EPA-R2-72-002 _ _ c
Environmental Protection Technology Series
Pyritic Systems:
A Mathematical Model
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington, D.C. 20460
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EPA-R2-72-002
November 1972
PYRITIC SYSTEMS: A MATHEMATICAL MODEL
By
Arthur H. Morth
Edwin E. Smith
and
Kenesaw S. Shumate
Contract No. 14-12-589
Project 1^010 EA.H
Project Officer
Dr. James M. Shackelford
Pollution Control Analysis Branch
Environmental Protection Agency
Washington, B.C. 20460
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, B.C. 20^60
For sale by the Superintendent of Documents. U.S. Government Printing Office, Washington, D.C., 20402 - Price $2.25
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents neces-
sarily reflect the views and policies of the
Environmental Protection Agency, nor does mention
of trade names or commercial products constitute
endorsement or recommendation for use.
11
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ABSTRACT
A mathematical model of an acid mine drainage system has been developed
for underground mines. The model relates the rate of acid formation to
the rate of pollution discharge from the system.
The calculational model was developed using a digital computer to simu-
late an existing mine as the sum of many micro scale mines, each repre-
senting a small reactive volume in the system being modeled. The input
to the model is a physical and chemical description of the system. Day-
to day simulation requires data on temperature, rainfall, and oxygen
concentration at the exposed coal face. The output of the model is
estimates of daily acid load and drainage flow, plus monthly and yearly
summaries.
Acid removal kinetics were related to three removal mechanisms: (l)
leaching by water trickling downward through oxidized pyritic material,
(2) flushing of oxidation products by movement of the water table, and
(3) diffusion of oxidation products by continuous oxidation and adsorp-
tion of moisture.
The calculational model was based on a carefully described physical
model so that a predictive model can be constructed with little or no
experimental data. However, methods for constructing the computational
model are given which can utilize the field data available to increase
the reliability of the model.
Underground mines for which drainage data were available were modeled
to test the ability of the model to predict flow and acid load data
from different mines. The model accurately predicts yearly flow and
acid loads and duplicates seasonal patterns.
This report was submitted in fulfillment of Project lUOlOEAH, Contract
No. 14-12-589» under the sponsorship of the Environmental Protection
Agency, Office of Research and Monitoring.
iii
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CONTENTS
Section
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
CONCLUSIONS
RECOMMENDATIONS
INTRODUCTION
LITERATURE REVIEW
Historical
Oxidation Mechanism
Electron Transport
Microbiological Oxidation
Geological Studies
Discussion
Model Oriented Studies
EXPERIMENTAL PROGRAM
Acid Removal from Isolated Coal Blocks
Removal Rates in High Humidity Chamber
Sulfate and Acidity Analyses
Comments
THEORETICAL BASES OF A PYRITIC SYSTEM MODEL
Derivation of Oxygen Concentration Gradient
Influence of Reaction Rate Constant
Effects of Reaction Order
Oxidation Product Removal
DEVELOPMENT OF DRIFT MINE MODEL
Description of Micro-System
Computer Programming of Model
VERIFICATION OF MODEL
UTILIZATION OF MODEL
Predictions
Generalization of Model
STATUS OF MODEL DEVELOPMENT
ACKNOWLEDGEMENTS
3
5
7
7
8
9
10
11
13
19
19
19
21
23
25
25
36
37
38
57
67
93
93
96
103
105
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COFTENTS (continued)
Section Page
XII APPENDIXES 107
Appendix A - Gradient Computer Program 109
Appendix B - Estimation of Potential
Evapotranspiration 119
Appendix C - Drift Mine Programming and Sample
Output for 1970 of Auger Hole Ho. 1 121
Appendix D - Instructions for Use of Main
Program 153
Appendix E - Evaluation of Parameters and
Constants for Subroutine "Remove" 159
XIII REFERENCES 16?
XIV LIST OF PUBLICATIONS 171
vi
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LIST OF FIGURES
Figure No.
1 Rate of Acid Removal from Isolated Coal Block 20
2 Effect of "Breathing" on Oxygen Gradient 30
3 Effect of "Breathing" on First Order Oxidation
Rate 31
4 Effect of First Order Rate Constant on Oxygen
Gradient 32
5 Effect of Rate Constant on First Order Oxida-
tion Rate 33
6 Effect of Zero Order Rate Constant on Oxygen
Gradient 34
7 Effect of Pore Length on Oxidation Rate 35
8 Sketch of Underground Pyrite System from Smith
and Shumate (3?) 46
9 Stratum in Seam Divided into Micro-Volumes 47
10 Storage Volume Material Balance 47
11 Location of Water Table 55
12 Main Program Flow Chart 58
13 Flow Chart of Subroutine DAYS 59
14 Flow Chart of Subroutine EVAP 60
15 Flow Chart of Subroutine REMOVE 6l
16 Drainage Flow for McDaniels Test Mine 68
17 Drainage Flow for Auger Hole #1 69
l8 Drainage Flow for Auger Hole #3 70
19 Drainage Flow for Auger Hole #4 71
20 Drainage Flow for Auger Hole #5 72
21 Drainage Flow for Auger Hole #6 73
vii
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LIST OF FIGURES (continued)
Figure No. Page
22 Drainage Flow for Decker #3 Mine (196^) jk
23 Acid Load for McDaniels Test Mine 75
2k Acid Load for Auger Hole #1 76
25 Acid Load for Auger Hole #3 77
26 Acid Load for Auger Hole #h 78
27 Acid Load for Auger Hole #5 79
28 Acid Load for Auger Hole #6 80
29 Acid Load for Decker #3 Mine (1964) 8l
30 HEAD vs TANK from Experimental Data l6k
viii
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SECTION I
CONCLUSIONS
1. A mathematical model has been developed which can be used to predict
drainage flow rates and acid loads from an underground mine.
2. Basic scientific principles and laboratory data can be used to
develop a quantitative model of a natural pyrite oxidation system.
3. The oxidation of pyrite within a natural pyritic system can be
accurately described beginning with fundamental kinetic equations for
the chemical reactions and transport of oxygen. The major difficulty
in obtaining accurate short-term predictive capabilities is in de-
scribing the removal mechanisms.
k. The computational model was developed from a carefully described
physical model of an underground pyritic system, thereby permitting
derivation of a computational model from geologic-hydrologic features
only. With this capability, the influence of new mines and effects of
different mining procedures on a watershed can be predicted.
5. Although it is possible to complete the computational model without
the benefit of field data, the reliability of the model can be greatly
increased with only a few representative flow and acid load data.
6. Methods for utilizing field data to increase reliability of the
model are available. The more comprehensive the field data, the more
reliable the model can be made.
7. The model can predict yearly flow and acid load data within ± 10
percent when field data are available. The general pattern of daily
flow and acid load observed is also predicted.
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SECTION II
RECOMMENDATIONS
Monitoring of the mine and auger holes in the McDaniel's research com-
plex should be continued. McDaniels mine has been under nitrogen for
more than 2 1/2 years and has now reached the point where 90$ of the
oxidation products stored under equilibrium condition (in air) have
been removed. A step change in oxygen concentration, together with
careful monitoring of drainage, would permit an independent analysis
of removal mechanisms.
Other underground mines, for which flow and acid load data are available,
should be modeled using the techniques described in this report. The
generality of constants used in the mathematical expressions for calcu-
lating flows could be determined, or the effect of geological parameters
on these constants could be evaluated.
The effect of changing the form of the ADD equation on the predictive
capability of the model should be investigated. A linear relationship
between ADD (the water leaving the soil layer per day and going to
underground storage) and WOVERW (the ratio of water in the soil layer
to the water content at saturation) was assumed. An exponential form,
where ADD increases markedly as WOVERW approaches unity (as soil layer
approaches saturation) would give more rational HEAD vs. TANK relation-
ships .
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SECTION III
INTRODUCTION
The natural formation of acid as a by-product of mining operations has
been observed throughout the world. This acid has been formed by the
reaction of oxygen and water with sulfur-bearing minerals, such as
pyrite (FeS2).
The formation of sulfuric acid from pyrite has become a major problem
in the coal mining areas of the eastern United States, particularly
Ohio, West Virginia, and Pennsylvania. The formation of an acid dis-
charge, popularly known as "acid mine drainage," or simply AMD, is
responsible for ruining many streams and lakes as recreation areas, for
numerous fish kills, and for general wasting of natural resources and
beauty. The acidity also causes corrosion of bridge piers, locks, boat
hulls, and pumps.30
The acid mine drainage problem has been attacked from many angles,
ranging from treatment of acid water and sealing of abandoned mines to
laboratory scale research. Research on AMD has included studies in the
areas of chemical kinetics, microbiology, mineralogy, geology, hydrology,
and treatment methods. Thus far most work has been confined to specific
areas with little interaction among disciplines. To coordinate this
diverse information, researchers at The Ohio State University have
undertaken a systematic analysis of acid mine drainage. The object of
the analysis is to develop a mathematical model of acid mine drainage
systems.
