EPA 910/9-84-121
United States
Environmental Protection
Agency
Region 10
1200 Sixth Avenue
Seattle WA 98101
Alaska
Idaho
Oregon
Washington
Environmental Services Division
January, 1984
A Time-Dependent,
Two-Dimensional Model for
Predicting the Distribution
of Drilling Muds Discharged
to Shallow Water \ ^
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A Time-Dependent, Two-Dimensional Model for
Predicting the Distribution of Drilling Muds
Discharged to Shallow Water
John R. Yearsley
EPA Region 10
Seattle, Washington
January 5, 1984
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A Time-Dependent, Two Dimensional Model for
Predicting the Distribution of Drilling Muds
Discharged to Shallow Water
Introduction
In drilling exploratory and production oil wells in offshore areas it
nas become common practice to discharge the drilling muds and cuttings to
marine waters. In general, the whole mud fraction has been found to be
more toxic tnan tne aqueous or particulate pnases. Trie 96-hour LCgQ
values for drilling muds are as low as 100 mg/1(Petrazuolo(198l )) for
some marine organisms. To protect water quality, National Pollution
Discharge Elimination System (NPDES) permits issued for such discharges
must oe in compliance with Ocean Discharge Criteria (40 CFR Part 125).
In oraer to write the permits for specific discharges it is necessary
to nave methods for estimating water quality impacts of the discharge.
Brandsma et al (1983), for example, have described a model predicting the
snort-term fate of drilling muds discharged to the marine environment.
Tnis model, called the Offshore Operating Committee (OOC) Model, is based
upon tne toork of Koh and Cnang (1973). The model has been used to
simulate field test conditions in the Gulf of Mexico (Ayers et
al(1982)). This model describes the behavior of drilling muds in terms
of turee processes: 1) convective descent; 2) dynamic collapse; and 3)
passive diffusion and has reproduced observed features of drilling mud
discnarges.
Ti/e reportec applications of the OOC Model have been in water depths
of greater than 20 meters. Many of the proposed offshore drilling sites
are in waters as shallow as five meters. Two important assumptions made
in tne OOC Mooel lead to plume characteristics in shallow water which can
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-2-
t>e adequately described by a simpler model. The first of these
assumptions is that the extremely fine material with low settling
velocity is forced from the jet when the discharge is characterized by
low aensimetric Froude numbers, Fr < 2.0, where:
Fr.
and,
2
g = the acceleration due to gravity, 9.8 meters/sec ,
ft -t:ie ambient density kg/meters ,
o
P = the fluid density, kg/meters ,
D = the diameter of the discharge pipe, meters,
u = the discharge velocity, meters/second.
For toese particles, if the settling time, H/w., where H is the water
ueptn, is greater than the vertical mixing time, H /^ , where ^
is tne coefficient of turbulent diffusion in the vertical, then the
tnree-aimensional problem can be approximated by a two-dimensional
analysis. This is tne case for fine material with settling velocities of
4
10 meters/second, in water depths of 10 meters, or less, and assuming
3 ?
a coefficient of turbulent diffusion of 5x10 meters /second.
The second assumption is that the settling speed of a cloud of
particles is greater than the settling speed of individual particles.
Brandsma et al (Iy83) suggest the use of an enhancement factor, F, such
tnat.
F = 0.013 C
4/3
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where C is the local concentration of suspended material in mg/1. In the
OOC Model, F is restricted to the range 1 to 28. For drilling muds,
_3
maximum particle settling rates are 10 meters/second. Concentrations
of drilling muds are typically greater than 1000 mg/1 IP the vicinity of
the discharge, giving rise to a maximum enhancement factor of 28. In
water depths of 1U meters and for current speed of the order of 0.2
meters/second, dimensional analysis shows that the OUC Model would
predict that the convective descent and dynamic collapse phases would
occur primarily in a region within 100 meters of the discharge. Beyond
this point, passive diffusion and settling of the remaining material
would characterize the distribution of solids.
