USDA
EPA
United States
Department of
Agriculture
Northeast Watershed
Center
University Park PA 16802
United States
Environmental Protection
Agency
Office of Environmental
Processes and Effects Research
Washington DC 20460
EPA-600/7-84-032
March 1984
Research and Development
H
III
- en
Atmosphere and
Temperature Within a
Reclaimed Coal-
Stripmine and a
Numerical Simulation of
Acid Mine Drainage from
Stripmined Lands
Interagency
—Energy/Environment
R&D Program
Report
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ATMOSPHERE AND TEMPERATURE WITHIN A RECLAIMED
COAL-STRIPMINE AND A NUMERICAL SIMULATION OF
ACID MINE DRAINAGE FROM STRIPMINED LANDS
by
D. B. Jaynes, A. S. Rogowski, and H. B. Pionke
U.S. Department of Agriculture, ARS
Northeast Watershed Research Center
University Park, Pennsylvania 16802
EPA-IAG-D5-763
Project Officer
Clinton W. Hall
Office of Energy, Minerals and Industry
Washington, D. C. 20250
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D. C. 20250
U S. Environmental Protection Agency
Region 5, library CPU 2J)
77 West Jackson Boulevard, 12th Ftoqr
Chicago, IL 60604-3590
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ii
DISCLAIMER
This report has been reviewed by the Office of Energy, Minesoils and
Industry, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection
Agency, nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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FOREWORD
The Federal Water Pollution Control Act Amendments of 1972, in part,
stress the control of nonpoint source pollution. Sections 102 (C-l), 208
(b-2,F) and 304(e) authorize basin scale development of water quality
control plans and provide for area-wide waste treatment management. The
act and the amendments include, when warranted, waters from agriculturally
and silviculturally related nonpoint sources, and requires the issuance of
guidelines for both identifying and evaluating the nature and extent of
nonpoint source pollutants and the methods to control these sources.
Research program at the Northeast Watershed Research Center contributes to
the aforementioned goals. The major objectives of the Center are to:
• Study the major hydrologic and water-quality associated
problems of the Northeastern U.S. and
• Initial emphasis is on land uses in the Northeast which
most severely impact surface and subsurface hydrology
and water quality.
Within the context of the Center's objectives, stripmining for coal
ranks as a major and hydrologically severe land use. In addition, often
the site is reclaimed and the conditions of the mining permit are met,
stripmined areas revert legally from point to nonpoint sources. As a
result, the hydrologic, physical, and chemical behavior of the reclaimed
iii
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land needs to be understood directly and in terms of control practices
before the goals of Sections 102, 208 and 304 can be fully met.
Signed:
Harry B. Pionke
Director
Northeast Watershed
Research Center
iv
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ABSTRACT
Oxygen, 0_, carbon dioxide, CO 2 and temperature were measured
with depth along a transect of an acid, reclaimed, coal stripmine
over a two year period. Spoil-atmosphere 0_ concentrations decrease
with depth but approach zero only in a small portion of the transect.
Most of the mine remains well oxygenated (0_ > 10% by volume) down
to 12-meters depth. C0? concentrations ranged from near atmospheric
levels to greater than 15%. At some locations, especially within 2
meters of the surface, variations in 0» and C0_ are correlated with
changes in the spoil temperature. Spoil temperatures in layers
below 3 meters remain in a range conducive to iron-oxidizing
bacterial activity year around. Flux ratios of C0_ and Q~ and the
source/sink rates of the two gases indicate that carbonate neutral-
ization of the acid produced by pyrite oxidation is the dominant
source of CO™.
In a second phase of the study, a numerical model describing
the production and removal of acid and acid by-products from
reclaimed coal-stripmines is presented. Both direct oxygen and
bacterially catalyzed pyrite oxidation is considered. The pyrite
oxidation rate is assumed to be controlled by first-order, solid-
liquid kinetics and simple diffusion of oxidant into reactive,
coarse, stone fragments. Oxygen supply into the reclaimed profile
is considered to be governed by one-dimensional, gas diffusion.
v
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Activity of the iron-oxidizing bacteria is controlled by the ferrous-
ferric ratio, from which they obtain their energy, and from a combination
of potentially inhibiting factors—the oxygen and hydrogen concentrations
and the spoil temperature. Under all conditions modeled, excess acid, in
the form of free hydrogen, must be removed if bacteria are to play an
important role in accelerating pyrite oxidation. Leaching of the spoil
by normal precipitation is insufficient in removing the excess hydrogen.
Neutralization and buffering by the host rock is required for prolonged
bacterial activity—the degree of hydrogen removal determining the
maximum sustainable activity. At optimum conditions, bacteria can greatly
increase pyrite oxidation.
As an offshoot of the diffusion portion of the study a comparison of
Pick's Law for the diffusion of gas, i, in a vapor to the equations based
on the kinetic theory of gases was made. The comparison shows that only
for certain special conditions is the Fickian diffusion coefficient, D^ ,
Fi
independent of the mole fraction of i and the diffusional fluxes of the
other gases. These conditions include the diffusion of a trace concen-
tration of a gas through a gas mixture of any composition and equi-molar
counter-current diffusion in a binary gas mixture, or in a ternary
mixture where the third gas is stagnant. In an 0 , CO., N« atmosphere,
variations in the diffusion coefficient of at least 10% from the tracer
values are possible with variations in the mole fraction or flux ratio.
The temperature and pressure dependence of the diffusion coefficient must
also be recognized.
VI
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CONCLUSIONS
Oxygen, carbon dioxide and temperature measurements within a
reclaimed coal-stripmine indicate that at this site, the spoil
atmosphere is seldom depleted of oxygen despite the continuing
oxidation of pyrite within the spoil." Increases in carbon dioxide
concentrations were correlated with decreases in oxygen concentra-
tions at most depths of each site. Oxygen and carbon dioxide con-
centrations-were significantly correlated with spoil temperature
at several locations but in general the correlation was weak.
Average spoil temperatures to at least 60 cm deep are, in general,
higher than temperatures found in a natural soil. Temperatures in
the spoil below 300 cm remain within the tolerance range of iron-
oxidizing bacteria year round.
We have presented a comprehensive model describing the in situ
oxidation of pyrite and the removal of the oxidation products from
reclaimed coal—stripmines- The rate of pyrite oxidation is assumed
to be controlled by both the reaction kinetics and the diffusion
rate of the products and reactants to the reaction site, where both
oxygen and ferric iron may serve as the oxidant. Ferric iron' con-
centrations are controlled by iron complexation and precipitation
reactions which are assumed to be rapid. The only important source
of ferric iron is oxidation of ferrous iron by iron-oxidating
vii
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bacteria. This model is unique in that the "activity" of the bacteria,
which determines the rate of ferric iron production, is calculated from
the energy available from the energy substrate and the deviation of the
bacterial environment from ideal growing conditions. Pyrite oxidation
and bacterial "activity" are linked through their modification of a
shared environment.
Simulations, using the model, indicate that the lack of oxygen is
the primary rate controlling factor in both pyrite oxidation and atuo-
trophic bacterial "activity." In zones where oxygen is not limiting,
autotrophic activity can greatly increase the rate of pyrite oxidation.
Whether or not bacteria are important in these zones, depends on the
solution pH. The oxidation rate of pyrite will be affected by
bacterially produced ferric iron only if the solution pH can be
maintained in the range between reduced bacterial efficiency (pH > 2.0)
and reduced ferric iron solubility (pH < 3.0). The interaction between
hydrogen, produced by pyrite oxidation, and the rock matrix appears to
be crucial in establishing the pH of the spoil solution.
Extensive testing of the model was not possible at this time,
although its behavior seemed consistent with our current knowledge
of acid formation in spoils. Further refinement of the model is
necessary. The model is very sensitive to changes in the gas dif-
fusion properties of the spoil. Although this property has been
2
measured for spoils in the laboratory (Colvin, 1977) , field-based
measurements, capable of incorporating the great heterogeneity of
reclaimed spoil, would be desirable. The values of E'. , x_, x TT
min T pH
and x_ , although based on experimental data, represent only best
estimates. Laboratory experiments designed specifically to
viii
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determine these values and the form of their mathematical relationship
would help establish the validity of the autotrophic "activity" model
and the magnitude of the model parameters.
In view of the extreme sensitivity of the autotrophic "activity" to
solution pH, the interaction of rock matrices with acid needs further
study. These interactions are complex and varied mainly due to the wide
range of minerals and reactions possible and the slow reaction kinetics
associated with most interactions. It may be possible to develop a
simple analytical technique, similar to that used to measure the acid
potential of spoil (Caruccio, 1968), that combines all of the
neutralization reactions into a simple empirical representation.
Carbonate neutralization was considered separately in this model because
of the great potential these materials represent for acid consumption.
Further research on the reaction kinetics of carbonates, incorporating
the effects and the development of iron coatings and diffusion control
of reactants needs to be pursued.
IX
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CONTENTS
Page
Foreword ............................ iii
Abstract . . . ......................... v
Conclusions ........................... vii
Figures ............................. xii
Tables ............................. xvi
Notation for Section 2 ..................... xviii
Notation for Section 3 ..................... xix
Notation for Section 4 ..................... xx
Notation for Appendix A ..................... xxv
Notation for Appendix B ..................... xxvii
1. Introduction ...................... 1
References .................... 4
2. Spoil Atmosphere and Temperature in a Reclaimed
Coal Stripmine ..................... 6
Introduction ................... 6
Materials and Methods ............... 8
Results ...................... 16
Discussion .................... 31
References .................... 36
3. Flux and Production Rates of Oxygen and Carbon
Dioxide in a Reclaimed Coal-Stripmine ......... 39
Introduction ................... 39
Theory ...................... 42
Materials and Methods ............... 44
Results and Discussion .............. 48
Conclusions .................... 55
References .................... 58
4. A Numerical Model of Acid Drainage from Reclaimed
Coal-Stripmines .................... 60
Introduction ................... 60
Description of Model ............... 62
Basic Reactions ............... 62
Basic Equations ............... 63
Oxygen Diffusion ............... 69
Chemical Species ............... 83
Ferric Precipitation .......... 84
Ferric Complexes ............ 85
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Page
Removal of Reaction Products . 86
Acid Neutralization. . . . 86
Leaching 90
Solution Method 93
Results and Discussion 97
Role of Iron Oxidizing Bacteria 97
Model Sensitivity and Versatility 112
Effective Diffusion Coefficient 112
Pyrite Distribution 119
Inhibition of Bacteria 123
Carbon Dioxide Generation 125
References 129
Appendices
A. Applicability of Pick's Law to Gas Diffusion 135
B. Parameter Values Used in the Pyrite Oxidation
Model . 160
C. Computer Listing and Example Output of Acid Mine
Drainage Model 173
XI
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LIST OF FIGURES
Figure PaSe
1 Location of monitoring sites 1-6 and the depth of
the gas sample-chambers (crossbars) at each site
in relation to the strip-mine stratigraphy ..... . 11
2 Schematic of gas sample-chambers design ...... . 12
3 Schematic of CL measuring-chamber used in the field 14
4 Variation of temperature { C) over time for six
depths at site 2. Depths shown are (A) 30cm,
60 cm, (o) 170 cm, (o) 320 cm, (A) 625 cm and (•)
945 cm . ...................... 20
5 Variation of temperature ( C) and the mole fractions
of 0_ and C02 over time for the composite record at
site 1. The temperature plot is shown as a line
connecting the individual data points for clarity . 22
6 Variation of temperature ( C) and the mole fractions
of Q£ and C02 over time for the composite records at
site 2. The temperature plot is shown as a line
connecting the individual data points for clarity . 23
7 Variation of temperature ( C) and the mole fractions
of ©2 and C02 over time for the composite record at
site 3. The temperature plot is shown as a line
connecting the individual data points for clarity . 24
8 Variation of temperature ( C) and the mole fractions
of 02 and C02 over time for the composite record at
site 4. The temperature plot is shown as a line
connecting the individual data points for clarity . 25
9 Variation of temperature ( C) and the mole fractions
of 02 and C02 over time for the composite record at
site 5. The temperature plot is shown as a line
connecting the individual data points for clarity . 26
10 Variation of temperature ( C) and the mole fractions
of 02 and C02 over time for the composite record at
site 6. The temperature plot is shown as a line
connecting the individual data points for clarity . 27
XII
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List of Figures (Continued)
Figure Page
11 Schematic of spoil profile showing the division of
the profile into layers as determined by the depths
of the gas concentration measurements, Y and Y _ .
Fluxes, Nn and N . , are calculated for 2 2
°2 C°2
the top of each layer and assumed to' be 0.0 at the
profile bottom. Source terms, Q. and Q . , are
calculated for each layer. . . . 2 • . • • 2 • • • • ^'
12 Cross section of a coarse fragment containing
pyrite ........................ 64
13 Plots of the inhibition factors (solid lines) .
a) XT- versus termperature (°C) ; dashed line is
normalized data from Malouf and Prater, 1961;
(o) normalized data from Silverman and Lundgren,
1959; (A)normalized data from Belly and Brock,
1974. b) Xpg versus pg; (») normalized data from
Silverman and Lundgre, 1959; (A) normalized data
from Schnaitman, et al . , 1969. c) XQ versus
oxygen mole fraction ..... . ... 2 ....... '°
14 Neutralization curves as calculated from equation
in text. Gg equals 1.0 in both plots. G^ equals
2.5 in plot 1 ( •) and 2.8 in plot 2 (• ) ...... 91
15 Example leaching curve shows the normalized con-
centration versus water— filled pore volumes.
Profile was 10 meters deep, divided into 20 layers
with a water-filled pore volume of 0.13 and an
infiltration rate of 50 cm/year ........... 94
16 Fraction of pyrite oxidized within entire profile
versus time for Run 1 and Run 2 ........... 98
17 The rate of leaching out of the profile of all iron
species versus time for Run 1 and Run 2 .......
xiii
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List of Figures (Continued)
Figure Page
18 Oxidation rate of pyrite for each layer after 5
years of oxidation. Fine cross-hatching is total
oxidation rate for Run 1. Open cross-hatching is
. rate of oxidation by direct osygen reaction with
pyrite in Run 2. While cross-hatching on black
is oxidation rate due to ferric iron reaction
with pyrite in Run 2. Below 1 meter, ferric
oxidation is negligible. Below 4 meters, oxida-
tion rate of Run 1 and Run 2 are identical ..... 102
19 The ratio of ferric iron to ferrous iron in the
water leaving the profile for Run 1 and Run 2.. . . 103
20 Fraction of pyrite oxidized within entire
profile versus time for Runs 2, 3 and 4 ...... 105
21 The rate of leaching out of the profile of all iron
species versus time for Runs 2, 3 and 4 ...... 107
22 The rate of leaching out of the profile of the
potential and active acid for Runs 3 and 4 ..... 110
23 Fraction of pyrite oxidized within entire profile
versus time for Run 3 and Run 5 .......... HI
24 Fraction of pyrite oxidized within entire profile
versus time for Runs 3, 6 and 7 ..........
25 -The rate of leaching out of the profile of all
iron species for Runs 3, 6 and 7 .......... 116
26 The mole fraction of oxygen within the. profile
versus depth (m) after 5 years for Runs 1 and 6 . . 117
27 The mole fraction of oxygen within the profile
versus depth (m) after 5 years for Runs 3 and 7 . . 118
28 The distribution of pyrite (wt./wt.) with depth (m)
for a) Run 3; b) Run 8; c) Run 9 .......... 120
xiv
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List of Figures (Continued)
Figure Page
29 Fraction of pyrite oxidized within entire profile
versus time for Runs 3, 8 and 9 121
30 The mole fraction of oxygen within the- profile
versus depth (m) after 10 years for Runs 8 and 9. 122
31 The rate of leaching out of the profile of all
iron species for Run 7 (no inhibition) and Run
10 (complete inhibition after 2 years) 124
Al Values of the reduced Fickian diffusion coeffici-
ent, Dp , in a binary gas mixture plotted against
the gas^ mole fraction of component i. Curve
labels are the values of the flux ratio, r.., for
which the curve was calculated 143
A2 Values of the Fickian diffusion coefficient, D ,
for 0? in an O^-CO^-U- atmosphere (in m /sec) .
The N_ mole fraction is held constant at 0.790,
while the 02 mole fraction, plotted on the
abscissa, is varied between 0.0- to 0.21. C07
comprises the balance of atmosphere. Values
are for 20°C and 101 KPa with the N,, flux being
set to 0.0. Curve labels are the values of the
flux ratio r _ ,0,,. Point represents value cal-
culated in 2 text 149
A3 Values for the Fickian diffusion coefficient, D_,
for C02 in an 02~C02-N2 atmosphere (in m^/sec).
The N2 mole fraction is held constant at 0.790,
while the 02 mole fraction, plotted on the
abscissa, is varied between 0.0 and 0.21. C0~
comprises the remainder of the atmosphere.
Values are for 20°C and 101 KPa with the N2
flux being set for 0.0. Curve labels are the
values of the flux ratio r^- , 0-• Point repre-
sents value calculated in 2 text 150
xv
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LIST OF TABLES
Table Page
1 Mean and range of selected properties of the spoil
and drainage waters from the reclaimed stripmine
used in this study 9
Average, maximum and minimum values for 0~ and C0_
concentrations and temperature.for each depth of
sites 1-6 17
Correlation, r, and regression coefficients, a and
b, between the mole fractions of CO- and decreased
02 (0.210-YQ ) for each depth at sites 1-6 29
Correlation coefficients, r, between the mole frac-
tion of CO- and temperature between the mole
fraction of C02 and temperature for each depth at
sites 1-6. ,,,,.,,,.,,,,,,, 30
Pyrite and sulfate concentrations expressed as
percent by weight sulfur for ten representative
spoil layers from research site (Rogowski, 1977).
Also, the C0_ equivalent of the carbonate content
required to neutralize the acid produced from
columns 2 and 3 and the measured carbonate content
expressed as C0_ (columns 4 and 5). The last column
gives the ratio CO- measured/C02 required in percent. 41
Means and coefficients of variation, C.V., for 0~
and C0£ fluxes at the surface of the six sites and
for all sites combined. The ratio of the fluxes,
r = N _ /Nn , was calculated from the mean values. . 49
" OUn U_
Mean values and coefficients of variation, C.V., of
the source terms for D£ and C02 and for the ratio
rq = QQQ at the individual depths at each site.
The correlation between Q n and Q , r, is also
listed .2. . . U.2 52
Mean values and coefficients of variation, C.V., for
the production rate of 0» and CO- and for their
ratio, r_ = QCQ /QQ . Rates are for the entire spoil
profile at each site averaged over time 56
xvi
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List of Tables (Continued)
Table Page
9 Coefficients used to calculate typical values of
t and t, . . . 68
c d
10 Measured IL, values and calculated X_, Xn , X „ and
M T 0_ pH
E . values from phase II of experiment run by
mm 4
Bailey (1968)* 81
11 Measured and calculated coefficients for the
bacterial "activity" model from phase I of experi-
ment run by Bailey (1968)^ 82
12 Iron complexes and log of the equilibrium constants
for their formation and for sulfuric acid dissoci-
ation and amorphous ferric hydroxide precipitation. 87
13 Ratio of the flux of CO to 0^ for Run 12 (hetero-
trophs active in layer I only;, Run 13 (hetero-
trophs active in layer 20 only) and Run 14 (acid
neutralization by carbonates in layer 20) 128
*
Al Coefficients for calculating D.. for gas pairs of
interest in research (after Marrero and Mason,
1972). Coefficients were fit to data over the
temperature range'shown. The uncertainty in the
calculated values is for the lower end of the
temperature range listed 154
Bl K values for Fe and 09 systems 164
5 ^
xvii
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NOTATION FOR PART II
a,b empirical constants,
a activity of H-CO, moles
H2C03
pCO- partial pressure at CO-, atmosphere (101 kPa)
r correlation coefficient, -
T temperature, K
T_n temperature at 30 cm depth, K
X mean value, (variable)
Yn? mole fraction of oxygen, -
Y - mole fraction of carbon dioxide, -
co2
xviii
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NOTATION FOR PART III
C.V. coefficient of variation, -
2
D Fickian diffusion coefficients for component, cm /sec
i
DZ weighing factor, cm
-2 -1
N. flux rate of component i, moles-cm -sec
P total pressure, kPa
Q. source term for component i, moles-cm -sec
r flux ratio, r = N n /N , -
n n oU- u_
r source ratio, r * Q n /Qn , -
q q CU2 U2
R gas constant, kPa-cm -mole -k
t time
T temperature, K
X mean
Y. mole fraction of component i
Z depth, cm
T tortuosity, -
3 3
$ air-filled porosity of spoil, cm /cm
xix
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NOTATION FOR PART IV
A fragment surface area per volume spoil water, cm
b stoichiometric ratio between pyrite and oxidant
consumption, -
C ff normalized concentration of solute, in effluent, -
C. normalized concentration of -solute in layer i, -
C normalized concentration of solute in influent, -
in
C oxident concentration at the fragment surface,
ox moles /cm-*
d. distance between layers, cm
D effective diffusion coefficient for coupled oxidant-
c ' product counter diffusion, cm^/sec
Dn effective diffusion coefficient for 0- in an Q~, N~
2 and C0» atmosphere, cm^/sec
D diffusion coefficient at 0~ water, moles-cm -sec
*Vi rn ^n binary diffusion coefficients for the gas pairs 0»
°2' 2' 2' and C00, 0~ and N0 and C00 and N0, respectively
_ o,z/ / z /
D _ cm^/sec
E electromotive force, volt
E energy per unit time available to bacterial
population, W
E energy per unit time available to bacterial popu
lation for growth, W
E energy per unit time available to bacterial popu
lation for maintenance, W
E , energy per mole of electrons oxidized available
to bacterial population, measured as a driving
force, volts
xx
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Notation for Part Iv (Continued)
' minimum energy per mole of electrons oxidized re-
min quired to sustain bacterial population, measured
as a driving force, volts
F the Faraday, C
3+
Fe total iron concentration (all species), moles/L
FFR fraction of coarse fragments in spoil, g/g
FPY fraction of pyrite in coarse fragments, g/g
G ,G empirical constants, -
I ionic strength, moles/kg
K first-order surface reaction rate constant for pyrite
oxidation per unit surface area of pyrite, cm/sec
K equilibrium constant for chemical reactions, -
K_ first-order reaction rate coefficient for bacterial
oxidation of ferrous iron, sec
K first-order surface reactioiurate constant for
carbonate dissolution, L-cm -sec"
K solubility constant for amorphous iron hydroxide, -
sp
IC.,K2 reaction coefficients_for chemical oxidation of
ferrous iron, mole -L -sec"1 and sec~l,
respectively
H one-half thickness of fragment, cm
MW molecular weight of pyrite, g/mole
Nn , N _ ,Nn gas flux of oxygen, carbon dioxide and nitrogen,
2 22 respectively, moles-cm~2-sec~l
P total pressure, kPa
Q oxygen source term, due to iron-oxidizing bacteria,
moles-cm~3_sec-l
xxi
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Notation for Part IV (Continued)
Q rate of carbonate consumption per surface area of
carbonate, moles-cm~^-sec~^
Q oxygen source term due to chemical oxidation of
ferrous iron, moles-cm~3-sec~^-
Q oxygen source term due to heterotrophic respira-
tion, moles-cm~3-sec~l
Q base rate of oxygen consumption from heterotrophic
H KB . _ o _1
respiration, moles-cm -'-sec -1-
Q total oxygen source term, moles-cm -sec
0 oxygen source term due to direct pyrite oxidation
*^ by oxygen, moles-cm~3_sec~l
'r ,r2 ratios of the fluxes of CO , 0_ and N2 to 02,
respectively, -
R gas constant, cm -KPa-mole -K
R rate at which bacterial population oxidizes iron,
moles of electrons/sec
R radius of carbonate particles, cm
D
t time, sec
t_ time required for complete pyrite oxidation if
chemical reactions are the rate controlling
process, sec
t total time required for complete pyrite oxidation
if diffusion processes are the rate limiting
steps, sec
T temperature, K
x. general inhibition factor, -
x ,x TT,X_ inhibition factors dependent on temperature, pH,
^ 2 and oxygen concentration, respectively, -
x fraction of pyrite remaining in a fragment, —
xxii
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Notation for Part IV (Continued)
x fraction of carbonate particle remaining, -
U
Y mole fraction of oxygen in spoil atmosphere, -
z d ep th, cm
z. . charge of the 9th chemical species, -
a surface area of pyrite per unit volume fragment, cm
T..,T2,Y_ activity coefficients for H , Fe and Fe ,
respectively
8 effective thickness of pyrite within which pyrite
is oxidized
A£", thickness of water film covering fragments, cm
AG energy released in iron oxidation, J
AG change in standard free energy, J
K.
AH actual increase of H in solution, moles
AH H produced through chemical reactions, moles
II product operator
p bulk density of spoil, g/cm
B
p_ molar density of carbonate in carbonate spheres,
moles/cm^
p molar density of oxygen in the vapour phase,
2 moles/cm
P molar density of pyrite in fragments, moles/cm
I. summation operator
T tortuosity of gas diffusion path, -
xxiii
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Notation for Part IV (Continued)
<|> air-filled porosity, cm /cm
A.
3 3
water-filled porosity cm /cm
w
[] concentration operator, moles/L
xxiv
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XXV
NOTATION FOR APPENDIX A
a,b,c semi-empirical constants
C. concentration of gas component k, kg m
v.,v. average velocity of gas i and j, respectively, m sec
D Fickian diffusion coefficient for component i,
i m^ sec~l
2 -1
D.. binary diffusion coefficient, m sec
D. . temperature dependent, pressure independent binary
^ diffusion coefficient, kPa m^
2 -1
D coefficient of thermal diffusion, m sec
F.,F. external force field acting on gas i and j, N/Kg
m.,m. mass of molecules of gas i and j, respectively, Kg
M Avagadrops number, mole -1
o
n.,n. number density of gas i and j, respectively, m
nm = n.-hn.
T i j
-2 -1
N. molar flux of gas i, moles m sec
P total pressure, KPa
_2 —]_
q. mass flux of gas i, kg m sec
r direction vector, m
R universal gas constant, m KPa mole K
r.. flux ratio, - N.N.
Ji Ji
t time, sec
T absolute temperature, K
Y. mole fraction of component i
xxv
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z distance or depth, m
a combined air-filled porosity, tortuosity term
II product operator
p.»P.»PT density of gas i, j and the combined gas density
^ respectively, Kg m~3 '
£ summation operator
xxvi
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NOTATION FOR APPENDIX B
b shorthand notation, see text
3
C concentration, moles/cm
3
C.,C- integration constants, moles/cm
C concentration at the leached rim - oxidation zone
interface, moles/cm^
C, C1, C- shorthand notation, see text
C. same as C_ , moles/cm
jL &
2
D diffusion coefficient in the spoil fragment, cm /sec
c
FFR fraction of spoil mass composed of coarse fragments, -
FPY fraction of fragment mass that is pyrite, -
K first order reaction coefficient for pyrite oxidation
s per unit area, cm/sec
£ one-half fragment thickness, cm
£' thickness at leached rim, cm
-3 -1
R reaction rate per fragment volume, dx, moles-cm -sec
R total reactionrate per unit surface area of fragment,
moles-cm -sec
X thickness, cm
a surface area of pyrite per unit volumn of fragment, cm
3
p bulk density of spoil, g/cm
B
p molar density of pyrite in fragment, moles/cm
py
3 3
4>A air-filled porosity in spoil, cm /cm
3 3
water-filled porosity in spoil, cm /cm
w
T tortuosity of diffusion path is spoil, -
xxvii
-------
-------
SECTION 1
INTRODUCTION
The United States has the most extensive deposits of coal in
the world. The rate at which we mine this coal must accelerate in
the next century if we are to satisfy our increasing energy appetite
and decrease our reliance on foreign sources of energy. Much of
this coal will be mined by surface operations, such as stripmining.
Stripmining will disturb millions of acres of land; land that must be
restored if it is to become productive again. Unfortunately,
reclaimed stripmines in the humid eastern United States have a
tremendous potential for both acute short-term and significant long-
term pollution of surface streams and lakes and subsurface aquifers
(Collier et al., 1970). Water leaving many reclaimed stripmines
contains acid, iron, sulfates and other constituents at levels far
exceeding their concentration in natural waters. Agnew and Corbett
(1973) found a large increase in the acidity of water draining from
stripmined lands, especially during "flush outs" (large stream flows)
caused by periods of heavy rain. Striffler (1973) found similar
results for eastern Kentucky stripmine waters and concluded that
primary watersheds, those directly draining stripmined areas, have a
serious problem. Caruccio (1973), among others, has measured acid
water draining from stripmine sites to have pH's as low as 2.8. At
such low pH's, Warner (1973) found a severe decrease in stream
invertebrates and algae populations and Kinney (1964) documented the
adverse effects on fish and other vertebrates. Even though acid
-------
pollution of streams caused a decrease in the stream biota, it does not
directly cause any visual degradation. Iron pollution, on the other
hand, can be readily observed when it precipitates in surface waters to
color them from red to yellow-orange. These stairiings, commonly
referred to as "yellow-boy," can greatly impact the scenic value of
streams in the Appalachian coal region.
Fortunately, the amounts of pollutants leaving a mined area can be
considerably reduced if proper reclamation techniques are used (Grimm
and Hill, 1974). However, we can intelligently develop these proper
reclamation techniques or best management practices only if we under-
stand the basic physical and chemical processes that lead to acid
drainage. Researchers have been intensively investigating acid drainage
problems for more than 50 years. A synopsis of their finding can be
found in many articles including review papers by The Ohio State
University Research Foundation (1971) and Rogowski et al. (1977). A
crucial area of the acid drainage problem in reclaimed stripmines that
has not received sufficient attention is the oxygen status of the mine
environment (Ohio State University Research Foundation, 1971). The
first portion of this research was to investigate the oxygen status of
a reclaimed stripmine. The results from this part of the study are
presented in Part II. Part II expands upon the oxygen concentration
findings and presents calculations of the oxygen and carbon dioxide
gas fluxes and the related rates of consumption and production of these
gases within the reclaimed mine spoil.
-------
Another productive avenue for developing best reclamation techniques
is to develop and use mathematical models that describe the acid drainage
process. A model, based on basic chemical and physical processes, can
serve as a useful tool for identifying and gaining insight into the
important, rate controlling processes of acid drainage. A model that
accurately predicts the behavior of actual stripmines can be used to
develop alternative reclamation techniques where the consequences of each
modification can be tested rapidly and inexpensively. Part IV presents
the development of a general model for acid formation and leaching from
reclaimed coal stripmines.
Included in the appendices is a review of the process of gas diffu-
sion in the vapor phase and a listing of the magnitude and derivation of
some of the parameters used in the model for acid drainage. Also listed
in the appendices is a listing of the FORTRAN program of the model and
example output for the program.
-------
-------
REFERENCES
1. Agnew, A. F. and D. M. Corbett. Hydrology of a Watershed Containing
Flood-Control Reservoirs and Coal Surface-Mining Activity,
Southwestern Indiana. In: Ecology and Reclamation of Devastated
Land, R. J. Hutnik and G. Davis, eds. Gordon and Breach, New York,
1973. pp. 159-174.
2. Caruccio, F. T. Characterization of Strip-Mine Drainage by Pyrite
Grain Size and Chemical Quality of Existing Groundwater. In:
Ecology and Reclamation of Devastated Land, R. J. Hutnik and G.
Davis, eds. Gordon and Breach, New York, 1973. pp. 193-226.
3. Collier, W. R., R. J. Pickering, and J. J. Musser. Influences of
Strip Mining on the Hydrologic Environment of Parts of Beaver Creek
Basin, Kentucky, 1955-56. U.S. Geological Survey Professional
Paper 427-C, 1970.
4. Grimm, E. C. and R. D. Hill. Environmental Protection in Surface
Mining of Coal. EPA-670/2-74/093, Environmental Protection
Technology Series, U.S. Environmental Protection Agency,
Cincinnati, Ohio, 1974. pp. 1-277.
5. Kinney, E. C. Extent of Acid Mine Pollution in the United States
Affecting Fish and Wildlife. U.S. Department of the Interior,
Bureau of Sport Fisheries and Wildlife Circular 191, 1964.
6. Ohio State University Research Foundation. Acid Mine Drainage
Formation and Abatement. Water Pollution Control Research Series
Program 14010 FPR, U.S. Environmental Protection Agency,
Washington, D.C.
-------
7. Rogowski, A. S. , H. B. Pionke, and J. G. Broyan. Modeling the Impact
of Strip Mining and Reclamation Processes on Quality and Quantity of
Water in Mined Areas: A Review. J. Environ. Qual., 6:237-244, 1977.
8. Striffler, W. D. Surface Mining Disturbance and Water Quality in
Eastern Kentucky. In: Ecology and Reclamation of Devastated Land,
R. J. Hutnik and G. Davis, eds. Gordon and Breach, New York, 1973.
pp. 175-192.
9. Warner, R. W. Acid Coal Mine Drainage Effects on Aquatic Life. In:
Ecology and Reclamation of Devastated Land, R. J. Hutnik and G.
Davis, eds. Gordon and Breach, New York, 1973. pp. 227-238.
-------
SECTION 2
SPOIL ATMOSPHERE AND TEMPERATURE IN A
RECLAIMED COAL STRIPMINE
Introduction
Within the past two decades, the problems caused by acid-
drainage from reclaimed coal stripmines in the eastern United States
have been the focus of numerous studies. These studies have shown
the primary source of acid to be the oxidation of the iron sulfide
mineral, pyrite. Two mechanisms for pyrite oxidation have been
demonstrated (Ohio State University Research Foundation, 1971) . The
first involves oxygen reacting directly with pyrite and water and
is summarized in Eq . [1] .
+ 3.5 02 + H20 + Fe + 2S0" + 2H [1]
The second mechanism, shown in Eq. [2], uses ferric iron as the
electron acceptor.
14Fe3+ + FeS2 + 8H2
-------
1968). Thus Eq. [2] is considered to be bacterially catalyzed
within acid stripmine spoils because the ferric iron is produced by
Eq. [3]:
bacteria
14Fe + 14H + 3.5 02 > 14Fe + 7H20 [3]
Summing Eqs. [2] and [3] gives Eq. [1], thus regardless of mechanism,
the result of pyrite oxidation is the same; two moles of H are
produced for every three and one-half moles of oxygen consumed..
Moreover, significant oxidation of pyrite cannot take place far from
the presence of gaseous 02 because of the slow diffusion rates of Q~
in water (Ohio State University Research Foundation, 1971). Thus,
the presence of oxygen in the spoil atmosphere is critical for in
situ oxidation of pyrite.
The temperature of the spoil environment is also critical in
determining the oxidation rate of pyrite. The rate of direct pyrite
oxidation by 0» and thus 0? consumption increases with temperature
(Clark, 1965). Autotrophic bacteria are also sensitive to temperature
showing maximum activity at temperatures near 30 C and almost no
activity for temperatures below 4 C and above 55 C (Malouf and
Prater, 1961; Ehlrich'and Fox," 1967; Cathles and Ap'ps, 1975).
Although the mechanics of pyrite oxidation and leaching have
been studied for years, almost no information is available on the
environmental status of reclaimed stripmines (Ohio State University
Research Foundation, 1971). As part of a comprehensive investigation
of the chemical and physical processes of a reclaimed stripmine, we
measured temperatures and spoil atmosphere compositions over an ex-
tended period of time and for the entire depth of the mine site.
-------
Materials and Methods
Oxygen, carbon dioxide and temperature profiles were measured
within a reclaimed bituminous coal stripmine. The sparsely grassed
mine-site, located in Clearfield County, west-central Pennsylvania,
has been described in detail elsewhere (Pedersen et al., 1978;
Pedersen et al., 1980; Pionke and Rogowski, 1980). The mine was
developed in Pennsylvanian-age deposits. Two coal seams were mined
at the site, the middle Kittanning (C) coal seam and the lower
Kittanning (B) seam that underlies the C. Noncalcareous, thin bedded
sandstones and shales overlay the middle Kittanning seam while
predominantly silt stones and shales overlay the lower seam. High
pyrite contents are usually associated with the shale layers (Rogowski,
1977; Lovell et al., 1978). Typical values of some of the important
properties of the mine spoil and drainage waters are shown in Table 1.
All the parameters vary greatly, but the water draining the site has
been consistently low in pH and high in acidity indicating that pyrite
oxidation and leaching are taking place.
In the first 10 months of the study, the spoil atmosphere composi-
tion was monitored at four locations along a transect of the mine
(sites 1-4, Fig. 1). Site 1 was located in an area between two strip-
mines composed of 440 cm of spoil overlying unmined, coal-bearing
strata. Site 2 was placed in 1250 cm of spoil from Kittanning B-seam
and sites 3 and 4 were placed in 700 and 1060 cm of spoil from the
Kittanning C-seam. In general, the shale and pyrite content of the
spoil decrease from sites 1-4, while the vegetation cover increases
from virtually 0.0 to 3.2 metric tons/ha (Pionke and Rogowski, 1980).
-------
Table 1. Mean and range for selected properties of the spoil and
drainage waters from the reclaimed stripmine used in
this study'.'