A useful mathematical model must quantitatively relate the physical and
chemical parameters of a pyritic system to the rate of pollution dis-
charge across the boundaries of the system. Such a model would accu-
rately predict the long-term effects of mining operations, abatement
procedures, and other conditions imposed on the system.
Of equal importance is the ability to predict surges and peak flows of
acid. In many pyritic systems, "normal" runoff can be absorbed without
effect on receiving streams. It is the heavy slugs of discharge that
periodically cause extensive damage to receiving waters. Prediction
of these would allow design of protective neutralizing systems.
The development of a mathematical model of a system usually follows a
step-by-step approach. The first step is the identification of what
is known about a system (and by inference, what is not known). This
may be done by reviewing the literature and work of previous investi-
gators. The second step is filling in the gaps in existing knowledge.
The preferred technique is experimentation; however, if the problem is
not amenable to experimental solution, approximations can be generated
starting from basic scientific principles. The final step is comparing
the model behavior with that of the real system. At this time, variables
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are free to interact, and the validity of the basic assumptions is
proved or disproved. Once the model has been refined and can predict
previous data, then it is possible to forecast the effects of pertur-
bations imposed on the system.
Such a step-by-step procedure will be followed in developing a model
of a pyritic oxidation system. In this case, the examination of exist-
ing knowledge includes reviewing both general acid mine drainage liter-
ature, and experimental studies of natural pyrite oxidation systems.
The experimental work is reported along with numerical computation
techniques used to evaluate undefined quantities.
Next, the actual model and computational methods are developed and
proved, based largely on information from a specific mine. Then the
model is evaluated for generality by applying it to other underground
pyritic system.
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SECTION IV
LITERATURE REVIEW
HISTORICAL
The problem of acid production in coal mining regions has been the sub-
ject of studies since before 1900. The earliest studies were essentially
reports of local acid production and high acid concentrations in streams
after heavy storms. The reports frequently traced the acid source back
to abandoned coal mines, and more specifically to iron pyrite associated
with the coal. In some manner, the pyritic sulfur was reacting and
oxidizing to form sulfuric acid and iron sulfate.
Early attempts were made to stop this oxidation by using mine sealing
techniques. This was done with some success in the 1920's in West
Virginia, but in other states records of methods and results have been
lost. Moulton2"6 has presented a good review of the early studies in
Ohio.
Since 1965, Bituminous Coal Research, Inc.21 has issued annual bibli-
ographies of acid mine drainage. The next step beyond reporting of acid
production was experimental laboratory work starting as early as 1926.
Some of the earlier investigators include Burke and Downs,6 and Nelson,
Snow, and Keys.28
OXIDATION MECHANISM
In recent research, the emphasis has been on solution chemistry and the
definition of the precise oxidation mechanism. Birle,4 Kim,16 Jutte,15
and North2"3 studied the basic kinetics of the oxidation of concentrated
pyritic material.
Birle4 performed a general study of the oxidation of iron pyrite. He
measured relative surface areas of different structural forms of pyrite.
Sulfur ball material of the type found in coal had much greater surface
area per unit weight than did highly crystalline museum grade pyrite
(fool's gold). In parallel work Stiles41 showed that the reactivity of
pyritic material is proportional to its surface area.
Kim16 studied the oxidation kinetics of concentrated pyritic material
in liquid and vapor phase reactions. The liquid or vapor referred to
the phase being recirculated through a pyrite bed. He found that the
oxidation rate depended on oxygen concentration. Vapor phase oxidation
rates seemed to increase with temperature, but Kim attributed this to
the increase in humidity.
Morth23 also worked with liquid and vapor phase reactions. He found
that oxidation rate doubled with a 10°C increase in temperature. He
observed that vapor phase oxidation increased with humidity, and that
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at 100 per cent relative humidity, the vapor phase rate is the same as
the liquid phase oxidation rate. Morth suggested that water is b'oth a
reactant and a reaction medium.
Jutte1'0 studied the influence of oxygen concentration on the oxidation
rate. The relative oxygen concentration was controlled by applying
nitrogen pressure on a liquid phase oxidation. The oxidation rate
decreased with increasing pressure. This result led to the conclusion
that there was competition between nitrogen and oxygen for a "reactive
site." The concept of a "reactive site" has led research into the
area of the actual reaction mechanism in addition to the kinetics or
rate of reaction.
ELECTRON TKANSPOKI
Singer and Stumm34; Smith, Svanks, and Shumate39; Smith, Svanks} and
Halko38; Sasmojo29; Grove14 have studied the electron transport mecha-
nisms of iron pyrite oxidation. Singer and Stumm34 investigated the
liquid phase oxygenation of ferrous ions and the hydrolysis of the
resulting ferric ion. They found that sulfate ions retarded the rate
of ferrous ion oxidation, and that high surface area materials such as
alumina catalyzed the oxidation. They erroneously concluded that (l)
ferric ion could not exist in contact with pyrite, (2) the overall rate
of pyrite dissolution is 'independent of the surface structure of the
pyrite, and (3) the oxidation rate controlling step is the ferrous iron
oxidation.
Smith, Svanks, and Shumate39 studied the anaerobic (oxygen free) oxida-
tion of pyrite using ferric ion as the oxidant. Working with various
ratios of ferric and ferrous ions, Smith et al. concluded that the
oxidizing species is a surface-adsorbed ferric ion. The rate-controlling
step is the surface transfer of electrons. It was also suggested that
aerobic (oxygen) and ferric ion oxidations follow different reaction
paths. In a continuation of the above study, Smith, Svanks, and Halko38
reported that the aerobic oxidation rate was a function only of the
oxygen concentration at the reactive site; however, the ferric ion
oxidation rate was dependent on the ferric-ferrous ratio and the total
iron concentration in solution.
Sasmojo29 studied the kinetics of both aerobic and ferric ion oxidation
and attempted to determine if there was an interdependence between the
two reactions. He compared the aerobic oxidation rate in the presence
and absence of ferrous ions in solution and found no difference. Then
using identical total iron concentration, ferric-ferrous ratios, and
pH, Sasmojo measured the ferric ion oxidation rate. This rate was
about one-third of the aerobic oxidation rate. He concluded that the
rate of pyrite oxidation by oxygen is not controlled by the oxidation
reaction of ferrous to ferric ion in solution. Sasmojo studied ferric
ion oxidation at varying ferric-ferrous ratios and total iron concen-
trations. At constant total iron concentration, the rate increased
8
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•with ferric-ferrous ratio, and at constant ferric concentration, the
rate increased with decreasing ferrous concentration. From this, he
concluded not only that ferric ions increased the oxidation rate, but
that ferrous ions had an inhibiting effect.
Grove14 also investigated ferric ion oxidation and the effects of the
ferric-ferrous ratio. He found that the real variable was the free
ferric-ferrous ratio. He defined free ions as those which were not
complexed nor associated with the solution anions in any manner. He
developed a set of equations to estimate the effects of anions on the
free ferric-ferrous ratio.
Smith and Shumate^7 in a final project report have summarized and put
in proper perspective the various pyrite oxidation studies performed
at The Ohio State University. The time interval covered includes the
work of Birle through that of Sasmojo. The report is particularly
significant since it is a unified presentation of information from
different approaches to the problem of defining the sulfide-to-sulfate
reaction mechanism.
MICROBIOLOGICAL OXIDATION
Microbiology has been another area of laboratory scale investigations.
Bacteria, such as Ferrobacillus ferrooxidans, enhance the rate of pyrite
oxidation. Lorenz and Tarpley^u and Konecik17 reported 10- to 50-fold
increases when these bacteria were added to pyritic systems. Bailey2
found that bacteria increased the oxidation rate, but only after 70 to
80 per cent of the iron in the reaction medium had been oxidized to the
ferric state.
Dugan and Lundgren12 investigated the metabolism of Ferrobacillus
ferrooxidans. The organisms were found to use the oxidation of ferrous
to ferric ions as their energy source. Hence, the bacterial enhance-
ment of oxidation rate arises from the increase in ferric ions during
F. ferrooxidans metabolism.
Lau, Shumate, and Smith19 studied the role of bacteria in the kinetics
of pyrite oxidation. They studied the growth of Ferrobacillus species
in a medium where pyrite was the only source of reduced iron. The
bacteria multiplied and increased the rate of pyrite oxidation by
maintaining a high (in excess of six) ferric-ferrous ratio in the solu-
tion around the pyrite. Lau et al. noted the influence of the water-
pyrite ratio on the rate of oxidation. For low ratios, the oxidation
rate was limited by the number of bacteria in the water while at high
ratios there were excess bacteria and the pyrite surface area influ-
enced the reaction rate. They suggested that bacterial catalysis is
much more likely at the surface of a pyritic system such as a refuse
pile than in an underground mine environment. This is attributed to
the fact that oxygen is the ultimate electron acceptor and must be
readily available for bacterial activity to occur.
