1 . 1 . 1 .
1. 1 . 1.
1 . 1.
1. 1.
1 . 1.
1. 1.
1. 1.
1 . 1.
1. 1.
1. 1.
1. 1.
1 . 1 .
1 . 1.
1
C
1
0
c
0
i.
0
0
0
0
0
0
0
0
0
0
3
0
1
1 .
1
1 .
0.0
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
.0
.0
1 .
1 .
1.
1
1
1
1
1
1
0
0
1
1
1
1 . 1 . 1.
1 . 1 . 1 .
1. 1. 1 .
1111
1111'
1111
1111
1111
1101
1101
1111
1111
1111
1111
.
.
.
0
0
0
0
A
0
0
0
0
0
0
0011111100
0000000000
0111111110
1 0.1
1 1.0
10.0
250 250 25C 250 250 250
20 25 30 35 40 45 50 55
C 10.0
-------
CLASS PROBLEM ~ Input data for Run 19
(*indicates lines modified or inserted in comparison to base conditions)
ROCKY
1
10. .
6 5
3 5
6 o
3 &
? 5
3310 0
0510 0
071C 0
0605 -1
1 0.01
0
0
0
0
0
0
0
0
0
0
0
1 40.0
MT ARSENAL — 10-YR CONTAMINATION + 10-YR FLUSHING
2 10 132000 1 7 5 100 4 9 1 1 0 0
001 0.23 100. 0.0 0.0 C.02000.2000. 0.3 0.5 1.0
.2
.2
.2
.0 1000.
1.
1 .
1.
1.
1.
1.
1.
1 .
1
1.
i .
1. 1.
1. 1.
1 . 1.
1. 1.
1. 1.
1. 1.
1. 0
1 . 0
1 . 1 .
1. 1.
1. i.
,
.
.
B
m
f
f
\ .
i.
i.
. 1. 1.
. 1. 1.
. 1. 1.
. 1. 1.
. 1. 1.
. 0 1.
. 0 1.
. 1 . 1 .
1 . 1 . 1 .
1 . 1. 1.
. 1. 1.
1.
1 .
1.
1.
1.
1.
1.
1 .
1
1.
1.
0
1
0
0
0
0
0
u
0
0
0
0
0
0.
1.
1
1
1
1
1
1
1
1
1
1
1
0
0
0011111
1
1
1
1
1
1
1
1
1
1
1
100
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 C 1
1 0 1
1 1 1
1 1 1
1 1 1
1 1 1
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 o
0000000000
0111111110
1 0.1
1 1.0
10.0
250 250 250 250 250 250
20 25 30 35 40 45 50 55
0 10.0
1
1 1 7 100 4 5 0 0 0
0310 0.2
0510 0.2
0710 0.2
0605 -1.0 10.
10. 0.0 0.0
------- |