Spoil property x
% pyritic S 0.18
(st/wt)
bulk density 1,560
(kg/m3)
% coarse fragments 78
(wt/wt)
% carbon 4.4
(wt/wt)
pH 4.9
(1:1 spoil-water
extract)
acidity 16.4
(meq/100 g)
Drain-water property x
PH 2.8
acidity 15 . 0
(meq/L)
range
0.02
640-1,790
54-93
0.4-22.8
3.7-6.0
4.0-24.0
range
2.3-3.7
9.0-19.0
'Data from Pedersen, et al., 1978; Pedersen, et al., 1980;
Rogowski, 1977; Rogowski, et al., 1982; and Rogowski, A. S.,
personal communication.
-------
At each site, a 15 cm (6 in) diameter bore-hole was drilled with
a standard well-drilling rig down to or slightly deeper than the
deepest extent of the stripmining process; a depth of between 870 and
1250 cm. Five or six gas-sampling chambers were placed at selected
depths between 150 cm of the surface and the bottom of each bore-hole
(Fig. 1). After location of the chambers, the bore-holes were
backfilled a few centimeters at a time; each layer being packed with
a metal rod. Clean, coarse, silica sand was placed around each chamber
with a 10-cm thick bentonite berm placed above the sand. The remaining
space between samplers was filled with spoil material that had been
screened to remove stone fragments. Two additional holes were drilled
at sites 1-4 with a Giddings soil auger . The holes were 5 cm in
diameter, 30 and 50 cm deep. Each hole was fitted with a gas sampler
and backfilled as described above.
After the first 10 months of monitoring, two additional sites
were added. Site 5 was located close to the buried highwall of
the Kittanning B-seam. Site 6 was placed in an adjacent area
overlying the unmined Kittanning B seam where the top 30 cm were
composed of disturbed spoil material.
Design of the gas samplers is shown in Figure 2. The samplers
consisted of an 8.25-cm chamber of either 2.5- or 5-cm (1- or 2-in)
diameter pvc pipe. A series of 0.48-cm (3/15-in) holes were drilled
The mention of trade names does not constitute an endoresement of
the product by the U.S. Department of Agriculture over other
products not mentioned.
10
-------
340
EZ2 Unmlned-Dliturbed
CD B-Stripped
C-Strlpped, B-0«ep Mined
Reclaimed Spoil\
300
Figure 1. Location of monitoring sites 1-6 and the depth of the gas sample-chambers
(crossbars) at each site in relation to the stripmine stratigraphy.
-------
Nylon Tubing
Wire Lead
to Meter
\ 1.1 r'
— Plastic Fastener
Rubber Stopper
—5.1cm OD PVC
(2 in)
/Rubber-backed Tape
-PVC Coupling
-Rubber Stopper
-0.48cm (3/16") Holes
—Thermocouple
-Nylon Screen
—PVC End Cap
Figure 2. Schematic of gas sample-chambers design.
12
-------
in each sample-chamber and were screened with a medium-mesh, nylon
screen. The chambers were coupled to lengths of pvc pipe so that
they could be placed at the desired depth. The sample-chambers were
connected to the surface by a 0.64-cm (0.25-in) diameter nylon tube.
At the surface, this tube was capped with a rubber septum except
when gas samples were withdrawn. Each sample-chamber was also
equipped with a thermocouple so spoil temperatures at each site could
be measured. The thermocouple consisted of a 0.082-cm (0.032-in)
diameter, copper/constantin, low-temperature element (Omega Engin-
eering, Type T) silver soldered to 24-gauge, copper/constantin,
unshielded wire (Omega Engineering, Type T Poly Rip Control).
Soldered connections were protected by ceramic insulators. Each
thermocouple was calibrated before installation. Temperature was
measured directly using a Leeds and Northrop detector (Model 934
Numatron Digital Thermocouple Recorder, Type T, battery operated).
An ice-water bath was used as a reference temperature when measure-
ments were made.
Oxygen, carbon dioxide and temperature were measured at each
sampler periodically (approximately every month). -Initially, oxygen
and carbon dioxide concentrations were measured in the field
independently of each other. A gas sample was obtained by connect-
ing the gas chamber access tube to a rubber bulb equipped with one-
way valves. The bulb was used to pump air out of the gas samplers.
For oxygen measurements, gas was pumped into a measuring chamber
(Fig. 3) equipped with a dissolved oxygen probe (Lazar Research Labs,
13
-------
f
5
<
c
a
Temperature
Probe -j
Rubber | V
Stopper^ II
1
j
3
/
i
^
1
! ' '/
l i \L
i i y -
/ ' '
J
n '
1 \:
To
Millivolt Meter
,Dissolved-Oxygen Probe
SAMPLE CHAMBER
I I
7.5cm 00 PVC
(3*)
0.6cm Plastic
Tubing
0
-
>
o
— Holes
GAS TRAP
- nil
25 ml Vial
Tubing
From Pump
Figure 3. Schematic of C>2 measuring-chamber used in the field.
14
-------
Inc., Model 00-166 Dissolved Oxygen Probe). Sufficient gas was
pumped from the gas sampler to ensure a representative sample in the
measuring chamber as indicated by steady 0_ readings. The required
gas volume was approximately 1.6 liters, which corresponded to
removing gas from a 9.4-liter spoil volume (1.5 g/cm bulk density,
70% saturation) or a 26-cm diameter sphere centered at each probe.
Oxygen levels were read directly from a millivoltmeter (Orion
Research, Model 407A), which had been calibrated for 0_ concentrations
in air (21% 0_) and bottled N_ gas (0% 0-). C02 concentrations were
measured by pumping a gas sample directly into a Lab-Line CO- Analyzer
(Lab-Line, Inc.) which gave the CO 2 levels directly in percent.
For the past twelve months of the study, CO- and 0,., concentra-
tions were measured in the laboratory. Field measurements were dis-
continued because the technique did not allow for measurements in the
winter. For laboratory measurements, gas samples were collected in
air tight bottles (150 ml volume), returned to the lab and measured
with a gas chromatograph (Varian Aerograph, Model 1820) as described
by Bollag and Barabasz (1979). The laboratory and field techniques
were correlated with each other and found to be in good agreement
for both 0- and C0~ measurements.
Statistical analysis was performed using standard procedures.
Duncan's new multiple-range test, adjusted for unequal sample size,
was used to compare the means of 0~ and C0_ for each layer at each
site (Steel and Torrie, 1960, p. 114). Homogeneity of regression
equations was tested as described by Steel and Torrie (1960, p. 319).
15
-------
Results
Average, maximum and minimum values for O-* CO 2 and temperature
for each depth at the six sites are shown in Table 2. The average
mole fraction of 09 ranged from 0.010 to 0.207, while the range in
individual values was between atmospheric levels (0.210) to below
the detection limit (< 0.001). Considerable variation in measured
values was found for most layers. Several layers near the surface
had variations in 0- levels of less than 0.02 but most layers showed
variations of greater than 0.05 mole fraction. In general, the
average values decreased with depth at any one site, as did the values
measured at any one time. At sites 1, 2 and 3, the 0_ concentrations
showed a tendency to decrease with depth until a minimum was reached
and then start to increase again. This pattern was consistent over
time. Site 1 showed the extreme decrease of 02 with depth, where
average 07 values dropped to 0.01 within 410 cm of the surface. The
low 0_ levels in the deeper layers of sites 1 and 6 were distinctly
different from the other values as indicated by Duncan's new
multiple-range test. Other than at sites 1 and 6, however, the oxygen
levels were consistently high indicating that most of the reclaimed
mine site was well oxygenated.
Oxygen and carbon dioxide concentrations in the surface layers
were in general not very different from atmospheric levels. One
reason for this may have been the contamination of gas samples by air
from the soil surface. The gas samplers used in this study were
primarily designed for obtaining samples at deeper depths. The large
16
-------
Table 2. Average, maximum and minimum values for 0_ and CO,
depth at sites 1-6. 2 2
concentrations and temperature for each
Site 1
Site 2
Site 3
Depth
cm
30
60
105
260
410
565
30
60
170
320
625
945
1250
30
60
150
305
455
610
810
X
.205
.206
.147
.022
.010
.016
.190
.194
.178
.171
.143
.152
.156
.207
.203
.191
.194
.183
.155
.188
at
a
g
j
j
j
abed
abc
cd
de
g
fg
efg
a
a
abc
abc
bed
efg
abed
°2
max
.210
.210
.210
,.082
.066
.115
.210
.207
.210
.209
.187
.199
.204
.210
.210
.207
.209
.205
. .194
.208
co2
min
ole fracl
.170
.190
.090
n.d.
n.d.
n.d.
.143
.154
.129
.126
.103
.090
.121
.185
.195
.169
.149
.140
.116
.153
X
.0045
.0046
.040
.132
.144
.147
.011
.010
.017
.023
.048
.040
.039
.0022
.046
.013
.012
.013
.030
.012
a
a
ef
i
ij
j
ab
ab
be
cd
fg
ef
ef
a
a
abc
ab
abc
de
ab
max
-
.025
.020
.104
.168
.187
.187
.034
.033
.045
.052
.082
.082
.060
,009
.014
.024
.027
.033
.055
.033
min
n.d.T
n.d.
.002
.062
.104
.088
n.d.
.001
.001
.002
.027
.013
.006
n.d.
n.d.
.004
.002
.002
.011
.004
Temperature
X
14.2
16.0
13.9
12.3
12.2
10.8
14.5
16.6
12.6
11.6
11.8
12.2
12.3
13.9
13.8
12.6
12.2
11.4
11.3
11.5
max
o..
C —
25.2
24.0
24.5
17.5
14.8
13.4
23.7
24.5
20.4
16.1
13.6
12.9
13.3
25.2
23.5
21.2
18.7
15.3
13.2
12.4
min
-2.6C
1.28
-2.5
3.0
5.3
7.6
-2.3
-1.8
1.5
6.6
10.4
11.2
11.2
-1.4
-1.0
0.8
4.4
7.0
9.5
9.9
-------
Sire 4
Site 5
Site 6
30
60
185
335
490
790
30
145
325
630
935
1240
150
305
.201 a
.179 cd
.194 abc
.199 ab
.192 abc
.189 abed
.197 abc
.193 abc
.186 abed
.186 abed
.179 cd
.170 df
.114 h
.046 i
.210
.207
.204
.209
.206
.208
.210
.210
.204
.208
.207
.190
.156
.141
.160
.097
.177
.181
.175
.141
.169
.152
.131
.155
.134
.139
.040
n.d.
.0032
.012
.010
.008
.015
.018
.005
.011
.014
.015
.022
.032
.056
.098
a
ab
ab
ab
abc
be
ab
ab
abc
abc
bed
de
8
h
.018
.024
.022
.019
.028
.050
.019
.033
.036
.034
.044
.048
.103
.136
n.d.
.002
.002
n.d.
.002
.001
n.d.
.001
.004
.002
.004
.020
.015
.059
14.0
14.2
11.9
12.6
12.5
12.2
10.0
10.2
10.8
11.5
11.6
11.8
9.9
11.1
23.4
23.4
20.6
18.6
16.4
13.7
25.0
19,7
15.4
13.0
12.6
12.4
19.7
14.7
-0.9
-0.1
3.1
6.1
8.3
10.4
-3.0
1.2
6.2
10.1
10.5
10.6
0.0
6.1
•I-
Numbers followed by the same letter in a column are not significantly different at p = 0.05.
Below detected limits (< .001).
§Data during the winter is missing.
-------
volumes of air required to obtain a sample may have permitted short-
circuiting of surface air through large pores to the sample chambers
located near the surface.
Table 2 also shows the mean and extreme values of CO- for each
site and layer. Average CO- mole fractions ranged from 0.009 to
0.147. Individual measurements ranged from less than 0.001 to 0.187.
High CO- concentrations (< 0.10) were observed only at sites 1 and 6.
The high average values of CO- at those two sites and for the 625 cm
layer of site 2 were .tested to be distinctly different than the other
values. Site 4 consistently had the lowest CO- concentrations with
no average value over 0.02 mole fraction for any layer. The surface
layers at every site normally showed the lowest CO- concentrations
with the concentrations increasing with depth. As in the case of
0-, sites 2 and 3 showed a tendency to reach maximum CO,, concentra-
tions at an intermediate depth and then start to decrease with depth.
Mean and extreme values for temperature are also shown in
Table 2. Mean values for sites 5 and 6 are considerably lower than
sites 1-4 because temperatures were measured over a period including
two winters and only one summer, while the data for sites 1-4 span
a period including two summers and winters. As expected, spoil
temperatures showed an annual cyclic fluctuation, with the amplitude
of the fluctuation decreasing and the phase lagging as depth increased.
This behavior is shown in Figure 4, where the temperature is plotted
for five depths at site 2 for a portion of the data record.
Temperature showed little variation at depths below 500 cm.
19
-------
30
O
20
Ni
O
W
H
«<: 10
cs
W
(X.
S
W 0
H
-10
n i i i i i i i i i I i i i i i i i i i r
i i i i i i i i i i i i i i i i i i i i i
J A S O N D
1980
J FMAMJ JA BOND
1981
J F M A
-1982-
DATE, MO8.
Figure 4. Variation of temperature ( C) over time for six depths at site 2. Depths shown are
30 cm, (D) 60 cm, (•) 170 cm, (o) 320 cm, (A) 625 cm, and (•) 945 cm.
-------
Although the mean values shown in Table 2 give a good indication
of the spoil atmosphere characteristics, the oxygen and carbon
dioxide levels also showed distinct seasonal tendencies. These
tendencies are best shown in Figures 5-10 where 0« and C0_ mole
fractions and temperature are plotted against time for each layer at
the six sites. Data spanning three years are superimposed on a
single Julian year. In Figures 5-10 temperature is shown as a con-
tinuous line connecting the individual data points for clarity.
Much of the discontinuity in the temperature plot is due to the
superimposition of the three years of data. Figures 5-10 illus-
trates that, at least for some depths at each site, there is a strong
tendency for the C0» levels to increase during the summer months
(150-273 days), while remaining low during the remainder of the year.
The increase in C0~ is accompanied by a decrease in 0~ concentrations.
This behavior is especially well illustrated at the 105 cm depth of
site 1 (Fig. 5) and all layers of site 2 (Fig. 6). Near the surface,
the increase in CO- and decreases in 0- coincide with the maximum
in the spoil temperatures. However, at the lower depths these ex-
tremes in CO- and 0? still occur during the summer while the tempera-
ture either experiences a maximum later in the year (320 cm, site 2,
Fig. 5) or exhibits almost no variation over time (625 cm and deeper,
site 2, Fig. 5).
A relationship between 02 and C0» concentrations and between 0-
and temperature and C0_ and temperature is suggested by Figures
21
-------
O
<
-------
Z
o
o:
u.
LU
_J
o
d -
d -
J 1 1 1 1 1 ' I i I I
CM
. . . a ' "• " «
4D CM
.8) « . B
. . .1
n a
320 CM
" f
ft« I t t
i • ' • i r
0. tfl. 122.
n nr
JL! L.
a« I
go
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- d
12PO CM
0° Og.
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61. 122. 172.
- O
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H-
(T
UJ
CL
- d
UJ
I-
30?.
30?.
JULIAN
DATE
Figure 6.
Variation of temperature and the mole fractions of CL
(X) and CO^ (0) over time for the composite record at
site 2. The temperature plot is shown as a solid line
connecting the individual points for clarity.
23
-------
o
-------
-------
d -
d .
»- d -
o
I I
d -
£30 CM
. d
. d
> o
12-tfl CM
000
d —
- d
- d
d
i
<
cr
Q.
s
LLJ
- d
I jj «_, , , , «_| , , , , 1
0. (51. 122. 155. 2-M. 3DS. 166. 6\. 122. 153. 2-M. 3D?. 364. '
JULIAN DATE
Figure 9. Variation of temperature and the mole fractions of £)„
(X) and CO, (0) over time for the composite record at
site 5. The temperature plot is shown as a solid line
connecting the individual points for clarity.
26
-------
cr
LU-
LL)
_j
o
a -
IPO CM
3DP CM
- =5
a
Ml
•CM
O
LU
tr
Z)
a:
LL)
a.
S
UJ
I-
JUL1AN DATE
Figure 10. Variation of temperature and the mole fractions of 0_
(X) and C0_ (0) over time for the composite record at
site 6. The temperature plot is shown as a solid line
connecting the individual points for clarity.
27
-------
5-10. To test the relationship between 02 and C02, regression and
correlation coefficients were calculated for the relation:
YCQ = a + b (0.210 - YQ ) [4]
where Ypr. and Y_ are the mole fraction of C09 and 0_, respectively
C02 U2 2. /
and a and b are regression coefficients. Table 3 shows the values
for a, b and r, the correlation coefficient, for 0- and C02 at the
different layers of each site. Correlations between Y__ and the
term 0.210 - Yn range between -0.29 and 0.97, although the smallest
absolute value for r, significant at the 5% level, is -0.51. Values
for b range from 0.19 to 0.88 and for a. from -0.014 to 0.074.
Although the degree of correlation is high in most cases, the frac-
tion of the variation in Yrn that can be attributed to variation in
2 2
Yn (represented by r , Steele and Torrie, 1960, p. 187) ranges from
0.26 to 0.94 when the r value is significant at the 5% level.
To test the relationship between temperature and Yn and Y _ ,
°2 2
correlation coefficients were calculated for temperature, T,and Y_ ,
T and Y n , and also between temperature at the 30 cm depth for
sites 1-5 and Yn and Y^,.. . These r values are listed in Table 4.
°2 C°2
Correlations between Y- and T are in general rather poor with only
2
5 values having an absolute value greater than 0.75 (excluding site
6). Correlations between Y__ and T are even poorer with only 6
layers having an absolute correlation greater than 0.75 (excluding
site 6). Correlations between T and Yrn and Yn are much stronger
co2 o2
for most depths when the temperature at the 30 cm depth of each site,
T-,njis used. Thirteen layers have an absolute correlation greater
28
-------
Table 3. Correlation, r, and fegression coefficients, a and b, between the mole fractions
of C0_ and decreased 0 (.210-Y ) for each depth at sites l-6f.
K)
Site 1
Site 2
Site 3
Depth
(cm)
30
60
105
260
410
565
30
60
170
320
625
945
1250
30
60
150
305
455
610
810
a
.0029
.0016
.0030
.050
.074
.028
.0018
.0016
.0015
.0004
.0192
.0141
.0075
.0013
.0016
.0033
.0050
.0025
.0098
.0026
b
.38
.88
.59
.43
.35
.62
.48
.58
.50
.60
.43
.46
.59
.34
.51
.51
.44
.39
.32
.42
r
.51* Site 4
.68**
.87**
.57**
.29
.59**
.10** Site 5
.97**
.91**
.96**
.77**
.81**
.93**
.74** Site 6
.72**
.85**
.81**
.77**
.80**
.84**
Depth
(cm)
30
60
185
335
490
790
30
145
325
630
935
1240
150
305
a
.0009
.0061
.0021
.0016
.0026
.0057
.0014
.0013
.0052
.0029
.0081
.014
-.0145
.028
b
.27
.19
.55
.61
.70
.58
.31
.56
.39
.52
.47
.46
.74
.43
r
.76**
.69**
.87**
.91**
.93**
.82**
.72**
.98**
.89**
.95**
.78**
.83**
.90**
.89**
Significant at the 5% level.
Significant at the 1% level.
- a + b (.210-Y- ).
t.
-------
Table 4. Correlation coefficients, r, between the mole fraction of 0,
and temperature and between the mole fraction of CO- and
temperature for each depth at sites 1-6.
Site 1
Site 2
Site 3
Site 4
Site 5
Site 6
Depth
(cm)
30
60
105
260
410
565
30
60
170
320
625
995
1250
30
60
150
305
455
610
810
30
60
185
335
490
790
30
145
325
630
935
1240
150
305
02-T
.40
-.27
-.92**
.11
.13
.08
-.72**
-.53*
-.79**
-.54**
.34
.28
-.30
.40
-.31
-.70**
-.49*
-.56**
-.13
.16
.50*
.36
.56**
-.09
.11
-.26
-.80**
-.80**
-.30
.77**
.55
.13
-.83**
-.82**
C02-T
.05
.56**
.84**
-.06
.08
.03
.74**
.57*
.85**
.60**
.12
-.06
.39
.01
.38
.74**
.80**
.74**
.19
-.19
-.30
.03
-.58**
-.02
-.21
.44*
.88**
.84**
.53
-.73**
-.62*
-.41
.72**
.80**
VT30
—
-.28
-.91**
.34
.02
.34
—
-.53*
-.84**
-.91**
-.90**
-.80**
-.93**
—
-.32
-.66**
-.42
-.77**
-.78**
-.51
—
.34
.58**
.25
.58**
-.13
—
-.86**
-.78**
-.87**
-.78**
-.82**
•W
—
.53*
.84**
-.16
.10
-.13
—
.55*
.87**
.92**
.70**
.68**
.88**
—
.40
.68**
.70**
.56**
.65**
.56*
—
.06
-.50*
-.29
-.58**
.20
—
.88**
.82**
.91**
:57
.92**
*Significant at the 5% level
**Significant at the 1% level
^Correlation coefficients between oxygen and tenperature; carbon di-
oxide and temperature; oxygen and the temperature at the 30 cm depth,
T • and carbon dioxide and T,_, respectively.
30
-------
than 0.75 between Y and T,n, while eight layers have absolute
values greater than 0.75 for Y _ and T,n. The number of signifi-
OU ~ jU
cant correlations at the 5% level increases from 12 to 17 for T__
and Yn and from 15 to 19 for T,n and Yr_ . For layers where the
U- JU 9
correlation is significant at the 5% level, the correlations are
positive between Y _ and temperature and negative between Y and
C°2 °2
temperature. Two layers at site 4 exhibit the reverse behavior but
the correlations for these two layers are fairly weak (1r| < 0.6)'.
Discussion
Oxygen concentrations remained fairly high for sites 2-5 during
the entire period of this study. This is a fairly surprising result
considering the abundance of pyrite within the spoil at this site
and is contrary to earlier calculations and observations of in situ
pyrite oxidation in reclaimed mines and refuse dumps where only
2
limited penetration of 02 was calculated or measured (Colvin, 1977 ;
Good, 1970 ). The increase in 0- concentrations with depth after
reaching a minimum value at several sites indicates that gaseous ex-
change ibetween the spoil and atmosphere may also be accompanied by
exchange between the spoil and a deeper layer, perhaps the water
table or more likely the zone of deep-mined, B coal (Fig. 1).
Carbon dioxide showed the same behavior with depth.
Colvin, S. L. 1977. Oxygen diffusion in strip-mine soils. Un-
published M.S. Thesis, Iowa State Univ., Ames, Iowa.
3
Good, D. M. 1970. The relation of refuse pile hydrology to acid
production. Unpublished M.S. Thesis, The Ohio State Univ., The Ohio
State Univ., Columbus, Ohio.
31
-------
Only at sites 1 and 6 did Y approach 0.0. At both of these sites,
trace levels of methane were detected during spring measurements when
Y was below detection levels indicating that anaerobic conditions
existed at least during part of the year. Low CL levels at site 6 can
be attributed in part to slower diffusion rates than at the other sites
since this site was located in undisturbed shale-overburden. Low CL
concentrations at site 1 must be due to higher consumption rates than
at sites 2-5 with perhaps impeded diffusion at the lowest depth where
again undisturbed material was encountered. The low 0 concentrations
at sites 1 and 6 were accompanied by very large increases in CO . We
have not found any other reports of such high CO. values in soil or
spoil materials. At all sites, the decrease in 0_ is strongly
correlated to the increase in CO . This behavior suggests that
respiration of plant roots or soil organisms is responsible for the
changes in 0 and CO . The high carbon content of these spoils
(Table 1) may support considerable activity by heterotrophic bacteria.
Another possible source of C0_ is neutralization of acid by
carbonate minerals. The acid produced by pyrite oxidation will
react with the gangue material (Rogowski et al., 1971). If the
gangue contains carbonates or other salts of weak acids, they will
react to neutralize the acid. For carbonate reactions in acid
stripmines (pH < 4), carbonic acid will be the dominant species
present since the first pK for H CO is 6.4 (Garrels and Christ,
3. Z j
1965, p. 76). The reaction for any carbonate species is:
32
-------
M - C03 + 2H+ •+ M2+ + H2C°3 . [5]
s aq
Carbonic acid will in turn be in equilibrium with gaseous" C0_, the
relation being governed by Henry's Law (Garrels and Christ, 1965,
P, 76).
" C6]
•*"*•') O *» '
where:
pCO- is the partial pressure of C0_ (atmospheres)
a is the activity of carbonic acid in solution,
where by convention, all C0_ is treated as
aq
H2CO_ (see Kern, 1960 for further discussion
aq
on this relationship).
Lovell, et al. (1978) have observed almost complete carbonate
neutralization of acid in stripmine spoils and data presented by
Rogowski, et al. (1982) indicate that some carbonate neutralization
is taking place at this site. Where carbonates are present in
stripmine spoils, appreciable CO,, can be generated over much of the
active lifetime of a reclaimed stripmine.
The correlation between 0. and T and C0_ and T is fairly weak.
This is similar to the result found by DeJong (1981) between C02 and
T in native and cultivated soils. The stronger correlation between
the temperature at 30 cm and the gas concentrations in some of the
deeper layers, particularly for sites 2, 3 and 5, indicates that
processes taking place near the surface are the dominant processes
33
-------
controlling the 02 and CO. concentrations in these deeper layers.
We should expect this to be true only if gas diffusion through the
spoil was the dominant process of gas movement and if consumption
and production processes for 0^ and CO- in the deeper layers were
considerably less than in the surface layers.
The mean values for temperature at the 30 and 60 cm depth for
sites 1-4 were 14.2 and 15.2 C, respectively. These values are
about five degrees higher than those measured by Carter and Ciolkosz
(1980) for a natural soil at approximately the same elevation and
location as the research site. They found average temperatures of
about 9.2°C at 25 cm and 9.3°C at 50 cm. Part of this difference is
due to a bias in the data used to calculate the means, since more
measurements were taken during the summer months. However, even the
time-weighted average for mean temperature, 10.4 C at 30 cm and
11.0°C at 60 cm, is 1.2 to 1.7°C higher than the natural soil. These
higher temperatures are probably due to the differences in vegetative
cover, allowing greater solar heating of the surface spoil materials
(Deely and Borden, 1978). The natural soil was located under a
closed forest canopy while the mine spoil had no tree cover and only
a sparse covering of grasses and herbaceous plants (Table 1). The
spoil showed a greater temperature variation in the top 30 cm layer
than the natural soil studies by Carter and Ciolkosz (1980), with
the temperature dropping below 4 C in the top 300 cm for a portion of
o
the year. Temperatures below 4 C should inhibit autotrophic bacteria
activity if the autotrophs are present in these layers (Ehlrich and
34
-------
Fox, 1967). The deeper soil stayed within the temperature tolerance
range of iron-oxidizing bacteria, though apparently 10-20 C below the
temperature of maximum activity (Table 2, Silverman and Lundegren,
1959).
35
-------
REFERENCES
1. Bollag, J. M. and W. Barabasz. Effects of Heavy Metals on the
Denitrification Process in Soil. J. Environ. Qual., 8:196-201,
1979.
2. Carter, B. J. and E. J. Ciolkosz. Soil Temperature Regimes of
the Central Appalachians. Soil Sci. Soc. Am. J., 44:1052-1058,
1980.
3. Cathles, L. M. and J. A. Apps. A Model of the Dump Leaching
Process that Incorporates Oxygen Balance, Heat Balance and Air
Convection. Metall. Trans., 63:617-624, 1975.
4. Clark, C. S. The Oxidation of Coal Mine Pyrite. Ph.D. Thesis,
John Hopkins University, University Microfilms International,
Ann Arbor, Michigan, 1965.
5. Deeley, D. J. and F. Y. Borden. High Surface Temperatures on
Strip-Mine Spoils. In: Ecology and Reclamation of Devastated
Land, R. J. Hutnik and G. Davis, eds. Gordon and Breach, New
York, 1973. pp. 69-79.
6. DeJong, E. Soil Aeration as Affected by Slope Position and
Vegetation Cover. Soil Sci., 131:34-43, 1981.
7. Dugan, P. R. and C. I. Randies. The Microbial Flora of Acid Mine
Water and its Relationship to Formation and Removal of Acid.
Project Completion Report A-002-2410, to Office of Water Resour.
Rec., U.S. Department of the Interior, 1968.
8. Ehlrich, H. L. and S. I. Fox. Environmental Effects on Bacterial
Copper Extraction from Lower Grade Copper Sulfide Ores. Biotech.
Bioeng., 9:471-485, 1967.
36
-------
9. Garrells, R. M. and C. L. Christ. Solutions, Minerals and
Equilibria. Freeman, Cooper and Company, San Francisco,
California, 1965.
10. Kern, D. B. The Hydration of Carbon Dioxide. J. Chem. Ed., 37:
14-23, 1960.
11. Lovell, H. L., R. R. Parizek, D. Forsberg, M. Martin, D. Richardson,
and J. Thompson. Environmental Control Survey of Selected
Pennsylvania Strip Mining Sites. Final Report to Agronne National
Laboratory, Contract No. 31-109-38-3497, 1978.
12. Malouf, E. E. and J. D. Prater. Role of Bacteria in the Alteration
of Sulfide Minerals. J. Metals., 1961:353-356, 1961.
13. Ohio State University Research Foundation. Acid Mine Drainage
Formation and Abatement. Water Pollution Control Research
Series Program 14010 FPR, U.S. Environmental Protection Agency,
Washington, D.C., 1971.
15. Pedersen, T. A., A. S. Rogowski, and R. Pennock, Jr. Comparison of
Morphological and Chemical Characteristics of Some Soils and
Minesoils. Reclam. Rev., 1:143-156, 1978.
16. Pedersen, T, A., A. S. Rogowski, and R. Pennock, Jr. Physical
Characteristics of Some Minesoils. Soil Sci. Soc. Am. J.,
44:321-328, 1980.
17. Pionke, H. B. and A. S. Rogowski. Implications for Water Quality
on Reclaimed Lands. In: Economics, Ethics and Ecology: Roots
of Productive Conservation, W. E. Jeske, ed. Soil Conservation
Society of America, Ankeny, Iowa, 1981. pp. 426-440.
37
-------
18. Rogowski, A. S. Acid Generation within a Spoil Profile: Pre-
liminary Experimental Results. In: Seventh Symposium on Coal
Mine Drainage Research, NCA/BCR Coal Conference and Expo IV,
Oct. 18-20, Louisville, Kentucky, 1977. pp. 25-40.
19. Rogowski, A. S., H. B. Pionke, and J. G. Broyan. Modeling the
Impact of Strip Mining and Reclamation Processes on Quality and
Quantity of Water in Mined Areas: A Review. J. Environ. Qual.,
6:237-249, 1972.
20. Rogowski, A. S., H. B. Pionke, and B. E. Weinrich. Some Physical
and Chemical Aspects of Reclamation. Preprint, paper presented
at the North Atlantic Region ASAE 1982 Annual Meeting, 1982.
21. Singer, P. C. and W. Stumm. Acidic Mine Drainage: The Rate
Determining Step. Science, 167:1121-1123.
22. Steele, R. G. D. and J. H. Torrie. Principles and Procedures of
Statistics. McGraw-Hill Book Company, Inc., New York, 1960.
38
-------
-------
SECTION 3
FLUX AND PRODUCTION RATES OF OXYGEN
AND CARBON DIOXIDE IN A RECLAIMED
COAL-STRIPMINE
Introduction
In Part II we presented data on the oxygen and carbon dioxide
status within a reclaimed coal-stripmine. An unexpected finding was
the prevalance of C0_ within the spoil profile. Carbon dioxide
concentrations ranging from 0.02 to 0.16 mole fraction were found in
the stripmine atmosphere. The higher values were restricted to only
one portion of the study area, but greatly'exceed the highest values
reported for natural soils (DeJong, 1981; Russell and Appleyard,
1915). We proposed two possible sources for the observed CO^: i)
heterotrophic respiration by soil bacteria within the spoil bank
and ii) carbonate neutralization within the mine of the acid produced
by pyrite oxidation with subsequent release of CCL gas. If either
of these mechanisms accounts for the observed C02> the implications
for acid generation and leaching within reclaimed stripmine is
significant. In the first case, uptake of 0- by micro-organisms
would help reduce pyrite oxidation by reducing the 0^ concentration
in the spoil atmosphere since the oxidation rate of pyrite is
directly proportional to the gaseous 0_ concentration (Clark, 1965;
Ohio State University Research Foundation, 1971). On the other hand,'
if the CO, is from carbonate neutralization of acid, the effect would
be to reduce the acidity leaving the stripmine, while the production
39
-------
rate of pyrite oxidation products remains unchanged. Both mechanisms
would serve to reduce the amount of acid leaving a stripmine.
However, in the first case, the reduction is from a decrease in the
production rate of acid, while in the second case, the reduction is
from an in situ neutralization of the acid produced. The objective
of this study was to see if either i or ii could be identified as
the dominant process at this reclaimed mine.
Neither mechanisms can be ruled out at this site. Heterotrophic
respiration in the surface layers must take place at this site since
a plant cover is well established. Also, heterotrophic activity
appears to be occurring in the deeper depths as indicated by the
formation of methane during the wet, presumably most poorly aerated
times of the year (Part II). Carbonate neutralization of acid is
also a possibility at this site, despite being located in an area
low in carbonate-containing overburden. Water quality data presented
by Rogowski, et al. (1982) indicates that some carbonate neutraliza-
tion is taking place at this site.
Table 5 shows the pyrite and sulfate content expressed as percent
by weight sulfur for ten representative spoil layers from this
reclaimed mine (Rogowski, 1977). The fourth column in Table 5 repre-
sents the amount of carbonate, expressed as percent by weight C00,
required to neutralize all the acid produced if all the pyrite oxi-
dizes as shown in Eq. [8] and one-half of the sulfate content is in
the form of sulfuric acid. The fifth and sixth column show the
40
-------
Table 5. Pyrite and sulfate concentrations expressed as percent by weight sulfur for
ten representative spoil layers from research site (Rogowski, 1977). Also,
the CO- equivalent of the carbonate content required to neutralize the acid
produced from columns 2 and 3 and the measured carbonate content. The last
column gives the ratio CO,, j/COo j j *n percent.
6 2 measured 2 required
Layer
1
2
3
4
5
6
7
8
9
10
Pyritic S
.095
.112
.136
.088
.124
.082
.064
.060
.066
1.967
Sulfate S
.085
.079
.089
.070
.049
.059
.056
.077
.055
.738
2 required
i . |
.122
.130
.158
.108
.118
.096
.082
.094
.082
1.86
C00 ,
2 measured
.03
.01
.01
.02
.03
.03
.03
.30
.01
1.16
Potential
neutralization
%
25
8
7
19
25
31
37
319
12
62
-------
amount of CCL forming minerals present in these layers and the per-
centage of the C02 requirement these minerals represent. From these
data it can be seen that appreciable CO- can be generated over much
of the active lifetime of a reclaimed stripmine.
Theory
One possible means of identifying whether mechanism i or ii
dominates the production of C0~ is to compare the consumption and
production rates of 02 and CO-- For aerobic hetertrophic respiration
by plant roots or microorganisms we would expect the ratio of con-
sumption of C02 to 02, r to be near -1.0 although values between
-0.6 and -4.0 have been reported (Bridge and Rixon, 1976; Rixon and
Bridge, 1968; Bunt and Rovira, 1955). To estimate r for mechanism
q
ii, the stoichiometry of carbonate neutralization of acid and pyrite
oxidation must be considered. For pyrite oxidation we know that
3.5 moles of 02 will oxidize 1.0 mole of pyrite to form 2.0 moles
of H+.
FeS2 + 3.5 02 + H20 •+ Fe2+ + 2S02~ + 2H+ [8]
This result is true regardless of whether 0_ reacts directly with
pyrite or if an intermediary oxidant, such as ferric iron, is
involved (Ohio State University Research Foundation, 1971). The
ferrous iron produced in Eq. [8] may or may not oxidize and pre-
cipitate within the mine to form more acid:
Fe2+ + 1/4 02 + 2.5 H20 -»• Fe (OH) + 2H+ [9]
42
-------
Thus, from 0.57 to 1.07 moles of H can be produced for every mole
of 0_ consumed during pyrite oxidation.
For carbonate neutralization in acid stripmines (pH < 4),
carbonic acid will be the dominant species in solution since the
first pKa for H.CO- is 6.4 (Garrels and Christ, 1965, p. 76). The
equation for any carbonate species is :
M-C03 + 2H+ -»• M2+ + H2C03 . [10]
aq
The carbonic acid formed in Eq. [10] will in turn be in equilibrium
with gaseous C0», the relation being governed by Henry's Law
(Garrels and Christ, 1965, p. 76).
where a is activity, pCO. is the partial pressure of C0_ (atmospheres)
P is total pressure (kPa), and Y_n is the mole fraction of C0_ (-) .
If we assume that the movement of water through the spoil is suffi-
ciently slow so that the water is always in equilibrium with gaseous
C0_, we can rewrite Eq. [10].