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GEOLOGICAL STUDIES
Since acid mine drainage causes stream deterioration not in a laboratory,
but in the real world, studies in the earth sciences, geology, hydrology,
and mineralogy are as important as laboratory investigations. In such
studies, pyrite is not isolated but is distributed in a binder such as
coal or shale.
Caruccio and Parizek8 and Caruccio7 have conducted extensive investiga-
tions of geologic factors in acid mine drainage around Clearfield,
Pennsylvania. Two locations were compared, one having acidic strip
mine drainage, the other nonacidic drainage. Caruccio and Parizek con-
ducted leaching studies to determine if the acid potential of a coal
could be related, to its sulfur content. While increased sulfur led to
greater acidity, this factor did not explain drainage differences of
the observed area.
Caruccio7 found that finer pyrite grains led to higher acidic activity.
He also suggested that shales may generate more acid than coal binders.
Coal is relatively "tight" and seals the pyrite from the atmosphere
while the relatively permeable shale permits oxidation of the enclosed
pyrite. Finally, Caruccio noted that if the ground water in a mining
area contains calcium carbonate, alkalinity will develop to counteract
acidity. Thus, even if acidic oxidation is occurring, the net effluent
will not be acidic.
Vimmerstedt and Struthers43 studied the weathering of spoils material
from Ohio Strip mines. They packed the spoils into columns and exposed
these to natural weather conditions. The leachate leaving the bottoms
of the columns was collected and analyzed for soluble salts, sulfate,
and various cations. The investigators found the the amount of leachate
and weight of salts followed the annual rainfall pattern. Through
regression analysis it was also determined that there was an overall
decrease with time in the weight of salts leached. This simply in-
dicated that the pyrite in the samples was being consumed.
Several investigators have checked the effects of coal mining on the
hydrology of an entire water shed. Corbett10 and Agnew and Corbett1
have studied the hydrology and chemistry of coal mine drainage in
Indiana. In particular, they were concerned with flushouts during
storms in strip mined areas. Corbett observed that the refuse piles
acted as aquifers to store water, during storms; the stored water would
then "be released gradually during dry weather. On the average, about
30 per cent of a given storm was retained in the heavily mined areas
as opposed to 15 per cent retention in less mined regions. The peak
stream flow during a storm was also considerably less in the stripped
area. Corbett did observe that if the refuse piles were already satu-
rated or if there had been heavy compaction during grading of the
mined areas, the surface runoff would be enhanced relative to undis-
turbed land.
10
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Agnew and Corbett1 emphasized the need for continuous data when studying
flushouts and natural systems. Peak flows occurred over a period of
hours rather than days. The flushouts increased the concentration of
deleterious ions (sulfate, hardness, acidity, and iron) in the receiving
streams from 30 to 1000 per cent over normal levels. These concentra-
tions increased at the start of the storm and remained high even after
flows had receded. Agnew and Corbett also suggested that some standard
method of reporting acidity be determined. In particular, it seemed
that both "acidity" and "alkalinity" should be reported rather than
just a net acidity. A number of other questions were raised about the
analysis of mine waters.
DISCUSSION
The investigations discussed to this point can be considered no more
than a sampling of the total acid mine drainage literature. They axe
typical of the varying points of view which must be considered in any
model of pyritic systems. Although methods and interpretation of re-
sults may vary, investigators have well defined the kinetics of iron
pyrite oxidation.
The importance of oxygen has been stressed as would be expected in an
oxidation reaction. In kinetic terms, the oxidation rate is a frac-
tional order with respect to oxygen concentration. Jutte15 estimated
the dependency as three-fourths power. Over the normal range of atmos-
pheric concentrations this can be taken as a linear (or first-order)
dependence.
The rate of pyrite oxidation has been shown to depend more on the pyrite
surface available than on the absolute weight of pyrite present. Stiles41
came to this conclusion for concentrated, crushed, sieved pyritic
material. Caruccio and Parizek8 observed a similar dependence for
pyrite still embedded in coal. Their observation was based on a quali-
tative estimate of the fineness of pyrite grains rather than on exact
measurements.
As the stoichiometric chemical reaction equation showed, water is also
part of the pyrite oxidation reaction system. Kim18 and Morth23 inves-
tigated the influence of water on the oxidation rate. In liquid phase
reactions, water was present in excess and did not enter the oxidation
rate equation. It was only in vapor phase reactions where humidity
could be varied that water concentration appeared to influence rates.
No specific reason for this influence was put forth until investigations
of the actual reaction mechanism were undertaken. The mechanism studies
led to the conclusion that water was necessary as an oxidation product
dissolution medium. The influence of humidity was then related to how
much of the pyrite surface contained adsorbed water and was available
as a reaction zone. Hence, for the rate limiting step, the basic func-
tion of water is to provide a means for the removal of oxidation products.
11
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The determination of the oxidation mechanism involved not only chemists
but also geochemists and microbiologists. Here differences in philosophy
and technique tended to cause divergent interpretations of similar
experimental data. Singer and Stumm3 in their studies of liquid phase
oxygenation of ferrous ions and dissolution of pyrite, concluded that
ferric ions could not exist in contact with pyrite. They also stated
that the ferric ion was the only actual oxidizing agent even though
oxygen might be the ultimate electron acceptor. The first conclusion
perhaps is based on a thermodynamic approach where infinite time is
allowed for a reaction to reach equilibrium rather than on a kinetic
approach where concentrations are considered as functions of time.
There is strong evidence to contradict the conclusion that ferric ions
in solution are the only species capable of directly oxidizing pyrite.
In studying liquid phase oxidation Morth2" placed an Amberlite®
IRA-120 ion exchange resin bed in series with the pyrite bed in a
recirculating solution. No iron was found in this solution using
ortho-phenanthroline spectrophotometric analysis. However, the oxi-
dation rate, as measured by oxygen consumption, was the same as in
runs where iron concentrations were at the 1000 ppm level.
Smith, Svanks, and Halko3p' also refuted Singer and Sturam by showing
that there are parallel oxidation mechanisms whereby oxygen and ferric
ions simultaneously and independently oxidize pyrite. In addition,
Sasmojo29 showed a direct surface reaction of pyrite with adsorbed
oxygen. Finally, as a practical matter, in a real system there is no
recirculation of iron-containing water over the pyrite. In experimental
work, iron-containing solutions were contacted with pyrite, and the
reduced iron then reoxidized to the ferric state after returning to the
bulk solution. In nature, the only way that the reduced iron can leave
the oxidation site is by gravity flow. If the water flow is away from
the oxidation site, it is improbable that the iron ions, when reoxi-
dized, return to the pyritic surface. This is not to deny the possi-
bility that drainage from one mine could come in contact with pyritic
material in a lower elevation mine.
In discussing the two mechanisms of pyrite oxidation Smith and Shumate27
stated that at low ferric-ferrous ratios, oxygen oxidation is dominant.
As the ratio increases, the relative importance of ferric ion oxidation
increases until at ratios in excess of five, ferric oxidation is domi-
nant. In a natural system, the only way to reach this ratio is through
Ferrobacillus species oxidation of ferrous to ferric ions, since at a
pH of two or three the rate of oxygenation of ferrous to ferric ions is
too slow to maintain a high ferric concentration in solution. This
requirement of bacterial assistance is in accord with Bailey's2 obser-
vation that in a laboratory oxidation system containing Ferrobacillus
species, the pyrite oxidation rate increased only after the bacteria
had oxidized 70 to 80 per cent of the iron in the reaction medium to
the ferric state.
12
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While laboratory investigations were concerned with detailed examination
of the oxidation reaction, there have been few detailed studies of what
happens once oxidation products have been formed. There is a middle
ground such as that taken by Vimtnerstedt and Struthers43 who worked with
spoils material. They observed that trickling flow such as that pro-
duced by rainfall removes oxidation products. This same observation
has been made by nearly everyone who was concerned by acid flushouts
after heavy storms. Overall, no great effort has been expended in
defining the exact mechanism whereby acid products move from the reac-
tion site to the receiving stream.