Tne UOC Model is a complex one, requiring large, sophisticated
computing equipment for execution of the moael software. In the case of
shallow water discharges, the dimensional analysis above shows that the
processes described by tne OOC Model at distances from the discharge
greater than lOu meters are relatively simple ones. Under these
circumstances, it seems reasonable to apply simpler models requiring less
computing time and smaller computers. For the processes of advection,
passive diffusion and settling, analytical solutions to the
advective-diffusion equation have been described for which such simple
algorithms can be written.
In tne following development, the modular solution technique, as
described by Lleary and Adrian (1973) and Cleary et al (1974), has been
used to develop a method for estimating the impact of drilling mud
discharge in shallow waters. The method can be used for planning
purposes, as well as for the design of permits. Simulations
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from this simple model, which can be implemented on a micro-computer, are
compared to actual field data, as well as to test case results from the
OOC Model. The comparisons with field data provide the potential user
witn measures for determining how well the simple model simulates actual
conditions. Comparisons with the OOC Model can oe used to evaluate
differences in results between the simple model and the OOC Model and
gives the user some perspective on the trade-off between mode"! complexity
and model accuracy.
Model Development
For discharges of drilling muds to shallow waters, the analysis
assumes that important processes determining the distribution of solids
in tne water column include:
1. Horizontal mixing under conditions of isotropic turbulence
2. Horizontal advection
3. Settling of solids
In addition, the model all discharges are treated as vertical line
sources. That is, the discharge is mixed instantaneously and uniformly
from top to bottom at the point of discharge in a line of infinitely
small radius and vertical extent equal to the water depth, H. The
equation describing the
conditions is given by:
equation describing the mixing of the j_ particle class under these
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where,
C. = the concentration of the i particle class, rag/1,
u - the current speed in the x-direction, meters/second,
w. = the settling rate of the i particle class,
meters/second,
D = the water depth, meters,
S = the strength of the source, mg/1/second,
= the coefficient of eddy diffusivity in tne
A
2
x-direction, meters /second,
= the coefficient of eddy diffusivity in the
2
y-direction, meters /second,
x = the coordinate in the downstream direction,
meters,
y = the coordinate in the crossstream direction,
meters,
t = time, seconds.
For those conditions in which the influence of horizontal boundaries can
be neglected and for wnich ocean currents are uniform and constant
tquation (l).can be solved by transform techniques (Cleary et al (1973),
Cleary et al (1974)). These methods are easier to apply if Equation (1)
is put in the form:
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(2)
where the substitutions:
X = X - Ut
y1 = y
t' = t
C(x,y,t) = C'(x',y',t';e-wt /D
SU,y,t) = S'ix',y',t')e~
nave been made.
in the x-, y-domain, the Fourier transform is appropriate for solving
Lquation (1) ana the transform pair is defined as:
=0=0
'' (3.
-CO -00
Since tne proolem is concerned with the analysis of a discharge which
begins at t' = 0, the Laplace transform is appropriate in the time domain:
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-7-
00
--fv-
0 / • . i.\ . \ I '
(5)
For the following boundary and initial conditions:
S(x,y,t) = SQ(t) at x = y = 0,
C(x,y,t) = 0 -00<
Ux,y,t) = 0, x-*-
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-8-
and is tne solution to tquation (lj when SQ(t) is a unit impulse:
SQ(t) = 1, t = 0,
= 0, otherwise
The results for a general source term, S (t), are obtained from the
superposition of scaled unit impulses which "add" up to make S ft). A
particular impulse is introduced at time/t, and the effect of all (an
infinite number, in theory) the impulses occurring between time, t=0, and
time, t=£, are added up to determine tne concentration at some location,
(x,y) at time, t (see Figure 1). This formulation can be used to
simulate tne time-dependent distribution of extremely fine particles
with low settling velocities which are separated from the plume. In
audition, tne effects of enhanced settling in the plume, due to elevated
concentrations, can also be simulated crudely by the choice of an
appropriate, enhanced settling rate.