M-CO- + 2H+ -»• M2+ + H20 + C02 [12]
g
Thus, the neutralization of 2.0 moles of H will produce 1.0 mole of
cor
The areas in the mine where 0- is consumed would correspond to
the areas containing pyrite, whereas C0? production would take place
only in zones where acidic waters come in contact with carbonates.
These areas may not be the same. Table 5 shows that the presence of
43
-------
CO producing materials does not correspond to pyrite abundance. If
all the acid produced by Eq. [8] is neutralized by carbonates, before
it moves far in the profile, r would equal -0.29. If no neutraliza-
tion occurs, r could be 0.0 and could go as high as -0.54 or higher
q
if iron precipitates within the mine as described by Eq. [11] or if
acid formed in one area of the mine is concentrated by leaching to a
high carbonate zone where it is neutralized. Even if this latter
case is true, the r value for the reclaimed site on the whole will
be between 0.0 and -0.54. This range is considerably different from
the range expected for heterotrophic respiration (-.6 to -4.0). The
difference in the two ranges for r may serve as a means of
differentiating between mechanisms i or ii, making it possible to
identify the dominant process of C02 production.
Materials and Methods
Oxygen and carbon dioxide concentrations for selected depths at
6 sites on a reclaimed coal-stripmine were presented in Part II. The
consumption and production rates for 0? and C0? at these sites can be
calculated from the gas concentration profiles if we assume that the
dominant means of gas movement through the spoil material is by
diffusion in the vertical direction only (Evans, 1965). The
diffusion of gas component i into the spoil can be described in one
dimension by:
- d/dz (N±) + Q± = d/dt (
-------
-2 -1
where N. is the flux of component i (moles-cm -sec , positive
downwards), Q. is the source/sink (+/-) term for component i (moles-
cnT^sec"1), $ is the air-filled fraction of the spoil (-), Y. the
mole fraction (-), z is depth (cm), and t is time (sec). At steady
or quasi-steady state, the gas concentration per unit volume of soil
is constant or changing slowly. The right side of Eq. [13] can then
be set equal to zero since <(>, p. and Y. are constant with time and
Eq. [13] can be rearranged:
d/dz (N.) = Q. [14]
The molar flux, N., can be found from the mole fraction form of Fick's
Law '(see Appendix A) .
N± = - */T Dp |^r dYi/dz [15]
3 —1 —1
where P is pressure (kPa), R the gas constant (kPa-cm -mole -K ),
T is temperature (K), T is the tortuosity (-) and D the Fickian
2
diffusion constant for component i (cm /sec, see Appendix A). The
Fickian diffusion coefficient in an open system, D , is adjusted
Fi
by (j>/T in Eq. [15] to account for the reduced air-filled cross
section and tortuous path of gas diffusion in soils (Troeh, et al.,
1982). A constant tortuosity term of 5 was used for the coarse spoil
material at sites 1-5 (Cathles and Apps, 1975). was assumed to be
0.12 at these sites based on an average bulk density of 1.57 g/cm
and a water-saturation percentage of 0.7 for the stripmine land
(Pedersen, et al., 1980). Since site 6 was located in an undisturbed
area, values of 10 and 0.06 were used for T and , respectively.
45
-------
D was calculated by assuming that CL and CO* diffusion were taking
i
place in a four -component atmosphere comprised of 0-, CCL, Ar and
, where N and N. were 0.0. Since
N Ar
and D^ are dependent
*
on N and Npn (Appendix A) , an iterative scheme was used to solve
°2 C°2
for N- , N-^ , D_ and D . Nitrogen and argon concentrations
°2 C°2 F02 FC02
were not measured directly so their values were set by assuming
Y^T + YA =1 —'%, - Y_-. and that the nitrogen-argon ratio was
? Ar . U_ <-u
constant and equal in the atmospheric ratio of 0.012. At each site,
the mine profile was divided into a number of layers corresponding
to the depths at which O^-and CO^ were measured (Fig. 11). Flux
values for 0- and C0_ were calculated at each layer by using the
unequal-spacing, central-difference form of the first-order space
derivation in Eq. [15] (Peaceman, 1977, p. 38). In general:
N.
[16]
where the subscript j refers to the depth, increasing downwards, and
DZ is the distance weighing factor;
t)7 = J+l J _ fl71
j+1/2 (z.-z.)(2.-z) + (z.-z.)^
At each site the flux was assumed to be 0.0 at the spoil-bedrock or
spoil-water table boundary. Oxygen and carbon dioxide concentrations
at the spoil surface were assumed to be at atmospheric levels. After
- V'l
Y. .
Ti '
\.i >
Y. . "
i, 3— 1
T. . T
1,3-1.
t
I
"Y< '+1 Yi •"
Ti -+1 Ti '
DZj-l/2'
46
-------
layer
spoil surface _ r
I _ - ~~ \J • £.J-\J .
N N : 02,1
°2'1 C°2'1 Y = 0.0003
L»Urt j J-
Qo2,i Qco2,i
Y Y
^2,2 C02,2
Q02,2 QC02,2
water table of bedrock
YC02,4
Figure 11. Schematic of spoil profile showing the division of the
profile into layers as determined by the depths of the
gas concentration measurements, Y and Y. . Fluxes
0_ Cu_
N and N are calculated for the top of each layer
2 2
ano are assumed to be 0.0 at the profile bottom. Source
terms, Qn and Q , are calculated for each layer.
U2 C02
47
-------
the fluxes were calculated, the average Qn and Q n values were
°2 CU2
found for the layers between the probes (Fig. 11), by using the
difference form of Eq. [14] :
Fluxes and source terms for CL and C0_, and the rates, r =
Q /Q and r T = N /Nn were calculated from the data presented
CUn U „ N CU. Li-
earlier.
Results and Discussion
The calculated fluxes showed considerable variation over time
at each site. Table 6 shows the flux values, averaged over time,
for oxygen and carbon dioxide at the soil surface of the six sites
and for all sites combined. Coefficients of variation, C.V., for
both Nn and N_n are also shown in Table 6. The C.V. values range
°2 C°2
from 37 to 390%. Site 6 consistently showed less variation than the
other sites and was also the only site located in undisturbed bed-
rock. This was probably because the diffusional process was more
consistent and uniform in the bedrock than in the spoil material.
This isn't surprising since we would expect greater heterogeneity of
both porosity and pyrite content in the spoil, which would lead to
nonuniform patterns of diffusion. In the extreme, heterogeneity
could negate our assumption of one-dimensional diffusion, although
the generally uniform variation of CL and CO concentrations with
48
-------
Table 6. Means and coefficients of variation, C.V., for 0- and
CO fluxes at the surface of the six sites and for all
sites combined. The ratio of the fluxes, r = N 0 /
N , was calculated from the mean values. 2
Site
1
2
3
4
5
6
all
v
X
moles
2
cm -sec
0.78
2.2
0.49
0.96
1.41
.45
1.2
io10
c:v.
%
160
110
140
110
130
37
130
"CO,
X
moles
2
cm -sec
-.27
-.82
-.07
-.10
-.23
-.20
-.37
xlO10
c.v.
%
210
110
270
390
200
43
170
r
™
-.35
-.37
-.14
-.10
-.16
-.46
-.31
49
-------
depth (Part II) indicates that vertical flow still dominates at this
reclaimed mine.
No significant difference at the 10% significance level was
measured between any site for the flux of 0^ anc* COo- For all the
—10 —2
sites the average flux of 0- at the surface was 1.2 x 10 moles-cm
-sec , while for CO the average flux was -.37 x 10 moles-cm
-sec . The CO^ fluxes measured for these minesoils are, in general,
less than the fluxes of C0_ measured by DeJong (1981) in grassland
and cultivated soils. DeJong (1981) found CO.. fluxes ranging from
-i r\ _n —1 c _9 *L
near 0.0 to -7 x 10 moles-cm -sec (-3 x 10 g-cm -sec ),
with fluxes normally near -2 x 10 moles-cm -sec . The lower
CO fluxes in the minesoils may be due to the lack of plant cover
and freshly deposited organic matter at the sites measured,
although no consistent pattern was obvious in the data.
Undoubtedly, much of the variation found in the flux values
was due to the fact that we assumed a constant air-filled porosity -
tortuosity term in the diffusion calculation when, in fact, this
term would vary over time as the water content of the minesoils
changed (Troeh, et al., 1982). The value we used was only approxi-
mate, thus, the magnitude of the flux terms shown in Table 6 are
also approximate. However, the ratio of the C02 flow to 0_ flux is
an absolute comparison since the effect of diffusion path in the
spoil is identical for 0,, and C02 (Penman, 1940) and cancels out
when we take the ratio, r = NCQ /NQ . Table 6 lists the TN for the
50
-------
average of the fluxes at the surface of each site. The r ranges from
-.10 at site 4 to -.46 at site 6 and is equal to -.31 for all the
sites combined. The lower values for rN occur at sites 3, 4 and
5 which are located on the upper portion of the mine site in the
predominantly sandstone overburden. The differences between r at
sites 3, .4 and 5 and 1, 2 and 6 are not significant however, because
of the great variability in the flux values. These r values indi-
cate that, on the average, from 2 to 10 times as much 0 is entering
the spoil material as C0_ is leaving.
The source term Q was calculated for 02 and CO,, for each layer
at the six sites. Table 7 summarizes the results, showing the mean
—3 —1
values of Qn and Q n (moles-cm -sec ) and the coefficients of
°2 UU2
variation for these values. The variation in the Q terms was large
enough that no significant difference could be found between the
different layers, but several trends are obvious from the data.
The layers of greatest consumption of 0- are the surface layers
at almost every site. The rate of 0« uptake in these layers is con-
sistently greater than for the deeper layers. This finding is
consistent with the fact that plant roots and soil organisms are
most active in the surface layers and would be removing oxygen during
respiration. The rate of 0_ uptake in the surface layer at the six
-12 -3 -1 -1 —1
sites averaged -1.2 x 10 moles-cm -sec or 0.065 uliters-g -hr
if a bulk density of 1.57 g/cm is assumed. This value is much lower
than the values found by Stroo and Jencks (1982) for 0~ uptake in
minesoils. Even for barren minesoils they found the lowest 0- uptake
51
-------
Table 7,
Mean values and coefficients of variation of the source terms for 09 and CO
and for the ratio rr
correlation between Q _ and Q
C°2 °2
/Q^ at the individual depths at each site. The
r, is also listed.
Ul
Site 1
Site 2
Site 3
Depth
cm
15
45
82
182
335
488
602
15
45
115
245
472
785
1098
15
45
105
228
380
532
v
X
moles
3
cm -sec
-3.6
3.6
3.1
- .92
- .55
- .073
.048
-5.5
-3.0
1.0
- .079
- .013
- .045
.027
-2.1
- .51
.003
- .072
.17
- .12
io12
c.v.
%
123
64
36
110
42
260
720
150
110
120
270
280
62
99
150
220
7900
140
92
-80
Qco2x
X
moles
3
cm -sec
1.5
-1.8
-1.4
.41
.23
.021
.13
2.5
1.2
- .38
.020
.010
.029
- .014
.35
- .004
.033
.059
- .064
.039
io12
C.V.
%
150
88
33
110
64
580
220
98
81
79
410
130
59
86
240
8000
350
71
56
92
X
—- —
-.38
-.48
-.49
-.50
-.47
-.15
-.29
,-.51
-.48
-.24
-.45
-.18
-.54
-.59
-.32
-.78
-.53
-.79
-.23
-.45
rq
c.v.
%
87
44
32
100
57
930
470
180
130
200
130
310
140
130
50
290
340
160
270
110
r
— —
-.85**
-.90**
-.63**
-.84**
-.47*
-.36
-.42
-.86**
-.85**
-.68**
-.77**
-.15
-.63**
-.49*
-.81**
-.88**
-.60**
-.71**
-.46*
-.58**
-------
Site 4
Site 5
Site 6
15
45
122
260
412
640
900
15
88
235
478
782
1088
75
228
342
.22
.082
-1.10
.12
.029
.003
- .010
-2.5
- .58
- .028
- .009
.007
- .014
- .090
- .052
- .20
1400
180
93
140
140
1500
580
160
130
327
310
270
120
110
90
78
.18
-.27
.28
-.027
-.017
.004
.006
.055
.13
.017
-.001
-.008
.011
.038
.030
.075
750
180
96
160
100
630
560
1620
160
170
1500
130
110
110
100
80
-.25
-.56
-.24
-.36
-.42
-.45
-.39
-.23
-.32
-.29
-.16
-.56
-.91
-.53
-.52
-.46
365
390
200
92
120
87
53
245
100
120
310
130
44
110
75
51
.22
-.77**
-.53*
-.59**
-.79**
-.69**
-.66**
-.30
-.63*
-.50
-.91**
-.81**
-.83**
-.86**
-.88**
-.88**
t
Significant at the 5% protection level.
it
Significant at the 1% protection level.
-------
rates to be 0.58 uliters-g -hr or about ten times the values
found in this study. This large difference may be due to differ-
ences in the studied site, but is more likely due to the different
techniques used to measure Q; a laboratory respirometer by Stroo and
Jencks (1982), and concentration gradients in this study. Also,
since only estimated values for the porosity - tortuosity term were
used here to calculate Nn and thus Q , the absolute magnitude of
U2 °2
Q is unknown. Comparing the two data sets, the coefficient 4>/T
would have to be increased by a factor of 10 for ,the uptake rates to
agree. Such an increase is certainly feasible but would result in
greater C« flux rates for the minesoil than for the natural soils
studied by DeJong (1981). Problems in measuring Yn at shallow
depths, discussed in Part II, may also contribute to the difference,
as well as smearing of the 0« gradient as a result of atmosphere-
pressure fluctuations (Morth, et al., 1972). Smearing of the gradi-
ents because of pressure fluctuations and deviation from strictly
vertical diffusion because of spatial variability in the porosity of
the minesoil may also account for the seemingly contradictory result
that the layers just below the surface act as 0 sources and CO
sinks (Table 7).
Problems with using the data resulting from uncertainty in the
absolute magnitude of Qn and Q _ is avoided by comparing the ratio
U2 CU2
of the fluxes r = Q _ /Qn and the correlation of the relative up-
Q 2 2
take terms. Table 7 shows the correlation coefficient between Q n
LU2
and 0- and the ratio, r , for each layer. In general, the
54
-------
correlation is strongest near the surface at each site indicating a
greater dependency of the changes in CCL and CL. The rQ values are
extremely variable and range from -.15 to -.91. Table 8 shows the
average values for the source term of 0~ and C0» and the r values
for the entire depth at each site. Again the values are extremely
variable which prevents any significant statistical comparison
between the sites. However, there is a trend in the data for rQ
similar to that found for r.T where the r-. values for sites 3, 4 and
N Q
5 are less than sites 1, 2 and 6. The average rQ value for all the
sites was -0.30 which indicates that more than 3 times as much 0?
is being consumed as CO .
Conclusions
Both the ratios of the diffusional flux of CO. to 0^ and the ratios
of the source terms for C0,j and €>„ showed considerable variability.
Site 6 showed considerably less variation than the other sites possibly
because it was the only site located in undistrubed bedrock where our
assumption of strict vertical diffusion was more valid. The r ranged
from -.10 to -.46 for the six sites and was equal to -.31 for all the
sites combined. The rQ for the entire profile at each site ranged from
-.12 to -.46 and averaged -.30 for the combined site. Both r and r
indicate that from 2 to 10 times as much 0 is being consumed as CO-
with 3.3 times as much for all the sites combined. These values lie
well within the range expected for carbonate neutralization of the acid
formed from pyrite oxidation and indicate that this mechanism accounts
for the bulk of the CO™ measured at this site although heterotrophic
55
-------
Table 8. Mean values and coefficients of variation, C.V., for the
production rate of 0~ and CO- and for their ratio, rn =
Q /Q . Rates are for the entire spoil profile at each
CU ty 'y
site averaged over time.
Site
1
2
3
4
5
6
all
v]
X
moles
2
cm -sec
-.66
-1.9
-.47
-.24
-1.0
-.45
-.91
C.V.
%
210
130
140
480
170
37
180
Qco2x
X
moles
2
cm -sec
0.22
0.78
0.063
-.047
0.16
0.20
0.29
io10
C.V,
%
280
110
300
880
250
42
220
rQ
-.44
-.40
-.15
-.24
-.12
-.46
-.30
C.V.
%
350
180
550
450
230
33
330
56
-------
respiration is undoubtedly still taking place. The more negative ratios
at the sites located on the lower portions of the mine site may be as a
result of greater concentrations of carbonate in this portion of the
mine. The more negative ratios may also be due to waters containing
acid formed in the upper reaches of the mine site flowing through the
lower sites and producing increased amounts of CCL for neutralization
reactions. This may also explain the poor correlation between Q- and
Q n at the 488 and 602 cm layers at site 1, where Y was very high.
LU— CUrt
The rn values indicate that a considerable amount of the acid produced
within the mine is being neutralized before it leaves the site.
57
-------
-------
REFERENCES
1. Bridge, B. J. and A. J. Rixon. Oxygen Uptake and Respiration
Quotient of Field Soil Cores in Relation to their Air-Filled
Pore Space. J. Soil Sci., 27:279-286, 1976.
2. Bunt, J. S. and A. D. Rovira. Microbial Studies of Some Sub-
antartic Soils. J. Soil Sci., 6:119-128, 1955.
3. Cathles, L. M. and J. A. Apps. A Model of the Dump Leaching Process
that Incorporates Oxygen Balance, Heat Balance and Air Convection.
Metall. Trans., 66:617-624, 1975.
4. Clark, C. S. The Oxidation of Coal Mine Pyrite. Ph.D. Thesis,
John Hopkins University, University Microfilms International,
Ann Arbor, Michigan, 1965.
5. DeJong, E. Soil Aeration as Affected by Slope Position and
Vegetation Cover. Soil Sci., 131:34-43, 1981.
6. Evans, D. D. Gas Movement. In: Methods of Soil Analysis, C. A.
Black, ed. American Society of Agronomy, Madison, Wisconsin, 1965.
Agronomy 9:319-330.
7. Garrels, R. M. and C. L. Christ. Solutions, Minerals and Equilibria.
Freeman, Cooper and Company, San Francisco, California, 1965.
8. Morth, A. H., E. E. Smith, and K. S. Shumate. Pyritic Systems: A
Mathematical Model. Environmental Protection Agency Technology
Series 14010 EAH, Contract No. 14-12-589, Report No. 665771, U.S.
Environmental Protection Agency, Washington, D.C., 1972.
9. Ohio State University Research Foundation. Acid Mine Drainage
Formation and Abatement. Water Pollution Control Research Series
Program 14010 FPR, U.S. Environmental Protection Agency,
Washington, D.C., 1971.
58
-------
10. Peaceman, D. W. Fundamentals of Numerical Reservoir Simulation.
Elsevier Scientific Publishing Company, New York, 1977.
11. Pedersen, T. A., A. S. Rogowski, and R. Pennock, Jr. Physical
Characteristics of Some Minesoils. Soil Sci. Soc. Am. J.,
44:321-328, 1980.
12. Penman, H. L. Gas and Vapour Movements in the Soil. II. The
Diffusion of Carbon Dioxide through Porous Solids. J. Agr. Res.,
30:570-581, 1940.
13. Rixon, A. J. and B. J. Bridge. Respiratory Quotient Arising from
Microbial Activity in Relation to Matric Suction and Air-Filled
Pore-Space of Soil. Nature, 218:961-962, 1968.
14. Rogowski, A. S. Acid Generation within a Spoil Profile: Preliminary
Experimental Results. In: Seventh Symposium on Coal Mine Drainage
Research, NCA/BCR Coal Conference and Expo IV, Oct. 18-20, Louisville,
Kentucky, 1977. pp. 25-40.
15. Rogowski, A. S., H. B. Pionke, and B. E. Weinrich. Some Physical and
Chemical Aspects of Reclamation. Reprint, paper presented at the
North Atlantic Region ASAE 1982 Annual Meeting, 1982.
16. Russell, E. J. and A. Appleyard. The Atmosphere of the Soil: Its
Composition and the Causes of Variation. J. Agric. Sci., 7:1-48,
1915.
17. Stroo, H. F. and E. M. Jencks. Enzyme Activity and Respiration in
Minesoils. Soil Sci. Soc. Am. J., 46:548-553, 1982.
18. Troeh, F. R., J. D. Jabro, and D. Kirkham. Gaseous Diffusion
Equations for Porous Materials. Geoderma, 27:239-253, 1982.
59
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SECTION 4
A NUMERICAL MODEL OF ACID DRAINAGE
FROM RECLAIMED COAL- STRIPMINES
Introduction
Acid drainage from reclaimed coal stripmines can be a severe
problem in the humid Eastern United States (Collier, et al., 1970).
The amount of pollutants leaving the reclaimed site can be reduced
by using proper-reclamation techniques when restoring the land
(Grim and Hill, 1974). However, the development and evaluation of
best reclamation and management techniques is difficult because of
the great expense and time required to implement and assess the
value of a specific practice and because of the great variability
between even adjacent-stripmine sites. The development of a mathe-
matical model that describes the acid production and leaching from
stripmined lands would facilitate the development of sound-
management practices by allowing assessment of each technique for
any given condition to be made in minutes rather than years. Although
several models for pyrite weathering have been presented (Morth, et
al., 1972; Colvin, 1977? Cathles and Apps, 1977; Cathles, 1979) none
is completely suitable for describing the process in reclaimed coal-
stripmines. The model described by Morth, et al., (1972) is for
pyrite oxidation in deep mines and assumes that pyrite oxidation
takes place only on the surface of cracks and voids and not within
the rock matrix. They assumed oxygen flux due to diffusion and
60
-------
atmospheric-pressure fluctuations. Their model is reasonable for
deep mines but does not seem representative of pyrite oxidation
within mine spoil composed of coarse fragments. Colvin (1977)
describes a model for pyrite oxidation of reclaimed stripmines where
diffusion serves as the mechanism of replacing oxygen with the
profile. However, the model uses representative values of pyrite
oxidation rates and does not attempt to relate the oxygen consumption
rate to pyrite content and distribution within the spoil fragments
nor does it differentiate between pyrite oxidation mechanisms.
Cathles and Apps (1977) present a model for oxidation and leaching
of sulfide-bearing fragments where the pyrite distribution, degree
of weathering, and oxidation kinetics are considered. However, they
assumed air-convection to be the main mechanism of oxygen movement
and that pyrite was oxidized by ferric iron, where the ferric iron
was maintained at a constant concentration by bacterial activity.
While these conditions represent reasonable assumptions for the
very coarse, copper-waste dumps they modelled, they do not apply
well to reclaimed coal-stripmines where diffusion processes probably
dominate and the role of iron-oxidizing bacteria is unclear. This
paper presents a parametric model of in situ oxidation of pyrite
and subsequent leaching of the acid products from reclaimed coal-
stripmines, based on oxygen diffusion, pyrite oxidation kinetics
and combined oxygen and ferric iron oxidation of pyrite, where the
activity of iron—oxidizing bacteria depends on the energy available
61
-------
from their substrate and the suitability of their environment for cell
viability and is calculated independently.
Description of Model
Basic Reactions.
The chemistry of pyrite oxidation is extremely complex and only
partially understood. However, the overall stoichiometry of the
reaction can be summarized by four equations (Singer and Stumm, 1968).
Two mechanisms for pyrite oxidation are possible (Ohio State University
Research Foundation, 1970). One possibility is that oxygen can react
directly with pyrite to form sulfate and acid.
FeS2 + 3.5 02 + H20 -»- Fe2 + 2S02~ + 2H+ [19]
Alternatively, ferric iron can replace oxygen as the direct oxidant.
FeS2 + 14Fe3+ + 8H20 -> 15Fe2+ + 2S02~ + 16H+ [20]
In stripmine spoil, the only important source of ferric iron in Eq.
[20] is assumed to be the in situ oxidation of ferrous iron (Lau, et
al., 1970; Singer and Stumm, 1968);
14Fe2+ + 3.5 02 + 14H+ -»• 14Fe3+ + 7^0 [21]
While the oxidation of ferrous iron is thermodynamically favorable,
the kinetics are extremely slow "at normal pH's of stripmine waters
(pH < 4; Singer and Stumm, 1970). However, certain chemoautotrophic
bacteria (Thiobacillus ferrooxidans) are known to use the energy
released by Eq. [21] as their energy source and can significantly
increase the oxidation rate (Lundgren, 1975; Beck, 1960). Thus, Eq.
62
-------
[21] and consequently Eq. [20] are thought to be bacterially catalyzed
since ferric oxidation of pyrite can be significant only when bacteria
are active.
As a final step in the pyrite oxidation process, the ferric iron
produced by Eqs. [19] and [20] may precipitate as a ferric hydroxide.
Fe3+ + 3H20 •*• Fe(OH)3 + 3H+ [22]
This reaction often takes place after the iron has been leached from
the stripmine site, with the iron hydroxide precipitation in surface
streams and ponds. Summing Eqs. [20] and [21] results in Eq. [19],
thus regardless of mechanism the result is the same; two moles of
acid are produced for every mole of pyrite and three and a half moles
of oxygen consumed.
Basic EOuations
The reclaimed-mine environment in which Eqs. [19]-[21] and
possibly [22] take place can be described as consisting primarily of
coarse (> 2mm) fragments. Pedersen, et al. (1980) and Ciolkosz, et
al. (1977) found coarse fragments composing 50-90% of the spoil
volume. In this model, we consider all the pyrite oxidation to take
place within coarse fragments. Since pyrite oxidation is a surface
reaction (Garrels and Thompson, 1960), the oxidant must diffuse from
the fragment surface through the fine pores of the fragment, which we
assume to be water saturated, to the pyrite mineral surface (Fig.
12). Evidence indicates that the fine-grained or framboidal form
of pyrite is the most reactive (Clark, 1965 and Caruccio, 1973).
63
-------
Liquid
Pyrite
Blebs
.. — Fe
Y//////////////,
Figure 12. Cross section of a coarse fragment containing pyrite.
64
-------
The framboidal form may be the result of the mineral being deposited
by microorganisms that were active in the original sediments (Emrich
and Thompson, 1968). Possibly for this reason, framboidal pyrite is
evenly distributed within the rock formations in which it is found
and the fragments derived from these strata during mining (Arora,
et al., 1978). The rate at which pyrite and oxidant react may be
controlled either by the chemical reaction rate or by the rate of
diffusion of oxidant into the fragment, or by both. This process
can be described by a standard shrinking-core model (Levenspiel,
1972). If we consider the fragments to be thin plates and the oxida-
tion of pyrite to be first order with respect to oxidant concentration
and pyrite surface area, we can express the oxidation rate of pyrite
within a fragment by:
dX/dt
2tn(l-X)+tr
U L*
where:
X = fraction of pyrite remaining in fragment, (-)
t = time for complete oxidation of fragment if diffusion of
oxidant is much slower than reaction ra.te, (sec)
t = time for complete oxidation of fragment if chemical
oxidation is much slower than oxidant diffusion, (sec)
and
t = time (sec)
tn represents the total time required to oxidize all the pyrite
within a fragment when the diffusion of reactants and products
between the fragment surface and the pyrite grain is the rate-
controlling step. t^ can be calculated from (Levenspiel, 1972):
65
-------
C ox
where:
p = molar density of pyrite within the fragment,
(moles/cm )
£ = one half thickness of fragment, (cm)
b = stoichiometric ratio between pyrite and oxidant
consumption, (-)
D = effective diffusion coefficient for coupled oxidant-
2
product counter diffusion, (cm /sec)
C = concentration of oxidant at fragment surface,
ox
(moles/cm ).
tp is the total time required for complete pyrite oxidation
within a fragment if the resupply rate of oxidant to the pyrite
surface is much faster than the chemical oxidation of pyrite. t
L*
can be calculated from, (after Levenspiel, 1972; Cathles and Apps,
1975):
ppy
CC bK.C 3d [25]
o OX
where:
K = first-order surface reaction rate constant for
O
pyrite oxidation per unit surface area of pyrite,
(cm/sec); i.e.,
p £ dx/dt = -bK_C
py S ox
a = surface area of pyrite per unit volume of fragment,
(cm )
66
-------
and
3 = effective thickness of fragment within which pyrite
is oxidized (cm, see Appendix B) .
From Eq. [23] it is obvious that the oxidation of pyrite will
be independent of diffusion rates at initial times, (X = 1) , but
may or may not become important as the pyrite 'is leached, depending
on the magnitudes of tc and t . For t » t , diffusion will never
be an important rate-controlling step and the fragment will weather
uniformly throughout its thickness. For t_ » tr, diffusion is the
rate-controlling step and a rim depleted of pyrite will form and
slowly grow at the fragment surface.
When both oxygen and ferric iron are present the rate of pyrite
oxidation is the sum of the rates of each oxidant acting alone (Ohio
State University Research Foundation, 1970) and their reaction rates
can be summed.
tD(02)(l-X)+tc(02)
[26]
Values for t_ and tn can be calculated from typical values for spoil
U D
and Eqs. [24] and [25]. For the values shown in Table 9, the
Q *> t Q
calculated values are t^CL) = 27 x 10 sec, t_(Fe ) = 35 x 10
Q -31 r
sec, t (09) = 4 x 10 sec, and t (Fe ) = .7 x 10 sec. These
Ll Am \*t
calculated values indicate that we would expect diffusion to be the
rate-controlling step for both the oxygen and iron oxidants and
would expect that a leached rim, surrounding a relatively unweathered
core, would form in the fragment. This agrees with the weathering
67
-------
Table 9. Coefficients used to calculatee typical values of t
and tn.
Parameter Value
p 4.4 x 10~ moles cm" (.13% pyrite S)
py
£ 1 cm
b(02) 1/3.5
b(Fe3+) 1/14.
D 10 cm -sec
c
C (0.) 0.29 x 10~ moles-cm" (.21 mole
ox 2 fraction)
C (Fe3+) 0.89 x 10~6 moles-cm"3 (50 mg/£)
K (0») 83. x 10~ cm-sec"
Ks(Fe3+) 4.4 x 10~6 cm-sec"1
a 217 cm"1
3 (02) .0745 cm
3 (Fe3+) .0102 cm
68
-------
pattern observed for sulfide-bearing fragments (Cathles, 1979;
Braum, et al., 1974).
Oxygen Diffusion
We assume the main mechanism for resupply of 0- to the fragment
surface to be diffusion within the interfragment voids of the spoil
profile. Atmospheric pressure fluctuations (Morth, et al., 1972),
air pumping from rising and falling water»table levels, convection
due to temperature and compositional differences (Cathles, 1979)
and dissolved oxygen contained in percolating water may contribute
to the 09 flux within the spoil but diffusion should dominate,
especially where a fine-textured, surface soil layer is present
(Evans, 1965). For one-dimensional diffusion of 0- into a r
spoil-bank at constant total pressure in which uptake of CL is
taking place and the water content remains constant over time,
the process can be described by:
Do2
d/dt " v * '"
Q0 [27]
2
where:
= air filled porosity, (-)
A
3
Pn = molar density 0-, (moles/cm -air)
Yn = mole fraction of 0- in gas, (-)
P = total pressure, (kPa)
R = universal gas constant, (8.31 kPa-cm /mole-K)
T = temperature, (K)
T = tortuosity of gas diffusion path, (-)
Q = 0 uptake rate, (moles/cm )
Z = depth, cm
69
-------
Dn is the effective diffusion coefficient of 0_ in an 0~, CO-,
N2 atmosphere and is found from the binary diffusion coefficients
and the flux ratios, r. = N /Nn and r_ = N /Nn (Appendix A).
1 C02 02 2. N2 02
-1
D
D
_ V
o, co
[28]
J ry ) O " o » ^ v O
For gaseous diffusion into spoil banks, the bottom of the spoil
profile can be assumed to act as an effective diffusion barrier
since below this boundary the air-filled porosity of the bedrock
is significantly less than the spoil and commonly coincides with
the water table.
Qn in Eq. [27] may be partitioned into four separate processes
U2
of CL consumption:
Q02 = QPY + QAB + QCHOX + QHB
Qpy represents oxygen consumption by direct pyrite oxidation. Q.
is the oxygen consumption rate of iron oxidation by autotrophic
bacteria as shown in Eq. [21]. Qr-rmv ^-s t^e rate of 0» uptake by
CntJA £.
chemical oxidation of ferrous iron, and Q,TT1 represents the uptake
HU
of oxygen due to respiration by plant roots or other soil organisms. •
The magnitude of each factor in Eq. [29] can be calculated separately.
QpY. Q_Y can be calculated from Eq. [23], modified to account
o
for the number of fragments per cm of spoil, ( _ ^) and the
•MTJ
^PY
stoichiometric ratio of pyrite consumption to 0? consumption, b (()-
70
-------
-b(0 ) -1- FFR FPY
QPY = £ -1 r301
2tD(02)(l-X)+t(,(02) MWpy LJUJ
For a given fragment configuration and pyrite content, the magnitude
of QpY depends on the 0» concentration at the fragment surface and
the degree to which the fragment has weathered.
Q . Q represents the rate at which 00 is consumed through
HB HB /
respiration by plant roots and other soil organisms. The magnitude
of Q depends on type and extent of plant cover, time of the year
HB
and the presence of biodegradable organic matter in the reclaimed
profile. Since Q does not affect pyrite oxidation other than
nJi
decreasing the available 0^ (Colvin, 1977), we have chosen a simple
temperature and 0- concentration dependent function to describe the
process. 0- uptake rates for bare (winter) and cropped (summer)
surface soils have been measured to range between 1.5 and 16.0 x
10 moles 0 -sec-cm (soil) (Russell, 1973). If we let the rate
equal zero at 0 C and a maximum value of 16.0 x 10 moles 0^-sec -
-3 o
cm at 30 C and assume that the observed values occurred at an 02
mole fraction of 0.17, but would drop to zero linearly as the 02
concentration goes to zero, we can represent Q _ as:
Q ?Y T n T > n r
HB ^ 0_ %BB T > U 0
[31]
=0.0 T < 0°C
Where Q is -the base rate of 0 production by respiration and
HBB 2.
would be equal to 0.0 when no plants or biodegradable organic
Y
-12 -1
matter are present in the soil and to -1.5 x 10 moles O.-sec
cm - C. for a well established agronomic soil.
71
-------
Q . The rate of chemical oxidation of ferrous iron is very
CHOX
slow at low pH's and pH dependent throughout the remaining pH range.
Singer and Stumm (1970) found that for pH > 4.5 the rate of ferrous
iron oxidation at normal atmospheric pressure can be expressed by:
d [Fe2+]/dt = - ^ [Fe2+] YQ [H+]~2 [32]
with ^ - 1.3 x 10~16 mole2-L~2-sec~1
where the brackets indicate concentration. Below a pH of 3.0, the
rate can be expressed as:
drFe2+]/dt = -K2 [Fe2+] YQ [33]
K2 = 1.7 x 10~9 sec"1
For the entire pH range, Eqs. [32] and [33] can be combined and since
the oxygen uptake rate is equal to one fourth of the ferrous iron
oxidation rate (Eq. [21]), we find the 0~ uptake rate per cubic centi-
meter to be:
A 1 — 9
= - 4W IFe'+J V KiIH+J
chem 2
where is the water-filled porosity.
Q . The rate at which chemoautotrophic bacteria can oxidize
ferrous iron, consuming 0^ in the process, is extremely variable
and depends on the size of the bacterial population and the condition
of the bacterial environment. Expressing Q in a manner similar to
chemical oxidation we have:
- *w d [Fe2+], *w
, w f , . ,
AB ~ 4000 dt ~ ~ 4000 *B LFe J Y02 [35]
Where 1C is the factor that accounts for the bacterial "activity
the reclaimed spoil. The lower limit for K^ is 0.0 when the auto-
trophs are not active. An upper limit to 1C is set by assuming that
72
-------
at maximum "activity," the bacteria are limited by the diffusion
rate of 0- to their surface. If we assume the bacteria are attached
to the fragment surface within the water film surrounding the frag-
ment (Malouf and Prater, 1961), the maximum oxidation rate must
just equal the diffusion rate of 0? through the film.
Y = /A£' [36]
4003 o2 2
where A^ is the fragment surface area per milliliter spoil water,
D,, is the diffusion rate of 0- in water, where 0_ concentration is
W 2. L
expressed as mole fraction and 101 kPa (1 atmosphere) total pressure
is assumed, Yn is the mole fraction of 0_ at the film surface (the
°2 ^
CL concentration at the fragment/bacterial surface is set equal to
0.0), and AX." is the film thickness. Rearranging Eq. [36]
40°°
For A£' = 0.01 cm (ElBoushi, 1975) and Dy = 2.75 x lO' moles 02~
cm— sec, the upper limit of K_ can be calculated for any pyrite and
fragment content. Between the upper and lower limits, the magni-
tude of K_ is found from the bacterial "activity," which depends on
the energy available to the bacteria.