Field studies have emphasized that neutralization by naturally occurring
alkalinity is as important as the formation of acid. Caruccio and
Parizek8 and Agnew and Corbett1 reported that calcium and magnesium
carbonates neutralize acidic drainage. The difficulty arises in de-
fining how much acid was originally produced at the source. Should
just sulfuric acid be included or should the acidity of metallic
sulfates such as ferrous or ferric sulfate also be considered? Sulfuric
acid is important because of biological effects, but total acidity
determines the cost of treatment. Most analytical techniques determine
the total acidity by hot titration to a phenolphthalein end point.
Agnew and Corbett1 also observed that if the acid equivalent of hardness
was added to the value of measured acidity in their samples, the sum
was quite close to the sulfate level. The implication of this equality
is that hardness is indicative of neutralized acidity. The only short-
coming of all these calculations is that none considered the effects of
precipitation of iron hydroxy sulfates or other metallic sulfates. The
main conclusion that can be drawn is that natural alkalinity of ground
water should be considered and that hardness may be taken as a good
estimate of the alkalinity which had been available.
MODEL ORIENTED STUDIES
While much has been written in the area of acid mine drainage, there
are a number of studies of particular importance to the development of
a mathematical model of a pyritic system.
Smith36 laid the basis for the development of such a model by discussing
the engineering aspects of acid mine drainage. In particular, he showed
how basic laboratory rate data and "first principles" of engineering
could be used to estimate acid mine drainage discharge rates.
Basic Concepts of Model
A mathematical model of pyritic systems was first suggested by Shumate,
Smith, and Brant33 in 1969. They expressed the belief that a model
would greatly reduce the time and expense of studying acid mine drain-
age. They described pyrite oxidation within the framework of a basic
engineering system in the hope of stimulating critical discussion.
Shumate et al. summarized five characteristics common to all pyrite
systems which must be considered in any model:
13
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1. The oxidation is a heterogeneous reaction involving
crystalline pyrite with oxygen in water. The environment
at the reaction site determines the reaction kinetics.
2. Oxygen transport is in the gas phase.
3- Pyrite exposed to a vapor phase will oxidize at a rate
similar to pyrite in water, provided the relative humidity
is near 100 per cent.
k. Removal of oxidation products has no influence on the
rate of oxidation.
5. In general, the reaction does not occur on the bulk
surface, but on pyrite embedded in a porous structure.
These five criteria are little more than restatements of the research
results already discussed. However, they are indicative of the orderly,
logical approach which must be used in the development of a mathematical
model of a pyritic system. Shumate e_t al.33 also suggested methods of
relating rates of oxidation, and acid release, to system characteristics.
The thrust of the suggestions was to treat a pyritic system as the sum
of many micro-systems.
McDaniels Research Complex
There have been two major investigations of natural systems by workers
at The Ohio State University. The development of a natural laboratory
by Shumate and Smith31 and the study of a refuse pile by Good13 have
furnished much of the information for development of a mathematical
model.
Shumate and Smith have developed the McDaniels Research Complex in
Vinton County in southeastern Ohio. The complex, administered by The
Ohio State University, includes the McDaniels Test Mine and six experi-
mental auger holes. The mine is located in the extensively mined upper
reaches of Sandy Run in Brown Township in the Middle Kittanning (No. 6)
coal bed. Moulton36 has described the geology of the area as follows:
There is a discontinuous shale layer overlying the coal, but
a shaly sandstone is present most frequently. The sandstone,
though shaly or silty at the base grades upward into a mas-
sive, medium grained, well cemented rock....The sandstone
over the Middle Kittanning coal bed is about hO feet thick,
_and at its top there is a thin stained zone which indicates
the horizon of the Lower Freeport coal....The general charac-
ter of the remaining upper part of the geologic section is
of sandstone or silt composition, with exception of more or
less minor occurrences of shale; 'limestone, and thin clay
and coal beds.
-------
In selecting a mine suitable for field research, investigators examined
four mines in the Sandy Run area. The McDaniels Mine was selected be-
cause it best met the following four criteria:
1. It was physically separated from all other mines.
2. There was only one opening to be sealed.
3. The strata near the opening were sound so that a tight
seal could be constructed.
^4. The mine produced a significant quantity of acid mine
water.
McDaniels Mine was also relatively small and in a good state of repair.
The test mine is a small drift mine extending 35 to hO feet into the
hillside. The refuse and other material left during mining was removed.
A concrete seal was placed on the only entrance to the mine. The seal
contains sampling ports and connections for injecting gases for' con-
trolling the atmosphere in the mine. The geology and hydrology of the
mine was determined. Six observation wells were drilled in the hillside
above the mine.
The most important aspect of the test mine work has been the continued
periodic measurements of drainage flow rates and chemical analyses for
more than five years. The data are important both because of their
frequency and because they represent a relatively well-defined system.
Besides collecting data, Shumate and Smith31 have attempted to use the
mine as one would use a chemical engineering pilot plant to perform
experiments.
The main variable available for experimentation was the atmosphere within
the mine. Since the mine is located in a "tight" geologic formation and
has only one man-made opening, the initial test was simply to put a seal
at the entrance. With a seal, the oxygen concentration in the mine
atmosphere dropped to 10 per cent, but no lower. This behavior, which
has been observed in a number of other "sealed" mines, has been attrib-
uted to "breathing." "Breathing" is the pushing and pulling of air
through the fine channels in the overburden by atmospheric pressure
variations. To counter-act breathing, positive atmospheric control was
maintained by injecting gases into the mine to maintain a slight posi-
tive pressure relative to the outside atmosphere. The gases that have
been injected include oxygen, nitrogen, and air. The oxygen was added
to raise the oxygen level. The nitrogen was added to minimize the
oxygen level, and air was injected to hold a constant 21 per cent
oxygen level.
The expectation of the investigators was that the results of a change
in the atmosphere would become apparent in one or two months. This
15
-------
hypothesis was based on the assumption that oxidation was occurring
close to water flow channels and that products were washed out soon
after formation. It was only after 6 to 8 month delays that anticipated
acid load changes occurred. This response lag indicated that oxidation
was occurring in areas away from normal flow channels. Product in
unleached volumes would only be removed by gravity diffusion as de-
scribed in Section VI. Hence, no changes in acid removal would be
noted until the previously accumulated oxidation products had been
removed from the system. In light of this conclusion, the most recent
experiment, addition of nitrogen to maintain a slight positive pressure
of nitrogen at all times, has been in progress since the middle of 19&9-
One of the best checks of any model which is developed is that it will
show a long lag time similar to the observations at the McDaniels Test
Mine. In other experiments, the permeability of the over-burden was
estimated, and core drill samples were taken from behind the exposed
coal faces. These cores showed that pyrite oxidation had occurred as
much as 50 feet into the coal away from the bulk atmosphere.
Six experimental auger holes were drilled in the same coal seam as the
McDaniels Test Mine, but on the other side of the valley. The flow
rate and drainage characteristics from these holes have been monitored
since they were drilled in the summer of 1969- The most notable obser-
vation has been the change from alkaline to acidic discharges. The
change is a sign of increasing acid production rather than a decrease
in the natural alkalinity of the ground water. A publication describing
all of the research at the McDaniels Research Complex has been prepared
by Smith and Shumate.37
In Situ Oxidation Rates
Larez18 determined the oxidation rates of pyrite contained in natural
coal and shale. He obtained blocks of coal and shale from the walls
of Auger Hole No. 3 at the McDaniels Research Site. The oxygen uptake
rate of each of the blocks was measured in a Warburg-type apparatus.
The oxygen consumption for shale was about 3 |ag-hr~1-cm~3 of solid.
For the coal binder, the uptake was only 1 |ag Os'hr'1 «cm"3. In engi-
neering units, these rates are in the range from 0.01 to 0.1 pound per
day per cubic foot solid. This difference in rates was attributed to
the higher pyrite content and greater porosity of the shale. Since the
blocks used were only about a centimeter in thickness, the observed
rates are probably the maximum possible at the operating conditions
used. These rates can be used as boundary conditions in developing a
model.
Larez .exposed the sample blocks to chlor^e to kill any bacteria present.
This treatment had no influence on the shale block oxygen uptake rate,
and slightly decreased the coal rate to 0,7 Wg'hr~1»cm"3 solid. These
results prove nothing concerning the effect pf bacteria on acid pro-
duction and may only indicate the totai absence of bacteria.
16
-------
Refuse Piles
Good13 has investigated acidic drainage from the refuse pile of the
New Kathleen Mine. This mine, near DuQuoin, Illinois, was operated by
the Truax-Traer Coal Company. The pile covers an area of about ^-0
acres and rises ^0 to 65 feet above the surrounding farm land. The
pile contains about two million cubic yards of coal refuse. Good
described the hydrology and oxidation characteristics of the refuse
pile.