An algorithm incorporating the concepts expressed in Equations (6)
and (7) has been coded in FORTRAN and implemented on the EPA Region 10
PUP 11/70. In addition to predicting concentrations of suspended
sediments, the code includes an expression for integrating the flux of
sediment through the bottom boundary. The resulting quantity is used to
estimate deposition rates along tne plume centerline. If there is a need
to estimate the concentration of dissolved substances in the water
column, it is a simple matter to include that in the code, as well. A
listing of the source code and a description of input variables and their
format are given in Appendix I.
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Model Application
Field Stuaies
Simulations of solids concentrations were obtained using Equation (6)
and compared with the results of three field studies. Two of the studies
were conducted in the summer of 1978 from the drilling rig, Penrod 63, in
the Gulf of Mexico. The third test was conducted at the Morton Sound
COST well in the Bering Sea during September 1982. Oceanographic and
Grilling mua discnarge parameters for eacti test are given in Table 1.
The diffusion coefficient,^. , was estimated from the relationship given
in Brooks (1^00):
(8)
4
where the constant, 4.64x10 , leads to values of the diffusion
coefficient in mks units corresponding to the value of 0.01 suggested by
Brooks for cgs units. Since the mixing zone is of primary concern in the
development of permits, the characteristic length, L, was chosen to be
IUU meters, that beiny a typical mixing zone size for drilling mud
discharges. It should oe kept in mind that this mixing zone has no
pnysical significance, out was chosen so that the analysis would be
consistent with the mixing zone size defined in the Ocean Dumping
Criteria.
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Drilling muds vary in type and composition. The characteristics of
tne drilling muds used by Brandsma et al (1980) in the Gulf of Mexico
tests are given (Table 2). No comparable data are available from the
Morton Sound COST well test. The characteristics of the mud used in the
Gulf of Mexico tests were, for want of better information, used for the
COST well simulations, as well.
Comparisons of model simulations and field results are shown in
Figures 2 through 4. For each test condition, two different simulations
usiny trie simple model (Equation 1) were performed. The first,
designated as Model I, uses settling rates for the individual particle
classes (Table 2). Tne second, Model II, is an attempt to incorporate
the two mechanisms for settling described by Brandsma et al (1983) and
aiscusseu earlier in the Introduction. In Model II, 90% of the solids
iiave a settling rate which is ten times that of Particle Class 1,
2
b.57xlu meters/second. The purpose of this is to provide for the
eiMiancernent of settling which occurs when the concentration of solids is
irigii. Tne remaining 10% has a settling rates equal to the lowest rate
used in Model I. This snould result in the forced early separation from
tne jet of tne extremely fine particles, as has been observed in actual
field measurements. As Brandsma et al (1983) point out, there is as yet
no physical explanation for this phenomenon. Rather it is an artificial
hiecrianisin incorporated into the model to duplicate what has been observed
in field experiments.
For the tests conducted in the Gulf of Mexico, the field results
snown in Figures 2 and 3 are maximum concentrations measured during the
oO-minute period following the initiation of discharge. In the case of
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-li-
the 275 uol/hr test, the discharge period was 54.5 minutes and 23.3
minutes for the 1000 bDl/hr test. Simulation results shown in Figures 2
ano o are also the maximum values obtained during the 60-minute period
following initiation of discharge. Although Ayers et al (1982) show the
decline in maximum plume concentrations as a function of transport time,
trie scale used in tneir presentation makes comparison difficult. As a
result, maximum simulated values are compared with maximum observed
values at a given location, using the data in Table 4 of Ayers et al
(1982). The time at which a maximum occurs at a given location may,
therefore, oe different between model results and field data.
Kurtuermore, it should be kept in mind that the field results are maxima
from some point in the water column, while the simulated results are
maximum depth-averaged results.
In the case of tne Norton Sound COST well, the duration of the
discharge was 62 minutes, but measurement times were not reported.
Values shown in Figure 4 are all those measured during the experiment
ana are also the maximum values observed at a particular point in the
water column. Tne simulation results are the maximum depth-averaged
values observed during the 62-minute period following the initiation of
discnarge. The time of the simulated maxima may not necessarily coincide
witn tne observed maxima, but there is no way of determining this, given
the available data.