K,,. The primary concern of rhis model is the long term (e.g.,
months) leaching of stripmined lands. Since on this time scale
bacterial population fluctuations are comparatively rapid, we can
consider the bacterial "activity" to be in dynamic equilibrium with
the environment at all but initial times. It is also desirable to
include the effects of the bacterial "activity" directly without
73
-------
having to be concerned with the exact population size and metabolic
kinetics. Most bacterial models are thus of little use to us since
they are concerned with population size or growth rate (Lacey and
Lawson, 1970; Schaitman, et al., 1969; Landesman, et al., 1966;
Lundgren, 1975). Instead, we must devise a scheme that accounts
for the activity of chemoautotrophic bacteria directly.
Treating the bacteria population as a single, idealized organ-
ism, we can represent the energy available to the population per unit
time, E , as being divided into two separate parts. First, the
A,
population must obtain sufficient energy in order to maintain its
current activity. This maintenance energy, E , represents energy'
required to obtain nutrients from the environment, regenerate cell
components, and sustain metabolic porcesses. E^ also includes the
energy required to shield each cell in the population from hostile
environmental conditions such as too low or too high of a pH or
high-salt concentrations. If E exceeds £1 then the remainder of
the energy available per unit time is put into population growth.
The total energy available to the population is partitioned
between maintenance needs and growth.
EA = SM + EG ™
An increase in cell numbers will only occur if E. > EL. and the cells
will cease to function or "die" and the population collapse when
E > EL., where both E^ and E have incorporated into them the
efficiency with which the specific organisms transfer energy from
external sources to internal uses.
74
-------
The energy requirement of an organism can be related to the
rate at which it consumes its energy substrate. Arkesteyn (1980)
found that Thiobacillus, ferrooxidans serves as the primary auto-
troph in increasing the oxidation rate of pyrite. These organisms
use the energy released from the ferrous-ferric oxidation reaction
as their only energy source. He found that the sulfur-oxidizing
bacteria were incapable of oxidizing pyrite directly but could use
the sulfur released from chemical or T_. ferrooxidans induced
pyrite oxidation. Therefore, in this model we'll assume that the
ferrous-ferric oxidation reaction is the sole energy source for
the pyrite-oxidizing autotrophs. If we let RC represent the rate
at which the entire population oxidizes iron (moles of electrons/
unit time) and let AG represent the energy released in iron oxida-
tion (energy/mole of electrons) then:
EA = Rc AG - ^ + EG [391
which, when the population is stable, (Ep - 0), reduces to:
(3
RC AG = EM [40]
Since we are assuming that the population can adjust itself rapidly
enough to always be in equilibrium with its environment, Eq. [40]
should always be true.
We can combine the bacterially dependent terms in Eq. [40]
by solving for AG:
AG = VRc • V I4l!
The magnitude of AG can be calculated if we know the iron ion
concentrations in the spoil solution. AG can be found from:
AG = - FE [42]
75
-------
where F is the Farady and E (volts) is found from the combined
Nernst equations for the exchange of one electron in the ferrous
iron oxidation and oxygen reduction half-cell reactions at normal
pressure.
0.46 - 8.6 x 10 5 T In
Y3[Fe3+]
[A3]
> + 2+
where y-, y_ and y_ are the activity coefficients for H and Fe and
Fe , respectively. Since AG is proportional to the driving force, E,
we will -consider the two interchangeable and talk of the energy as
though it were measured by the driving force, E and thus let E.* = E
at constant cell population size.
The value of E/J will vary in relation to the environment of the
organism, increasing when adverse conditions are encountered. This
can be represented by:
n
!£ = E'. / H x. [44]
a. mm . , i J
i=l
where E'. is the minimum value of E.' for ideal conditions and x.
mm rl i
represents the inhibiting effect caused by the ith inhibition agent.
x. varies from 1.0 for no inhibition to 0.0 for total inhibition
and subsequent cell "death" and population collapse. For T.
ferrooxidans, we will consider only 3 inhibition agents. These are
defined as:
x H Temperature dependence of cell viability. T.
ferrooxidans are mesophiles and based on work by
Silverman and Lundgren (1959), Landesmann, et al.
76
-------
(1966), Belly and Brock (1974), Lundgren (1975)
and Malouf and Prater (1961), we have assigned
the peak cell activity (x =1.0) to be at 28°C,
falling to zero at 4°C (Ehrlich and Fox, 1967)
and 55°C (Cathles and Apps, 1975). A cubic
equation was fit through these points such
that
x =-1.23 x 10~5 T3 - 4.33 x 10~4 T2 + .0657 T - .255 [45]
4°C < T < 55°C
x =» 0.0 otherwise
Figure 13a shows, the calculated value of x versus the
normalized cell "activity" data from Belly and Brock
(1974), Silvertnan and Lundgren (1959) and Malouf and
Prater (1961).
x = T. ferrooxidans are sensitive to pH. At low pH's, cell
PH
activity decreases probably due to acid attack of cell
membranes. At high pH's, activity also decreases
perhaps due to a decrease in efficiency of metabolic
processes that are tuned to low pH's. From the work
by Silverman and Lundgren (1959), Landesmann, et al.
(1966), Schnaitman, et al. (1969), Ehrlich and Fox
(1966) and Malouf and Prater (1961), the maximum
activity is between pH 2.5 and 4.0. A quadratic
expression was fit to the data given by Silverman
and Lundgren (1959) and Schnaitman, et al. (1969) and
is shown in Fig. 13b. From this data:
77
-------
00
to
.8
.6
-*
.4
.2
0
a.
10 20 30 40o 50 60
Temperature °C
a.
1.0
.8
w .6
O.
X!
.4
CM
O
X
3
pH
1.0
.8
.6
.4
.2
0
C.
b.
0 .05 .10 .15 .20 .25
Oj Mole Fraction
C.
Figure 13. Plots of the inhibition factors (solid lines). a) x versus temperature ( C) ;
dashed line is normalized data from Malouf and Prater, 1961; (•) normalized data
from Silverman and Lundgren, 1959; (±) normalized data from Belly and Brock, 1974.
b) x versus pH; (•) normalized data from Silverman and Lundgren, 1959; (A)
pH
normalized data from Schnaitman et al., 1969. c) x versus oxygen mole fraction.
U2
-------
x = -.348 pH2 + 2.26 pH - 2.66 1.54 < pH < 4.95 [46]
= 0.0 otherwise
the maximum (x „ = 1.0) occurring at pH = 3.25.
pn
Q = Oxygen dependence of chemoautotrophic bacteria. T.
ferrooxidans are obligate aerobes whose activity
ceases when 0_ is depleted.. At 25 C, Myerson (1981)
found their activity to decline when 0_ concentra-
tions fell below 5% of saturated levels. Thus, at
normal atmospheric pressure:
Xo2 = 1'° Yo2
Xo2 = Yo2'-01 Yo2
[47]
The x - 0 relation is shown in Fig. 13c
Thus, E' can then be written as:
the magnitude of E' varying with environmental conditions. At this
point, we need to evaluate E'. . No a priori relationships seem
obvious so instead we must turn to experimental data.
We have found only one report in the literature with sufficient
4
detail to evaluate E' . . Bailey (1968) ran culture experiments with
pyrite solutions innoculated with iron-oxidizing bacteria. From his
observations of ferric, ferrous and bacterial concentrations as a
function of time, we can evaluate E/.. Initially, his solutions showed
4
Bailey, J. R. 1968. Biological oxidation pyrite. Unpublished M.S.
Thesis, The Ohio State University, Columbus, Ohio.
79
-------
rapid bacterial growth (doubling time ^ 10 hr), but as the system
approached steady state conditions the population stabilized, in
agreement with our model, and remained fairly constant thereafter
(AG = E£) .
4
Analysis of the results of Bailey 0.968) are shown in Tables
10 and 11. The experimental results are divided into two phases.
Phase 1 represents the growth phase of the bacterial population
when AG > EC,, while phase 2 represents the steady state condition
when AG = E^. To evaluate for E'. , the data from the second phase
a. mm
of the experiment was used to calculate E and EC, from Eq. [43] and
to find x , xn and x . E'. was then found by rearranging Eq.
T U — pti mxn
[48]. The average value for E". from eight measurements during
phase 2 was 0.173 volts (Table 10). This value was then used with
the data from phase 1. Table 11 shows the analysis of the results
from five measurements during the intial growth phase. The values
for EC. were---calculated by correcting the value for E'. found in
Table 10 for x_, x.- and x „. Values for AG were found from Eq.
T 02 pH
[43]. E' is the difference between AG and E.', in each case E'>
G M G
0.0 indicating that a surplus of energy is available for population
growth. The last column in Table 11 shows the normalized growth
rates of the bacteria. Comparing the last two columns, we find
that the growth rate is roughly proportional to the surplus energy,
E_ (especially after 224 hours) which is consistent with our simple
I?
growth model.
80
-------
Table 10. Measured E., values and calculated x_, X- , x TT and
M I U7 pn
E . values from Phase II of experiment by Bailey
mm
(1968).4
hr
593
639
688
758
833
880
929
1002
PH
3.10
3.05
2.95
2.85
2.80
2.80
2.80
2.70
XT
.80
.80
.80
.80
.80
.80
.80
.80
\
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
XPH
1.00
.996
.979
.954
.940
.940
.940
.905
**
.224
.231
.202
.230
.223
.209
.249
,240
E'.
mxn
.179
.184
.158
.175
. .168
.157
.187
.173
Ave. = .173
81
-------
00
Table 11. Measured and calculated coefficients for the bacterial "activity" model
from Phase I of experiment run by Bailey (1968) .
hr
224
362
412
439
459
pH
3.71
3.90
3.50
3.40
3.35
XT Xn XnH AG
1 U_ pH
.8QO 1.00 .935 .312
.800 1.00 .861 .301
.800 1.00 .987 .258
.800 1.00 1.00 .233
.800 1.00 1.00 .226
C ^
.231 .081
.251 .050
.219 .039
.216 .017
.216 .009
RR§
0.42
1.00
0.55
0.39
0.26
V
rl
\
is calculated
= EA - V
based on E . of 0.173.
min
§
RR is the measured normalized growth rate of the bacterial population.
-------
On the basis of this model of bacterial growth, we can calcu-
late the ferric/ferrous ratio at any time and for any conditions
by rearranging Eq. [43] and by using Eq. [48] to calculate Ej.
2+ -v L J n
Fe T3 2 T 8.8 x 10 "
2+
The actual oxidation rate of Fe by bacteria must be such that Eq.
[49] is satisfied. That is the valueof K^ in Eq. [35] is adjusted
such that the ferric/ferrous ratio calculated in Eq. [49] is met.
To extend the model of pyrite oxidation beyond steady-state
conditions of bacterial population "activity", allowances for popu-
lation growth and decline must also be included. Population growth
is modeled by allowing the "activity" (K,,) to double every 12 hours
if conditions are favorable (e.g., AG > E/l) . This compares to the
4
doubling times for population size found by Bailey (1968) of
between 7.5 and 51 hours. When environmental conditions deteriorate
in relation to sustaining population size, the population "activity"
is assumed to respond instantly and K^ decreases.
Chemidal Species
Chemical species that are followed in the model include H ,
2+ 3+ 2-
Fe , Fe , SO , HSO, and the complexes of ferric iron. Concentra-
tions for each are calculated using the activity coefficient for the
ion as calculated by the Davies equation (Davies, 1967, p. 60).
y. = exp
- 0.5 z
- 0.31
[50]
83
-------
which is satisfactory for ionic strengths less than about 0.3 moles/
kg.
Ferric Precipitation. The precipitation and complexation of
ferric iron must be considered. One such step, is the precipitation
of ferric hydroxide:
Fe3+ + 3H20 ->- Fe(OH)3 + 3H+ [51]
c
The change in standard free energy per mole of electrons for this
reaction is AG = -210.kJ and thus is spontaneous as written. The
K
equilibrium concentrations of Fe can be calculated from this
reaction, but the very low values for ferric concentration don't
agree well with measured values from acid—mine drain-waters
(Nordstrom, et al., 1979), when crystaline forms of iron hydroxide
are used. This is probably due to one of two factors, either the
kinetics of the above reaction have not been considered and may be
slow or the crystaline form of Fe(OH)_ may not be the controlling
3+
species for Fe solubility. Amorphous Fe(OH)_ or some other
species may instead be the control (Langmuir and Whittemore, 1971).
Fresh solutions can be significantly supersaturated with respect
to ferric hydroxide precipitates (Langmuir, 1971), but this seems
to be primarily a function of nucleation kinetics. In strip mines,
where nucleation surfaces are abundant, precipitation of ferric
hydroxide would not be a problem. Analysis of acid-mine drain-
waters has, in fact, shown this to be true (Nordstrom, et al.,
84
-------
(1979), the waters seldom being supersaturated with respect to
Fe(OH), :
3 amor
Fe(OH)3 anor + 3H+ •+ Fe3+ + 3H2
4. Yet many measurements of total ferric iron concentrations exceed
A
the calculated values (Bailey, 1968 ; Pionke, et al., 1980). This
is primarily due to ferric complexes. Ferric iron complexes strongly
with hydroxides and sulfates, which can raise the aqueous concentra-
3+
tion of Fe a hundred to a thousand times at moderate pH's (pH ^ 5).
Thus, the complexed forms of ferric iron must be accounted for.
Another reason we must take account of iron complexes is that
in most kinetic studies of pyrite oxidation or bacterial catalysis
of ferrous iron, ferric complexes have been ignored and values
reported as Fe concentrations, are in reality, total aqueous
3+ 3+
Fe , Fe_ . Thus, the reaction kinetics are based on total dissolved
ferrous iron not just the Fe ion.
For calculating the pyrite oxidation rate in this model, the
3+
Fe concentration in solution is used in the rate expressions.
85
-------
3+
Fe is found in one of two ways. If the hydroxide solid is present
Eq. [52] is used to calculate the ferric iron concentration from
which the concentration of the complexes can be found. The solid
iron hydroxide is then adjusted for changes in total dissolved iron
minus pyrite dissolution. If no solid hydroxide is present, the
dissolved iron species are adjusted so that the mass balance is
preserved and the species are in equilibrium with each other. The
complexes considered in this model and their equilibrium constants
are shown in Table 12.
Removal of Reactio'n Products
The dissolved products of the pyrite and bacterial-oxidation
reactions must be removed from the spoil profile. Two possible
methods exist for H removal; acid neutralization with a possible
increase in reserve acidity and leaching by deep percolation. For
sulfate and iron, only leaching is assumed to remove the ions from
the profile.
Acid Neutralization. Acid produced by pyrite oxidation may be
neutralized or modified by the surrounding rock matrix or gangue
material (Rogowski, et al., 1977). These H - gangue reactions
appear to be quite significant. Lovell, et al., (1978) found that
in situ neutralization reactions were significant in all three
mine sites they studied, effectively removing all of the acidity
in two of the sites. Although not of the same magnitude, consider-
able neutralization and transformation to reserve acidity was
observed in a small column-leaching study (Pionke, et al., 1980).
86
-------
Table 12. Iron complexes and log of the equilibrium constants
for their formation and for sulfuric acid dis-
sociation and amorphous ferric hydroxide precipitation.
Reaction logK
H._0+Fe -*->-Fe(OH) +H - 2.94
2H-0+Fe -*-»-Fe(OH)9+2H - 5.70
2H?0+2Fe -^-HFe,, (OH)9 +2H - 5.22
3+ +
3H20+Fe «-»Fe(OH)- +3H -12.
aq
4H20+Fe3+^Fe(OH)~+ 4H+ -21.60
Fe +HSO.-«->-FeHSO, 0.60
4 4
4 4
3H++FeOOH+H2CK->-Fe3++3H 0 4 . 9
Reference
1
1
1
2
2
1
1
3
References refer to: 1) Sapieszko, et al., 1977; 2) Baes and
Mesmer, 1976; and 3) Nordstrom, et al., 1979.
87
-------
Although not reported in the study, approximately 10% and 20%
of the H formed from pyrite oxidation was consumed by neutraliza-
tion and transformation to reserve forms of acidity (mostly
aluminum), respectively (H. B. Pionke, personal communication).
Column studies by Braun, et al., (1974) have shown similar results.
Carbonates may be very reactive with H and are capable of
maintaining the water percolating through them at pH's near
neutrality (Freeze and Cherry, 1979). The carbonate-H reaction is
treated separately from other gangue-H reactions because of this
large neutralization capacity and because of their use as liming
materials on reclaimed stripmines. The reaction of carbonates
with H is assumed to be controlled by the chemical kinetics. The
rate of carbonate consumption per unit area of carbonate can be
described by (Wentzler, 1977).5
Qc = - Kc [H+] [53]
' -1 -2
where 0 is the rate of carbonate consumption (moles-sec -cm )
c
—6 2
and K the first-order rate constant (2.9 x 10 L/cm -sec).
c
Assuming the carbonate is in the form of distinct, pure fragments
that dissolve completely with time, we can describe the consumption
of carbonate mathematically in a manner similar to the consumption
of pyrite [Eq. 23] but without the diffusional control term (t ).
For spherical particles, Levenspiel (1972) gives the rate of change
of the fraction of carbonate sphere remaining, X , to be:
Wentzler, T. H. 1977. A study of the interactions of limestone
in acid solutions. Unpublished M.S. Thesis, The Pennsylvania State
University, University Park, Pa.
88
-------
3 X 2/3 K [H+]
= °p R C [54]
c s
where p is the molar density of the sphere and R its original
c s
radius. The rate of carbonate consumption and thus H consumption
can .then be calculated from Eq. [54] and the number of carbonate
fragments per volume.
Reactions between H and other gangue minerals that need to be
considered include neutralization of H to form weak acids, such
as orthoclase reacting to form kaolinite (Birkeland, 1974, p. 61).
+ . . H*
(orthoclase) (kaolinite)
or the exchange of H for other cations on clay colloids and oxides.
Reserve acidity in the form of aluminum and aluminum hydroxides may
also serve as a sink for hydrogen. In general, the amount of pH
modification caused by the gangue would depend on the mineralogy
and pH. For this model a simple empirical relation was used to
partition the H produced into active solution-H and combined
neutralized- or reserve—H . The relation has the form:
AH+ = AH* (1.0 - exp (G_(G -pH)) ) [56]
K 15 A
4- + +
where AH and AIL are the actual increase in free H and the amount
A. f J\
of H produced by all the remaining reactions respecively, and G.
and G,, are empirical constants. G. has the physical significance
jj A
that when the solution pH equals G. all the H produced is consumed
A
by the gangue and the pH remains constant. G_ is a scaling factor
D
which determines the rate at which the condition of constant pH is
89
-------
approached. The shape of the neutralization curves used in this
study are shown in Fig. 14.
Leaching. Water percolating through the reclaimed-spoil
profile will flush the oxidation products out of the profile.
Intuitively, it would seem unrealistic to assume that Darcy type
flow governs the movement of water in coarse-spoil material.
Indeed, ElBoushi (1975), measuring infiltration into coarse-stone
rubble, and Rogowski and Weinrich (1981), modeling infiltration
into reconstructed-spoil profiles, have demonstrated the short-
comings of Darcy's Law for describing water movement in coarse
materials. In addition, since it is assumed in this model that
the water content of the spoil remains constant over time, infil-
tration studies like those quoted above are of limited help here.
Considerable progress has been made in understanding and modeling
the leaching of coarse materials (Rao, et al., 1980 a and b), but
such treatments are beyond the intent of this model where only a
simple removal mechanism of solutes is desired.
Instead, we first recognize that the model will be solved
by finite-difference techniques and therefore divide the spoil
profile into a number of horizontal layers. Within each layer,
the water is assumed to be completely mixed and homogeneous, which
represents a major simplification of the leaching process. In
strongly structured soils, it has been shown that infiltrating
water can penetrate very deeply in a short time with very little or
no interaction with the intervening soil layers (Quissenberry and
90
-------
NEUTRALIZATION CURVE
a
1.
2. 3. 4
EXPECTED PH
Figure 14. Neutralization curves as calculated from equation in
text. G_ equals 1.0 in both plots
o
G equals 2.5 in
A
plot 1 (•) and 2.8 in plot 2 (•).
91
-------
Phillips, 1976;.Bouma and Dekker, 1978). Incorporating this
phenomena into the leaching process, we assume that water leaving
any layer is partitioned to the underlying layers in proportion to
the inverse of the distance separating them, 1/d. Water traveling
between two layers does not interact with the intervening layers.
For an n layer system, water infiltrating the surface is
partitioned among all layers proportional to the inverse of the
depth to the layer (the distance is measured from the surface to
the center of the layer). The fraction of infiltrating water enter-
ing any layer, i, is:
n
fraction = 1/d./ I 1/d. [57]
1 3-1 J
Water leaving any layer will also be partitioned proportional to 1/d
to the underlying layers. The fraction entering any layer j from
layer i where layer 1 is at the surface is:
n
fraction. . = l/(d.-d.)/ £ l/(d -d.) [58]
13 J 1 k=i+l * x
The amount of water leaving any layer is equal to the amount
entering, which is just the sum of all the fractional contributions
from overlying layers, the 0 layer indicating surface precipitation:
j-1 n
outflow. = I [l/(d.-d.)/ E I/(d-d.)] outflow.. [59]
J i=0 3 X k=i+l k 1 X
+ 2-f
H , Fe , total sulfur, total dissolved ferric iron, and the
acid-neutralization products are carried with the percolating water
and leached from the mine profile. The chemical load entering any
layer is equal to the sum of water coming from each overylying layer
92
-------
multiplied by the species concentration in the layer. The amount of
each constituent leaving a layer is just the concentration of the
species in the layer multiplied by the outflow.
An example of leaching as described by Eq. [58] is shown in
Fig. 15. The figure shows the normalized concentration of a non-
interacting solute in the water leaving a 10-meter deep profile
that is divided into 20 layers. The profile has a water-filled
pore volume of 0.13 and the water is infiltrating at a constant
rate of 50 cm/year. The initial and boundary conditions for the
solute concentration are:
C. = 1.0 1 < i < 20; t = 0.0
1 [60]
C. = 0.0 t > 0.0
in
Figure 15 shows a considerable smearing of the solute front, with
the concentration slowly tailing off to zero after more than 3
pore-volumes have passed through the profile. The method of in-
verse weighting of water flow between layers mimics a system where
diffusion - dispersion processes are of considerable magnitude
(Rose, 1977).
Solution Method
Equations [27], [28], [30], [31], [34], [35] and [49] serve as
the basis of a model for describing in situ pyrite-oxidation.
Equations [53], [56], [59] and the expressions listed in Table 12 are
used to adjust the concentrations of each species and calculate the
leaching rate of the reaction products, where water is assumed to
93
-------
1.0
0.8
PORE VOLUMES
1 2
0.6
'EFF
0.4
0.2
0.0
1000 2000
DAYS
O Q
3000
Figure 15.
Example leaching curve showing the normalized concen-
tration versus water-filled pore volumes. Profile was
10 meters deep, divided into 20 layers with a water-
filled pore volume of 0.13 and an infiltration rate of
50 cm/year.
94
-------
move downward only at a uniform annual rate. For air movement in
the vertical direction only, Eq. [27] is a nonlinear, nonhomogeneous,
parabolic equation. Equation [27] can be solved using an implicit,
finite-difference technique in which the reclaimed-mine profile is
divided into N horizontal layers.
The solution of these series of equations is very unstable due
to the complicated interdependence of the variables and to the non-
linear form of some of the equations (e.g., Eq. [49]. The solution
procedure involved estimating values for all of the variables at
time t + At, calculating the diffusion coefficients and source/sink
terms from Eq. [28], [30], [31], [34] and [35] and then solving Eq.
[27]. The calculated values for the 02, CO , Fe , Fe and H con-
centration were then used to recalculate the diffusion coefficients
and source/sink terms and Eq. [27] was solved again. This procedure
was repeated until the values for 0», CO-, Fe. , Fe and H con-
centrations had converged. Values for IL, and the leaching rates of
each chemical species were then updated for t + At and the entire
process repeated a maximum of 25 times or until all values had con-
verged. The iterative scheme has proven to be stable and capable
of handling large (^ 6 months) time steps for all cases studied.
A comprehensive testing of the model, comparing the model
results to measured values, was not possible due to the lack of a
sufficiently complete data set for an active, oxidizing-leaching
pyrate body. However, several simulations were run to determine the
95
-------
interaction of several parameters in the model and to compare the
simulator results to known stripmine behavior. For all simulations, a
reclaimed profile, 10 meters deep and divided into 20 equal horizontal
layers, was used. Unless otherwise noted, each layer contained 75%
(wt/wt) coarse fragments (£ = 1 cm), containing a pyrite content of
0.25% (wt/wt) and a 20% water-filled porosity. The bulk density of
each layer was 1800 kg/m and a constant water saturation of 70% was
used.
At the beginning of each simulation the profile air-space contained
0.21 mole fraction 0 and 0.0003 CO . The spoil water contained 0.28
2+ 3+
mg/L Fe ,4.8 mg/L sulfate, less than 1 mg/L Fe and was at a pH of
5.0. No soluble ferric hydroxide was assumed to be present. These
values for dissolved species may be unrealistically low for spoil water
in newly reclaimed mine-sites because of the large content of soluble
salts in spoil material (Lovell, et al., 1978), but were used so that
the formation of oxidation products could be observed more easily. After
the pyrite started to oxidize, the water infiltrating the surface of the
profile was assumed to be at a pH of 5.0 and contain no dissolved iron,
with sulfate at a concentration of 4.8 mg/L. In the simulations where
iron-oxidizing bacteria are active, a 32 day "innoculation" period was
assumed. During these first 32 days, the bacteria were assumed not to
be active. After this time a base "activity" for the bacteria,
represented by K = 10~ , was used. That is, the base rate of ferrous
oxidation catalyzed by bacteria was set to less than 0.1% of the
minimum chemical oxidation rate of ferrous iron.
96
-------
Results and Discussion
Two major aspects of the model were investigated. The signi-
ficance of iron-oxidizing bacteria was studied, since the way in
which the model calculates their "activity" from the energy subtrate
and environmental conditions is unique. Several other simulations
were also performed to illustrate the flexibility of the model and
compare the model output to expected behavior.
Role of Iron Oxidizing Bacteria
Since this model is unique in the way that the activity of
iron-oxidizing bacteria is accounted for, the effect of bacteria on
pyrite weathering as predicted by the model was examined. In the
first simulation, Run 1, iron-oxidizing bacteria were assumed not to
be active and thus the only source of ferric iron was chemically
oxidized ferrous iron. Figure 16 shows the fractional amount of
pyrite consumed within the entire profile from 0 days, when pyrite
oxidation begins, to 10,000 days or approximately 27 years. The
pyrite is consumed slowly, with just over 22% consumed after 10,000
days, the consumption is due almost exclusively to direct 0,, reaction.
The ferric iron concentration never exceeds 0.5 ymoles/L at any time
in any layer. The rate of pyrite oxidation due to ferric iron is
never greater than 0.07% of the direct 0., pyrite oxidation rate.
The rate of pyrite oxidation is slightly faster at initial times, but
is virtually constant (slope in Fig. 16 is constant) after 3000 days.
A similar trend is observed in Fig. 17, where the rate of total iron
97
-------
86
(K
C
Tl
n
03
o
O
3
o
>-tl
•a
O
X
H-
o.
H-
N
fD
O.
•3"
H-
3
m
3
it
O
H-1
fD
CO
c
CO
O
b
FRACTION PYRITE
pop
ro
o 01
> O
•< o
CP o
so
CD
3
Cu
pa
o
o
o
o
p
In
—r
p
CD
C C
Z 2
PO —•
-------
2
being leached from the profile (moles/m -day) is plotted against time
for the 0 to 10,000 day period. A marked peak in the leach rate is
observed at 2^.00 days (5.75 years), which then levels off slowly to
2+
an almost constant value. The average concentration of Fe within
the profile after 2J.OO days of pyrite oxidation is 0.005A moles/L.
The average pH of the spoil water is 1.99. After 10,000 days of
weathering, the ferrous iron concentration and average pH of the
spoil water are 0.0032 moles/L and 2.22, respectively. While the
2+
Fe concentrations seem to be well within the range of values found
for water samples removed from below a reclaimed stripmine, the pH
values appear to be about 0.5 of a pH unit lower than measured
values (Rogowski, et al., 1982).
In the second simulation, Run 2, iron-oxidizing bacteria were
allowed to interact with the pyrite system as predicted by the
model. Figure 16 also shows the amount of pyrite consumed over time
for this simulation. The consumption of pyrite is almost identical
to the results of Run 1, where no bacteria are active, the relative
increase in oxidation being less than 3%, which represents an abso-
lute increase in pyrite oxidation of 0.7% after 10,000 days. The
plot for Run 2 in Fig. 17 shows the same behavior, almost no differ-
ence is observed in the rate of total-iron removal for Run 1 and
Run 2.
The lack of impact by the bacteria in this case is explained
by the fact that the pH of the spoil water drops rapidly below
2.6 for all layers after only 200 days and remains between 1.8 and
99
-------
H
O
O
l.f
<£
1'°
UJ
io.e
O
o
x 0.6
z
o
£ 0.4
H
O no
1- U.2
0.0
(
i i i i i i i i l
o RUN 1
o RUN 2
-
*P*A*to^
cP ^cP^i
o
o
cf
D
IP
1 1 1 1 1 1 1 1 1
D 5000 10000
DAYS
Figure 17. The rate of leaching out of the profile of all iron species versus time for Run 1
and Run 2.
-------
2.3 for most layers for the remainder of the simulation. Examina-
tion of Fig. 13b shows that at these lower pH's, x _ drops to
pH
between 0.2 and 0.7 indicating decreased "activity" of the bacteria
because of adverse H activity and a decreased role for ferric iron -
pyrite oxidation. However, it is misleading to believe that the
bacteria exert no influence under these conditions. Figure 18 shows
the rate of pyrite oxidation (moles/cm -sec) as a result of direct
02 and ferric oxidation for Runs 1 and 2 after 5 years of oxidation.
Although the overall rate of pyrite oxidation is similar, in Run 1,
0- is the only important oxidizer while in Run 2 bacterially
produced ferric iron begins to become important in the surface layer,
where the pH remains higher due to infiltration of water at pH 5.
This increase in ferric iron concentration can also be seen in Fig.
19 where the ferric/ferrous concentration ratio in the water leaving
the profile is plotted against time. The ratio is about 100 times
greater during Run 2 than during Run 1.
Two additional simulations were run under the same conditions,
but where interactions between the acid produced by pyrite weather-
ing and the rock matrix were assumed to occur. Figure 20 shows the
fraction of pyrite consumed versus time for these two runs compared
to Run 2. In Run 3, the gangue material is assumed to react with
H so that the pH never falls below 2.5 (G = 2.5). In Run 4, the
A.
system is maintained at a pH of 2.8 or above (G = 2.8"). The H
A
produced by pyrite oxidation, but not assumed to contribute to the
101
-------
0
1
2
3
J *
f 5
Q.
S 6
7
8
9
10
Pyrite Oxidation Rate x1014 (moles/cm3-sec)
01 2 3
^XX^XXXXXXXXXX
vXXXXXXXXXXXXXXXXXV
\XXXXXXXXXXV\X1
\XXXXXXXX1
^OOsXXXXXXXXXXXX
xxxxxxxxxxx-
XXXXXXXXXXi
XXXXXXX1
XXXXX1
Figure 18. Oxidation rate of pyrite for each layer after 5 years of
oxidatio'n. Fine cross-hatching is total oxidation rate
for Run 1. Open cross-hatching is rate of oxidation by
direct oxygen reaction with pyrite in Run 2. White cross-
hatching on black is oxidation rate due to ferric iron
reaction with pyrite in Run 2. Below 1 meter, ferric
oxidation is negligible. Below 4 meters, oxidation rates
of Run 1 and Run 2 are identical
102
-------
IU
UJ
1—
X
o
UJ 10~4
0
<
A lcf5
Ul
rO
UJ
U_
10~6
r ' ' ' ' ' L 00°°^
D oQo ao o -
"^ nO^^ ~
~o Qo° ~
a o°
~° oa"00
_ ° o RUN 2 -
_ —
— *~"
™~ D 1 I Kl 1
« r\ w mi rt O "™"
•-• f\ rt O O ^ "•"•
~ ' 0ooOo0000° I
Ooooooo° °
O o 1 1 1 1 1 1
10OO 3000 50OO 7000
DAYS
Figure 19. The ratio of ferric iron to ferrous iron in the water
leaving the profile for Run 1 and Run 2.
103
-------
H activity, is represented by the reserve acidity in the spoil
solution.
Raising the pH of the system has the effect of increasing
the x _ function value and thus increasing bacterial "activity."
pH
In Run 3, where the pH is maintained at 2.5 or higher, Fig. 20
shows a considerable increase in the amount of pyrite consumed over
time. After 10,000 days, 30.5% of the pyrite is consumed for a
relative increase of 36% over the unbuffered, bacterial Run 2.
Most of this increase occurs before 2,000 days, after which the rate
of pyrite consumption is very similar to Run 2 (plots are parallel).
When the system pH is maintained at 2.8 and above, 36% of the pyrite
is consumed after 10,000 days for a relative increase of 61% over
the unbuffered run. Again, most of this increase over Run 2 occurs
before 2,000 days, but the rate of pyrite oxidation continues to
be greater than Run 2 or Run 3 as indicated by the continuously
diverging plots.
To maintain the pH at 2.5 and 2.8, a considerable proportion of
the H* formed by Eqs. [18], [19] and [21] must be converted to
acidity by reactions with the gangue. In Run 3, 39% of the acid
formed from pyrite oxidation is converted to acidity after 10,000
days of oxidation. Again, it should be remembered that in this
model the acidity term represents both neutralization and conversion
to reserve forms of acidity such as Al . In Run A, 56% of the acid
104
-------
0
10000
Figure 20. Fraction of pyrite oxidized witliin the entire profile versus time for Runs 2, 3, and A,
-------
from pyrite oxidation is converted to acidity in order to maintain
the pH at 2.8 or higher. Although these percentages seem high,
they certainly fall within the range of observed behavior for strip-
mine lands (Lovell, et al., 1978).
Figure 21 shows the rate of removal of total iron over time
for Run 3 and Run 4. Run 2 is replotted on this figure for ease of
comparison. For Run 3, where the pH is maintained at 2.5 or higher,
the peak in the total iron-leaching rate occurs at 1,750 days
(°u 5 years). The rate of leaching is considerably greater than Run 2
throughout most of the simulation, being almost double when the maxi-
mum rate is observed. Although greater in magnitude, the shape of
the rate vs. time plot for Run 3 is very similar to Run 1 and Run 2,
Run A, however, shows a considerably different behavior. The plot
for Run 4, where the pH is maintained at 2.8 or higher, shows a
tendency for the rate to reach a plateau value of about 0.0065
2
moles/m -sec and then slowly oscillate around this value while the
plateau rate slowly decreases with time. This behavior is due to
two factors. As 0_ penetrates a layer at a sufficient rate to
permit bacterial activity, the ferric iron concentration increases,
*
which increases the overall rate of pyrite oxidation, which in
turn increases the total iron in solution and in the leachate. This
process is what is occurring within the 250 to 300 cm layer between
3,300 and 4,000 days in Run 4. A point is reached, however, where
the bacterially catalyzed-ferric iron concentration within the
106
-------
5000
DAYS
10000
Figure 21. The rate of leaching out of the profile of all iron species versus time for Runs 2, 3,
and 4.
-------
layer .exceeds the ferric iron solubility as controlled by amorphous
ferric hydrooxide at pH 2.8. The ferric iron then starts to pre-
cipitate, removing iron from solution and from the leaching water.
3+
The rate of leaching then starts to decline because the Fe oxi-
dant is maintained at a stable concentration while the pyrite
concentration decreases. From Eq. [26], where t is greater than
t (pyrite oxidation rate is controlled by diffusion), it can be
W
seen that as X decreases the rate of pyrite oxidation decreases.
This is what is occurring between 4,000 and 5,100 days, where X,
for the layer between 250 and 300 cm in which the maximum rate of
pyrite oxidation is taking place, decreases from 0.646 to 0.449.
After 5,100 days the pyrite concentration in the layer is suffi-
ciently low that the oxidation rate and consumption of 0« has
decreased to a point that increased levels.of 0- are diffusing
to the next deepest layer raising that layer's 0« concentration.
The process is then repeated in the deeper layer. The iron con-
centration in the deeper layer and the profile as a whole and in
the leach water starts to increase again. Thus, the oscillating
behavior of Run 4 in Fig. 21 is due to the division of the profile
into distinct layers, while the constant value of the leaching rate
is controlled by the precipitation of ferric iron within the profile
when the pH is maintained at 2.8 or higher. This is the first simu-
lation discussed where iron precipitation is observed.
A better indication of the rate of pyrite oxidation and acid
leaching for Run 4 compared to Run 3 is shown in Figure 22, where
108
-------
the total acidity being removed from the profile in. the leach water
versus time is plotted. The total acidity is the sum of the con-
centrations in the leachate of H , one-half the acidity value
calculated from the gangue-H interaction, and three times the ferric
iron values. One-half of the acidity value is used in calculating
the total acidity in an attempt to partition the gangue-H inter-
action between neutralization processes and the formation of reserve
acidity. As can be seen in Fig. 22, the two plots are of similar
shape with the plot for Run 4 indicating an increase in the rate of
acid leaching of about 30% over Run 3 after 1,950 days of pyrite
oxidation.