Oxidation appeared to occur in a h- to 10-inch thick outer mantle. The
clay was washed out of this layer by rainfall to form a layer of clay
just beneath the outer mantle. This clay layer was tightly packed and
about an inch thick. The layer had low permeability, but there were
cracks and crevices where water could enter the main part of the pile.
The clay layer did serve as an oxygen and water barrier over most of
the pile. The remainder of the pile showed little evidence of oxidation.
The pile had several distinct drainage areas. Instruments were set up
to measure the flow rate and water quality from each of these areas.
There were also a number of springs around the base whose flow rates
were measured. These springs were fed by some sort of internal storage
pool in the pile. Test wells in the pile confirmed the existence of
such a pool, but did not define its exact nature. This pool was re-
charged by precipitation and supplied a significant flow rate between
storms. Depending on the section of the pile, ho to 75 per cent of the
precipitation was recovered as surface runoff. The runoff was analyzed
for sulfate and acidity. Generally, these were at a maximum concentra-
tion at the beginning of the storm, and tailed off as the acidic products
were removed.
Since the runoff data had some scatter, Good developed a 0.1-acre irri-
gation sprinkler plot. Precipitation could be simulated by sprinkling
uncontaminated water on the plot at any desired rate. Again, the
drainage was measured and analyzed. Based on all data, Good estimated
that about 30 per cent of the water from a given storm entered the pile
and later emerged via springs. The daily acid production was estimated
as 200 Ib/acre.
Brown5 studied the transport of oxygen through layers of soil and mater-
ial from coal refuse piles. He attempted to model the transport, but
he encountered difficulty in estimating the diffusivity of air through
the soil. Brown obtained laboratory scale oxidation rates for material
from the Truax-Traer pile Good had studied. The small-scale rates
checked closely with those obtained by Good.
The projects discussed in this section have been oriented toward devel-
oping information about natural pyrite systems. The results have been
in accord with the reaction kinetics developed in laboratory investiga-
tions. Although Smith and Shumate37 and Good13 furnished data on acid
17
-------
removal rates, no removal mechanisms were suggested and evaluated. This
subject of removal mechanisms and rates is one of the areas where infor-
mation and theories will be developed as the model is constructed.
18
-------
SECTION V
EXPERIMENTAL PROGRAM
While much experimental information is available on oxidation rates, no
work has been done to determine removal rates. To counteract this
deficiency, several relatively simple experiments have been performed.
ACID REMOVAL FROM ISOLATED COAL BLOCKS
Blocks of coal were isolated from the main seam in Auger Hole No. 2B at
the McDaniels Research Site. One-foot square blocks were isolated by
cutting channels 6 to 12 inches deep around the blocks, and then filling
the channels with polyurethane foam. The foam provides a barrier to
oxygen and water vapor. The block is exposed to the atmosphere only
on the front face and only to other coal on the rear face. At the time
of the foaming, Plexiglas® drainage trougns were placed in the hori-
zontal channels.
Periodically, at h to 8 week intervals, the faces of the blocks have
been washed. One liter of water was placed in a polyethylene squeeze
bottle and the block was sprayed. The wash water was collected and
returned to the laboratory for analysis. About 65 to 75 per cent of
the water was recovered; the remainder was lost by splashing. The
recovered water was assumed to be the average composition, and all
calculations have been based on one liter of wash water.
The wash water was analyzed for acidity by hot titration to the phenol-
phthalein endpoint, and for sulfate by barium sulfate precipitation.
The wash water- was acidified, and atomic adsorption spectrophotometry
was used to determine the iron concentration.
The acidity and sulfate are virtually identical since the wash water
contained no alkalinity. The acid removal rates for a block are shown
in Fig. 1 as a function of time. After an initial peak at the begin-
ning of the test in March, 1970, the rate fell off through the summer.
In October, the rate began to rise and reached a peak in January, 1971.
This seasonal variation corresponds to the variation observed by Smith
and Shumate37 in the drainage from the auger holes at the McDaniels
Research Site. This similarity indicates that large-scale acid removal
rates can be explained by micro-scale rate variations as in the case of
oxidation rate calculations. A detailed explanation of removal mecha-
nisms and rates will be presented in Section VI.
REMOVAL RATES IN HIGfl HUMIDITY CHAMBER
During the cutting of channels in the above experiment, several large
blocks of coal were dislodged. Two blocks3 about 1 x 2 x h inches in
size, were placed in the bottom of a desiccator. Water, instead of
drying agent, was placed in the bottom of the desiccator. With the
19
-------
ro
o
0
Mar. May
1970
Nov.
July Sept.
Figure 1 - Rate of Acid Removal from Isolated Coal Block
Jan. Mar.
1971
-------
normal good seal of the desiccator, 100 per cent relative humidity was
maintained in the chamber. Periodically, the lid was removed to renew
the oxygen supply.
Although the blocks were sitting above the water, they gradually became
wet, and occasionally drops of water would fall back into the main body
of water. This experiment was continued for several months. At the
conclusion of the run, the bottoms of the blocks were rinsed with dis-
tilled water. This water was added to the water in the chamber and
analyzed in the normal manner for acidity, sulfate, and ferrous and
ferric iron.
During the first test of 196 days, the acid removal rate for both blocks
was l^A mg/day, the sulfate removal was 2.^ mg/day, and the iron rate
was 3.3 mg/day. The ferric-ferrous ratio was 1.6. When the test was
repeated for a 72-day period, the acid removal rate was 5.5 mg/day and
the sulfate rate was k.2. The iron rate increased to 13.1 mg/day,
while the ferric-ferrous ratio was only 0.2^. These two sets of data
have much scatter, but they do give an order of magnitude estimate of
the rate of the gravity diffusion type of removal mechanism which will
be presented in Section VI.
The weight of each blocks was about 200 grams. When a removal rate per
day per gram of coal is calculated, values are in the range of 1 to 10
(j.g/day. It is interesting to observe that Larez'18 estimates of oxygen
uptake by coal and shale samples fell in this same range. This agree-
ment is particularly significant since there has been very little other
experimentation with naturally occurring materials regarding oxidation
and product removal rates.
SULFATE AND ACIDITY ANALYSES
In their work with acid mine drainage in Indiana, Agnew and Corbett1
raised questions about methods of analyzing drainage. In particular,
they observed that calcium and magnesium hardness (CaCQs and MgC03)
should be considered in drainage analyses. Their results showed that
the sum of acidity plus hardness, in consistent units, was equal to
the sulfate.
To check this observation, samples from McDaniels Mine and the six
auger hole mines at the McDaniels Research Site were taken in the
usual manner. A small portion of the sample was acidified to prevent
precipitation. The usual sulfate and acidity analyses were run on the
bulk sample. Atomic absorption spectrophotometry was used to determine
calcium and magnesium in the acidified samples. The acidity, sulfate,
and calcium and magnesium data are tabulated in Table 1. The concen-
tration of each has been converted to an equivalent calcium carbonate
basis as is usually done for the acidity determination. The sum of
acidity and hardness are in excellent agreement with the sulfate values
in all cases. These results are in accord with the observations of
Agnew and Corbett.1
21
-------
TABLE 1
DKAINAGE ANALYSES DATA
ro
Source
(Date)
McDaniels Mine
(12-15-69)
McDaniels Mine
(8-6-70)
Auger Hole No. 1
(8-12-70)
Auger Hole No. 2A
(8-12-70)
Auger Hole No. 2B
(8-12-70)
Auger Hole No. 3
(8-12-70)
Auger Hole No. h
(8-12-70)
Auger Hole No. 5
(8-6-70)
Auger Hole No. 6
(8-6-70)
Metal Ions (ppm)
Ca Mg
15
16
70
118
25
107
90
81
111
10
9
22
57
11
23
27
22
35
CaC03 Equivalent
(ppm)
Ca Mg
36
38
168
290
60
126
216
191+
266
1+0
35
87
225
U3
91
106
87
138
Acidity (ppm)
CaC03
72
87
265
1665
60
270
152
225
3^7
Total CaC03
Equivalents
(ppm)
ll+8
160
520
2180
163
1+87
1+71+
506
751
Sulfate
(ppm)
133
15U
533
2108
169
1+91
1+53
525
757
-------
COMMENTS
These relatively simple and crude experiments have provided .inform-'t,j on
about the rate of product removal from a small volume of coal. Vher,"
data, along with all of the oxidation information, wall be used in ihc
development of a model of a pyritic system in the following section,,.
The calculations involving water hardness have shown that the alkalinity
of the receiving waters must be considered in our- model.
-------
SECTION VI
THEORETICAL BASES OF A PYRETIC SYSTEM MODEL
"Iron pyrite reacts in the presence of oxygen and water to form iron
sulfate and sulfuric acid. These products are removed and frequently
have deleterious effects on the receiving body of water." The preceding
phrases are a verbal model of acid mine drainage. A mathematical model
of acid mine drainage starts with the verbal model and precisely quan-
tifies and computationally defines each event in the verbal model.