Comparisons with tne OOC Model
Tetra Tech (1b83) has evaluated the OOC Model predictions of drilling
muu dispersion in the outer continental shelf area of Alaska Seven of
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test cases examined by Tetra Tech (Table 3) are compared with maximum
aeptn -averaged concentrations obtained from Equation (6) using both
Models I and II. In the test cases examined by Tetra Tech, the velocity
profile varied linearly from zero at the bottom of the water column to
some constant value at the surface. The solutions to Equation (6) in
this report assume tnat the velocity profile is uniform. In each of the
test cases, tnerefore, the average value of the current (one-half the
surface current) was used to obtain results from Equation (6). Results
of the comparisons are shown in Figures 5 through 11. The OOC Model
results are maximum depth-averaged concentrations, too, although it is
not clear from the Tetra Tech (1983) study what time is associated with
eacn ooservation. Values reported for the solutions to Equation (6)
(Model 1 and II) are the maximum values obtained during the two-hour
simulation period following initiation of discharge. Discharge duration
was eitner 30 or 60 minutes (Table 3).
Discussion
Comparisons of suspended solids concentrations estimated with
Equation (6) and those obtained from the field studies (Figures 2 through
4) showed that Model I generally predicted concentrations higher than
those observed, while Model II predicted lower concentrations. The
exception to this was in the vicinity of discharge where maximum observed
concentrations were several times higher than depth-averaged values pre-
aicteu by the simple model. This is not surprising given that the
characteristic vertical mixing times associated with actual field
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-13-
conciitions are large compared to the time it takes for a particle to
reacn sampling points five to ten meters away from the discharge. For
these locations the assumption that the water column is well-mixed is not
a good one, and the depth-averaged values obtained from model will
underestimate maximum observed concentrations.
Comparisons between the OOC Model and the Models I and II (Figures 5
through 11) show that Model I predicts generally higher concentrations
than the OOC Model and Model II, except for the shallowest (five meters)
discharge, predicts lower levels than the OOC Model. For the shallowest
water the very large concentrations in the vicinity of the discharge give
rise to maximum settling rates in the OOC Model which are 30 times that
of Model I ana three times tnat of Model II. Under these conditions the
OOC Model predicts that the percentage of solids deposited within 15
meters of the discharge is 79% or greater (Appendix B in Tetra Tech
(1983)). Similar results could be obtained from the simple model by
substantially increasing the enhanced settling velocity in Model II.
Wnether or not this is warranted would have to be determined by
laboratory and field testing.
In some cases, the slope of the concentration curves with respect to
distance for both the OOC Model and for Models I and II showed a sharp
citange. For the OOC Model simulation this occurred in the shallowest
discharges and appeared to be due to the large percentage of solids which
settle out in the vicinity of the discharge. In the case of Models I and
II tne snarp change in slope was most noticeable in the case of low
ambient current speed and was due to the fact that the simulation was not
run long enough to reach the actual maximum.
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Tetra Tech (1983) found that OOC Model predicted that at a fixed
distance from the discharge dilution increased as velocity decreasesd.
%
For the test cases in Table 3, the Models I and II obtained opposite
results. The principal reason for this being that the vertical mixing in
the OOC Model is not coupled directly to the magnitude of the ambient
current as is the case for Models I and II. In Models I and II the
discharge is distributed instantaneously over the water column and
diluted by the amoient current. In the case of a steady state discharge
this leads to an increase in dilution as velocity increases. However,
for some time-dependent discharge schedules this will give rise to
increases in dilution as velocity decreases, depending upon the ratio of
discharge time to travel time and the ratio of settling time to travel
time. For the OGC Model, the passive diffusion phase following
convective descent and dynamic collapse includes vertical, as well as
horizontal diffusion processes. If advection increases relative to these
mixing processes and relative to the settling processes then during a
given time period the advective length scale will increase while the
diffusion and settling length scales will remain approximately constant
In the OOC Model this will lead to an increase in concentration at a
given point as the magnitude of the ambient current increases.