One other simulation was run to investigate the response of
the bacterial "activity" model. Run 5 was conducted assuming no
gangue-H interaction but where the x „ function [47] was lowered
ptt
one-half pH unit so that the maximum, x = 1.0, occurred at pH
pti
2.75. This simulation was run because the mathematical form and
value of the coefficients in Eq. [48] represent only a first
approximation and are not absolute. Differences in bacterial strains,
substrate type, and means of measuring bacterial activity may cause
discrepancies between the leaching studies cited in estimating the
x. values and bacterial activity within stripmine material. Figure
23 shows the plots of pyrite consumed versus time for Run 5 and
Run 3. The plots are of similar magnitude, although buffering the
pH at 2.5 or higher results in greater consumption of pyrite at
109
-------
OTI
to
3
0.
-C-
•
(TO
C
ID
NJ
NJ
TOTAL ACIDITY |MEQ/M2-DAY)
H ,.
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u
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o
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o RUN 3
a RUN 5
Qa
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5000
DAYS
J I
10000
Figure 23. Fraction of pyrite oxidized within entire profile versus time for Run 3 and Run 5,
-------
early times, but less consumption after 8,800 days or after about
28% of the pyrite is consumed.
Runs 1-4 indicate that, at least for the parameters used, the
iron-oxidizing bacteria increase the pyrite oxidation rate only if
the pH is maintained above ambient levels of interactions with the
rock matrix. Removal of H by leaching alone (Run 2), was insuffi-
cient in preventing the pH in dropping to levels where the bacteri-
ally produced ferric iron only compensates for the loss in direct
0_ pyrite oxidation caused by the drop in 02 concentrations due to
bacterial consumption of 0-- The oxidation rate in Run 4, where
the pH is maintained at 2.8 or higher is controlled intermittently
by ferric solubility and bacterial "activity," with bacterial
"activity" controlling the oxidation rate until the solubility of
ferric iron is exceeded. The solubility then controls the oxida-
tion rate until bacteria start to increase in the next deepest
layer because of increased 0? levels.
Model Sensitivity and Versatility
Although it is beyond the scope of this paper to perform an
extensive sensitivity analysis of all the parameters in the model or
to model all possible management alternatives to reclaiming a given
mine profile, several possible combinations of parameters were
studied to demonstrate the versatility of the model.
Effective Diffusion Coefficient. Ultimately, the rate of pyrite
oxidation can exceed the rate at which 02 is supplied to the oxida-
tion zone. In this model, 0- is assumed to be transported through
the mine profile by gas diffusion which is very sensitive to the
112
-------
air-filled porosity and tortuosity of the flow path. To observe the
effect of varying the porosity and tortuosity on the results, two
simulations were run where the air-filled porosity from Runs 1-5
was doubled and the tortuosity was halved. Examining Eq. [27], it
can be seen that this combination results in increasing the effective
diffusion coefficient, D ", by a factor of A. In Run 6, iron-
2
oxidizing bacteria are assumed not to be active within the profile,
analogous to Run 1. For Run 7, bacteria are assumed to be active
as calculated by the model, with the spoil solution pH maintained
at a pH of 2.5 or higher (G. = 2.5). This is comparable to Run 3.
Figure 24 shows the plots for Run 6 and 7 for the consumption of
pyrite over time. Run 3 is included for reference. The oxidation of
pyrite increases significantly with the increase in the effective
diffusion coefficient. Run 6, without the bacteria, shows a signi-
ficant increase over Run 3, with 40% of the pyrite consumed after
10,000 days. 'When the bacteria are allowed to be active, Run 7
shows that a very large increase in the amount of pyrite consumed
is obtained, with 70% of the pyrite consumed after 10,000 days.
This represents a 133% increase in pyrite oxidized over Run 3 and
a 75% increase over Run 6. At the reduced air-filled porosity,
when bacteria were included at a buffered pH of 2.5 the amount of
pyrite oxidized increased by 24% over the case where no bacteria
were present (Run 3 compared to Run 1, Figs. 16 and 20). Thus, at
the greater air-filled porosity, the effect of bacteria is increased
(75% increase in pyrite oxidation versus a 25% increase). The
113
-------
00
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i-l
01
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rr
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3
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FRACTION PYRITE
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3
CO
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-------
effect of increased pyrite consumption is even greater at early
times. After 500 days, 3 times as much pyrite is consumed in Run 7
than Run 6.
The effect of increased diffusion can also be seen in Fig. 25
where the rate of total iron leaching from the profile is plotted
*
against time. The plot for Run 3 is also shown for comparisons
with Runs 6 and 7. The leach rate of iron shows a similar pattern
over time for the three runs, however, the magnitude is greater at
all times for Runs 6 and 7 compared to Run 3. The leaching rate is
particularly greater in Run 7 where iron-oxidizing bacteria are
present.
The effect of increasing the diffusion rate is perhaps better
shown in Fig. 26 and 27 where the 0? concentration with depth after
1,825 days (^ 5 years) of pyrite oxidation is plotted. Figure 26
shows Runs 1 and 6 where bacteria are not allowed to be active. 02
concentrations at the deeper depths are much higher for Run 6.
The shape of the curves reflect a process where the consumption term
is proportional to the concentration (Kirkham and Powers, 1972).
This is in contrast to Fig. 27 where Runs 3 and 7 are plotted.
These 0« profiles show a near linear decrease with depth similar to
diffusion through a non-interacting zone to a layer of complete
0,, consumption. 0^ does not penetrate as deeply in the profiles
where bacteria are active due to the concentration of pyrite oxida-
tion in the first few layers of high pyrite concentration rather
than slower oxidation rates distributed over several layers as is
the case when bacteria are not active.
115
-------
CJ
\3.0
UJ
O
2
2.0
z
o
a:
1.0
0.0
1 1
A
A
^/T-0.0216
- o
OA-0.0054
1 1 1 T
o RUN 3
o RUN 6
A RUN 7
J I I L
5000
DAYS
I I
10000
Figure 25. The rate of leaching out of the profile of all iron species versus time for Runs 3,
6, and 7.
-------
CL
UJ
Q
0.0
MOLE FRACTION
0.05 0.10 0.15 0.20
8
o
9 -
10
T
T
o
o
o
o
o
o
o
o
o o
o o
O o
AFTER 5 YEARS
o RUN 1
o RUN 6
0.25
Figure 26. The mole fraction of oxygen within the profile versus
depth (m) after 5 years for Runs 1 and 6.
117
-------
MOLE FRACTION
2
X
1—
Q.
LJ
Q
0
0
1
2.
3
4
5
6
7
8
9
10
.0 0.05 0.10 0.15 0.20 0.;
1 1 1 1 -
0 0
O D
-
o o
0 0
-
0 0
0 D
_
0 0
00
- -
CD
r AFTER 5 YEARS
33 o RUN 3
Q RUN 7
D
D
O
D
D
D
— —
D
D
I.I.
Figure 27. The mole fraction of oxygen within the profile versus
depth (m) after 5 years for Runs 3 and 7.
118
-------
Pyrite Distribution. Runs 1-7 were conducted with a uniform
pyrite distribution with depth to simplify the comparisons between
the runs. Two simulations were performed to illustrate the depend-
ence of pyrite oxidation on pyrite distribution. The two simulations
were run under conditions similar to Run 3 except that the initial
pyrite distributions were as shown in Fig. 23. These distributions
are analogous to burying a "worst" pyrite layer at either 4.75
meters or 9.75 meters and replacing the best material or material
with the lowest pyrite content near the surface.
Figure 29 shows the amount of pyrite consumed from 0 to 4,000
days for these two runs and Run 3. Both Run 8, where the worst
layer is half-buried and Run 9 where the layer is completely buried,
show a marked reduction in pyrite oxidation. However, Runs 8 and 9
show very little differences in pyrite oxidation, indicating that
for the combination of parameters used, the position of the worst
layer is not as important as the position of the first layer having
a sufficient pyrite content to support an oxidation rate that
effectively consumes all of the oxygen. This is best illustrated
in the 0« versus depth plots for these two runs after 3,650 days
(10 years). Figure 30 shows these 0- profiles. In each case, 02
does not penetrate significantly beyond the first layer having a
pyrite content gerater than 0.25% (wt/wt), which is sufficient to
consume most of the 0--
119
-------
KJ
O
.01
.02
Fract ion Pyr ite
0 .01 .02 0
01
.02 .03
V
1
2
3
J 4
f 5
ex
» 6
Q
/
8
9
in
|
1
§
|
|
|
-------
o-
rr
H-
0
3
«•
?3
C
O3
X-N
cr
c
H-
(B
a.
o
rr
lj
Ln
<§-
C
3
O.
3
VO
^
buried
O
rr
vo
ui
-
>"x
00
r»
NJ
vO
T!
11
01
n
rr
H-
0
3
O
It!
-o
H-
rr
re
O
H-
D.
H-
N
re
D-
s:
rr
H-
3
re
D
H-
re
•o
o
i-h
H-
I—1
re
1
en
c
CD
rr
H-
3
re
i-n
O
?o
C
3
FRACTION PYRITE
POP
o *_ ro
P
O
O
0
g 8
K 0
01 o
GJ
8
O
O
BL. ! i '
Wt>
fi t>
Q. t>
S >
H. »
M >
S 0
%. >
B *> ooc>
ft ^ CD ao m
6 \ c c <
?, % m m z
8 p o o
8 * — — 2
jr» ^ ^^ ^^ C/^
0 *->! ^J H
§ t> 01 01
B > 2 S
fi &
8 &
8 p
8 p
8 *
8 . *
8 >
8 *
8 *
B *
8 p
ff »
JD C^
r? >
% >
HD >
O t>
1 I 1 1
o
0
re
3
rr
if
-------
0.0
MOLE FRACTION
0.05 0.10 0.15 0.20
X 5
D.
Lu)
Q
8
10
CD
CD
n>
x
at
DO
00
o o
0 0
Q O
O O
0 O
O O
O O
O O
DO
AFTER 10 YEARS
o BURIED (4.75 M)
o BURIED (9.75M)
0.25
figure 30. The mole fraction of oxygen within the profile versus
depth (m) after 10 years for Run 8 (buried at 4.75 m)
and Run 9 (buried at 9.75m).
122
-------
Inhibition of Bacteria
Comparing Run 1 to Run 3 or Run 4, it is apparent that, at least
under some circumstances, a considerable reduction in the oxidation of
pyrite over time can be achieved if a system can be shifted from
bacterially catalyzed Fe oxidation of pyrite to direct 02 oxidation.
Indeed, techniques for inhibiting bacterial activity have been pro-
posed as a means of reducing acid drainage from reclaimed stripmines
(Kleinmann and Erickson, 1981). If bacteria can be inhibited from
the beginning of pyrite oxidation, a reduction of the magnitude
represented by the difference between Run 3 or 4 and Run 7 and Run 6
may be possible. Amending the stripmine spoil after oxidation has
started and bacteria have been established in order to inhibit
bacterial activity and reduce acid drainage has also been suggested
(Kleinman and Erickson, 1981). To simulate the situation in which
iron-oxidizing bacteria are inhibited after they have become
established, a run was made identical to Run 7 but where the
bacterial activity was assumed to cease after approximately two
years of oxidation. This represents the extreme case where the
addition of a bacteriacide is 100% effective in destroying the
•
bacteria throughout the profile. Figure 31 shows the rate of
leaching of total iron over time for this simulation along with the
results of Run 7 for comparison. Although the bacterial activity
ceases after 700 days, allowing the oxidation system to shift from
Fe -dominant to O^-dominant, no difference in the leaching rate of
123
-------
K3
1
CM1
y
o
2
^ 2
x
z
o
ir
t
O
D
00
DO O
cP
O
a
o
o
o
o
O
KB=O.O
e
8
a
o
1000
a UNINHIBITED
a
INHIBITED
I
2000
DAYS
3000
O O
4000
Figure 31. The rate of leaching out of the profile of all iron species versus time for Run 7 (no
inhibition) and Run 10 (complete inhibition after 2 years).
-------
iron is observed until 250 days later. From 950 days onward, the
plots continue to diverge such that a large reduction is observed
after 3,000 days, or 2,300 days (6.3) years after bacterial inhibi-
tion. The system demonstrates an apparent sluggishness in response
to the decreased oxidation rate. One reason is that not until after
day 800 does the ferric iron concentration fall below levels allow-
ing the direct 0- oxidation mechanism to become dominant. Another
reason is that at the assumed leaching-rate of 50 cm/year, 2.16
years are required to remove one water-filled pore volume from the
10-meter deep profile. Thus, any change in oxidation rate will not
be fully expressed in the leach water until months and perhaps years
later.
Carbon DioxideGeneration
Several simulations were made to examine the way in which the
model handled carbon dioxide production and flux within the mine
profile. Four simulations were run for a period of five years;
Run 11, a control where no source of carbon dioxide was assumed,
Run 12, where heterotrophic respiration was assumed to be occurring
in the top 50 cm of the profile, Run 13, where respiration was
assumed to be occurring in the bottom layer of the profile only,
and Run 14, where darbonates were assumed present in the bottom
layer only. Run 12 is analogous to a mine profile with a well
-12
established vegetative cover, where Q__ = - 0.3 x 10 moles
DD
125
-------
0 -cm -sec - C in Eq . [31]. Run 13 represents the case where
heterotrophs are active deep within the mine profile, utilizing
buried organic matter or digestible coal. (}„„.., Eor Run 13 was
also set to -0.3 x 10 moles 0_-cm -sec - C . Run 14 was run
to simulate carbonate neutralization of acid . Only one layer was
assumed to contain carbonate at a content of 0.083% (wt/wt) . The
low carbonate content in the profile was used because the H -
carbonate reaction rate as predicted by the model was very rapid
and dominated the pyrite oxidation reaction even at very low-
carbonate contents. Although rapid reactivity of carbonates in
acid spoil has been observed (Geidel and Caruccio, 1977), we be-
lieved the neutralization rate used in this model to be unrealistic-
ally fast mainly because it was based on work with freshly exposed
limestone (Wentzler, 1977) and ignored diffusion controlled kinetics
and possible build-up of iron coatings on the carbonate surface
(Geidel and Caruccio, 1977) both of which would reduce the neutraliza-
tion rate. Even at the low-carbonate content used here, the pH of
the bottom layer remained above 5.0 compared to approximately 2.5 for
the other layers.
In every case the production of CO,, reduced the oxidation of
pyrite. After five years 73, 85 and 88% of the pyrite consumed in
the control was consumed in Runs 12, 13 and 14, respectively. The
reduction in pyrite oxidation is due primarily to the decreased
oxygen concentration in the spoil profile. The reduction in 0_
concentrations in Run 12 was due mainly to 0 consumption in the
126
-------
surface layers. In contrast, reductions in 0- concentrations in
Runs 13 and 14 were primarily due to increased resistance to oxygen
diffusion in the profile because of the counter-current C0_
diffusion up through the profile (see Appendix A) . In addition to
reducing pyrite oxidation because of C02 production, Run 14 showed
reduced levels of acid being flushed from the profile because of
carbonate neutralization.. Although Run 14 had a greater amount of
pyrite oxided than Run 12, the acid removed from the profile after
5 years was the same; 73% of the control value • for Huns 12 and
14 compared to 80% for Run 13.
Table 13 shows the flux ratio, r = N_n /Nn , for each layer
K LU- U „
in Runs 12-14. Even for these simple examples it can be seen that
the behavior of r with depth is fairly complicated. Values of r
are both positive and negative in each run and may not show a uni-
form increasing or decreasing pattern with depth. For example,
Run 12 shows a minimum r value below the surface layer at a depth
of 275 cm. This may, in part, explain some of the difficulties
encountered with the interpretation of measured fluxes in Part
III.
127
-------
Table 13. Ratio of the flux of
C02 to 0 for Run 12 (hetero-
trophs active in layer 1 only), Run 13 (heterotrophs
active in layer 20 only), and Run 14 (acid neutraliza
tion by carbonates in layer 20).
Layer
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Depth
(cm)
25f
75
125
175
225
275
325
375
425
475
525
575
625
675
725
775
825
875
925
975
Run 12
-.47
.16
.12
.10
.093
.089
.090
.096
.12
.21
.57
.76
.83
.86
.90
.94
.99
1.0
1.1
1.2
VNo2
Run 13
.0003
.0002
-.0009
-.0016
-.0018
-.0022
-.0028
-.0037
-.0053
-.010
-.028
-.074
-.10
-.14
-.18
-.24
-.33
-.45
-.61
-.72
Run 14
.0003
.0003
.0003
.0004
.0001
-.0013
-.0026'
-.0033
-.0048
-.0091
-.027
-.082
-.13
-.18
-.26
-.38
-.57
-.88
-1.4
-1.8
'Depth to middle of layer.
128
-------
-------
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134
-------
APPENDIX A
APPLICABILITY OF PICK'S LAW TO GAS DIFFUSION
135
-------
-------
Introduction
The exchange of gases between the soil and the atmosphere is of
primary concern to soil scientists. Gas movement in the soil can be
caused by both convection and diffusion. Convection results when a
difference in total gas pressure exists between two locations.
Diffusion will occur even if the total pressure is uniform as long as
there is a spatial difference in the chemical potential, normally
represented by differences in concentration or partial pressure, of
the components of a gas mixture (Kittel, 1969). While both processes
are important in soils, diffusion is considered to dominate during
normal gaseous exchange (Evans, 1965).
The fundamental equation used to describe one dimensional
diffusion in soil is Pick's First Law.
q± = - a DF dCi/dz [Al]
i
where q. is the mass transfer rate of component i per unit area
-2 -1
(ML T ), D is the Fickian diffusion coefficient for component i
2 -1 1 -3
(L T ), C. is the concentration of i (ML ), z is distance and a is
the correction term that accounts for the air-filled porosity and
tortuosity of the diffusion path in soils (Troeh, et al., 1982).
Since in the remainder of this paper the magnitude of a is inconse-
quential as long as its magnitude is independent of gas type
(Penman, 1940b), we will let it equal 1.0 and drop it from the
remaining equations.
136
-------
Alternatively, Eq. [Al] can be written in terms of mole fractions
by invoking the equation of state for ideal gases and Dalton's Law to
give:
Ni = -V fedVdz [A2]
where now N. is the molar flux, P is the total gas pressure, R the
universal gas constant, T absolute temperature, Y. the mole fraction
of component i and t is time. While useful in soil science, it must
be remembered that Fick's Law when applied to gases is strictly an
empirical relation, borrowed from studies with solutes and shown to
agree well with observed diffusional processes in air (Kirkham and
Powers, 1972, p. 429; Penman, 1940a and 1940b). The form of Eq.
[A2], the flux of a gas being equal to its gradient multiplied by a
single coefficient, is very misleading and requires closer
examination.
The equations for gaseous diffusion were developed by Stefan
(in Wilke, 1950) and Maxwell (1952) among others. The equations
are based on the statistical mechanics description of ideal gases
developed by Gibbs and Boltzman (Kittel, 1969). These equations
have been extensively developed in the literature and found to
agree very closely with experiments on gas-diffusion (Hirschfelder,
et al., 1964; Fairbanks and Wilke, 1950). Since the interest in
gas-diffusion in soils has increased in recent years (Smith, 1977;
Bakker and Kidding, 1970; DeJong, et al., 1979;and others) and Fick's
Law is used to describe the process in most soils literature (see
137
-------
Wood and Greenwood, 1971 for an exception) it would seem advisable
to compare Pick's Law (Eq. [A2]) to the Stefan-Maxwell diffusion
equations in order to gauge its validity. This paper will examine
several simple cases of diffusion of interest in soil science. It
is not our intention to develop the Stefan-Maxwell equations in
depth, nor to fully present the' theory underlying them. For this,
the reader is directed to the comprehensive works by Chapman and
Cowling (1939) or Hirschfelder, et al. (1964), or to the excellent
review by Marrero and Mason (1972). We shall, for the remainder of
the paper, consider only"diffusion in the gas phase, ignoring gas-
liquid interactions, convection, turbulence or other mass flow
phenomena, and for simplicity will consider only steady-state
diffusion.
Stefan-Maxwell Equations for Gas Diffusion
Chapman and Cowling (1939, p. 244) have shown that for dif-
fusion, the average velocity of one gas in relation to a second gas
is represented by:
n ^(.•njn^) n±n (m -nO
v,-v,= - —— D^ r r- + J J
9r p, 3r
3T/3r ] 1A31
where the terms are defined at the end of this paper. For our pur-
poses, it is only important to note that the difference in average
velocities of two gases (v.-v.) depends on four separate terms on the
right side of Eq. [A3], which may be thought of as the chemical
138
-------
potential for the gas pair (Kittel, 1969, p. 215). The first term
represents ordinary or concentration diffusion, which we are con-
cerned with in this paper* The second term represents diffusion
caused by differences in total pressure but should not be confused
with mass flow. As an example of pressure diffusion, lighter ele-
ments such as helium will concentrate in the upper portions of the
atmosphere due to diffusion driven by pressure differences in the
atmosphere. The gases respond to the pressure gradient created by
gravity and not to gravity directly. The third term represents a
diffusional flux created by an external force, such as a flow of
charged particles in an electric field giving rise to an electric
current. The final term represents thermal diffusion. In thermal
diffusion, a temperature difference will cause diffusion within a
gas mixture, with the lighter components concentrating near the
warmer zone. If the temperature gradient is maintained, the gas
components will continue to separate until ordinary diffusion
exactly balances thermal diffusion. Of the four terms, only con-
centration or ordinary diffusion is important under normal circum-
stances in soil and plant processes, although thermal diffusion is
used in commercial refining techniques for separating isotopes of
some gases (Jones and Furry, 1946; Vasaru, et al., 1969).
For ordinary diffusion in one dimension of one gas, i, through
another gas, j, where total pressure and temperature are constant,
Eq. [A3] reduces to:
139
-------
2
n d(n./n )
v.-v. --- 2— D.. - ^— — [A4]
i j n^ ij dz
nT
Dividing by - D.., Eq. [A4] can be rearranged such that:
ninj XJ
v n n -v n n d(n n )
Dividing both sides of Eq. [A5] by Avagadro's number, MQ, convert
the number densities to molar densities. Remembering that N. = v.
n./M , Eq. [A5] becomes:
NiWi = i d
-------
mixture and not just i and j. However, this difference is slight
(within the experimental error of measurement) and can be ignored
(Marrero and Mason, 1972).
In general, Eq. [AS] represents n-1 independent equations for
n
n unknowns (since Z Y. = 1.0) and as such the solution is indet-
i-1 1
erminate. However, under certain simplifying assumptions, solutions
can be found for the series of equations. We will examine several
of these situations applicable to soil and plant science.
Binary Gas System
For the simplest case of diffusion in a two-component system
(i and j), Eq..[A8] yields only one unique equation, identical to
Eq. [A7], since Y. + Y. = 1.0. Eq. [A7] can be rearranged inl:o a
form similar to Pick's Law (Eq. [A2]). By letting r.. equal the
negative value of the ratio of the fluxes, r.. = - N./N., and sub-
stituting 1-Y. for Y., we can rearrange Eq. [A7] to obtain:
ddz
X a
Comparing Eqs. [A9] and [A2] we find that:
DF. ' l-(l-r..)Y.
The Fickian diffusion coefficient depends not only on D.., but also
on the flux ratio and mole ratio of component i. Two special
circumstances immediately follow from Eq. [A10] .
141
-------
Tracer Diffusion
In cases where Y. is present only in trace amounts (i.e., Y. =
0.0), Eq. [A10] for the Fickian diffusion coefficient reduces to:
D = D [All]
i J
independent of flux ratios and concentration.
Closed System
A second possibility for binary gas diffusion is diffusion in a
closed system where, since the total pressure remains constant, N. =
- N , r = 1.0 and, from Eq. [A10], D_ again just equals D...
J Ji Fi ^
Open System
A more general situation is the steady state diffusion of gases
through an inert layer where the concentrations of the gases are
held constant at one end because of an infinite source/sink for the
gases (the atmosphere) and the concentrations are fixed at the other
end by consumption or production processes. An example would be
oxygen diffusing into a soil ped and oxidizing ferrous to ferric
iron where oxygen and nitrogen comprise the ped atmosphere. For an
open system Eqs. [A9] and [A10] cannot be solved without a_ priori
knowledge of r... FigureAL illustrates the variation of D with
J1 i
changes in r.. and Y. as calculated by Eq. [A10]. The reduced
*
Fickian diffusion coefficient, D_ = D_ /D.. is plotted for several
Fi Fi 1J
values of r.. and for 0.0 < Y. < 1.0. As discussed for equi-molar,
counter-current diffusion in a closed system and for tracer diffusion,
D is constant for all values of Y. when r.. =1.0 and for all
142
-------
2.0
Figure Al. Values of the reduced Fickian diffusion coefficient, D
F. '
i
in a binary gas mixture plotted against the gas mole
fraction of component i. Curve labels are the values of
the flux ratio, r.., for which the curve was calculated.
143
-------
values of r.. when Y. =0.0. D diverged rapidly however as Y.
31 i F± * i
increases, decreasing as r.. becomes less (reduced resistance to
diffusion) and increasing as r.. increases. In the extreme it can
be seen from Eq. [A10] that D can become negative when the two
i
gases are diffusing in the same direction (r.. < 0.0), that is,
gas i would diffuse against its gradient. This behavior has been
measured by Duncan and Toor (1962).
Three Component Gas Systems
The soil atmosphere can normally be characterized as a three-
component (ternary) system. In a ternary system composed of gases
i, j and k, where Y. + Y. + Y = 1, Eq. [A8] yields two unique
1 J *•
equations:
„ N.Y.-N.Y. N.Y-N.Y.
ij ik
N.Y.-N Y. N Y, -N, Y.
J ij Jk
Again, the general solution of these equations is impossible without
further simplifying assumptions.
Tracer Diffusion
If we let component i represent a gas at trace concentration, so
that Y. + Y, = 1, then Eq. [A12] which describes the diffusion of i,
J ^
becomes :
144
-------
y Y
ik
or upon solving for N,:
- D..D.
j ik4k ij
which is identical in form to Fick's Law with the Fickian diffusion
coefficient dependent only on D.., D.. and the mole fractions;'Y.
and Yk.
D..D
n
D
F. Y.D.n
i j ik k ij
In general, for tracer diffusion in a n-component gas mixture, the
tracer will diffuse according to Fick's Law where the diffusion
coefficient is equal to:
n n n
D = H D / I (Y ( n D ) [A17]
i j=l 1J j=l J k=l lk
or j
and is independent of the diffusional fluxes of the other components.
One Gas Stagnant
Eqs. [A12] and [A13] can also be simplified if we assume one
of the gases is stagnant. This is analogous to quasi-steady state
respiration in a soil where oxygen and carbon dioxide are being
exchanged with the atmosphere and nitrogen, the third gas component,
(k), is stagnant. In this case with N = 0.0, Eqs. [A12] and [A13]
&
become:
145
-------
P/RT dY±/dz = N±
P/RT dY./dz = N.
Y.
Y.
- N.
Y. Y.
i , I
D.. D
Y.
- N.
[A18]
[A19]
These equations can be solved for the molar fluxes N. and if Y ,
Y and Y, are known. In the case of counter-current, equi-molar
j k
diffusion, where N » - N. (r.± = 1.0), Toor (1957) has solved these
equations exactly and found that the solution must simultaneously
satisfy Eqs. [A20] and [A21].
K
Ni = - Nj = DT=5T
J jk ik
.
ln
D..
:r±i) (Y. - Y.
D., i, 10
jk 1 2
D
-
(Y - Y ) = ln(Y /Y
ik Jl 32 ^2
[A20]
[A21]
The second subscript on Y refers to the points 1 and 2 separated by
the distance z. These equations can be used to describe diffusion
in soils where the source and sink terms for CL (i) and CCL (j) are
determined by plant root or soil organism respiration and the res-
piration quotient, CO- produced/O- consumed, is near 1.0 (e.g., r =
1.0). However, it must be remembered that this is only a good
approximation for respiration in soils during quasi-steady state
conditions because if Y. or Y. is changing rapidly, N, 4= 0.0 and
i 3 K
the simplification is not justified.
In general, we can solve Eqs. [A18] and [A19] only if the ratio
r.. is known. Substituting r..N. for N. in Eq. [A18] and solving
146
-------
for N. and substituting N./r . for N. and solving for N in Eq „
i 3 31 i 3
[A19] yields
N =
i D..Y.-H)...D.lrT.
ik j 13 k 31 ik i
N
3 D.^D.VD Y/r-~ T
J jk i 13 k jk j 31
which are in the form of Fick's Law with diffusion coefficients
D..D
D
F. D..Y.+D..Y.+T..D..Y.
i ik 3 13 k 31 ik i
= ' i.1—1^
F. DMY.+D..Y.+D..Y./r..
i jk i 13 k jk 3 31
These equations demonstrate that the apparent diffusion coefficient
in Fick's Law depends not only on the binary diffusion coefficients
but also on the gas composition and the flux ratio, r^ . As am
example, D can be calculated for 0? from Eq. [A24] and for CCL from
Eq. [A25] in a ternary atmosphere where i = CL, j = CO., k = N. and
N =0.0. For this case Eqs. [A24] and [A25] become:
2
°2 02'N2XC02 02,C02"N2 rC02, 02°2ty2
[A26]
+D
Values for the binary diffusion coefficients can be calculated from
Table Al (next section). For a temperature of 20 C and a pressure of
101 kPa these values are 0.159 x 10~A , 0.202 x 10~4 and 0.159 :K 10~4
(m2/sec)for D D ^ respectively. The Flckian
147
-------
diffusion coefficients can then be calculated if values for Yn , Y n ,
U2 L 2
Y>T and r_. are known. For example, with Yn =0.15, Y = 0.06,
N2 C02 02 C02
Y,T =0.79 and r.,^ _ = 0.5, D_ and D_ are calculated to be
N, CO,,0- Fn F
2 , 2. L _, 2^2 ")
0.210 x 10 and 0.150 x 10 m /sec, respectively. These two points
are indicated on Fig. A2 and A3 where the values of D and D
°2 C°2
are plotted for various flux ratios. In both figures Y is held
2
constant at 0.790 while Y varies from 0.0 to 0.21. Carbon dioxide
comprises the remainer of the atmosphere (0.21 < Y < 0.0).
co2
The apparent diffusion coefficients for both 02 and CO- vary
little for r . n near 1.0. As the flux ratio deviates further
(JUn , \Jn
from 1.0, the 09 diffusion coefficient diverges rapidly as Y_
U2
increases (Fig. A2). D for C00 is less variable but can deviate
r 2.
markedly from its value at r _ n = 1.0 at low values of the flux
CU2'U2
ratio and high C0_ (low 02) concentrations (Fig. A3). Values for
the flux ratio in soils have been reported ranging between 0.6 and
4.0 (Bunt and Rovira, 1955; Rixon and Bridge, 1968; Bridge and
Rixon, 1976). Although none of these authors reported the 0_ and
C0_ mole fractions at which these ratios were found, extreme values
of 0.0 to 0.21 for 0- and 0.0 to 0.09 for CO- have been measured
(Russell and Appleyard, 1915). Using the values of 0.05 for Y
co2
and 0.15 for Yn and a flux ratio of 2.0, we can see from Figs. A2
and A3 that deviations in the fickian diffusion coefficients of 15%
for 0« and 9% for C0» from the values at r _ n =1.0 are possible.
Z 2. CU2,U2
Figures A2 and A3 illustrate the potential hazard of applying values
of the Fickian diffusion coefficient from one situation to another
148
-------
Q-20-
.14
Figure A2. Values of the Fickian diffusion coefficient, D , for 0_
2
in an 0--C02-N2 atmosphere (in m /sec) . The N« ;nole
fraction is held constant at 0.790, while the 0_ mole
fraction, plotted on the abscissa, is varied between 0.0
and 0.21. C0« comprises the balance of the atmosphere.
Values are for 20°C and 101 kPa with the N flux being
set to 0.0. Curve labels are the values of the flux
ratio r
text.
, O
Point represents value calculated in
149
-------
.20 .25
Figure A3. Values for the Fickian diffusion coefficient, D , for
2
C0_ in an 0 -CO -N_ atmosphere (in m /sec). The N? mole
fraction is held constant at 0.790, while the 0~ mole
fraction, plotted on the abscissa, is varied between 0.0
and 0.21. CO comprises the remainder of the atmosphere.
Values are for 20 C and 101 kPa with the N« flux being
set to 0.0. Curve labels are the values of the flux
ratio r n . Point represents value calculated in
C°2'°2
text.
150
-------
where the flux ratio and gas composition may not be the same. This
may be, at least in part, the reason why flux calculations based
concentration gradients do not compare well to other techniques for
measuring flux (DeJong, et al., 1979).
Equation fA8] also applies to diffusion in four-component or
greater gas mixtures. 02> C02> N2 and Ar or 02> C02, N2, Ar and H20
vapor atmospheres would be mixtures of interest in soils. However,
as in the ternary case, unless some simplifying assumptions can be
made, the exact solution for diffusion in these mixtures is not
possible.
Binary Diffusion Coefficient
D.. is the proportionality coefficient relating the flux of ±
and j to their gradient in a binary gas system. Conceptually D..
can be thought of as a macroscopic averaging of the interactions
or collisions between components i and j. The greater the number of
collisions, the more diffusion is impeded and the smaller D.. must
be. For this reason, D.. must be inversely proportional to density,
and thus pressure since the number of collisions will increase
linearly with pressure at constant temperature. Thus:
Dij = Dij/P [A28]
*
where D.. is the temperature dependent, pressure independent binary
diffusion coefficient. However, any decrease in D.. due to a
pressure increase will be exactly balanced by an increase in the
151
-------
number of molecules or flux carriers per volume of gas (increased
concentration, C) . This can be seen by substituting Eq. [A28] into
Eq. [A29] for the flux in a binary system:
Ni = - l-(l-r.')Y. fe dVd2 tA29J
the pressure terms drop out and the diffusion equation is pressure
independent when expressed in mole fractions:
[A30]
When working with the concentration form of the diffusion equation
(Eq. [Al]), the pressure dependence of the diffusion coefficient
must be retained:
where P. is the total pressure at which D.. is known and P2 is' the
pressure at which diffusion is taking place.
Relations for calculating D.. for any gas pair, based on
classical statistical mechanics were independently developed by
Chapman and by Enskog (Chapman and Cowling, 1939). The solution
*
involves successive approximations to D... The approximations con-
verge rapidly, so that the first approximation, which is temperature
dependent but independent of gas composition and at most the second
approximation, which introduces slight compositional variation, is
152
-------
*
sufficient for calculating D.. to within at most several percent
error (Marrero and Mason, 1972).
Values for D.. (more commonly D..), can be found in numerous
papers in the literature (see Marrero and Mason, 1972), with some
recent values for carbon dioxide, nitrous oxide, ethylene and
ethane presented by Pritchard and Currie (1982). Marrero and Mason
(1972) have compiled an extensive tabulation of binary diffusion
coefficients taken from the literature. Based on the Chapman-
Enskog equations and extensive experimental results, they have com-
piled semi-empirical relations for the first approximation of over
70 gas pairs. Diffusion coefficients for gas pairs of interest in
soil research are tabulated in Table Al. In all cases shown, the
*
second approximation to D.., which is based on the compositional
ratio of component i to component j, represents a correction to the
first approximation of less than 1.0% at normal temperatures for
the entire compositional range. This correction is within the;
experimental error of the measured values and can be neglected for
all the gas pairs listed. The equation used by Marrero and Mason
*
(1972) to calculate D.. is:
ln(D*.) = ln(a) + b ln(T) - c/T. [A32]
They computed the constants a, b and c by matching Eq. [A32], whose
form is suggested by the theoretical work of Chapman-Enskog, to a
compilation of experimental data for each gas pair. The temperature
153
-------
* t
Table Al. Coefficients for calculating D.. for gas pairs of
interest in soil research (after Marrero and Mason,
1972).
Gas
Couple
Ar-CH,
Ar-N2
Ar-02
Ar-air
Ar-C02
CH4"N2
CV°2
CH4-air
N2-02
N2-H20
N2-C02
02-H20
o2-co2
Air-H20
Air-C02
H20-C02
C02-N20
a x 107
KPa-m
0
0
0
0
1
1
1
1
1
0
3
0
1
0
2
9
0
b
2/sec-Kb
.792
.913
.987
.926
.76
.01
.68
.04
.14
.188
.18
.191
.58
.189
.73
.33
.284
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
.785
.752
.736
.749
.646
.750
.695
.747
.724
.072
.570
.072
.661
.072
.590
.500
.866
0
0
0
0
89
0
44
0
0
0
113
0
61
0
102
307
0
c
K
.0
.0
.0
.0
.1
.0
.2
.0
.0
.0
.6
.0
.3
.0
.1
.9
.0
T range
307-10~4
244-104
243-104
244-104
276-1800
298-104
294-104
298-104
285-104
282-373
288-1800
282-450
287-1083
282-450
280-1800
296-1640
195-550
Uncertainty?
limits
%
3
2
3
3
3
3
3
3
3
4
2
7
3
5
3
10
3
ln(D..) = ln(a) 4- b ln(T) - c/T, where T is temperature, (K) .