The items to be quantified include how much oxygen reacts with how imich
pyrite at what rate in the presence of how much water? Additional
questions include in what manner and how fast do the acidic products
get to the receiving waters? These factors as well as others suggested
by the previously discussed research investigations will be evaluated
in the following sections.
There are different kinds of pyritic systems such as drift mines, auger
holes, deep mines, and refuse piles. A single model capable of de-
scribing all of these systems would be cumbersome and difficult to use.
Therefore, a model will be developed to describe one particular system.
Suggestions and techniques for generaliizing the model to fit other
systems will then be offered.
A drift mine was selected for the initial model. This system was chosen
because Smith and Shumate37 have obtained detailed and fundamental in-
formation about a drift mine, and McDaniels Test Mine can furnish a
check on the validity of the model. In addition, the auger holes at
the McDaniels Research Site provide an opportunity to test the gener-
ality of the initial model.
An acid mine drainage system has two major subsystems; i.e., (l) pyrite
oxidation, and (2) oxidation product removal. Each of these areas will
be discussed separately. The oxidation presentation, based on experi-
mental and theoretical information, is applicable to all pyritic systems.
The removal section is based on general knowledge, but has less experi-
mental data to support the presentation than does the oxidation discus-
sion .
DERIVATION OF OXYGEN CONCENTRATION GRADIENT
The reaction mechanism and the kinetics of the oxidation of concentrated
pyritic material have been described in the review of previous laboratory
work. Certain conclusions will be reiterated to aid in the development
of the oxidation model.
One observation was that the oxidation rate was proportional to the
oxygen concentration. In the mine environment it is possible to
measure a bulk oxygen concentration in the main cavity. However, \.hic-
-------
concentration is only applicable to oxidation occurring on exposed coal
surfaces. Since oxidation products have been observed along cleavage
planes within coal away from an exposed face, oxidation obviously occurs
well back in the hill. Therefore, some method of estimating oxygen
concentration within the pyrite-containing material must be developed.
Since no direct analyses are readily available, a mathematical analysis
will be used.
The analysis begins by assuming that oxidation occurs along the walls
of small channels in the coal or shale. The channel has cross sectional
area, A, and extends distance, L, into the binder. Reaction occurs the
length of the channel at a rate proportional to the oxygen concentration
CQX. The rate may also be assumed so slow that no oxygen gradient
exists across the area A.
Consider an element in the channel of AZ length as shown in the sketch
below.
Z + AZ
The oxygen entering this volume at Z is ANQx A@ , where NQx is pound
moles per hour per square foot and A0 is the time increment in hours.
The oxygen leaving the volume at Z + A2 is ANQx A3. The oxygen con-
sumed by reaction is k^CQxAAZAQj where k^ is the reaction rate constant
with units of reciprocal hours and C0x is the oxygen concentration in
pound moles per cubic foot of gas. The accumulation of oxygen in the
volume is ACQ-^AAZ. These terms can be collected in the following form:
input minus output equals reaction plus accumulation, or
- AC0xMZ + kRC0xAAZAf)
If all terms are divided by>AA7'A&, and the limits are taken as the
differential elements approach zero, the following equation is obtained:
dC0x
- kRC0x = -~ . (l)
The oxygen concentration term, C0x, can be replaced by XQXC, where C
is the total gas concentration in pound moles per cubic foot and XQX
is the mole fraction of oxygen in the gas. This substitution yields
the general equation
26
-------
(2)
Equation (2) is a general relationship which can only be solved by
making specific assumptions and substitutions for given situations.
For this analysis, it is reasonable to assume that there is no time
dependence; an assumption that will be verified in the course of the
analysis. A second condition for the solution is that an "effective"
diffusivity, D, which is independent of position and concentration,
be defined such that
&nv
NO* = -CD ^2*.
This condition is based on the fact that coal and shale contain voids
and channels which are neither straight nor uniform. Because of the
nonuniformity of the diffusion path, the normal distinctions of diffu-
sion area, path length, and counter-diffusion become blurred. Bird,
Stewart, and Lightfoot3 have discussed the concept of effective diffu-
sivity in detail. They presented a similar situation of the first-order
consumption of a gas inside porous catalyst pellets.
When the two modifications are applied to Eq. (2) and derivatives taken,
the following equation is obtained:
This may be rearranged easily to give
dZ D
The general solution to Eq. (5) is:
XQX = A exp((kR/D)'/'Z) + B exp(-(kR/D)'''Z) . (6)
The integration constants may be evaluated by use of the two boundary
conditions (BC); i.e.,
BC 1: At Z = L, XQX =0.0
and :
BC 2: At Z = 0, fyx = XQX . .
27
-------
From BC 1, it is apparent that A is zero. Then, using BC 2,
XOXQ = B exp[-(0)] = B
or
In the evaluation of the oxygen gradient, some value must be assigned
to the effective diffusivity. Workers in soil mechanics (see Brown5)
have suggested using D = 0.6 DAB, where DAB ^s the normal oxygen in air
diffusivity.
Another solution to Eq. (2) may be developed by assuming that the
atmospheric pressure varies at the mouth of the channel. If the ambient
pressure increases, air containing 21 per cent oxygen will be pushed
into the pore. If the outside pressure decreases, part of the air in
the confined volume will be pulled out. This is now an unsteady state
problem which is more easily handled by numerical than by analytical
solution techniques. One simplifying assumption is that the pressure
alternately increases and decreases uniformly with time; i.e., a
"sawtooth" function. As in the previous analytical development, the
effective diffusivity will be used to describe other motion of the
oxygen molecules. These assumptions give for the oxygen movement:
NOX = -K
The first term on the right hand side of the equation is the molecular
diffusion of oxygen into the channel, and the second term is the bulk
flow of oxygen and nitrogen being pushed and pulled by the pressure
variations.
At atmospheric pressure the moles (£n) of an "Ideal" gas entering the
channel mouth are equal to V/RTAP(e), where V is the channel volume,
R is the gas constant, T is the ambient temperature, and AP(0) is the
change in atmospheric pressure as a function of time. When V is re-
placed by A*L and the entire equation divided by area to convert to a
flux, we obtain
£a = (NO
O
X
A x N ART
= LAP(e) (9)
RT
Finally it may be assumed that effects of gas entering (or leaving)
the channel are uniformly reflected over ths length of the channel;
28
-------
i.e., each incremental volume gains an additional 1/V moles of gas.
This in terms of the flux is
+ %)z - d-z/L) (10)
r\l
and
(Nox + NN)z = ^M (L - Z). (11)
Kl
Equation (ll) may "be substituted into Eq. (8) and the derivative taken:
= -CD yu* + a^«; (L-Z) ^ - Xox ^^/ (12)
Arr ^J TDT1 xn VJ JL TMTI ^ y
Equation (12) is substituted into Eq. (2) to give the second-order
unsteady state equation
= CD - £ (L-Z) 4 Xox £E -kRXOxC. (13)
^ RT ^Z^ ^X RT ^^
Three boundary conditions are required for the solution of Eq. (13).
Two are the same distance and mole fraction parameters as used in the
analytical solution. The third is a time and mole fraction parameter
describing the oxygen gradient at zero time.
BCl: At Z = L, 6 = 0; XQX = 0
BC 2: At Z = 0, 9 = 6; XQX = Xbx
BC 3: At Z = Z, 9 = 0; XQX = XQ-J, exp(-(k /D)P/'Z)
Equation (13) is of such complexity that there are no straightforward
analytical solutions. However, numerical techniques using a digital
computer can be used to generate solutions for different values of the
independent variables L and AP(#). Implicit finite differences are
used to estimate all derivatives, and a solution is obtained by iter-
ative techniques. The setup of the numerical solution and the computer
program "GRADIENT1' are shown in Appendix A.
The output of the program "GRADIENT" is sets of oxygen gradients for
given L and AP(0) values. An integrating function in the program
estimates the daily oxygen consumption in the channel at the stated
conditions. Since "GRADIENT" generates much data rapidly, the most
important information will be summarized in Figs. 2-7-
29
-------
0.24 -
LEGEND
O Inhaling Plus Diffusion
A Exhaling Plus Diffusion
E Diffusion Alone
0 5 10 15 20
Distance from Air-Solid Interface, Feet
Figure 2 - Effect of "Breathing" on Oxygen Gradient
25
30
-------
O
O
E
D
t_
cn
c
o
"a.