Conclusions
A simple model has been developed for evaluating the impact of
drilling muds and cuttings discharged to shallow marine waters. Depth-
averaged solids concentrations simulated by the model show reasonable
agreement with results of field tests when particle settling rates are
used. Agreement oetween predicted and observed maximum concentrations
increases when an enhanced settling rate is applied to 90% of the
discharged solids.
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The simple model with individual particle settling rates (Model I)
preaicts higher depth-averaged concentrations than the OOC Model for
several conditions representing shallow water discharges. The simple
model with enhanced settling rates applied to 90X of the solids (Model
II) predicts lower concentrations than the OOC Model except in the case
of the Shallowest (five meters) discharge. In general, the differences
between the simple model described in this report and the OOC Model was
yreatest for the shallowest discharge. This discrepancy is due to the
difference in initial plume dynamics between the OOC Model and Models I
and II. Tin's difference gives rise to higher deposition rates in the OOC
Model than in Models I and II. Adjustment of the enhanced settling
velocity in Woael II would result in deposition rates similar to those
predicted by the OOC Model.
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Bibliography
1983. Ayers, R.C., Jr., R.P. Meek, T.C. Sauer, Jr., and D.O. Stuebner.
An environmental study to assess the effect of drilling fluids on
water quality parameters during high-rate, high-volume discharges
to the ocean. Journal of Petroleum Technology. January, 1982.
pp. 165-173.
ly&U. Brandsrna, M.G., L.R. Davis, R.C. Ayers, Jr., and T.C. Sauer, Jr.
A computer model to predict the short term fate of drilling
discharges in the marine environment. Proc. Symposium - Research
on Environmental Fate and Effects of Drilling Fluids and Cuttings,
January, 1980. pp. 588-610.
1983. Brandstna, M.6., T.C. Sauer, Jr., and R.C. Ayers, Jr. MUD Discharge
Model, report and user's guide. EXXON Production Research Co.
Houston, Texas.
1%0. Brooks, N.H. Diffusion of sewage effluent tn an ocean current.
Proc. 1 Conf. on Waste Disposal in the Marine Environment.
Pergamon Press, Oxford, England, pp. 246-267.
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15/3. Cleary, R.W. and D.D. Adrian. New analytical solutions for dye
diffusion equations. Journ. of the Environmental Engineering
Division, ASCE. Vol. 99, No EE3. June, 1973. pp. 213-228.
1974. Cleary, R.W., D.D. Adrian and R.J. Kinch. Atmospheric diffusion
and deposition of particulate matter. Journ. of the Environmental
Engineering Div., ASCE. Vo.. 100, No. EEl. February, 1974.
pp. 187 ^00.
19/3. Kon, R.C.Y. and Y.C. Chang. Mathematical model for barged ocean
disposal of wastes. U.S. Environmental Protection Agency. Report
EPA-66U/2-73-029.
lydl. Petrazzuolo, G. Preliminary report: An assessment of drilling
fluids and cuttings released into the Outer Continental Shelf.
U.S. Environmental Protection Agency, Ocean Programs Branch.
Washington, D.C.
1963. Tetra Tech Inc. Draft report - Evaluation of drilling mud
dispersion predictions of the Offshore Operators' Committee
(OCC) model for Alaska Outer Continental Shelf areas. Prepared
for EPA Region 10, Seattle, Wash. July, 1983. 19 pp.
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Taole 1. Oceanographic and discharge parameters used to simulate
conditions during various drilling mud dispersion studies.
Norton
Gulf of Mexico Gulf of Mexico
Discharge rate 0.047
(meters**3/second)
0.011
0.044
Initial 302000.
concentration(mg/l)
1430000
1430000
Discharge period
(minutes)
62.
54.
23.
Water depth
(meters)
12.
23.
23.
Current speed
(cm/sec)
30.
15.
12.
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Table 2. Settling velocity and composition of components for drilling
muas used in model studies.
Particle Class
123456
Settling 0.657 0.208 0.0849 0.0437 0.0231 0.0130
velocity
(cm/sec)
% Volume 10. 10. 12. 20. 38. 10.