? 1J *
Uncertainty in D.. term at lower end of listed temperature range.
154
-------
range over which these coefficients were fit and the uncertainty
*
limits in D.. at the lower end of the temperature range are also
given in Table Al.
*
An example calculation of D.. using values in Table Al is as
follows. The pressure-independent, diffusion coefficient for the
gas pair 0»-C07 is calculated from Eq. [A32] with the coefficients
from Table Al of a = 1.58 x 10 , b = 1.661 and c = 61.3 At a
temperature of 293 K:
ln(D* _n ) « ln(1.58 x 10~7) + 1.661 ln(293) - 61.3/293. [A33]
°2'C°2
D* 0 = 0.00160 m2-KPa-sec~1
or at atmospheric pressure, from Eq. [A28]
Dn _n = 0.00160/101.
°2'C°2
[A34]
= 0.159 x 10~A m2/sec
The diffusion coefficients are highly sensitive to temperature with
a 30% variation possible under normal, seasonal soil temperature
fluctuations. For example, the binary diffusion coefficient for the
0,,-CO gas pair is equal to 0.136 x 10~ at 0°C (273 K) and 0.165 x
10~4 at 30°C (303 K) or D0 rf, is 22% greater at 30°C than 0°C.
°2'C°2
155
-------
SUMMARY
The comparison of the Stefan-Maxwell equations and Fick's Law
for diffusion of gas through vapor shows that only under certain,
special circumstances is the diffusion coefficient for Fick's Law,
D , a constant independent of the mole fraction of i and the
i
diffusion flux of other gases. These special cases are the diffusion
of a trace amount of component i and equi-molar, counter-current
diffusion in a binary gas mixture, or equi-molar, counter-current
diffusion of two gases in a ternary system with the third gas
stagnant. In general, D is dependent on the binary diffusion
i
coefficients, the composition of the gas mixture, and the diffusional
flux ratios of the gas components. Measured values of D can only
i
be accurately extrapolated to other circumstances when all the above
conditions are similar. In an CL, C02 and N» atmosphere where N? is
stagnant, variations on the order of 10% from the tracer value of
D for 00 and C0_ are possible with variations in the mole fraction,
c / /
or flux ratio. The diffusion coefficients are most sensitive to
changes in the flux ratio for ratios less than 0.8 or greater than
1.2. The temperature and pressure dependent nature of the diffusion
coefficient must also be considered.
156
-------
-------
REFERENCES
1. Bakker, J. W. and A. P. Ridding. The Influence of Soil Structure
and Air Content on Gas Diffusion in Soils. Neth. J. Agric. Sci.,
18:37-48, 1970.
2. Bridge, B. J. and A. J. Rixon. Oxygen Uptake and Respiratory
Quotient of Field Soil Cores in Relation to their Air-Filled
Pore Space. J. Soil Sci., 27:279-286, 1976.
3. Bunt, J. S. and A. D. Rovira. Microbial Studies of Some Sub-
anarctic Soils. J. Soil Sci., 6:119-128, 1955.
4. Chapman, S. and T. G. Cowling. The Mathematical Theory of
Nonuniform Gases. Cambridge University Press, London, 1939.
5. Curtiss, C. F. and J. 0. Hirschfelder. Transport Properties of
Multicomponent Gas Mixtures. J. Chem. Physics, 17:550-555, 1949.
6. DeJong, E., R. E. Redmann, and E. A. Ripley. A Comparison of
Methods to Measure Soil Respiration. Soil Sci., 127:299-306,
1979.
7. Duncan, J. B. and H. C. Toor. An Experimental Study of Three
Component Gas Diffusion. Am. Inst. Chem. Eng., 8:38-41, 1962.
8. Evans, D. D. Gas Movement. In: Methods of Soil Analysis,
C. A. Black, ed. American Society of Agronomy, Madison,
Wisconsin, 1965. Agronomy 9:319-330.
9. Fairbanks, D. F. and C. R. Wilke. Diffusion Coefficients in
Multicomponent Gas Mixtures. Indust. Eng. Chem., 42:471-475,
1950.
10. Hirschfelder, J. 0., C. F. Curtiss, and R. B. Bird. Molecular
Theory of Gases and Liquids. John Wiley and Sons, Inc., New
York, 1964.
157
-------
11. Jones, R. C. and W. H. Furry. The Separation of Isotopes by
Thermal Diffusion. Rev. Modern Phys., 18:151-224, 1946.
12. Kirkham, D. and W. L. Powers. Advanced Soil Physics. Wiley-
Interscience, New York, 1972.
13. Kittel, C. Thermal Physics. John Wiley and Sons, Inc., New York,
1969.
14. Marrero, T. R. and E. A. Mason. Gaseous Diffusion Coefficients.
J. Phys. Chem. Ref. Data, 1:3-118, 1972.
15. Maxwell, J. C. Scientific Papers, II. Dover Publications, Inc.,
New York, 1952.
16. Penman, H. L. Gas and Vapour Movements in the Soil. I. The
Diffusion of Vapours through Porous Solids. J. Agr. Res.,
30:437-462, 1940a.
17. Penman, H. L. Gas and Vapour Movements in the Soil. II. The
Diffusion of Carbon Dioxide through Porous Solids. J. Agr.
Res., 30:570-581, 1940b.
18. Pritchard, D. T. and J. A. Currie. Diffusion Coefficients of
Carbon Dioxide, Nitrous Oxide, Ethylene and Ethane in Air and
their Measurement. J. Soil Sci., 33:175-184, 1982.
19. Rixon, A. J. and B. J. Bridge. Respiratory Quotient Arising from
Microbial Activity in Relation to Matric Suction and Air-Filled
Pore-Space of Soil. Nature, 218:961-962, 1968.
20. Russell, E. J. and A. Appleyard. The Atmosphere of the Soil. Its
Composition and the Causes of Variation. J. Agric. Sci., 7:1-48,
1915.
21. Troeh, F. R., J. D. Jabro, and D. Kirkham. Gaseous Diffusion
Equations for Porous Materials. Geoderma, 27:239-253, 1982.
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22. Smith, K. A. Soil Aeration. Soil Sci., 123:284-291, 1977.
23. Toor, H. L. Diffusion in Three-Component Gas Mixtures. Appl.
Ind. Chem. Eng. J., 3:198-207, 1957.
24. Vasaru, G., G. Miller, G. Reinhold, and T. Fodor. The Thermal
Diffusion Column. Veb Deutscher Verlag der Wissenschaften,
Berlin, 1969.
25. Wilke, C. R. Diffusional Properties of Multicomponent Gases.
Chem. Eng. Prog., 46:95-104, 1950.
26. Wood, J. T. and D. J. Greenwood. Distribution of Carbon Dioxide
and Oxygen in the Gas Phase of Aerobic Soils. J. Soil Sci.,
22:281-288, 1971.
159
-------
-------
APPENDIX B
PARAMETER VALUES USED IN THE PYRITE
OXIDATION MODEL
160
-------
-------
D
c
The coupled counter-current diffusion coefficient for the
diffusion of reactants and products within the coarse fragments was
assigned a value comparable to measure diffusion coefficients in
—7 2
soil. Cathles (1979) used a value of 1.6 x 10 cm /sec for D in
c
stone fragments. Elgawhary et al. (1970) and Palmer and Blanchar
(1980) measured values of about 1.8 x 10 and from 0.3 - 1.0 x 10
2
cm /sec for zinc diffusion and for potassium diffusion in soils,
respectively. A value from the lower range was used for this model
-7 2
and was equal to 1.0 x 10 cm /sec.
K
s
Numerous workers have investigated pyrite oxidation rates,
unfortunately most have ignored the fact that pyrite oxidation is a
surface reaction, which makes estimation of K difficult. McKay and
Halpern (1958) and Braley (1954) showed pyrite oxidation rate is
proportional to pyrite surface area. Lorenz and Tarpley (1964)
studied the reaction rate for three different pyrite sizes under
a variety of oxidizing conditions. Clark (1965) combined their
results with those of Braley (1954), (which gave surface area of
pyrite fragments versus particle size as measured by screen sieving),
to show the relationship between reaction rate, oxidant concentration
and pyrite surface area. Making surface area determinations for
irregularly shaped, framboidal pyrite grains is extremely difficult.
161
-------
Extrapolating these results from one set of samples to another must
be done with extreme caution due to the great variety of pyrite
grain shapes and sizes. However, we can assume that the most finely
ground pyrite will tend to have the most uniform fragment shape and
use these values to calculate K from the data presented by Clark
5
—9
(1965). This gives a value of 1.8 x 10 cm/sec for K when oxygen
s
is the oxidizer (curve 1, Clark, 1965, Figure 12, p. 113), and 8.6 x
/ Q O_i_
10 cm/sec (curve 3) and 8.1 x 10 cm/sec (curve 4) when Fe is
the oxidizer.
Singer and Stumm (1968) in studying the reduction rate of Fe
by pyrite found that the reaction is first-order with respect to
3+
Fe concentration, but conversely, they found the reaction rate
constant was inversely dependent on the Fe concentration. They
had no explanation for this apparent contradiction, but from the
data it appears that their assumption of non-limiting pyrite surface
area was in error. This can be seen in their Figures 5-18 where
doubling the surface area at fixed Fe concentrations caused a
doubling of the reaction rate. If available surface area was not
limiting an increase would not be expected. Extension of the experi-
3+
ments to greater pyrite surface area-Fe concentration ratios should
verify this relationship. Using the Singer and Stumm (1968) values
for the reaction rate constant and the surface area information
presented by Clark (1965), we calculate K values for Fe oxidation
s
to be 4.4 x 10 cm/sec when available pyrite surface area is least
162
-------
limiting and 10.0 x 10 cm/sec when most limiting. The former
value is preferred in view of the argument above.
In a study by the Ohio State University Research Foundation
(1970) reaction rate and surface area determinations were made for
3+
both Fe and 02 oxidants of primary sulphur ball pyrite. They
_g
found the maximum value of K for 0~ reduction, to be 12.0 x 10
S £
cm/sec when dissolved 0,, concentrations were the least and a
—8
minimum K value of 4.4 x 10 cm/sec when dissolved 0- concentra-
s t
tions were the greatest. These values indicate a slight coupling
effect of available surface area with 0~ concentrations. They also
3+ —6
found K for the Fe system to equal a maximum of 4.4 x 10
3+ —8
cm/sec for the minimum Fe concentration studied and 7.5 x 10
3+
cm/sec for the highest Fe concentration.
Pionke, et al. (1980) measured pyrite oxidation rates for fresh
2-
shale fragments, exposed to 20% 0_, to be 0.45 mg SO, per hour.
They did not specify pyrite grain size or surface area, but measured
the pyrite concentration in the shale to be 3.8% by weight. From
the work of Caruccio (1973), we can assume that the active-pyrite
grains in their samples were on the order of 0.2 microns in size.
Using this approximation and assuming the grains to be spherical,
Q
we can calculate the K value for their material to be 8.3 x 10.
S
cm/sec, in excellent agreement with the other values. K values
S
3+ 3+
for the 0« system, K (0,), and for the Fe system, K (Fe ), are
^ s £ s
—8
summarized in Table Bl. In this model a value of 8.3 x 10
163
-------
3+
Table Bl. K values for Fe and 0- system
Source
K (cm/hr)
s
Fe
3+
Clark (1965)
Singer and Stumm
(1968)
OSURF (1970)
Pionke, et al.
(1980)
oxidant
8.6 x 10
-8
8.1 x 10
-8
4.4 x 10
,-8
-6
10. x 10
4.4 x 10
-6
7.5 x 10
—8
18. x 10
-8
12. x 10
-8
4.4 x 10
-8
8.3 x 10
-8
164
-------
cm/sec was used for K (0_) and a value of 4.4 x 10 cm/sec for
s ^
3+
K (Fe ) was used.
s
The surface area of pyrite per unit volume of fragment was
calculated from the pyrite content of a fragment. Donaldson, et al.
(1977) measured the surface area for sandstone to be approximately
4 2
10 cm /g. This surface area was then modified by the pyrite content
and the pyrite and fragment densities. In particular:
a = 104 . pFR . (FPY PFr/Ppy)2/3 [Bl]
where p is the fragment density (g/cm ), p is the pyrite density
(5.0 g/cm ), and FPY is the fraction of pyrite in a fragment (g/g).
For a fragment having a 0.002 pyrite fraction and a bulk density of
3 23
2.1 g/cm , ct equals 187 cm /cm .
The thickness of the fragment in which pyrite is being oxidized
can be calculated in a manner similar to that used by Cathles (1979).
First, we assume that the oxidant is diffusing through a leached rim-
of the fragment, where no uptake is occurring, to a zone where pyrite
is oxidizing at a rate proportional to the oxidant concentration.
DC d2C(x)/dx2 - a KsC(x) =0 [B2]
or:
2 ° Ks
^ - --=-D(x) - 0 [B3]
165
-------
where C is concentration of the oxidant, a the surface area of pyrite
per unit volume, D the diffusion coefficient of the oxidant in the
fragments, K the first-order reaction rate constant and x is depth
into the fragment. The solution to Eq. [B3] is of the form
C(x) = C, exp(a K /D )1/2 + C0 exp I-(a K /D )1/2J [B4]
J. a C ^ S C
Eq. [B4] can be solved subject to the boundary conditions:
dC(x)/dx =0.0 x = I, one-half thickness [B5]
of fragment
C(x) = C^ = C^ x = r = Ri [B6]
where i," is the depth of the leached rim and R = 1.0 - fraction
pyrite remaining/initial pyrite fraction. Taking the derivative
of Eq. [B4] with respect to x and using Eq. [B5] gives:
0.0 = b C^ exp(b£) - b GZ exp(-b£) [B7]
1/2
where b = (ctK /D ) '
s o
Rearranging Eq. [B7]:
CL = C2 exp(-b£)/exp(b«.) = C2 exp(-2b£) [B8]
From Eqs. [B4] and [B6] we find:
CD«, • cn exp(bR£) + C0 exp(-bR£,) [B9]
K.X X /
or rearranging:
CL = (CR£ - C2 exp(bR£ ) / exp(bR£)} [BIO]
Eqs. [B8] and [BIO] can be used to find the values of C and C^,
giving:
166
-------
- CR£exp(-2b£)
Cl = exp (bR£-2b£)+exp (-bR£) = CR£ Cl
__ _
2 = exp (bR£-2b£)+exp (-bR£) = CR£ C2
The reaction, rate, R, , for the fragment can be expressed for
a unit area and depth, dx,as:
R, = a K C(x) dx [B13J
dx s
The rate per unit surface area for the entire fragment is:
R^, = / a KsC(x) dx = /£ ex KsC(x) dx [B14]
Since no reaction is taking place in the leached rim, 0 < x < R£.
Substituting Eq. [B4] for C(x) and Eqs. [Bll] and [B12] for C and
C_, Eq. [B14] becomes
^ = Q Ks fRi [CR£ Cl exP(bx) + CR£ C2 exP(~bx>3 dx [B15]
which upon integration becomes:
R = a KC/b c [exp(bi) - exp(bR£)]
- C, [exp(-b£) - exp(-bR£)]l
Z j
[B16J
For the pyrite oxidation model, we want to replace the expression
for R,^ with one of the form
RT = a Ks Cx=o 3 [B17]
Combining Eqs. [B16] and [B17] and solving for 3 gives:
167
-------
C
7 - JC. I«cp(b£) - exp(bRJl)] - C, [exp(-b£)
x=a
8 [B18]
x=o
ffithin the depleted rim there is no uptake of oxidant and the
C(x) vs x curve will be linear. The flux of oxidant, Q0 , can be
expressed as:
*T = Q* = -Dc dC(x) = -Dc %5=IT [B19]
and
C
-s±- = 1.0 - R&/D Q /C
C co x=o
x=o
[B20]
- 1.0 - R£/D
c T
Substituting Eq. [B17] into Eq. [B20] gives
CL./C = 1.0 - R&/D a K 3 [B21]
R£ x=o c s l J
which when substituted into Eq. [B18] gives:
3 = C (1.0 - R2./D a K 3)/b [B22]
C S
which can be rearranged
3 = C /(b + R£/D a K C-) [B23]
c s
Eq. [B23] was then used to calculate 9 as a function of oxidant
concentration, reaction rate, diffusion rate and degree of pyrite
weathering.
168
-------
FFR
The fraction of fragments composing the spoil, FFR, was assumed
to 0.75 (wt./wt.) This compares with values measured by Pedersen,
et al. (1980) of from 0.5 to 0.9.
FPY and p
py
The average pyrite content of the spoil composing a reclaimed
stripmine was measured by Rogowski (1977) to be approximately 0.001
pyritic S by weight or 0.002 pyrite by weight. In this model we
assume all the pyrite to be contained within the coarse fragments
which comprise 75% of the total spoil weight. Thus, we set FPY
equal to .002/.75 or 0.0025. For a bulk density of 1.5 and a
fragment fraction of 0.75, this value of FPY corresponds to a molar
density of pyrite of p = 0.0025 • 0.75 • 1.5/120. = 23 x 10~6
py
moles pyrite/cm .
PB> *A and
The bulk density for minesoils was measured by Pedersen, et
3
al. (1980) to average about 1.57 g/cm , which corresponds to a
3
total porosity of 0.4 (particle density = 2.62 g/cm ). We have
assumed a percent water saturation of 75% in this model based on
measured values (Rogowski, et al., 1982). With these values for
total porosity and water content, a good estimate for the air-
33 33
filled porosity, ., is 0.12 cm /cm and 0.28 cm /cm for .
A Vr
169
-------
Unfortunately, a mistake was made in running the simulations where
was set to 0.06 cm /cm instead. This corresponds to a bulk
A
3
density of 1.7 g/cm , which is still within the range measured by
Pedersen, et al. (1980).
2
Colvin (1977) measured the diffusion coefficient for 07 in
shale spoil. He found the ratio of the diffusion coefficient in
spoil to the coefficient in air to be 0.013 at an air-filled
porosity of 0.13. For these conditions T can be calculated to be
T = 0.13/.013 = 10, which was the base value in the model.
170
-------
REFERENCES
1. Braley, S. A. Summary Report on Commonwealth of Pennsylvania,
Department of Health Industrial Fellowship, Nos. 1, 2, 3, 4,
5, 6 and 7. Mellon Institute, Fellowship No. 326B, 1954.
2. Caruccio, F. T. Characterization of Strip-Mine Drainage by Pyrite
Grain Size and Chemical Quality of Existing Groundwater. In:
Ecology and Reclamation of Devastated Land, R. J. Hutnik and G.
Davis, eds. Gordon and Breach, New York, 1973. pp. 193-226.
3. Cathles, L. M. Predictive Capabilities of a Finite Difference
Model of Copper Leaching in Low Grade Industrial Sulfide Waste
Dumps. Mathematical Geol., 11:175-191, 1979.
4. Clark, C. S. The Oxidation of Coal Mine Pyrite. Ph.D. Thesis,
John Hopkins University, University Microfilms, Inc., Ann
Arbor, Michigan. No. 65-10-278, 1965.
5. Donaldson, E. C., R. F. Kendall, and B. A. Baker. Surface-Area
Measurement of Geologic Materials. Soc. Petrol. Eng. J.,
15:111-116, 1975.
6. Elgawhary, S. M., W. L. Lindsay, and W. D. Kemper. Effect of EDTA
on the Self-Diffusion of Zinc in Aqueous Solution and in Soil.
Soil Sci. Soc. Am. J., 44:925-929, 1970.
7. Lorentz, W. L. and E. L. Tarpley. Oxidation of Coal Mine Pyrites.
Report of Invest. No. 6247, U.S. Bureau of Mines, 1963.
8. Mckay, 0. R. and J. Halpern. A Kinetic Study of the Oxidation of
Pyrite in Aqueous Suspension. Trans. Met. Soc., AIME 212:301-309,
1958.
171
-------
9. Ohio State University Research Foundation. Sulfide to Sulfate
Reaction Mechanism. Water Pollution Control Research Series
14010 FPS 02/70, Federal Water Pollution Control Administration,
Washington, D.C., 1970.
10. Palmer, C. J. and R. W. Blanchar. Prediction of Diffusion
Coefficients from the Electrical Conductance of Soil. Soil
Sci. Soc. Am. J., 44:925-929, 1980.
11. Pedersen, T. A., A. S. Rogowski, and R. Pennock, Jr. Physical
Characteristics of Some Minesoils. Soil Sci. Soc. Am. J.,
44:321-328, 1980.
12. Pionke, H. B., A. S. Rogowski, and C. A. Montgomery. Percolate
Quality of Strip Mine Spoil. Trans. ASAE, 23:621-628, 1980.
13. Rogowski, A. S. Acid Generation within a Spoil Profile:
Preliminary Experimental Results. In: Seventh Symposium on
Coal Mine Drainage Research, NCA/BCR Coal Conference and Expo
IV, Oct. 18-20, Louisville, Kentucky, 1977. pp. 25-40.
14. Rogowski, A. S., H. B. Pionke, and B. E. Weinrich. Some Physical
and Chemical Aspects of Reclamation. Preprint, paper presented
at the North Atlantic Region ASAE 1982 Annual Meeting, 1982.
15. Singer, P. C. and W. Stumm. Acidic Mine Drainage: The Rate
Determining Step. Science, 167:1121-1123, 1970.
172
-------
APPENDIX C
COMPUTER LISTING AND EXAMPLE OUTPUT OF
ACID MINE DRAINAGE MODEL
173
-------
-------
Computer Listing of Acid Mine Drainage Model
1. //MNWXXXXX JOB (DXJ79)
2. // EXEC PGM-UMSG,PARM-(INTERACT, 'TO D1J JOB RUNNING')
3. //DELETE DD VOL-REF-MEN.P65440.DlJ.LIB,
4. // DSN-MEN.P65440.D1J.DMNLS8,
5. // DISP-(OLD,DELETE)
b. /*
7. // EXEC FWCG.PARM-NOSOURCE
8. /'JOBPARM FULLSKIPS,UCS-TN,FORMS-16,V-NORMAL
9. //SYSIN DD *
10. IMPLICIT REAL'S (A-H.O-Z)
11. INTEGER O.OPRINT
12. REAL'S NA,NB,NAI,NBI,KB(50>,KBMAX,NC2,NC(50),NCI,NCIO,LSMAX,
13. 1KBO,KB1,KB2,KBO(50),KBA(50),KBH(50),KBU50),LS(50).LSO(50)
14. REAL** KSP,K11,K12,K13,K14>K22,K.ML,KMHL,KA2,KOX1,KOX2,INFILR,
15. IL,KSO,KSF,DCO,DCF,KLS,MWLS,DC02
16. DIMENSION X(50), YA(50),YB<50),NA(50),H2C03(50) ,OH2C03(50),
17. 1NB(50),R(50),T(50),PHI(50),FFR(50),RHOB(50),TE(50),TO(50),
18. 2FPY(50),RHOFR(50),UA(50),UB(50),UAN(50),EA(50),EB(50),
19. 3DX(50),DA(50),DB(50),FA(50),FB(50),TA<50),1AO(50),YBO(50),
20. 4PYO(50),QA(50),qB(50),PY(50),YAX(50),YBX(50),YAH(50),YAL(50),
21. 5PYX(50),NAI(50),NBI(50),UAO(50),UBO(50),U(50),RR(50),
22. 6ALPHA(50),DELTAO(50),DXFO(50),DXF(50),TB(50),C03FL(50),TFE3C(50),
23. 7AFE3T(50),FE2(50),FE3(50),PYFC50),PY02(50),TFE3CX(50),
24. 8ST(50),FE2X(50),YAXO(50),YBXOC50),GA(50),GB(50 ) ,
25. 9FFEO(50),WC(50),010(50),OH(50),OE3(50),OEOH(50 ) ,OEOH2(50),
26. 10EOH4(50),OE20H2(50),OES04(50),OEHS04(50),OEOOB(50),OS04(50)
27. 2,H(50),FEOOH(56),OEOR3(50),OST(50),OE2(50),OHBOX(50),HBACT(50),
28. 30E20XOO) ,OHS04(50),G1(50) .DELTAFC50) ,HC(50) ,AHLS(50) ,AHLSX(50),
29. 40E2B(50),OBC(50),FE3FL(50),FE2FL(50),HFL(50),DX2(50),
30. 5STFLC50),HCFL(50),CAFL(50),CA(50),OCA(50),RLS(50),FLS(50)
31. EXTERNAL DO,DC02,DAB,DBC,DAC,FLDX
32. COMMON/ADEL/KSO,DCO,KSF,DCF.L
33. 1/ACHEMI/FE31,H1,TFE3C,K.SP,KA2,K11,K12,K13,K14 , K22 , KML , KMHL , MCHEMI
34. I/ACHCAL/OIO,OEOH,OEOH2,OEOH3,OEOB4,OE20H2,OES04,
35. 20EHS04,0£OOH,OS04,OHS04,ST1FE2,OR>OE3,OE2,
36. 30ST,CA,OCA,H2C03,OH2C03,I/AHADJ/HC,OHC,HCFL,GA,GB/AFLUX1/H,FE3,X,
37. 4DX,DT,INFILR,N
38. EQUIVALENCE (FFEO.OE2B)
39. CALL ERRSET(208,256,-1,1)
40. CALL TIMREM(IREMO)
41. READ, IDUMP
42.
43.
44.
45.
46.
47 .
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
*5.
66.
67.
68.
69.
70.
71.
174
c
c
c
c
c
c
c
SET IN CONSTANTS
MCHEMI — 10
MM-MSMEEP-M-0
RHOPY-5.0
PI-3. 14159265
KSP-79433.0
KA2-.073
Kll». 00116
K12-2.0E-06
K13-1.0E-12
K14-2.5E-22
K22-6.0E-06
KML-84.0
KMHL-4.0
KOX1-1.3E-19
KOX2-1.7E-12
BO-1./3.5
BF-1./14.
EMIN-. 173
IFCIDUMP.EQ. 1 ) THEN
INITIALIZE VALDES IF T-0.
(IDUMP-1 )
C
C
c
c
c
c
c
-------
72. READ31,OPRINT,MBAT,1.,RADIUS,Y,Z,
73. 1DCO.KSO, DCF,KSF,KLS,P,RC,El,ET,KT,INFILR,MVLS,RHOLFi!
74. INFILR-INFILR/(365.*86400.)
75. PR-P/RC
76. DX(1)-1.
77. X(l) —.5
78. IP(MT.Eq.l) THEN
79. DDT-DT-86400.»2.
80. ELSE
81. DDT-DT-MT
82. END IF
83. READ35,DEPTH,ML,VINC.NPL
84. N-NL*liPl.+ l
85. IF(S.EQ.l) READ31.N
86. READ36,X(2),YAd ) ,YBd),Td) ,PHI(1),WC(1 ) ,FFR(I ) ,
87. 1RHOBO ),FPY(1 ) ,FFEO(1 ) , RHOFRd ) , TE ( 1 ) , GA C 1 ) , GB ( 1 },HBACT(1 ) ,
88. 2RLS(1),FLS(1)
89. DO 30 1-2,N
90. IF(X(2).GT.O.O) X(I)-X(I-I)+X(2)
91. IF(YA(1).NE.-1.) YA(I)-YAd-I)
92. IFmU).NE.-l.) fB(I)-YBd-l)
93. IF(FFRd ).NE.-1.) FFR(I)-FFRd)
94. IF(RBOB(1).NE.-1.) RHOB(I)-RHOB(1)
95. IF(FPY(1 ).NE.-1.) FPYd)-FPY(l)
96. IF(FFEO(1KNE.-l.) FFEO(I )-FFEO(1)
97. IF(RBOFR(1J.NE.-l.) RHOFRd )-8HOFR(l )
98. IF(Td).NE.-l.) TCI)-T(l)
99. IF(PHI(1).NE.-1.) PHKI)-PHI(l)
100. IF(WCd).NE.~l.) VC(I)-WCd)
101. IF(TE(I).HE.-25.) TE(I)-TEO)
102. IF(GAd).NE.-l.) GA(I)-GAd)
103. IF(GB(1 ).NE.-1.) CB(I)'GBd)
104. IFCRLSd ).NE.-1. ) KLS(I)-RLSd)
105. IFtFLSd ) .NE.-l. ) FLS(I)-FLSd )
106. IFCHBACTd ).NE. 1.) HBACT( I )-HBACT ( 1 )
107. IFCI.KE.21) FLSd)-0.
108. 30 CONTINUE
109. 31 FORMAT(I2,/,I2,/,13(G10.0,/) , I 10,3(/,G10.0))
110. 35 FORMAT(G10.0,/,I2,/,G10.0,/,I2)
111. 36 FORMAT(GIO.O)
112. IF(X(2).EQ.-1. ) READ,(X(I),I-1,N)
113. IF(X(2).EQ.O.) THEN
114. NI-NPL
115. DO 32 1-2,NL
116. NI-NI+NPL*VINC**(1-1)
117. 32 CONT1K0E
118. DI-DEPTH/NI
119. 11-2
120. DO 34 J-l.NL
121. DO 33 1-1 ,NP1.
122. DX(II)-D1
123. X
-------
151.
152.
153.
154.
155.
156.
157.
156.
159.
160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
172 .
172.
173.
174.
175.
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
191.
192.
193.
194.
195.
196.
197.
198.
199.
200.
201 .
202.
203.
204.
205.
206.
207.
208.
209.
210.
211 .
212.
213.
21*.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
40
1/,10X,'FFR- ' .F6.3.8X,'RHOB- ',F6.3,9X,'FPY- ',F7.4,/,1 OX,
2'FFEO- ',F6.3,7X,'RHOFR- ',F6.3,8X,'TE- ' , F6.3,/,1 OX,
3'GA- ',F8.4,7X,'GB- '.F6.3.11X,'HBACT- ',F6.3/,1 OX,'RLS- '.
4F8.4,6X,'FLS- ',F8.4,8X,'RHOLFR- ',F8.4,/,1 OX,'L- '.F6.3)
DO 40 J-l.N
I-N-J+1
RLSd)-2.*MULS*lCl.S/(RLSd)*RHOLFR)
FLSd)-FLSd)*RHOBd)/(2.*MVLS)
H2C03d)-DC02(TEd))*YB(I)
TO(I)-TEd)-TEd)+273.
ALPHAd)-(FPYd)*RHOFRd)/RHOPY)**(2./3. )*RHOFR(I )*10000.
Zl-WC(I); 22-PHId)
WC(I)-Z2*Z1
PHId)-Z2*(l .-Zl)
Td)-PHId)/T(I)
OHBOXd)-OE2Bd)-OE20Xd)-UBd)"0.
HCd)-1.0-20
KSA(I)-KZO(I)-KBd)-O.D-15
LSOd)-LSd)-PYOd)-UAOd)-DXFOd)-PYd)-1.0;PYF(I)-PY02(I)-1.0-25
IF(FPYd) .EQ.0.0) PY(I)-0.0
IF (RLS d)*FLSd). EQ.0.0) LSO d )-LS (I )-0 . 0
YAXOd)-YAXd)-YAOd)-YA(I)
YBXOd)-YBXd)-YBOd)-YB(I)
CALL DELCALC ALPHA d) , PY ( I ) , DELTAOd ) , DELTAF (I ) )
NAId)-NA(I)-1.0; NBI d )-NB d ) — 1 .
CAd)-OE2(I)-FE2(I)-5.00-07
STCD-5.0D-05
FEOOHd)-1000.«FFEO(I)*RHOBd)/C89.«UC(I))
H(I>-1.00-05
CALL CHEMI(-1,H d),FE 3 d),FEOOH d),AFE3T(I),G1d))
Hd)-OH(I); FE3d)-OE3d)
UANd)--DCO*RHOBd)*FFRd ) *DO (TE (I ) ) * ALPHA C I ) *KSO / ( 3 2 . *RHOFR d ) *L)
UAd)-YA(I)*UANd)*DELTAO(I)/(ALPHAd)*DELTAOd)*KSO*
1L*(1 .-PY(D)-f-DCO)
U(I)-UAd)/YAd)
DXFCD —120.* BF*DCF* ALPHA ( I) *KSF/( RHOFR d )«FPY(I)*L)
R(D—0.05
CONTINUE
LSOO )-LS(l )-PY(l )-UA(l )-DXF(l)-OAOd)-UAK( 1)-FEOOH(1 )-0.0
OCA(1)-CA(1)-ST(1)-FE2(1)-HC(1)-FE3(1)-1.OE-15
C
C
C
C
ELSE
READ(43,202)
1TZ1,TZ2,TZ3,1
READ(43,201)
READ(43,201)
READ(43,201)
READ(43,201 )
READ<43, 201 )
READ(43,20I )
READ(43,201 )
READ(43,201)
READ(43,20j )
READ(43,201 )
READ(43,201 )
READ(43,201 )
READ(43,201 )
READ(43,201)
READ(43,201)
READ(43,201 )
READ(43,201 )
READ(43,201)
READ(43,201)
READ(43,201)
READ(43,201)
READ(43,201 )
READ(43,201 )
READC43.201 )
READ(43,201 )
C
RETRIEVE DUMPED VALUES C
CIDDMP-0) C
C
OPRINT , 0, N , NBAT ,MBAT ,MT ,E 1 , PR, DT , DDT , TT , ET , TUT ,
rZ4,TZ5,TZ6,TZ7,TZ8,KSO,DCO,KSF,DCF,L, IKFILR.TFEO
(PY(I),I"1,N)
(PYOd).l-l .N)
(TECI ) ,1-1 ,N)
(TOd) ,1-1 ,NT)
CX(I),I-1,N)
(DXd),I-l,N)
(Td),l-l,N)
(UANd ) ,1-1 ,N)
(UA(I),I-1,K)'
(UAOd).I-J ,N)
(ALPHAd) ,1-1 ,N)
(PHId) ,1-1 ,N)
( WC (I ) , I - 1 , N )
(RHOBd).I-l ,N)
(RHOFRCI) ,1-1, K)
(FFRd ) , 1-1 ,N)
(FPY(I) ,1-1, K)
(FEOOHd) ,1-1 ,N)
(ST(I),I-1,K)
(FE3d),I-l ,N)
(FE2(I) ,1-1, N)
(Hd).I-l.N)
(DXFd ) , 1-1 , K)
176
-------
226. READ(43,201) (DXF0(1 ) , I-1, )O
227. READ(43,201) (OE2B(I ) . I - 1,K)
228. READ(43,201) (OE20X(I),1-1,N)
229. READ(43,201) (KB(I),I-1,N)
230. READ(43,201) (KBOCI ) ,1-1,N)
231. READ(43,201) (010(1),I-l,N)
232. READ(43,201) (HC(I),1-1.N)
233. READ<43,201) (HBACT(I).I-l ,N)
23*. READ(43,201) (OHBOXd) .1-1 ,N)