E
C
O
o
c
0)
X
O
0
0
L EGEND
In Cycle
A Out Cycle
KR= 0.03 Hour'1
AP= 12 mm Hg / Day
I
0
100 200 300 400
Channel Length, Feet
500
Figure 3 - Effect of "Breathing" on First Order Oxidation Rate
31
-------
0.24 -
0,20
£ 0.16
o>
x
O
c
o
0.12
0.08
o 0.001
0.0
A 0.03
0.04 -
0
Distance from Air-Solid Interface, Feet
Figure h - Effect of First Order Rate Constant
on Oxygen Gradient
32
-------
o
Q
E
o
c
o
"o.
E
C
o
o
c
CD
X
O
1000.0 -
100.0 -
1.0
0.001
0.01
O.I
1,0
Reaction Rate Constant, Hour"'
Figure 5 - Effect of Rate Constant on First Order
Oxidation Rate
33
-------
0.24
0.20
0
LEGEND
KR, Hour H
O 0.001
n 0.01
A O.I
05 10 15 20
Distance from Air-Solid Interface, Feet
Figure 6 - Effect of Zero Order Rate Constant
on Oxygen Gradient
-------
2 -
o 10
Q
\
c/)
E
o
i_
en
E 8
c
o
Q.
E
D
(/)
C
O
O
c
0)
01
>>
X
O
0
0
O Zero Order
o First Order
KR = 0,03 Hour
1
1
100 200 300
Channel Length, Feet
400
Figure 7 - Effect of Pore Length on Oxidation Rate
35
-------
The AP(0) function was treated as a sawtooth variable that linearly
moves between some maximum and minimum value. The maximum has been
fixed at 7^5 mm Hg pressure and the minimum is established by the AP.
Figure 2 shows the maximum and minimum oxygen gradients for a daily
pressure change of 12 mm Hg and an L of 200 feet. At the minimum
pressure, the channel has been partially evacuated, and the oxygen
gradient is at its lowest level, since the highest oxygen content air
has been pulled out. At the maximum, relatively oxygen-rich (21 per
cent), atmospheric air has been forced into the channel to raise the
gradient. For comparison, the gradient from the analytical solution
(no breathing) is also shown. The analytical gradient is slightly
closer to the minimum than to the maximum. Calculations for more nor-
mal, 1 to 3 mm Hg, daily pressure changes give maximum and minimum
gradients closer together. At these low pressure variations, the time
average of the gradients approaches the analytical gradient.
The channel length, L, is representative of the volume of gas available
for compression and expansion rather than being a perpendicular distance
from the channel mouth. Figure 3 shows the influence of L on the amount
of oxygen consumed in the channel. As expected, more oxygen is con-
sumed on the "in" than on the "out" breathing cycles. Longer channels
increase the oxidation on the "in" steps, but give less oxidation on
the "out" cycles. The net result is a slight increase of oxidation
with increasing L.
The evidence presented in Figs. 2 and 3 leads to the conclusion that
"breathing" has little effect on oxidation in closed-end channels. If
channels between the atmosphere and a very large void volume, such as
a mined out volume, were considered, "breathing" might be of greater
importance. This is indicated by the rapidly increasing oxygen con-
sumption at longer pore lengths in Fig. 3. In such a case nearly all
of the pyr it e- containing channel would be swept with a new atmosphere
during each pressure change. However, in the current development, it
seems reasonable to use the analytical oxygen gradient.
INFLUENCE OF REACTION RATE CONSTANT
The rate constant k^ also influences the oxygen gradients and amount of
oxidation. Generally kR is defined in terms of the reacting materials.
In the case of a heterogeneous reaction a very careful definition is
required. The reaction rate equation is written below in the usual
symbolic language for a first-order reaction:
The derivative, ^Cox/d0, is the change in moles per unit volume per
unit time. The rate constant, RR, has the units of reciprocal time,
and C0x> ^he §as concentration, has the units of moles per unit volume.
-------
i^rite is embedded in the channel walls in small quantities so the
•].e l.uol concentration must be considered in determining kR. Since the
true pyrile distribution is not known, it is necessary to assume a
di st ri but Ion. For example, in the laboratory? one gram of 60-mesh,
iv on cent .rated, pyritic material consumed 2rj fig 02/hr in air at 25°C .
The enii!i of pyrite can be assumed to be distributed along the walls of
:'.oint- volume, V, of channel, or,
Rate x gram pyrite _ mole oxygen
__
FniJrTpyrite Volume Volume
x 10" '"' gram oxygen ._. k x 0.21 x 32 grams oxygen
V hour LR 22.4 liters
k -
.3 x 1Q-4 liter
V hour
If a channel cross sectional area of 1 mm" is considered, it is likely
that the reactivity equivalent of 1 g of crushed pyrite would be found
in a length of 100 m. This would give a volume of 0.01 m3, or a kp>
value of 0.083 per hour. Since this can only be considered an educated
guess, Fig. h has been drawn to show the effect of the rate constant
on oxygen gradients. The higher the rate constant, the more rapidly
the gradient drops to aero. The influence of rate constant on the
amount of oxidation is shown in Fig. 5 as a logarithmic plot. This
plot has a slope of 0.5, indicating that the rate is proportional to
the square root of the rate constant. This is the result for any rate
calculation using a concentration term based on Eq. (?)• The preceding
observation leads to the conclusion that for a reasonably accurate
oxidation model, the rate constant should be known, within an order of
magnitude .
EFFECTS OF REACTION ORDER
All of the discussion to this point has been based on the premise of
first-order, or oxygen concentration dependent, reaction kinetics.
However, in microbiological work, particularly that of Lau et al. ,xu?
it has been observed that above a certain minimum concentration of
oxygen, the oxidation of pyrite is independent of the oxygen concentra-
tion. The oxidation rate appears to be some function of the Ferrobacillus
concentration, or zero-order with respect to oxygen.
The "GPADIENT" program was modified to do zero-order calculations of
oxidation above a minimum oxygen level and first-order below that level.
Based on the work of Lau et al . , two per cent oxygen was used as the
cut-off point. The oxidation rate above two per cent oxygen was con-
sidered to be the same as the rate observed at normal (21 per cent)
atmospheric oxygen level.
37
-------
The results generated using these assumptions lead to the same conclu-
sions as the first-order case. Some differences in form do exist. For
example, the zero-order oxygen concentration gradients shown in Fig. 6
are steeper than the first-order curves in Fig. h. The most important
difference between the two orders is shown in Fig. 7> where the amounts
of oxidation are plotted against pore length for the different orders.
The zero-order reaction gives a consistently higher level of oxidation
than does the first-order. This occurs because the zero-order concen-
tration gradient, the driving force for diffusion, is steeper as more
oxygen enters the channel to be used in oxidation.
The difference between zero- and first-order rates is not important in
the development of a model for three reasons. As a practical matter,
the 30 per cent difference is minor compared to some of the other in-
fluences such as rate constants. More importantly, Smith35 and others
have stated that the significant bacterial activity, ferrous to ferric
oxidation, occurs in the drainage rather than on the surface of the
oxidizing pyrite. This means that in a natural system the pyrite is
oxidized, the products move to a receiving stream or pool, and then
the bacteria oxidize ferrous ions to the ferric state. In the labora-
tory research, the bacterial enhancement of oxidation rates was observed
only in systems where the culture medium was recirculated over the
pyritic material. In a natural system recirculation does not occur.
Finally, in a natural system, the water-to-pyrite ratio is low at the
reaction sites. Under this condition, as explained by Lau et al.,19,
there will be relatively few bacteria growing, and therefore, no en-
hancement of the oxidation rate.
OXIDATION PRODUCT REMOVAL
Generally speaking, the removal of pyrite oxidation products has been
investigated much less than oxidation of pyrite. The basic removal
problem is to describe and evaluate the flow rate of oxidation products
through various porous media by both water movement and by molecular
diffusion in aqueous solution (i.e., without net flow of water).
The rate of removal is primarily a function of the hydrologic character-
istics of the system. Conditions describing the extremes of removal
rate compared to oxidation rate can be imagined as varying from oxida-
tion sites in close proximity to flowing ground water to sites far
removed from the water table which are never inundated or flushed by
blowing water. All other factors being equal, oxidation rates at these
sites would be the same, but the rate of acid transport to the effluent
stream would be quite different. To estimate the rate of transport, we
must first describe possible transport mechanisms.
Removal Mechanisms
On the basis of laboratory observations and physical considerations, it
is possible to visualize three parallel transport mechanisms.
38
-------
The first is simply a direct washing. As ground water percolates through
flow channels in the coal seam, products from the walls of the pores
are dissolved. These products may have formed at times when the channel
was not filled with water or the products may have diffused from adja-
cent channels that are not normally used for water flow. As flow
increases, more channels are utilized, and more product is removed.