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TaDle 3. Oceanographic and discharge parameters used for comparison of
OOC Model and two-dimensional analytical solution (Equation 6).
Test Case #
1 234567
Discharge rate 0.044 0.011 0.044 0.011 0.011 0.044 0.044
(meters**3/sec)
Initial 1430000. 1430000.
concentration(mg/l)
Discharge period 30. 60. 30. 60. 60. 30. 30.
(minutes)
Water depth 5. 5. 15. 15. 15. 5. 15.
(meters)
Surface current 10. 10. 10. 10. 2. 2. 30.
speea(cm/sec)
-------
c
tf = time at which scaled
impulse is discharged
time at which concentration
in receiving water is to be
computed
Figure 1.
Schematic showing relationship between scaled impulse and unit
impulse. Impact at time, t, is determined by summing up the
effects of all the impulses discharged prior to time, t.
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FIGURE 8. COMPARISON OF TWO-DIMENSIONAL MODEL RESULTS AND
FIELD STUDIES IN THE GULF OF MEXICO - 275 BBL/HR TEST
9
L
0
G
1
• 4
S
U
S
p
E 3
N
0
E
D
s 2
0
L
I
D
S
^ *
n '
G
/
L
i i i i i i i i i
X nooEi i
•f 0 noDEt u
+ FIELD DAT*
_
1,
0 X
X
o x
X
* X
0
0
0
0
0
4
1 1 1 1 1 1 It 1
50 100 150 300 850 300 350 400 450 5<
DISTANCE - METERS
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FIGURE 3. COMPARISON OF TUG-DIMENSIONAL MODEL RESULTS AND
FIELD STUDIES IN THE GULF OF MEXICO - 1000 BBL/HR
L
0
G
1
e
S
U
S
p
E
N
D
E
D
S
0
L
I
D
S
N
G
X
0
NODCl I
nonet, ii
FIELD DATA
0
U)
I
50 100 150 800 850 300
DISTANCE - METERS
350 400 450 500
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FIGURE 4. COMPARISON OF TUO-DIMENSIONAL MODEL RESULTS AND
FIELD STUDIES AT THE NORTON SOUND COST UELL - 1065 BBL/HR
L
0
Q
1
e
S
U
S
P
E
N
D
E
D
S
0
L
I
D
S
n
G
X
0
NODEl I
HODEI II
FIELD DATA
* x x
000
X
0
X
0
X
0
\
lee aee
3ee 4ee see see
DISTANCE - METERS
?ee aee see teee
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FIGURE 5. COMPARISON OF OOC MODEL AND TUG-DIMENSIONAL
MODEL RESULTS. CASE tl (TABLE 3)
L
0
G
1
e
s
u
s
p
E
N
D
E
D
S
0
L
I
D
S
M
G
X
0
•f
nODEL I
MODEL II
OOC HODEL
I
NJ
50 100 150 800 850 300
DISTANCE - METERS
350 400 450 500
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FIGURE 6. COMPARISON OF OOC MODEL AND TUG-DIMENSIONAL
MODEL RESULTS. CASE t3 (TABLE 3)
»
L
0
G
1
! 4
S
U
S
p
5 3
N
D
E
D
5 8
L
I
D
S
1
M
G
L
•
i i r i i i i i i
X HODCL I
0 HODEL II
* OOC HODEL
X
X
X
* X
0
+ X
0 o
0
0
i
4
+
1 1 1 1 1 II 1 1
50 100 150 800 250 300 350 400 450 5(
I
to
DISTANCE - METERS
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FIGURE 7. COMPARISON OF OOC MODEL AND TUG-DIMENSIONAL
MODEL RESULTS. CASE *3 (TABLE 3)
L
0
G
1
0
S
U
S
P
E
N
D
E
D
S
0
L
I
D