235. READ(43,201) (Rd>.I-l.N)
236. READC43.201) (OE3(I) .1-1,N)
237. READ(43,201) (OE2(I),I-1,N)
238. READ<43,201) (OH(I),1-1,N)
239. READ(43,20I) (YAO(I ) ,I-1 ,N)
240. READ(43,201) (YBO(I ) ,I-1 ,N)
241. READ(43,201) (GA(I),1-1,N)
242. READ(43,201) (GB(I ) ,I-1,N)
243. READ(43,2Q1) (CA(I),1-1,N)
244. READ(43,201) (LS(I ) , I-1 ,N)
245. READ(43,201) (LSOd),I-l,N)
246. READ(43,201) (RLS(I),I-1,N)
247. READ(43,201) (FLS(I),I-l,N)
248. READ(43,201) (H2C03(I),I-1,N)
249. READ(43,201) (OH2C03(I),I-1,N)
250. FPY(1)-0.0; PYF(1)-PY02(1)-l.OD-25; E1-.00001
251. DO 38 I-l.N
252. CALL DELCAL( ALPHA d),PYd),DELTAO(I),DELTAF(I))
253. CALL CHEMIU,H(1),FE3(I) ,FEOOH(I) ,A.FE3T(I) ,Z)
254. KBACI)-KB(I)
255. NAI(I)-NA(I)-1.0; NB1(I)-NB(I)"-!.
256. GKD-1.0
257. 38 CONTINUE
258. IF(l.EQ.Z) THEN; TT=TT-DT/86400.
259. DT-D0T-DT*2.
260. TT-TT+DT/86400. ; END IF
261. END IF
262. HCFLCD-0.
263. EB(1)-EA(1)-1.0
264. EA(1)-DB(1)-0.
265. PYX(1)-PYO(l)-PY(l)
266. B(l)-NA(l)-NBC1)-0.0
267. OHCU)-HC(l)
268. KBAd)-KB(l)
269. QA(l)«YAX(l)-YA(l)
270. QB(l)«YBX(l)-TB(l)
271. NAI(N)-NB1(N)-TB(N)-TA(N}-0.
272. Z-FLUX(O)
273. c***«»*********«**********««*******«****«****«*******************C
274. C C
275. C CONSTANT PART OF TRANSMISSIBILITIES ARE CALCULATED C
276. C C
277. c*»***«**««*******»*******•»««*»**•»*«**«**»***•*«»****«***«.*«**c
278. 400 CALL TIMREM(IREM)
279. 1F(2.*IREM-IREMO.LT.50) GO TO 200
280. IF(TT.GT.1850. ) GO TO 200
281. IREMO-IREM
282. PRINT789
283. 789 FORMAT('l')
284. DO 70 I-l.N
285. TEMP-TE(I)
286. TA(I)-Td)*DAB(TEHP)«DAC(TEMP)/TE«P
287. TBd )-Td)*DAB(TEMP)*DBC(TEMP)/TS>lP
288. 70 CONTINUE
290. C C
291. C CALCULATE EXTRAPOLATED VALUES AND LEACH RATES C
292. C C
293. C****************************************************»****«****««c
294. YAXOd )-YAX(l )-YA(l); YBXO ( 1 ) -YBX ( 1 )-YB (1 )
295. DO 50 1-2,N
296. ASX-LSd) + (LSd)-LSOd))
297. LSOd)-LS(l)
298. LSd)-DMAXl(ASX,O.OD+00)
299. YAXd)-YAd)-KYAd)-YAOd))
300. YBXd)-YBd) + (YB(I)-YBO(I))
301. IF(YAXd)-LT.O. ) YAXCI)-YA(I)/2. ; IF ( YBX (I )-LT. 0. ) YBX (I )• YB < I)/2 .
302. IF(O.GE.l) THEN
303. Z3-H(I) + (Hd)-OHd»
304. Zl-FE3d)-HFE3d)-OE3(D)
305. Z2-FE2(I) + (FE2d )-OE2(I ))
30b. OE3d)-FE3(I)
177
-------
307. OE2U )-FE2(I )
3oe. mzi.cT.o.) THEN; FE3(i)-zi; ELSE; FE3(i)-FE3d)/2.; END IF
309. IF; OBC2-DEC(TE2 )
178
-------
390. NC2-(NC1-NC10 ) r. .-t-NCU'
391. NCIO-NCI
392. IF(M.CT.O) NC2-(NC2+NC(I))/2.
393. NCd)-NC2
394. 2-1.; MKM-0
395. WHILE U.GT.1.OD-1i. AND . MMM .LT.2 2)
396. Zl-NA(I); Z2-NBCI)
397. NAd)-T2«DAB2*DAC2/(YB2*(DAC2-DAB2)-'SA2*DA»2-H>AB2><'(22«YA2/
398. 1(T2*DAB2) + NC2*YA2/(T2*DAC2)-PR/TE2»((YA3-YA2)«XXH-(YA2-YA1)»XX2))
399. NB(I)-T2*DAB2*DBC2/(YA2*(DBC2-DAB2)-YB2*DAB2+DAB2)*(NA(I)«YB2/
400. 1(T2*DAB2)+NC2«YB2/(T2*DBC2)-PR/TE2*((YB3-YB2)*XX1+(Y82-YB1)*XX2))
401. Z"DABS(NA(I)-Z1 )-t-DABS ( NB ( I )-Z 2 )
402. MMM-MMW+1
403. END WHILE
404. 74 IF(NAd).EQ.O.O) THEN
405. RRCD-R2 — 1.0D-H6
406. IF(NBd).EO.O.O) RR( I )-R( I )-R2-PI
407. DA2-1.
408. ELSE
409. R2-RR(I)-NBd)/NA(I)
410. RMAX-DMAX 1(RMAX,1.-DABS(R(I)/R2)}
411. Rd)-R2-(R.Rd)-»-Rd))/2.
412. DA2-YB2*(DAC2-DAB2)-YA2*(R2*DAC2+DAB2)+DAB2
413. END IF
414. IF(R2.EQ.O.O) THEN
415. DB2-1.
416. ELSEIF(R2.EQ.PI) THEN
417. DB2-1.
418. ELSE
419. IF(R2.EQ.-1 .OD-H6) THEN
420. Z-0.0
421. ELSE
422. Z-DBC2/R2
423. END IF
424. DB2-YA2*(DBC2-DAB2)-YB2*(Z+DAB2)+DAB2
425. END IF
426. FAd)-4.»PR*TA3«TA2/(TA3*DA2+TA2*DA3)
427. FB(I)-4.«PR*TB3*TB2/(TB3*DB2+TB2«DE3)
428. DX2(I)-(X2-X1)*(X3-X2)+(X3-X2)**2
429. 80 CONTINUE
430. Z-0.0
431. D085J-:,N
432. I-N+2-J
433. DA(I)-FA(I-1)/DX2(I)
434. DB(I)-FB(I-1)/DX2(I)
435. FA(I)-FA(I)/DX2(I)
436. FB(I)-FB(I)/DX2(I)
437. FE21-FE2U)
438. Hl-H(I)
439. IF(NB(I) .EO.0.0) FB(I)-DBd)
440. Ud)-UAN(I)«DELTAO(I)/(ALPHA(I)*DELTAO(I)*KSO*
441. 1L*(l.-PY(I))+DCO)
442. IF(O.EQ.O) UAO(I)-U(I)«YA(I)
443. X1-DMIN1(0.OD+00,2.*HBACT(I)*(TE(l)-273.»
444. EAd)--(DA(I>+FA(I)-(0(l)-«CCI)/4-*FE21 * ( KB { I )-i-KOXl
445. l*Hl**(-2)+KOX2) + Xl ) )-PHI(I)*PR/(TE(I)*DT)
446. EB(I)--(DB(I)+FBd)+DC02(TE(I))/CDT*1000.)}
447. QAd)--PHId)*FR*YAO(I)/(TO(I)*DT)
448. OB(I)-X)*YA(I)-((OH2C03(I)+C03FL(I))/ 1 000 . +(LSO(I)-LS(I))»FLS(I))
449. 1/DT
450. Z-1 -+Z+DABS(QB(I))+YB(I )/TE(I )-YBOCI )/TOd )
451. IF(Z.EQ.O.O) THEN
452. QB(I)-YBd)
453. EB(I)-1.0
454. DB(I)-FB(I)-FBd-l)«0.
455. ELSE
456. EB(I)-EB'-E".A» "•:"".tv.v j>(Ay« A".* ^ -?Y'! AX "'•'": A>«F T>'/v" C. r
-------
87
120
C
C
C
CONTINUE
UT-0.
DO 115 J-l.N
I-N+l-J
PYRITE CONSUMPTION IS CALCULATED
C
C
C
475. IF(YAX(J).LT.O.) THEN; YAX{J)-YA(J> ; YA(J)-YA(J)/2 .
476. PRINT.J,YAX(J),'-YAX' ,YA(J) , '-YA'; END IF
477. IF(DB(J).EQ.O.) THEN
478. YBX(J)-YBX(J-1)«DEXP((NA(J)/T(J)+NA(J-l)/TfJ-l))«(X(J)-X(J-l))/
479. 1(2.*DAB(TE(J))«PR/TE(J)))
480. END IF
481. YAX(J)-YA(J)-(YA(J)+YAX(J))/2. ; YBX ( J )-YB(J )-(YB(J)+YBX(J))/2.
482.
483.
484.
485.
486.
487.
488.
489.
490.
491. IFd.EQ. 1) GO TO 115
492. TOE3C-OEOH(I)+OEOH2(I)+OEOH3(I)+OEOH4(I) + 2.*OE20H2U)+OEHS04(I)
493. l-t-OES04(I)-K)EOOH(I)
4 94 . AMAX-DMAX1(AMAX,DABS(YAX(I)-YAXO( I ) ) )
495. BMAX-DMAX1(BMAX,DABS(YBX(I)-YBXO(I)))
496. YA2-YA1-YA(I)
497. YBl-YB(I)
498. YAXOCI)-YAX(I); YBXO ( I )-YBX ( I )
499. IF(FPY(I).EQ.O.) THEN; Z3-Z4-0.0; GO TO 111; END IF
500. Z3-DT*U(I)*YA1«BO*120./(RHOB(I)*FFR(I) '
501. 1*FPY(I))
502. Z4-DT*DXF(I)*AFE3T(I)*FE3(I)*DELTAF(I)/(L*D£LTAF(I)«ALPHA(I )
503. 1*KSF»O .-PY(I))+DCF)
504. PY(I)-PYO(I )+Z3+Z4
505. IF(PY£I).LT.O.O) THEN
506. . PY(I)-PYO(I)/2.
507. Z3--Z3«PY(I)/(2.*(Z3+Z4))
508. Z4—(PY(I)+Z3)/2.
509. END IF
510. IF(O.NE.O)CALL DELCAL(ALPHA(I),PYO(I ) , DELTAO(I),DELTAF(I))
511. Ill IF(O.EQ.O) THEN
512. PYU)-PYO(I)
513. UAO(I)-0(I)»YA1
5U. END IF
515.
516.
517.
518.
519.
520. IF(O.EQ.O) THEN
521. AFE21-AFE22-DFE20X-AS04-0.
522. ELSE
523. FE32-FE31-FE3U)
524. FE32-FE31
525. H2-R1-HCI)
526. KB2--1.
527. KBl-KB(l)
528. AFE21—Z3»1000.*RHOB(I ) *FFR ( I ) *FPY ( I ) / ( 1 20. *WC( I ) )
529. AFE22— 1 5 . *Z4 * 1 000 . *RHOB ( I ) *FFR ( I) *FPY ( I ) / ( 1 20. *WC( I ) )
530. FE21-FE2(I)
531. FE22-FE2X(I)
532. TC-(TO(I)-HE(I))/2.-Z73.
533. XTE— 1 .23D-05*TC*«3-4.33D-04«TC**2 + 0.0657*TC-0.255
534. IFCH2.LE.O.) PRINT,I,E2, '-H2 ' , X
535. PH—DLOG10(H2)
536. XPH--.348*PH**2+2.26*PH-2.66
537. IF(XPH.LE.O.O) THEN; Z2 5-KB2-Z5-KB(I)-0.0; GO TO 803; END IF
538. X02-YA2/.01
539. IF
-------
476. PRINT,J,YAX(J), '-YAX' ,YA(J), '-KA'; END IF
477. IF(DB(J).EQ.O.) THEN
478. YBX(J)-YBX(J-1>*DEXP«NA(J)/T(J)+NA(J-1 ) /T(J-1))«(X(J)-X(J-l))/
479. 1(2.«DAB(TE(J))*PR/TE(J)))
480. END IF
481. YAX(J)-YA(J)-(YA(J)+YAX(J))/2. ; YBX ( J )-YB ( J )- ( YB ( J )+YBX( J ) ) t'l .
482. 87 CONTINUE
483. UT-0.
484. 120 DO 115 J-l.N
485. I-N+l-J
486. c******«*****»************«***************»*********************«C
487. C C
488. C PYRITE CONSUMPTION IS CALCULATED C
489. C C
490. c********•«**»*****«*******•******«**•**»*****•*««**«****»«**««**c
491. IFd.EQ.1) CO TO 115
492. TOE3C-OEOHd)-K>EOH2d)+OEOH3d)+OEOH4d )-f2.*OE20H2(I)+OEHS04(I)
493. l-K>ES04d)+OEOOHd)
494. AMAX-DMAXl(AMAX,DA.BS(YAXd)-YAXOd)) )
495. BMAX-DMAX1(BMAX,DABS(YBX(I)-YBXO(I)))
496. YA2-YAl-YAd)
497. YBl-YB(I)
498. YAXOd)-YAXd ); YBXO(I)-YBX(I)
499. IF(FPY(I).EQ.O.) THEN; Z3-Z4-0.0; GO TO 111; END IF
500. Z3-DT*Ud)*YAl*BO*120./(RBOBd)*FFRd)
501. 1*FPY(D)
502. Z4-DT*DXFd)*AFE3Td)*FE3d)*DELTAFd)/(L*DELTAFd)*ALPHAd)
503. l*KSF*d.-PYd))+DCF)
504. PYd)-PYOd)+Z3+Z4
505. IF(PYd) .LT.0.0) THEN
506. PYd)-PYOd)/2.
507. Z3 — Z3*PY(I)/(2.*(Z3+Z4))
508. Z4 —(PY(I)+z3)/2.
509. END IF
510. IF(O.NE.O)CALL DELCAL ( ALPHA ( I ) , PYO ( I ) , DELTAO ( I ) , DELTAF ( I) )
511. Ill IF(O.EQ.O) THEN
512. PYU)-PYO(I)
513. UAO(I)-U(I)*YA1
514. END IF
515.
516.
517.
518.
519.
520. IF(O.EQ.O) THEN
521. AFE21-AFE22-DFE20X-AS04-0.
522. ELSE
523. FE32-FE31-FE3CI)
524. . FE32-FE31
525. H2-H1-HCI)
526. KB2 — 1.
527. KBl-KBd)
528. AFE21—Z3*1000.*RHOB(I)*FFR(I)*FPYd)/(120.«UCCI))
529. AFE22 — 15.*Z4*1000.*RHOBd)*FFRd)*FPYd')/d20.*WCd))
530. FE21-FE2(I)
531. FE22-FE2XCI)
532. TC-(TOd)+TEd))/2.-273.
533. XTE--1.23D-05*TC**3-4.33D-0'*TC**2+0.0657*TC-0.255
534. IF(H2.LE.O.) PRINT,I,H2,'-H2',K
535. PH--DLOG10CH2)
536. XPH--.348«PH**2+2.26*PK-2.66
537. IF(XPH.LE.O.O) THEN; Z2 5-KB2-Z5-KB(I)-0.0; GO TO 803; END IF
538. XC2-YA2/.01
539. IF(X02.GT.1.) X02-1.0
540. EM-EMIN/(XTE*X02«XPH)
541. IFUTE.LE.O. -OR.XPH.LE.O.O.OR.X02.LE.O.) TREK
542. PRINT,l.XTE,'-XT',X02,'-X02',XPH,'-XPH',YA2,'-YA'
543. KB(I)-KB1/100.
544. GO TO 803
545. END IF
546. IFCEM.GT. 1. 18) THEN; KBd)-0.0; CO TO 803; END IF
547. Z25-Z5-G1(I)**(-4)*H2*YA2*«.25*DEXP(( .46-EM)/(8.6D-05*TE(I ) ) )
548. Z18-Z5-(FE31-Z5«FE22)/(1.+Z5)
549. Z5-FE22+Z5
550. KB2-KBd)-(0£2d) + AFE21*YA2/YAl+AFE22*d . -Z 1 8 /FE3 1 )+FE 2FL CI )
551. 1-Z5)/(Z5*ET*YA2*1000.)
552. IF(KBd). LT.0.0) KB ( I) - . 0 1 *DSQRT ( KB 1 ) *3 . 3D-08
553. 803 Z11-2.*DT/8640G.
554. Z11-DMIN1(2.0D+01,Z11)
555. KB(I)-DM1N1 (KB(I).KBO{I)*2.*«211 '.
55b. Z16-4.*WC(I)*2.75D-l]/f.O)**r*FE225
C
C KB IS CALCULATED
C
C
C
C
181
-------
557.
558.
559.
560.
561.
562.
563.
564.
565.
566.
567.
568.
569.
570.
571.
572.
573.
574.
575.
576.
577.
578.
579.
580.
581.
582.
583.
584.
585.
586.
587.
588. '
589.
590.
591.
592.
593.
594.
595.
596.
597.
598.
599.
600.
601.
602.
603.
604.
605.
606.
607.
608.
609.
610.
611.
612.
613.
614.
615.
616.
617.
618.
619.
620.
621.
622.
623.
624.
625.
626.
627.
628.
629.
630.
631.
632.
633.
634.
635.
636.
KBd )-DMlNl (KB(I) ,Z16)
KBAd)-KB(I)
KB(I)-KB1
IF(KBA(I)*YAl*FE21.LT.1.0D-22) KBA(I)-0.0
IF(K.BA(I)«KB(I).NE.O.) THEN; KBMAX-DMAX1 ( KBMAX, DABS (KB ( I )-KBA (I ) )
1/KBCD)
ELSE; JCBMAX-DMAX1 (KBMAX, DABS ( KBA( I) ) ) ; END IF
IF(KBAd).EQ.KB2) FERMAX-DMAX1 ( FERMAX . DABS ( Z25-FE3 1 /FE22 > /Z25 )
C C
C FE3.FE2 AND H ARE CALCULATED C
C C
FE2Xd)-(OE2d)+AFE21+AFE22+FE2FL(I)
1 >/{r.+DT*1000.«YAl*(KOXl*Hl**(-2)
2-t-KOX2+KBd)))
WHILE(FE2X(I) .LT.O. )
FE2FL
1F(H(I) .GT. AST) THEN -
STL-AST
ELSE; STH-AST; END IF
AST-(STH+STL)/2.
IF(TT.LT.O) PRINT,I,M,IST,STH,'-HH',H(I),'-H',AST,
1 '-AST' ,STL, '-HL' ,HFL(I) , '-HFL'
IST-IST+1
IFdST.CT.20) THEN
DFE2B-DFE2B/2.
KB(I)-KB(I)/2.
END IF
END WHILE
END IF
C
C S04 IS CALCULATED
C
AS04--2.*(Z3+Z4)*1000.*RHOB(I)*FFR(I)*FPY(I)/
1(120. *WC(I))
ST(I)-OST(I )+AS04+STFL(I)
IF(ST(I ) .LT.O. ) THEN
/
)
182
-------
637.
63E.
639.
640.
641.
642.
643.
644.
645.
646.
647.
648.
649.
650.
651.
652.
653.
654.
655.
656.
657.
658.
659.
660.
661.
662.
663.
664.
665.
666.
667.
668.
669.
670.
671 .
672.
673.
674.
675.
676.
677.
678.
679.
680.
681.
682.
683.
684,.
685.
686.
687.
688.
689.
690.
691.
692.
693.
69-.
695.
696.
697.
696.
699.
700.
701.
702.
703.
704.
705.
706.
707.
708.
709.
710.
711.
712.
713.
~T 1 i.
c
c
c
c
c
c
317
114
115
C
C
C
1ST-)
STH-2.*OST(I)+AS04
STL-0.0
AST-(STH+STL)/2.
WHILE (DABS
-------
715. 1F(«.GT.50) PR I NT 2,M,AMAX,BMAX,PYMAX,HMAX,FEMAX.FERMAX
716. : FORMATC/.1X,' M- ',13,' AMAX-' ,D11.3, ' BMAX-',Dl1.3,
717. 1' PYMAX-' ,D11.3,' HMAX-',011.3.' FE3MAX-' ,D 1 1.3,
718. 2* FERMAX-'.D11.3)
719. IF{OPRINT.GE.3) THEN
720. DO 900 1-1,K
721. 900 PRINT12,I,X(I),YA(I),YB(I),NACI).NB(I),UA(I).UB(I),R2,PYU>
722. END IF
723. IF(M.LT.35) THEN
724. IF(AMAX.CT.10.«E1) CO TO 500
725. IF(BMAX.GT.10.*E1) GO TO 500
726. IF(PYMAX.GT.El) GO TO 500
727. IF(HMAX.CT.£1*1000.) GO TO 500
728. IF(FEMAX.GT.E1*1000.) GO TO 500
729. END IF
730. 999 FORMAT(1X,I2,2X,6D11.4)
731. MSWEEP-MSWEEP+1
732. 901 IFCOPRINT.CE.1 .OR.MSWEEP.GT.20) PRINT902,MSWEEP,M,RMAX,KBMAX,
733. 1FLMAX.LSMAX.FCMAX
734. 902 FORMAT(37X,'AFTER SWEEP',14,5X,'AND' ,I 4 , ' ITERATIONS',/
735. 1,1 OX, 'RMAX-' ,D11.3,8X, 'KBMAX-' ,D11.3,8X, 'FLMAX-' ,D11.3,8X,
736. 2'LSMAX-',D11.3,'FCMAX-',011.3)
737. IF(OPRINT.GT.1) PRINT 2,M,AMAX,BMAX,PYMAX,HMAX,FEMAX,FERMAX
738. IFCMSWEEP.LT.25) THEN; M-0
739. IFCOPRINT.EQ.4) PRINT785,(I,YA(I),1-1,N)
740. IF(OPRINT.EQ.4) PRINT785,(I,YAX(I),I-1,N)
741. IF(OPRINT.EQ.4) PRINT788,(I,KB(I),1-1,N)
742. IF(OPRINT.EQ.3) PRINT788,(I,KBA(I),I-1,N)
743. DO 786 1-2,N
744. FE2(I)-(FE2X(I)+FE2(I))/2.
745. YA(I)-(YA(I)+YAX(I))/2.; YB(I )-
-------
796. Z8-FHJX(7)
797. DO 124 J-2.N
798. I-N-M-J
799. NC1-YBX(I)-PHI(I)*PR/TE(I)«DX(I)/DT*(YAO(I)-YA(I)+YBO(I)-YBCI) .
800. 1+YAOU-M )-TA(I + l )+YBO(I+l )-YB(I-H ))/2.+NCI
801. 124 CONTINUE
802. DO 125 I-l.H
803. H2C03(I)-DC02(TE(I))*YB(I)
804. IF(I.NE.N) THEN
805. Dl-DX(I)
806. D3-DX(I+1)
807. D2-D1+D3
808. T2-(T(I)*D3+T(I-H7*D1)/D2
809. TE2-(TE(I)*D3+TEU+1 )*D1)/D2
810. DAB2-DAB(TE2)
811. DAC2-DAC(TE2)
812. DBC2-DBCCTE2)
813. YA3-YACI+1)
B14. YAl-YA(I)
815. X3-XU + 1)
816. Xl-X(I)
817. YB3-YB(I+1)
818. YBl-YB(I)
819. YA2-(D1*YA3+D3*YA1 )/D2
820. YB2-(D1*YB3+D3*YB1)/D2
821. Z10-1
822. HHILECZ10.GT. l.OD-U)
823. Zll-NAI(I); Z12-NBKI)
824. NAI(I)-T2«I>AB2*DAC2/(YB2*(DAC2-DAB2)-YA2*DAB2+DAB2)*(Z12*
825. 1YA2/(T2«DAB2)+YBX(I)*YA2/(T2«DAC2)-PR/TE2*(YA3-YA1 )/(X3-Xl ))
826. NBI(I)-T2*DAB2*DBC2/(YA2*(DBC2-DAB2)-YB2*DAB2+DAB2)*(NAI(I)*
827. 1YB2/(T2*DAB2)-I-YBXCI)*YB2/(T2*DBC2)-PR/TE2*(YB3-YB1 )/(X3-Xl ))
828. Z10"DABS(NAI(I)-Z11)+DABS(NBI(I)-Z12)
829. END WHILE
830. END IF
831. R(I)-NB(I)/NA(I)
832. U3-U(I)*YA(I)
833. Ul-03
834. UAO(I)-U3
835. U3--U1*BO*2.
836. U3-03/DXU)
837. U4-DMIN1(O.OD+00,2.*YA(I>*HBACT(I)*(TE(I)
838. 1-273.))
839. Dl-X(I)-<-DX(I)/2.
840. OE20XCD — FE2(I)«YA(I)*(KOXl*H(I)**(-2 )+KOX2)
841. YAX(I)-U2-1./A.*VC(I)*0£20X(I)
842. U2-U2+1./4.«WC(I)«(-KB(I ) *YA(I ) *FE2(I))
843. Z-DMAX1(Z,DABS(?Y(I)-P10(I)))
844. . FE20X-YAX(I)*4.*DT
845. FE2B--KB(I)*YA(I)«FE2CI)
846. TFE2B-FE2B*DT««C(I)
847. OE2B(I)-FE2B
848. DXFO(I)-DXF(I)*AFE3T(I)»FE3(I)*DELTAF(I ) /(L*DELTAF(I)'ALPHA(I)"KSF
849. 1*(1.-PY(I))+DCF)
850. IF(DABS(NB(D) . LT . l.OD-20) NB(I)-0.0
851. 123 PRINT12,I,X(I),YA(I),YB(I),NA(I),NB(I),HI,U2,U4,FE20X,PYCI)
852. IF(MBAT.EQ.l) WRITE(NBAT,851 ) I,X(I),YA(I),YB(I),NA(I),NB(I),UJ ,
853. IZll.PY(I)
854. PRINT13,D1,NAI(I),NBI(I),PYF(I)/PY02(I),TFE2B
855. 1,1.5(1)
856. IFCMBAT.EQ.1) URITECNBAT,13) D1,NAI(I),DELTAO(I)
857. 126 FORMAT(1X,I3,8(1X,D10.4))
858. 125 CONTINUE
859. 12 FORMAT(1X,I4,1X.F8.1,2F10.4,3X,2(D10.4,3X),4(E!0.3,2X),2X,F&.3)
860. 13 FORMAT(6X.F8.1,20X,2(3X,D10.4),25X,2(2X,D10.3),4X,F6.3)
861. 851 FORMAT(IX,14,1X,F8.1,2F10.4,3X,2(D10.4,3X),/,2(D10.4,3X),
862. 1F7.4)
863. PRINT15
864. PRINT215
865. DZ7-Z7-TFE-0.0
866. DO 128 1*1,K
867. Z7-Z7-KPY02(I)+PYF{I))*FPY(I)
868. IF(I.CT.l) DZ7-DZ7+FPY(I)*DX(I)
869. IF(I.NE.l) CALL CHEMI(1 ,H(I ) , FE3(I),FEOOH(I),AFE3T(I),PYX WRITE(NBAT,16 ) I , PH,FE2CI ) , FE3(I),FEOOH
-------
876. 10S04(I),010(1).FE20X.TFE2E
877. FRINT16,I,PH,FE2(I),FE3d),FEOOHd).HCCI).OS04(I),010(1),
878. 1H2C03(I),CA(I),Z11
879. IFCTT.GE.32.) KBOCI)-DMAXI(KB(I),KBA{I),1.OD-15)
880. IF(KBd>+KBOd).LT.1.0D-12) GO TO 128
881. IF(KBd).NE.O.O) THEN; XI-DABS(KB( I )-KBO(I ) )/KB(I )
882. ELSEIF(KBOd).EQ.l.00-15) THEN; Xl-0.; ELSE; Xl-100.; END IF
883. KBMAX-DMAX1(DABS(KB(I)-KBO(I))/KBO(I),KBMAX. XI )
884. KBMAX-KBMAX
885. 128 CONTINUE
886. Z7-86400.*Z7/(DT*DZ7)
887. 15 FORMATC1 ' ,1X, 'LAYER',4X, ' PH ' , 7X , ' FE2 ' , 9X, ' FE3 ' , 7X, ' FEOOH ' ,
888. 17X,'ACIDITY',7X,'S04',6X,'IONIC STR',5X,'H2C03',
889. 28X,'CA',7X,'TFE3CMPLX')
890. 215 FORMAT(17X,' MOLES/L',
89 ! . j ' , 7X, '-'./)
892. 16 FORMAT(1X,I4,IX,F8.2,3X,9(D9.3,3X))
893. IF(OPRINT.EQ.3) PRINT?
894. 7 FORMATC5X, 'B',6X,'S04' ,5X, 'HS04' ,4X, 'FE3' ,5X, 'FEOH',
895. 13X,'FEOH2',3X,'FEOH3',3X,'FEOH4',
896. 22X,'FE20H2',3X,'FES04',2X,'FEHS04')
897. TFED-TFE-TFEO
898. TFEO-TFE
899. TFE-(TFED+(Z2+Z3)*DT/a64000.-DT*INFILR*(FE3(l)+FE2(l)))/TFE
900. IP(TT.EQ.O.O) TFE-0.0
901. DO 127 I-l.N
902. FH--DLOG10(B
-------
956.
957.
958.
959.
960.
961.
962.
963.
964.
965.
966.
967.
968.
969.
970.
971.
972.
973.
974.
975.
976.
977.
978.
979.
980.
981.
982.
983.
984.
985.
986.
987.
988.
989.
990.
991.
992.
993.
994.
995.
996.
997 .
998.
999.
1000.
1001 .
1002.
1003.
1004 .
1005.
1006.
1007.
1008.
1009.
1010.
101 1.
1013.
1014.
1015.
101 6.
1017.
1016.
1019.
1020.
1021.
1022.
1023.
1024.
1025.
1026.
1027.
1028.
1029.
1030.
1031.
1032.
1033.
1034.
1035.
END IF
DT-DMINl(DT,1.5768P+07j
END IF
140 IF(TT.LE.32.) THEN
IHTT+DT/86400. .GT.32.) DDT-DT-864 00 . *2 .
END IF
TT-TT+DT/86400.
END IF
MSWEEP-MM-M-0
IF(TT.GE.ET) GO TO 200
GO TO 400
c
c
c
c
DATA IS DUMPED IF TIME
LIMIT IS EXCEEDED
C
C
C
C
200 PRINT,' "'"EXECUTION EXCEEDS TIME ALLOWED, JOE DUMPED*'***'
WRITE(42,202) OPRINT,0,N,NBAT,MBAT,MT,E1,PR,DT,DDT,TT,ET,TUT,
lTZl,TZ2.TZ3,TZ4,TZ5,TZ6,TZ7,TZ8,KSO,DCO,K.Sr,DCF,L,INFILR,TFEO
WRITE(42,201 )
WRITE(42,201)
WRITE(42,201) (PY(I).I-l,N)
WR1TE(42,201 ) (?10(I),1-1,N)
URITEC42.201) (TE(I),1-1,N)
WRITE(42,201) (TO(I),I-1,N)
WR1TE(42,201) (X(I),I-1,JO
WRITEC42.201) CDX(I),I-1,N)
WRITE(42,201) (T(I),I-1,N)
WRITE(42,201) (UAN(I),1-1,N)
WRITE(42,201) (UA(I),1-1,N)
WRITE(42,201 ) (I)AO(I) ,1-1,N)
WRITE(42,201) (ALPHA(I),I-1,N)
WRITE(42,201 ) (FKI(I) ,1-1 ,N)
WRITE(42,201) (UC(I),1-1,N)
WR1TE(42,201 ) (RHOB(I),I-1,N}
WRITE(42,201 ) (RHOFRCI ) ,1-1 ,N)
WRITE(4:,201 ) (FFRCI),1-1,N)
•»RITE(42,201 ) (FPY(I) ,1-1 , K )
WRITEC42,201) (FEOOH(I),1-1,N)
«RITE(42,201) (ST(I),1-1,N)
WRITE(42, 201 ) (FE3CD , 1-1 ,N)
WRITE(42,201) (FE2(I),I-1,N)
WRITE(42,201) (H(I),1-1,N)
WRITE(42,201) (DXFCI),1-1,N)
WRITEC42.201) ,1-1 ,N)
WRITE(42,201) (CA(I),1-1,N)
WRITE(42,201) (LS(! ) ,1-1,N)
BRITE(42,201) (LSOCi;,1-1,N)
WRITE(42,201) (RLS(I),1-1,N)
WRITE(42,201) (FLS(I),1-1,N)
WKITE(42,201) (H2C03(I),1-1,N)
WRITE<42,20n (OH2C03U) ,1-1 ,N)
201 FORMAT(IX, 2D28. 1 8)
202 FORMAT(1X,515,110,2(1X,F10.8),/,lX,4D17.10,/,5(lX,D17.10),/,
11X,4D18.10,2E13.6,/,1X,4E13.6,D17.10)
STOP
END
D.O. FUNCTION
DO*YA - GRAMS 02 PER KL
187
-------
1036.
1037.
1038.
1039.
1040.
1041.
1042.
1043.
1044.
1045.
1046.
1047.
1048.
1049.
1050.
1051.
1052.
1053.
1054.
1055.
1056.
1057.
1058.
1059.
1060.
1061.
1062.
1063.
1064.
1065.
1066.
1067.
1068.
1069.
1070.
1071.
1072.
1073.
1074.
1075.
1076.
1077.
1078.
1079.
1080.
1081.
1082.
1083.
1084.
1085.
1086.
1087.
1088.
1089.
1090.
1091.
1092.
1093.
1094.
1095.
1096.
1097.
1098.
1099.
1100.
1101.
1102.
1103.
1104.
1105.
1106.
1107.
1108.
1109.
1110.
1111.
1112.
1112.
1114.
1115.
1116.
1117.
DOUBLE PRECISION FUNCTION DIM 1 ,)
REAL'S T
DO-.032*10."(2237.8/T-15.803+.018117«T)
RETURN
END
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
D.C02. FUNCTION
DC02-HENRY 'S LAW TEMP. DEPEND. COEFFICIENT
FUNCTION DC02(T)
REAL'S T
DC02-. 03388
RETURN
END
FUNCTION DAB
THIS FUNCTION CALCULATES THE TEMPERATURE DEPENDANT
02-C02 DIFFUSION COEFFICIENT.
DOUBLE PRECISION FUNCTION DAB(T)
IMPLICIT REAL'S (A-H.P-Z)
DAB-1 . 56D-05*T**1 . 661 /DEXPC61 . 3/T)
RETURN
END
FUNCTION DAC
THIS FUNCTION CALCULATES THE TEMPERATURE DEPENDANT
02-N2 DIFFUSION COEFFICIENT.
DOUBLE PRECISION FUNCTION DAC(T)
IMPLICIT REAL'S (A-H.P-Z)
DAC-1.13D-05*T"1.724
RETURN
END
FUNCTION DBC
THIS FUNCTION CALCULATES THE TEMPERATURE DEPENDANT
N2-C02 DIFFUSION COEFFICIENT.
DOUBLE PRECISION FUNCTION DBC(T)
IMPLICIT REAL'S (A-H.P-Z)
DBC-3. 15D-05'T"1 .57/DEXP(113.6/T)
RETURN-
FUNCTION FLUX
CALCULATES LEACHING RATE FOR H , HC , FE3 , FE2 , ST
AKD IS BASED ON CONCENTRATIONS AT OLD TIME STEP ONLY.
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
DOUBLE PRECISION FUNCTION FLUX(MO)
IMPLICIT REAL'S (A-H.O-Z)
REAL«4 INFILR
DIMENSION HCFL(50),OH(50),OE3(50),OE2(50),OST(50),OHC(50),S(50),
1X(50),DX(50),A(50,50),OEOH(50),OEOH2(50),OEOH3(50),OEOH4(50),
20E20H2(50),OES04(50),OEHS04(50),OS04(50),OHS04(50),010(50),
30EOOH(50),ST(50),FE2(50),H(50),FE3(50),HC(50),CA(50),CB(50),
4CA(50),OCA(50),H2C03(50),OH2C03(50)
COMMON/ACHCAL/OIO,OEOH,OEOH2,OEOH3,OEOH4,OE20H2,OES04,
20EHS04,OEOOH,OS04,OHS04,ST,FE2,OH.OE3,OE2,
30ST,CA,OCA,H2C03,OH2C03,I/AHADJ/HC,OHC,HCFL,GA,GB
4/AFLUXl/H,FE3,X,DX,DT,INFILR,N
IF(MO.GT.O) CO TO 25
NN-N+1
H(NN)-F£3(NN)-FE2(NN)-OH(NN)-OE3(NN)-OE2(NN)-OST(NN)-OHC(NN)-0.
HC(NN)-OEOH(NN1-OEOH2(NN)-OEOH3(NN)-OEOH4(NN)-OE2OH2(NN)-0.
CA(NN)-OCA(NN)-ST(NN)-OEHS04(NN)-OES04(NK)-OS04(NK>-OHS04(NN)-0.
H2C03(NN)-OH2C03(NN)-0.
X(NN)-X(N)->-DX(N)/:.
DO 10 II-2.N
188
-------
u5c»^c^U'^ww^o*cn^*^tn^u^jwo^oo^o*u>^u>lo»— o ^ cr>
OD
TVS0
~ -* •*. o
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1 1 O to
H NJ <_.
*"' *» "
31 -^s
KJ 4
O 3J
\_/ (-1
-- 1
CJ *—
ti ^
O
'£
)*
O
to
0
o
*".
f-.
\
V
•f
r>
» 4
to z n i z t-> 2; i i a;
o * t-t '-"•N :z o o itt-i^^rto
O Z M M » 3J2JMMI
O M (I^WOM ll^tJ
^ » O — » » O
»-* on »-* 3: z
*-» > > ^ no
o ii 3: (i
*_- O *-* CJ
v_* PI «^* pi
* 25 * X
O O O O
n :r 31 a:
> » n *
•^ o — • o
MO M 30
,_x >. vv n
i i
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\-^ -^f
n n
HJ M
tJ O
O "I -^
H 3!
^— • y-.
* M
•-v O
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11
C/l
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/-^
t-4
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35 1 » 0
1 1 1
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4 t
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•- x
^ 0
in ^
H <-
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t> w
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l->
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00 * H4 ^ ^
t J O '"N II
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M ^-v
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if ro
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10 pi
t-* U>
M ^-*
4 -*
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in u>
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M i>>
t/l x-»
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t Ct
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4- ^
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33 ^
Kl (-<
C. *-
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4 o
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Pt w
t/> t-t
O 1
t- •->
U 4
1 O
N- PI
^ o
o -->
tn (
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t_ o
1 PI
•- o
^ ffi
S^SMMS^^^^^!^
^ 4 *
O Hto OC1OOOO
33 M« OOOOOO
^> *
H 0 _)HHHHH
•^ 3! OOOOOO
5 V S^^JSSS
^* ^
P3 O
v^ t_<
1
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4.
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t
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4.
tc
c,
(
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4
n
1 h^ yO f^>
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O H •
1
5C
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W M
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f
r*
B
?4
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25
^^
w
f
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2
Mir)o>-ar'O>wMaon(
CJSSr4 O » [/I 7! | ^^l 5^ 35 M (/) ''> 35 I
>tot~»OKJ5^»~|t-Hp1C^KiNJHl
O|Mt—fOM« n*-^u*- • »o« *-4» n« OO*-'-'
— 25- *«1O ZU 35O S5r.I-.XM Z
O PI '^-f I P1?S1» llpl^-(-i» |f-|pl>
I t_, i (sj ^- ^- ^- -^- ( 35 M 0 I
>- ^«^_x*
-------
1200.
1201 .
1202,
1203.
1204.
1205.
1206.
1207.
1208.
1209.
1210.
1211.
1212.
1213.
1214.
1215.
1216.
1217.
1218.
1219.
1220.
1221.
1222.
1223.
1224.
1225.
1226.
1227.
1228.
1229.
1230.
1231.
1232.
1233.
1234.
1235.
1236.
1237.
1238.
1239.
1240.
1241 .
1242.
1243.
1244.
1245.
1246.
1247.
1248.
1249.
1250.
1251.
1252.
1253.
1254.
1255.
1256.
1257.
1258.
1259.
1260.
1261.
1262.
1263.
1264 .
1265.
1266.
1267.
1268.
1269.
1270.
1271.
1272.
1273.
1274.
1275.
1276.
1277.
1278.
1279.
1280.
1281 .
S2EI.
Y-2.*H2C03(1 )/CH2C03(I)+OH2C03(l ))«OH2C03O)
100 IF(I.EQ.NN) GO TO 110
FLUX-(CI-Y*TI)*INFILR*DT/DX(I)
RETURN
110 FLUX-CI*INF11.R*864000.
RETURN
EKD
c
C SUBROUTINE FOR CALCULATING DELTA
C
C
C
C
1
10
SUBROUTINE DELCAL(A,PY,DELTA,DELTB)
IMPLICIT REAL*8 (A-Z)
REAL*4 KSO,KSF,DCO,DCF,L
COMMON/ADEL/KSO,DCO,KSF,DCF,L
PYI-1.0
Y-DSQRT(KSO«A/DCO)
R-(1.-PY/PYI)*L
C-(DEXP(-Y«R)-DEXP(Y*(R-2.*L)))/(DEXP(Y*(R-2.'L))+D£XP(-Y*R))
DELTA-C/(Y*<1.+R«RSO*C/(DCO«Y)))
Y-DSQRT(KSF«A/DCF)
R-(1.-PY/PYI)*L
C-(DEXP(-Y*R)-DEXP(Y*(R-2.*L)))/(DEXP(Y*(R-2.*L))+DEXP(-Y*R))
DELTB-C/(Y*(1-+R*KSF«C/(DCF«Y)))
RETURN
END
••*******************»****»****».»*«**.****«**********«***»*C
C
THOMAS'S ALGORITHM . C
C
l**********»************»******»»*t*+»*»*t******************c
SUBROUTINE THOMAS(A,B,C,D,N,X)
DOUBLE PRECISION A(N),B(N),C(N),D(N),X(N),W(50),G(50),DEN(50)
DO 1 1-2, K
IF(I.NE.N) W(I)-C(I )/DEN(I)
G(I)-(DU)-AU)*Ca-l))/DEN(I)
CONTINUE
X(N)-GCN)
3t(N-l)-G(N-l )-W(N-l)«X(N)
N-N-1
IF(N.CT.l) GO TO 10
RETURK
END
SUBROUTINE HADJ
THIS ROUTINE ADJUSTS THE H PRODUCED TO
ACCOUNT FOR NEUTRALIZATION BY THE GANGUE MATERIAL.
SUBROUTINE HADJ(AH,OH,I,H)
IMPLICIT REAL'S (A-H,0-Z)
DIMENSION HC(50),OHC(50),HCFL(50),GA ( 50),GB(50)
COMMON/AHAEJ/HC,OHC,HCFL,GA,CB
MMM-0
IFCAH.LE.O..OR.GACI).LT.-9.) TREK
H-OH+AH
HC(I)«OHC(I)+HCFL(I)
WHILE(HC(I).LT.O.)
HCFL(I)-HCFL(I)/2.
HC(I)-HC(I)-HCFL(I)
MMM-MMM+1; IF(MMM.CT.10) THEN; PRINT,'
GO TO 732
END IF
ZND WHILE
732 RETURN
END IF
«-!; Zl-1.0
AL-OH
AC-DM INI (1 .OD+0!**(-GA(I» ,OH+AH)
AM-(AL+AC)/2.-OH
WHILE(DABS(Zl-AM).CT..0001*AM)
Zl-AM
APH—(DLOC10(OHHDLOC10(OH+AM))/2.
AAH-AH*(1.-DEXP(CBU ) * < CA (I )-APH)»
IFtAV.-LT. AAH) THEN
*«*ERROR***1120'
190
-------
1283.
1284.
1285.
1286.
1287.
1288.
1289.
1290.
1291.
1292.
1293.
1294.
1295.
1296.
1297.
1298.
1299.
1300.
1301.
1302.
1303.
1304.
1305.
1306.
1307.
1308.
1309.
1310.
1311.
1312.
1313.
1314.
1315.
1316.
1317.
1318.
1319.
1320.
1321.
1322.
1323.
1324.
1325.
1326.
1327.
1328.
1329.
1330.
1331 .
1332.
1333.
1334.
1335.
1336.
1337.
1338.
1339.
1340.
1341.
1342.
1343.
1344.
1345.
1346.
1347.
1348.
1349.
1350.
1351.
1352.
1353.
1354.
1355.
1356.
1357.
1358.
1359.
1360.
1361.
1362.
1363.
1364.
!365.
733
20
25
ELSi.
AC-AM+Oh
END IF
AM-( AL+AG)/2.-OH
M-H-fl
IF(M.CT.50) PRINT,I,OH,'-H' ,AAH,'-AAH' , '
IF(M.GT.SO) STOP
END WHILE
H-OH-t-AM
HC(l)-OHC(I) + AH-AM-t-HCFL(I )
WHILE(HC(I).LT.O.)
HCFLd)-HCFL(I)/2.
HC(I)-HC(I)-HCFL(I)
MMM-MMM-H ; IF(MMM.GT.SO) THEN; PRINT,'
GO TO 733; END IF
END WHILE
RETURN-
END
HC IS NOT CONVERGING*
***ERROR***1132'
c
c
c
c
c
c
c
c
SUBROUTINE CHEMI
THIS ROUTINE CALCULATES THE IONIC STRENGTH, ACTIVITY
COEFFICIENTS, AND CONCENTRATIONS OF THE FERRIC SPECIES FOR
ANT GIVEN PR, ST, TFE3, AND TFE2. IT RETURNS THE ACTIVITY
COEFFICIENTS AND THE TOTAL IRON(III) ACTIVITY.
.
i
1
t
(
(
I
SUBROUTINE CHEMI{MO,H,FE3,FEOOH,AFE3T,DELIO)
IMPLICIT REAL*8 (A-H.O-Z)
REAL*8 lO.DELFE(SO)
REAL*4 KSP.K11,Kl2,Kl3,Kl4,K22,KML,KMHL,KA2
DIMENSION OH(50),010(50),OE3(50),OEOH(50),OEOH2(50),HC(50),
10EOH4(50),OE20H2(50),OES04(50),OEMS 04(50),0504(50),OE2(50),
20EOH3(50) ,OHS04(50) , OE-OOH ( 50 ) , OST ( 5 0) ,ST(50),FE2(50),TFE3C(50),
3HCFL(50),OHC(50).GA(50),GB(50),CA(50),OCA(50),H2C03(50),OH2C03(50)
COMMON /ACHEMI/FE31 , HH 1 , TFE3C , K.S? , KA2 , K 11 , Kl 2 , Kl 3 , Kl 4 , K2 2 , KML , KMHL ,
1MCHEMI/ACHCAL/010,OEOH,OEOH2,OEOH3,OEOH4,OE20H2,OES04,
20EHS04,OEOOH,OS04,OHS04,ST,FE2,OH,OE3,OE2,OST,CA,OCA
3,H2C03,OH2C03,I/AHADJ/HC,OHC,HCFL,GA,GB
M-l; X-0.0
IF(MO.LE.O) THEN
DELFE(I)-0.
OEOOH(1)«FEOOfi
IO-0.5«H+1.5*ST(I)
FEOH-FEOH2-FEOH3-FEOH4-FE20H2-FES04-FEHS04-0.
ELSEIF(MO.GT.1) THEN
X2-Z1-FE3RI-FE3
HR-H
CALL HADJ(HR,OH(I),I,H)
H-HH1; FE3-X2-FE31
10-010(1); FEOH-OEOH(I); FEOH2-OEOH2(I )
FEOH3-OEOH3(I); FEOH4-OEOH4(I ) ; FE2OH2-OE20H2(I)
FESO4-OESO4(I); FEHS04-OEHS04(I); OFEOOH-OEOOH(I)+FEOOH
ELSE
R2-FE3; X-IO-OIO(I)
END IF
G1-10.**(-.5*(DSQRT(IO)/(1 .4-DSORT(IO))-.3»10))
G2-G1**4
C3-G1««9
G4-G1**16
GO TO 25
10-0.25*(H-fflS04-'-F£OH2+FEOH4+FES04+4.0*(FE2(I) + S04->-FEOH+FEHSOJi)
H-8.0*HC(I) + 9.0*FE3-H6.0*FE20H2)-HO/2.
IFdO.GT. 120. ) PRINT,I,'- I ' , M, '-M ' , ST ( I ) , ' - ST ' , FE2 (I ) , '-FEI '
IF(IO.GT.120.)PRIKT2,H,PH,S04,HS04,FE3,FEOH,FEOH2,FEOH3,FEOHi,
1FE20H2,FES04,FEHS04,FEOOK
IFdO.GT. 120.) PRINT,FE3R1, ' -FE3RI ' , FE3R , ' -FE3R',HR,' -HR',
ICELFEd) , '-DELFE' , FE3E , ' -FE3E ' , H6 , ' -H6 ' , HC (I ) , ' -HC ' , 10 , ' - I 0 '
IF(M.CT.IS) THEN; IO-X; END IF
G1-10.**(-.5*(DSQRT(IO)/(1.+DSQRT(IO))-.3*10))
C2-G1**4
G3-G1**9
G4-G1**16
1F(MO.EQ.4) THEN
Z1-FE3
H6-H-DKAX1(H,OH(I)/100.)
FE3E-KSP/C3*(G1*H)**3
FE3R-FE3R:-G3«FE3E*(KH / ( H*G 1 *G2 ) + K 1 2 / ( H** 2 *G ! ** 3 )-t-K 1 3 '
1(E*«3*C1**3)-HC)4/(H**4«G1**5)+G3*FE3E*K22/(G4«H**2«G1**2)
2*K«1,*SO4«C2/G!+KMHL*HS04«C1 /G2)+OEOH(l)^-
3+OEOH4(I)+OE20K2(I)*OIS04(I)+OEHS04(I)
191
-------
1306.
1367.
1368.
1369.
1370.
1371.
1372.
1373.
1374.
1375.
1376.
1377.
1378.
1379.
1380.
1381 .
1382.
1383.
1384.
1385.
1386.
1387.
1388.
1389.
1390.
1391.
1392.
1393.
1394.
1395.
1396.
1397.
1398.
1399.
1400.
1401.
1402.
1403.
1404.
1405.
1406.
1407.
1408.
1409.
1410.
1411.
1412.
1413.
1414.
1415.
1416.
1417.
141 8.
1419.
1420.
1421.
1422.
1423.
1424.
1425.
1426.
1427.
1428.
1429.
1430.
1431.
1432.
1433.
1434.
1435.
1436.
1437.
1438.
1439.
1440.
1441.
1442.
1443.
I 444.
1445.
88
27
28
IFCFEUOH.GT. Cl. ) THE:.
FE3-FE3E
ELSE
FEOOH-0.0
FE3-(FE3III+0£OOH(I)+OEOH(I)+OEOH2(I>+OEOH3 +
10E20H2+K13/(H**3*Gl**3)+K14/(H*«4*Gl**5>+C3*FE3«K22
3/(C4*H**2*Gl**2)-HCML*S04*G2/Gl-t-KMHL«HS04*Gl/G2))
END IF
IF(FE3.LE.O.O) FE3-DMAX1(O.OD+00,FE3R+DELFE(I))
H1-DMAX1(OH(I)/10..H); HA-10.; MMMM-1 ; IF(K.EQ.l) KMMM-1
WHILE(DABS(HA-H).GT..001«H.AND.MMMM.LT.2)
MMMM-MMMM+1; IFU.EQ.32) FRINT , MMMK , HA , ' -HA ' ,H . ' -H '
HA-H
AH-HR+3.*(FEOOH-OEOOH(I))-(OEOH(I)+2.*(OEOH2(I)+OE20H2(I))
H.3.*OEOH3(I)+4.*OEOH4(I)-t-OHS04(I)+OEHS04(I)) + FE3*G3*
2(K11/(H1*G1«G2)+2.«K12/(H1*H1*G1**3)+3.*K13/(H1**3*C1**3)+4.«K14/
3{H1**4«G1««5)+2.*K22*G3«FE3/(G4*H1**2*C1**2)+KMHL«HS04»G1/G2)
4+HS04
CALL HADJ(AH,OH(I),I,H)
H2-DMAX1(OH(I)/100.,H)
IF ( H . EQ . OH ( I ) / 1 00 . ) HC ( D-OHC ( I ) / 1 0.
END WHILE
IF(M.EQ.9)THEN
IFCH2.GT.H1) THEN
HH-H2; HL-H1
ELSE
HH-H1; HL-H2
B-(HL-HiH)/2.
END IF
ELSEIF(M.GT.9) THEN; IF(H.LT.Hl) THEN;HH-H1
ELSE; HL-H1; END IF
H-(HL+HH)/2.
1FCI.GT.35) PRINT88,HR,FE3R1,FE3R,FE3,FE3E,FEOOH,B,HL,HR,H2,IO
ELSEIF(M.LT.9.) THEN
H-(Hl+H2)/2.
IFC1.GT.33) PRINT,I,El,'-HI', P. 2, '-H2'
END IF
FORMAT(1X,F10.5,' -HR '.F10.5,'
1' -FE3 ',F10.5,' -FE3E ',F10.5,
2F1C.5,' -HL '.F10.5,' -HH '.FJ0.5,'
GO TO 27
END IF
IF(MO.LE.O) THEN
X2-Z1-FE3-.2*(H*G1)**3/G3
FEOOH-OEOOH(I)-FE3-FEOH-FEOH2-FEOH3-FEOH4-2.*FE20H2-FES04-FEHS04
IF(FEOOH.LT.O.O) THEN
FEOOH-0.0
END IF
END IF
IF(FE3.LT.O.O) THEN
PRINT28.I.M
FORMATC//,35X, 'WARNING' ,/, 10X, 'FE3 .LT. 0.0; TOTAL COMPLEXES
1EXCEED FEOOH',/,5X,'PROGRAM WAS EXECUTING LAYER',14,', ITERATION'
214,' IN SUBPROG CHEMI')
PRINT,FE3RI, ' -FE3RI',FE3R, ' -FE3R',HR,' -HR',
IDELFE(I), '-DELFE' ,FE3E, '-FE3E' ,H6, '-H6'
PRINT2,H,PH,S04,HS04,FE3,FEOH,FEOH2,FEOH3,FEOH4,FE20H2,
1FES04.FEHS04,FEOOH
STOP
END IF
S04-ST(I)/(l.+K«KA2*G2-t-KML«FE3*C3*G2/Cl+K>1HL*H«FE3*KA2*Cl*C3)
HS04-H*S04*KA2»G2
FEOF-FE3«K11*G3/(G1*G2*H)
FEOH2-FE3«K12"G3/(G1««3*H«*2)
IF(FEOH.GT.1000.)PRINT.FE3,'-FE3',FEOH,'-FEOH',R,G1,G2,G3,'1354'
FEOH3-FE3*K13*G3/(H**3*G1**3)
FEOH4-FE3«K14«C3/(H**4*G1**5)
FE20H2-(FE3/H)**2*K22*(G3/G1)*«2/G4
FES04-FE3*KML*S04*G2*G3/G1
FEHS04-FE3«KHHL*HS04»G1«G3/G2
IFCMO.GT.l) THEN
DELFE(I)-FEOH+FEOH2+FEOH3+FEOH4+2.*FE20H2+FEHS04+FES04-
10EOH(I>-OEOH2(1)-OEOH3(I)-OEOH4(I)-2.*OE20H2(I)-OEHS04(I>-
20ES04(I )
END IF
IF(DABS(FE3-X2).LE. -001«FE3) THEN-
IP (DABS(IO-X)flO.LE..01) GO TO 30; EKD IF
X-IO
X2-FE3
•FE3RI '.F10.5,' -FE3R '.F10.5,
-FEOOH ' ,/,IX,FlO.5, ' -H ',
•H2 '.FlO.5,'- 10 ',/)
192
-------
1447.
1448.
1449.
1450.
1451.
1452.
1453.
1454.
1455.
1456.
1457.
1458.
1459.
1460.
1461.
1462.
1463.
1464.
1465.
1466.
1467.
1468.
1469.
1470.
1471.
1472.
1473.
1474.
1475.
1476.
1477.
1478.
1479.
1480.
1481.
1462.
1483.
1484.
1485.
1486.
1487.
1488.
1489.
1490.
1491.
1492.
1493.
1494.
1495.
1496.
1497 .
1498.
1499.
1500.
1501.
1502.
1503.
1504.
1505.
1506.
1507.
1508.
1509.
1510.
1511.
1512.
1513.
1514.
1515.
1516.
1517.
1518.
1519.
1520.
1521 .
1522.
1523.
1524.
152S.
M-M+1
CO TO 20
30 AFE3T-((G1*(FEOH2+FEOH4+FES04) + G2 *(FEOH+FEHS04)+2.*G4*FE20H2
1+FEOH3)/(FE3*G3)+G3)/1000.
TFE3C(I)-FEOH+FEOH2+FEOH3+FEOH4+2.*FE20H2+FEHS04+FESO4+FEOOH
IF(MO.LE.l) THEN-
DELI 0-FE3+FE2(I)+FEOOH+FEOH+FEOH2+FEQH3+FEOHA+2.«FE2OH2+
1FES04+FEHS04
OEOH(I)-FEOH; OEOH2(I)-FEOH2; OEOH3(I)-FEOH3
OEOH4(t)-FEOH4; OE20H2 ( I )-FE20H2 ; OEOOH ( D-FEOOH ; OES04 ( I )-FES04
OEHS04(I)-FEHS04;OS04(I)-S04; OHS04(I )-HS04; OST(I)-ST(I)
OHC(I)-HCd); OCAd)-CA(I); OH2C03 ( I )-H2C03 ( I )
IF(MO.EQ.-l) THEN; OH(I)-H; OE2(I)-FE2(I ) ; OE3(I)-FE3; END IF
ELSE; DELIO-G1
END IF
OIOCD-IO
IF(I.EQ.32) GO TO 60
IF(MCREMI) 40,50,60
40 RETURN
50 PRINT1,I,M,10
1 FORMAT{/, 10X,'LAYER ',14,', I ITERATIONS - ',12,531,
1'IONIC STRENGTH - ',F6.4)
RETURN
60 PRINT1,M,IO
PH —(DLOG10(G1*H))
PRINT2,H,PH,S04,HS04,FE3,FEOH,FEOH2,FEOH3,FEOH4,FE20H2,
1FES04,FEHS04,FEOOE
2 FORMAT(7X,'H',8X,'PH',7X,'S04',7X,'HS04',6X,'FE3',7X,'FEOH',/,
13X,D8.2,3X,F6.3,3X,4(D8.2,2X),//,5X, 'FEOH2' ,5X, 'FEOH3',5X, '1-EOH4'
24X,'FE20K2',5X,'FES04',4X,'FEHS04',4X,'FEOOH',/,3X,7(D8.2,2S))
PRINT3,FE3,AFE3T*FE3
3 FORMAT(/,5X, 'FERRIC IRON', 87.,'TOTAL FERRIC',
1' IRON ACTIVITY',/.6X.D10.4,6X.D10.4)
- RETURN
END
//DATA.FT51F001 DD UNIT-BAT,FILES-SDXDT1
//DATA.FT52F001 DD UNIT-BAT,FILES-SDXDT2
//DATA.FT53F001 DD UNIT-BAT,FILES-SDXDT3
//DATA.FT54F001 DD UNIT-BAT,FILES-SDXD74
DD UNIT-BAT,FILES-SDXDT5
DD VOL-REF-MEN.P65440.D1J.LIB,
// DSN-MEN.P65440.D1J-DMNLS8,
// DCB-(RECF«-FB,LR£CL-100,BLKSIZE-3100) ,
// SPACE-(TRK, (3,5),RLSE),DISP-(NEW,KEEP )
//DATA.INPUT DD *
IDUMP
OPRINT
MEAT
L
RADIOS
T DIMENSION
Z DIMENSION
DCO
KSO
DCF
KSF
KLS
P
RG
El
ET
1 MT
INFILR (CM/YR)
MWLS
RHOLFR
DEPTH
NL
VINC
NPL
X2
YA
//DATA.FT55F001
//DATA.FT42F001
1
0
0
2.
4.
100.
100.
.0000001
.000000083
.0000001
.000004*
.00000291
1.
82.3
.0000!
10300.
50.
50.
3.
1000.
20
1.
1
0.
.21
.0003
10.
.313
.7
.75
1.80
0.0025
.0
2.1
T
PHK.180, .216)
WC
FFP.
RHOBC 1 .67,1 .80)
FPV
FFEC
RHOF?
193
-------
1526.
1527.
1528.
1529.
1530.
1531.
1532.
1533.
1534.
1535.
1536.
1537.
1538.
1539.
1540.
1541.
1542.
1543.
1544.
15.
2.50000000
1.11000
0.0
1.0
.00083
0.0 0.
.00025
.02325
.0025
0 0.0
.00025
.0025 •
.0025 .
TE
GA(0.
GB(1.
HBACT
RLS
FLS
.00025 .00025
.00025 .00025 .00025
.0025 .0025 .0025
0025 .0025 .0025 .0025
0.0 -0.30-12 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.00.00.0
//DATA.FT43F001 DD DSN-MEN.P65440.01J.DMNLS7,
// DISP-(OLD,KEEP),VOL-REF-MEN.P65440.D1J. LIB,
// DCB-(RECFM-FB,LRZCL-10C,BLKSIZE-3100),
// SPACE-(TRK,(17,3),RLS£)
/*
// EXEC PGM-UKSG,PARM-(INTERACT,'TO D1J JOB DONE')
194
-------
Example Output from Run 4
RMAX-
RHAX-
RMAX-
RMAX-
RMAX-
AHAX-
0
0
0
n
0
0.
I
I
.8710-03
.7870-03
. 1 15D-0?
.61fln-03
,R83n-m
162D-0'' BMAX
1 KB -
4 KB •
7 KB -
10 KB -
13 K II "
- 16 KB -
- 19 KB -
-
0
0
f)
n
0
0
n
AFTER
KRMAX-
AFTF.R
KBMAX-
AFTER
KBMAX-
AFTK.R
KBI1AX-
AFTF.R
KBMAX-
n. 1 1 '.n-i 7
.0
. 10910-07
,f>2?nn-o;
.n
.0
.n
. n
SWEEP 21
0,5170+00
SWBKP 22
0.277D400
SWEEP 23
0.226IUOO
SWEEP 24
n.!391MOO
SWEEP 25
o. ifl3n+on
PYMAX- O.I
2
5
•' 8
- 1 1
- 1'.
- 17
- 20
AND 5 ITERATIONS
FLMAX- 0. 1150-01
AND 4 ITERATIONS
FLMAX- 0.fi45D-02
AND 1 ITERATIONS
FLMAX- 0.7980-02
AND 3 ITERATIONS
FLMAX- 0.2690-02
AND 1 ITERATIONS
Fl.MAX- 0. 6690-02
74D-05 UMAX- 0.441D-04
KB - 0.99840-08 1
KB - 0. 1639D-07 I
KB • 0.7992D-07 1
KB - 0.0 I
KB - 0.0 I
KB - 0.0 I
KB - 0.0 I
LSMAX-
LSMAX-
LSHAX-
LSHAX-
I.SHAX-
0.0 FCMAX-
0.0 FCMAX-
0.0 FCHAX-
0.0 FCMAX-
0.0 FCMAX-
FE3MAX- 0. 3000-03 FERMAX- 0.
3
6
9
- 12
- 15
- 18
- 21
KB - 0
KB - 0
KB - 0
KB - 0
KB - 0
KB - 0
KB - 0
.77600-08
. 281 ID-07
.U08D-08
.0
.0
.0
.0
0. 2810-01
O.U5D-01
0.697D-02
0.397D-02
0.825D-03
1370*00
-------
AFTER 6166.0 DAYS
SOLUTION WAS FOUND IN 155 ITERATIONS
LAYER
1
2
3
4
.•i
6
7
8
9
to
1 1
12
13
I'l
15
16
17
18
19
20
21
DEPTH
-0.5
0.0
25.0
50.0
75.0
100.0
125.0
150.0
175.0
200.0
225.0
250.0
275.0
300.0
325.0
350.0
375.0
400.0
125.0
450.0
4 7 5 '. 0
500.0
525.0
550.0
575.0
600.0
625.0
650.0
675.0
700,0
725.0
750.0
775.0
800.0
825.0
850.0
875.0
900.0
925.0
950.0
975.0
1000.0
02
0.2100
0. 1 754
0.1411
0. 1081
0.0777
0.0500
0.0264
0.0091
0.0068
0.0053
0.0041
0.0032
0.0024
0.0019
0.0014
0.001 1
0.0009
0.0007
0.0006
0.0005
0.0005
C02
0.0003
0.0003
0.0003
0.0003
0.0003
0,0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
N02
0.6720D-10
0.67150-10
0. 53620-10
0. 31850-10
0.3050D-10
0. 29240-10
0.27770-10
0.26390-10
0.2472D-IO
0.2315D-10
0.2114D-10
0. 19220-10
0. 16440*10
0.1376D-10
0.7729D-
0. 1812D-
0. 14990-
0.1I8ID-
0. 10590-
0.9330D-12
0. 83330-12
0. 73070-12
0.6503D-12
0.56760-12
0.5033D-I2
0.4373D-I2
0. 38630-12
0.3340D-12
0.29370-12
0. 25240-12
0.2205D-12
0. 18780-12
0.1623D-12
0. 13630-12
0. 1 1550-12
0.94400-13
0. 76990-13
0. 59350-13
0.4406D-13
0.2863D-13
0. 1 'i 3 4 0-13
0.0
NC02
0.2024D-I 3
0.2023D-13
0. 16150-1 3
0.95930-14
0.91870-14
0.8806B-I4
0.8365D-14
0. 79490-14
0. 7450D-I4
0. 69770-14
0.637ID-I4
0. 5794D-I4
0. 49550-14
0.414HO- 4
0.23290- 4
0.54380- 5
0.44990- 5
0.3540B- 5
0.31771)- 5
0.27990- 5
0.250ID- 5
0.21930- 5
0.19530- 5
0.17040- 5
0.15120- 5
0.13130- 5
0.11610- 5
0. 10030-15
0.88250-16
0. 7582D-I6
0. 66250-16
0.56430-16
0. 48780-16
0. 40950-16
0. 34720-16
0. 28370-16
0.23140-16
0. 17840-16
0. 1324D-16
0. 86070-17
0.43100-1 7
0.0
II02I-Y
0.0
-0.2350-13
-0. 1640-13
-0. I 190-13
-0.857D-14
-0.584D-I4
-0.353D-I4
-0.205D-14
-0. 5670-14
-0.4920-14
-0. 4020-14
-0. 3240-14
-0.2590-14
-0.2050-14
-0. 1620-14
-0. 1290-14
-0. 1030-14
-0.8340-15
-0.6980-15
-0.612D-15
-0. 5700-15
U02FF.OX
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
8610-26
210D-I3
3600-13
4500-13
5600-13
727D-13
106D-12
238D-12
6930-14
1770-17
126D-17
91fll)-l8
681D-1B
5100-18
3860-18
295D-18
2290-18
1820-18
1500-18
130D-18
1210-18
U02HB/OR
0.0
0. 1000+01
0.0
0.810D+00
0.0
0.208D+01
0.0
0.3580+01
0.0
0. 6210+01
0.0
O.II9D+02
0.0
0.288D+02
0.0
0. 1150+03
0.0
0.176D+OI
0.0
0.31 ID+00
0.0
0.271D+00
•0.0
0. 2570+00
0.0
0. 2780+00
0.0
0.302D+00
0.0
0.336D+00
0.0
0. 3790+00
0.0
0.429D+00
0.0
0.482D+00
0.0
0.5300+00
0.0
0.560D+00
0.0
0.559D+00
CHOX/BACTOX
-0. 3810-18
0.0
-0.1660-09
-0.928D-06
-0.359D-09
-0. 159D-05
-0. 3200-09
-0.199D-05
-0.265D-09
-0. 2480-05
-0.200D-09
-0.322P-05
-0. 1320-09
-0.46BD-05
-0.230D-09
-0. 105D-04
-0. 122D-09
-0.307D-06
-0.784D-10
0.0
-0.556D-10
0.0
-0.4060-10
0.0
-0.3010-10
0.0
-0.226D-10
0.0
-0. 1 710-10
0.0
-0. 130D-10
0.0
-0. 101D-10
0.0
-0,8070-1 1
0.0
-0.665D-1 I
0.0
-0.577D-1I
0.0
-0. 533D-1 1
0.0
XPY/XLS
0.0
0.0
0.345
0.0
0.231
0.0
0.184
0.0
0.186
0.0
0.235
0.0
0.343
0.0
0.641
0.0
0.957
0.0
0.969
0.0
0.975
0.0
0.979
0.0
0.982
0.0
0.985
0.0
0.987
0.0
0.988
0.0
0.9B9
0.0
0.990
0.0
0.991
0.0
0.991
0.0
0.992
0.0
-------
LAYER
T
T
T
T
T
T
T
T
T
T
T
T
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
PH
5.
2.
2.
2.
2.
2.
2.
2.
2,
2.
2.
2.
2.
2.
2.
2 .
2.
2.
2.
2.
2.
00
91
BO
an
BO
BO
80
80
80
80
80
80
80
60
81
81
81
82
82
82
82
0.
0.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
FE2
. 1000-14
.3810-03
. 1040-02
.1210-02
. 1400-02
. 1640-02
.2040-02
. 1040-01
.7360-02
.6090-02
.5570-02
.5260-02
.5070-02
.4920-02
.482D-02
.4730-02
.4670-02
.4620-02
.4580-02
.4560-02
.*Mn-ft?
11
20540-02
II
1 1060+02
FE3 FF.OOII ACIDITY S04 IONIC STR
0. 1000-14 0.0 0.10011-14 0.1000-14 0.105D-03
0.2530-03 0. 2830-01 0.4900-09 0.1920-02 0.6810-02
0.7000-03 0.651D-OI 0.9520-03 0.415D-02 0.1890-01
0.8860-03 0,6!OD-01 0.3970-02 0.6310-02 0.3630-01
0.1050-02 0.5480-01 0.7370-02 0. 8700-02 0.5580-01
0.1230-02 0. 3840-01 0.1170-01 0.1170-01 0.802O-01
0. 1450-02 0.2700-01 0. 1840-01 0.1670-01 0.1180+00
0.1670-02 0.0 0. 2950-01 0.301D-01 0.2080+00
0.1120-04 0.0 0.2000-01 0.1890-01 0.1330+00
0.1380-05 0.0 0.1700-01 0.1610-01 0.1130+00
0.8620-06 0.0 0.157D-01 0.1490-01 0.1050+00
0.6050-06 0.0 0.1500-01 0.1430-01 0. 9980-01
0.4510-06 0.0 0.1450-01 O.I38D-01 0.9670-01
0.3520-06 0.0 0.1420-01 0.1350-01 0.9460-01
0.2830-06 0.0 O.I40D-OI 0. 1330-01 0.9310-01
0.2350-06 0.0 0.1390-01 0.132H-01 0.9210-01
0.2000-06 0.0 0.1380-01 0.1310-01 0.913D-01
0.1730-06 0.0 0.1370-01 0.130D-01 0.9070-01
0.1530-06 0.0 0.136n-01 0.1290-01 0.9030-01
0.1380-06 0.0 0.1360-01 0.1290-01 0. 90011-01
n. 1260-06 o.o n. iif.o-oi 0.1290-01 o. 8980-01
INCRF.lir.NTAL FRACTIONAL IRON MARS BAt.ANCF,
-.26440-03
FRACTIONAL PYRITF, CONSUMPTION PKR M*«2 PER DAY
-.29600-04
TOTAL FRACTIONAL PYRITE CONSUMPTION PER M'*2
-.25630+00
HOLES ENTERING THE WATER TABLE PF.R H**2 PER DAY
ACIDITY FE3 FE2 TOTAL SULFATE
0.18530-01 0.53550-04 0.6IJ6n-o? n^i'tOR-O! 0
TOTAL MOLES TO ENTKR THE WATER TABLE PER M**2
ACIOITY FE3 FE2 TOTAL SULPATR
0.14B5l)f03 0.27630 + 00 0.1**SDl-02 0.12770+03 0
II2C03
0.1020-04
0. 1020-04
0. 1020-04
0. 102D-04
0. 10211-04
0. 102D-04
0. 1020-04
0, 1020-04
0. 1020-04
0. 1020-04
0. 1020-04
0. 1020-04
0. 1020-04
0, 1020-04
0. 1020-04
0.1020-04
0. 1020-04
0. 1020-04
0. 1020-04
0. I02D-04
0.1020-04
CALCIUM
.2900i;-i2
CALCIUM
.62940-03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 .
0.
CA
. 1000-14
. 1000-14
. 1000-14
, 1000-14
. 1000-14
. 1010-14
. 1090-14
. 1460-14
.2570-14
.5150-14
. 1010-13
.1830-13
.3040-13
.4660-1 3
.6650-1 3
.893D-13
. 1 140-12
. 1380-12
.1610-12
.18111-12
.2020-12
H2C03
i 39iu-u»
1I2C03
85850-01
TFE3CMPH
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
n.
0.
216D+05
2680+01
2080+01
2260+01
2410+01
2570+01
2780+01
3190+01
2850+01
2750+01
271D+01
2690+01
2680+01
2690+01
270D+OI
2720+01
2730+01
2750+01
2770+01
2790+01
28011 + 01
-------
-TECHNICAL REPORT DATA
/Please read Instructions on the rcitrsc before completing)
' ~ " |3. RECIPIENT'
1 REPORT NO
kCCESSIOf
4. TITLE AND SUBTITLE
Atmosphere and temperature within a reclaimed coal-
stripmine and a numerical simulation of acid mine
drainage from stripmined lands
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTMOR(S)
D. B. Jaynes, A. S. Rogowski, and H. B. Pionke
8. PERFORMING ORGANIZATION
3
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Northeast Watershed Research Center
USDA-ARS, 110 Research Building A
University Park, Pennsylvania 16802
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA-IAG-D5-E763
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Research & Development
Office of Energy, Minerals & Industry
Washinaton, B.C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
Interim 9/1/75-8/31/80
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
This project is part of the EPA-planned and coordinated Federal Interagency
Energy/Environment R&D Program. _^^_____
16. ABSTRACT
Oxygen, 62, carbon dioxide, €62 and temperature were measured with depth along a
transect of an acid, reclaimed, coal stripmine over a two year period. Spoil-atmosphere
Q£ concentrations decrease with depth but approach zero only in a small portion of the
transect. Most of the mine remains well oxygenated (02 > 10% by volume) down to 12-
meters depth. C02 concentrations ranged from near atmospheric levels to greater than
15%. At some locations, especially within 2 meters of the surface, variations in 02 an<
C02 are correlated with changes in the spoil temperature. Spoil temperatures in layers
below 3 meters remain in a range conducive to iron-oxidizing, bacterial activity year
around. Flux ratios of CO- and 02 and the source/sink rates of the two gases indicate
that carbonate neutralization of the acid produced by pyrite oxidation is the dominant
source of C02>
In a second phase of the study, a numerical model describing the production and
removal of acid and acid by-products from reclaimed coal-stripmines is presented. Both
direct oxygen and bacterially catalyzed pyrite oxidation is considered. The pyrite
oxidation rate is assumed to be controlled by first-order, solid-liquid kinetics and
simple diffusion of oxidant into reactive, coarse, stone fragments. Oxygen supply into
the reclaimed profile is considered to be governed by one-dimensional, gas diffusion.
(Circle One or More)
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Energy Conversion
Physical Chemistry
[norganic Chemistr
^Organic Chemistry
Chemical Engineering
6F 8A 8F
8H IDA 10B
7B 7C 13B
13. DISTRIBUTION STATEMENT
19. SECURITY CLASS (Tins Report/
21. NO. OF PAGES
20. SECURITY CLASS (Thispage)
22. PRICE
EPA Form 222O-1 (9-73)
------- |