S
M
G
X
0
•f
meet i
(lODEl II
ooc nooEL
I
N3
4
0
iee ise aee ase see ase
450 see
DISTANCE - METERS
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FIGURE 8. COMPARISON OF OOC MODEL AND TWO-DIMENSIONAL
MODEL RESULTS. CASE t4 (TABLE 3)
L
0
Q
1
e
s
u
s
p
E
N
D
E
D
S
0
L
I
D
S
M
Q
X MODEL I
0 MODEL II
+ OOC HODEL
*
I
NJ
oo
I
•f
0
0
•f
0
se tee ise see ase aee
DISTANCE - METERS
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FIGURE 9. COMPARISON OF OOC MODEL AND TUO-DIMENSIONAL
MODEL RESULTS. CASE 15 (TABLE 3)
d
L
0
G
1
a 4
s
u
s
p
E 3
N
D
E
D
s a
0
L
I
D
S
M 1
G
L
— r • • r i i i i i i i
X RODEl I
0 C10DEL II
•f OOC HODEl
•f
- X
X
0 X
x
0 +
»
0 X
+
I I I A I I 141 I I
50 100 150 800 250 300 350 400 450 5(
DISTANCE - METERS
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FIGURE 10. COMPARISON OF OOC MODEL AND TUO-DIMENSIONAL
MODEL RESULTS. CASE *6 (TABLE 3)
L
0
G
1
0
S
u
S
p
E
N
D
E
D
S
0
L
I
D
S
M
G
X NODCL I
0 nooEL it
•f OOC nODEL
_L
_L
.L
_L
_L
_L
o
i
50 100 150 800 850 300
DISTANCE - METERS
350 400 450 500
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FIGURE 11* COMPARISON OF OOC MODEL AND TUO-DIHENSIONAL
PIODEL RESULTS. CASE *7 (TABLE 3)
9
L
0
G
1
* 4
S
U
S
p
D
E
D
s a
0
L
I
D
S
1
n
G
L
i i i i i i i i i
X noDCL i
0 flood n
•f OOC BODEt
Q
y
X
0 X x
0 +
0 .
5 0
*
— _
1 1 1 1 1 1 • 1 1 1
lee aee aee «ee see see ?ee see see le
I
CO
DISTANCE - METERS
-------
Appendix I
Data Card Input
and
Source Code Listing
for
Two-Uimensional Model
-------
-1.1-
Table i-i. Data card input description for FORTRAN source code which
solves Equation (6).
Card
Type
1
1
1
1
2
2
2
2
3
3
3
3
3
3
3
3
Column
1-5
6-10
11-15
lb-20
1-8
73-bO
1-8
17-24
1-10
11-20
21-30
31-40
41-50
51 -6U
61-70
71-80
Format
15
15
15
15
F8.0
F8.0
F8.0
F8.0
F10.0
F10.0
F10.0
F10.0
F10.0
F10.0
F10.0
F10.0
FORTRAN
Name
NWR
NTIME
NSCNDS
NDX
V ( 1 \
A \ I /
x(io)
v / n i \
A \ 1 i /
t>
X(13)
DEPTH
DT
DIFF
U
SRCE
TSTOP
CBRGND
RHO
Description
Unit number of output device
(5=CRT,6=line printer)
Total number of time periods to be
simulated
Number of seconds between time
periods. Algorithm obtains solu-
tions to Equation (6) at t=NSCNDS,
2*NSCNDS, ,NTIME*NSCNDS
Number of distances at which model
output is desired (NDX 13)
Distance from discharge point at
which output is desired, meters
Distance from discharge point at
whicn output is desired, meters
Distance from discharge point at
which output is desired, meters
Distance from discharge point at
which output is desired, meters
Water depth, meters
Integration time increment, seconds
Coefficient of eddy diffusivity;
meters**2/second
Ambient current speed, meters/second
Source strength,
meters**3-mg/l /second
Time at which discharge stops,
seconds
Background concentration, mg/1
Density of drilling mud,
grams/cubic centimeter
-------
-1.2-
Card FORTRAN
Type Column Format Name Description
4 1-10 F10.0 KATIO(l) Decimal fraction of volume of
particle class 1
4 11-20 F10.0 RATIO(2) Decimal fraction of volume of
particle class 2
* « • •
• e • •
Sl-oO F10.0 RATIO(6) Decimal fraction of volume of
particle class 6
5 1-10 F10.0 W(l) Settling velocity of particle
class 1, meters/second
5 11-20 F10.0 W(2) Settling velocity of particle
class 2, meters/second
5 51-60 F10.0 W(6) Settling velocity of particle
class 6, meters/second
-------
OIMENSIOK RATIfll6),W<6),XC13J,C(13).CTMPt6»,SONNT(13)
C
C PROGRAM FOR PREDICTING DISTRIBUTION CF SLBSTANCE SUBJECT TC DIFFUSION
C SETTLING AND HORIZONTAL AOVECTION IN A VERTICALLY WELL-MIXEE
C ENVIRONMENT. DEVELOPED FOR SPECIFIC APPLICATION TO DISTRIBUTION OF
C TRILLING PUDS IN A SHALLOW. MARINE ENVIRONMENT. SEE:
C "» TIME-CEPENDENTt TKO-OINENSIONAL MODEL FOR PREDICTING THE
C OISTRIBLTION OF DRILLING MUDS DISCHARGED TO SHALLOW HATERS"
C JOHN YEARSLEY
C EPA REGION '10
C SEATTLE. WASHINGTON
C JANUARY 5, 1984
C
C
C OPEN FILING CONTAINING CHARACTERISTICS OF PHYSICAL ENVIRONMENT, SETTLING
C VELOCITIES OF SOLIDS AND MASS EMISSION RATES. METHOD LSED TO OPEN
C PILE IS SPECIFIC TC POP 11/70
C
OP EN (UN I T-4f NAME-1 XFCRM.DAT', TYPE- 'OLD* I
C
C RHAO DATA
C
C CARD •!
R" AD (4, 1100) NHR.NTIME.NSCNOStNDX
OELT-NSCNDS
C
C C4RDI2
1EADI4,150G» (X(N) .N-l.NDX)
WR ITECNHR,2300) X
M.RITE(NURf?350)
C
C C*RD *3
R= AD (4. 1200 1 DEPTH, DT.DIFF,U,SRCE,TSTOP,RHOtCBGRNO
C
C CARD «4
R?AD(A,1200) RATIO
C
C CARD 19
I
M
•
10
PI-3.
NT-DT
C
C IE GIN SIMULATION
C
OT 199 I-1«NTIME
C
C EXAMINE A TOTAL OF NDX POINTS ALONG THE PLUME CEMERLUE
C
01 189 II-ltNDX
XL-X(II)
HNT-I*KSCNPS
XXNT-NNT
H1UR-XXHT/3600.
NINC-NNT/NT
C( ID-O.C
oa 49 m-1,6
CTMPIII I )-0.0
49 CONTINUE
C
C DIVIDE TIME STEP INTO MNC INCREMENTS. THE LARGER NINC THE MORE
C ACCURATE THE SIMULATION AND THE MORE CPU TIME RECUIREO. NUC INCREASES
C WITH TIME SO THAT MODEL HON«T "FORGET" ALL THE DISCHARGES THAT HAVE
C OCCURRED I* THE PAST.
-------
TI-III
TAU-OTMTI-P.5)
IF(TAU.GT.TSTOP) GO TO U9
TPRIME-XXNT-TAU
ARG-0 COMPUTATIONS ARE MADE WHEN
C FCTR IS LESS THAN C.01. THIS ALSO REDUCES ACCURACY SOfEWHfT, BUT
C **KES THE PPOGRA1 PUN MORE EFFICIENTLY, PARTICULARLY HI-EN LCNG TI1E
C PERIODS ARE BEING EVALUATED.
C
59 IF(FCTR.LT.0.01) GO TO 1*9
TO 99 IV-1,6
CT MP< IV)-CTMP( IV)
»RATIO«IV)*FCTR*EXP(-hCIV)*TPRIME/DEPTH)
99 CONTINUE
149 CONTINUE
00 169 111-1,6
C
C COMPUTE SEDIMENTATION PATES
C
SDHNTIIU«5D*NT
------- |