The second removal mechanism is the flushing of products from an inun-
dated volume. The inundation occurs as the water table rises during
the spring thaws or during heavy rains and covers a previously non-
saturated volume. The oxidation products gradually dissolve and are
carried to the receiving stream. This mechanism is partially respon-
sible for the high acid loads observed during the spring.
The final removal mechanism arises from the fact that the oxidation
products form a highly localized concentrated acid and salt solution.
This solution is hygroscopic and will absorb moisture from the air.
Since the relative humidity in a mine atmosphere is usually 100 per
cent, ample water is available for absorption. In addition, when warm
air from outside enters a mine and is cooled, moisture may be removed
by condensation. Eventually, sufficient moisture is collected at the
oxidized surface, and droplets of acidic solution form. As the drops
become heavier, they begin to flow by gravity and eventually reach the
receiving streams. This mechanism has been observed in laboratory
studies where water-saturated air was recirculated over a bed of pyritic
material. After about one week, acidic brown liquid began to drip from
the pyrite bed. The removal by condensation, or gravity diffusion in
the nomenclature of this model, is assumed to occur uniformly through-
out a pyritic system, but only the drops leaving the bottom of the
system are included in the net removal of acid.
While experimental data and theoretical calculations could be used to
closely estimate oxidation rates in a pyritic system, fewer data are
available for estimating the rate of removal by each of the described
removal mechanisms. However, using "common sense" and the engineering
approach of Smith,37 removal rates can be estimated in terms of what is
physically reasonable.
Gravity diffusion both adds and removes products from a volume of coal
or shale. The rate of removal by this method can be estimated in two
ways. The laboratory experiment with a small coal block in a 100 per
cent relative humidity chamber gave a removal rate, R^eu^ of about
100 (ig acidity per day per square foot of coal drainage surface. If
the rate of gravity diffusion is considered proportional to the quantity
of oxidation products stored in a volume, the above removal rate is a
maximum estimate since it represents a volume at the air-solid inter-
face where the oxygen concentration and oxidation rate are at a maximum.
If the rate of removal by gravity diffusion is assumed proportional to
the concentration of stored products, the total removal rate from a
one-foot wide row of volumes perpendicular to the interface may be
39
-------
estimated by integrating the exponential oxidation gradient of Eq. (7);
i.e.,
rL
Total removed = RRem J exp(-(kR/D)'/-')dZ.
0
Inserting the value of kp equal to 0.8 per day for coal, a diffusivity
of 10.0 square feet per day, and the RRem value of 100 mg acidity per
day and noting that at great values of L there are no oxidation products
to be removed, then
Total removed = (100/(0.8/10 )'A)exp(-(0.8/10)"»)
= 3^3 mg acid per day per foot of interface.
For the estimated wall length of 100 feet at McDaniels Mine this gives
3*1 g per day or about 2 Ib per month.
The second method of estimating gravity diffusion is to examine acid
output data from McDaniels Mine for periods such as late summer and
early autumn "when the ground is relatively dry and ground water flows
are low. Under these conditions, leaching and inundation removal of
oxidation products are minimal, and gravity diffusion is the dominant
removal mechanism. Over the 1§66 to 1970 period, acid loads in this
dry season have been in the range of 2-4 Ib per month at McDaniels Mine.
Since this range agrees with the rate estimated in the laboratory study,
a relationship must be included in the model to give this rate of re-
moval by gravity diffusion.
The removal of products by percolation or by flushing requires that
there be a description of underground water flow patterns. Hydrologic
equations have been developed to describe flow patterns in watersheds
covering hundreds of square miles. Even in these large areas, the non-
isotropic nature of the earth forces generalizations in the flow de-
scriptions. When the relatively small (at most two or three acres)
drainage area of McDaniels Mine is considered, flow can best be described
as "through cracks and crevices."32* It has been suggested that the
best mathematical description of this behavior can be obtained by
assuming a model and determining how well the model correlates previous
precipitation and flow data.
Soil Layer "Water Balance
Assuming that the source of water for mine drainage is precipitation as
rain or snow, over a hydrologic year the total drainage can be related
to the precipitation over a specific watershed area. However, the
degree of saturation of the soil affects water infiltration so that the
rate of water passing through the ground surface to the sub-surface
aquifer varies. If a water balance is made on the soil layer, the
-------
degree of saturation can be calculated and the amount of water going
to storage (for drainage flow) can also be determined. The following
paragraphs describe the development of the calculations.
Water balance
As a general rule in material balance, the amount of material coming
into a system minus the amount going out of a system must be equal to
accumulation. For water balance in the soil layer, precipitation as
rain or snow is the "in"; excess infiltrated water for drainage flow
(ADD), evapo-transpiration (PEVAP), and runoff (RUNOFF), if any, are
the "out"; and the water stored in the soil layer or root structure
(PWATER), is the "accumulation."
The equation describing the balance is
PWATER = RAIN + EMRNF + SWMELT - RUNOFF - PEVAP - ADD, (15)
where EMRNF is the difference between excess water and RUNOFF, and
SWMELT is the amount of melted snow.
During warmer weather [that is, when the mean temperature (TMEAN) is
greater than 32°F] any precipitation is considered as rain. If the
provisional water holding capacity (PWHC) can be determined by the
method of Thornthwaite and Mather,43 the difference between PWHC and
the moisture content of the soil (PWATER) is equal to the deficiency
of water in the soil (DEFICT). If the rainfall is larger than the
deficiency, excess water (EXCS) will be removed as surface runoff.
For our model, 92$ of the excess water is assumed to run off; the rest
(i.e., EMRNF ='EXCS - RUNOFF) is included in the water balance as "In."
When the mean temperature is less than 32°F, precipitation is considered
to be snow that will stay on the ground surface until the mean tempera-
ture is higher than 32°F and the ground thaws. Wisler and Brater44
estimated that 0.1 inch snow is melted for each degree day above freez-
ing. The melted snow (SWMELT) is then treated the same as rainfall.
The "out" for the water balance of the soil layer includes the water
going into storage for drainage flow (ADD), evapotranspiration (PEVAP),
and runoff (RUNOFF), if any. The method of Thronthwaite and Mather45"
can be used to estimate PEVAP (directions on how to use this method
are provided in Appendix B); however, PEVAP depends on the moisture
content in the soil layer. The efficiency factor (EFF) for PEVAP is
equal to the degree of saturation; i.e., the ratio of PWATER to PWHC.
For example, PEVAP is equal to 2.00 for the month of April, or an
average of 0.066 for each day in April. A day having 100$ soil satu-
ration will have a larger PEVAP value (0.066) than a day with a 50$
moisture saturation (PEVAP = 0.033). The excess infiltrated water,
ADD in Eq. (15)> will leave the soil layer and go into the storage
aquifer (TANK) for drainage flow.
-------
ADD was assumed to be a function of temperature and (PWATER/RJHC) =
WOVERW. For a "ballpark" estimation for the effect of WOVERW, a straight-
line relationship with ADD was assumed, since the more saturated the
soil, the more water will be available for entering storage. To con-
sider the effect of temperature, a factor (FADD) was defined which varied
from a low value at temperatures below 32°F to a high constant value for
temperatures above U5°F. Basically, FADD is used to describe the mobil-
ity of water in the soil layer. Equations for determining FADD are
given in Appendix E.
At this point, all the components in the water balance equation have
been defined. The root storage water for any day can be calculated by
adding the net amount of the water to the FWATER of the previous day
as shown in Eq. (l6).
PWATER = PWATER + RAIN + EMRNF + SWMELT - ADD - PEVAP - RUNOFF.
(new) (of previous (16)
date)
The amount of ADD for any one day can then be determined and added to
the aquifer storage of that day. The concept of the aquifer storage
(TANK) is discussed below.
Watershed area; storage and flow
Morth^5 suggested that drainage flow (FLOW) can be calculated as a
function of the storage and drainage area of the mine. Linear relation-
ships between these variables were found by Morth to give the best
results. For the purpose of finding the dependent variable, drainage
flow, the independent variables, watershed area, and storage, must be
determined first.
Watershed area (WSHED) is the ground surface area through which water
passes to provide the drainage flow water. Knowing the drainage for a
year and the annual ADD water, watershed area can be calculated. Since
the auger holes and McDaniels Mine have the same soil layer and temper-
ature conditions, McDaniels Mine should have a larger WSHED than the
auger holes, since higher annual drainage flow was recorded for the
mine.
The "out" of the water balance for the soil layer are PEVAP and ADD.
The latter will enter the aquifer of the mine. This aquifer can be
treated as storage for the drainage flow.
The concept of TANK representation for the storage of drainage flow is
hypothetical. For a one-tank representation, the volume of storage
water would be the height or the value of TANK times the watershed area,
WSHED. In other words, the storage is a very flat rectangular box,
since the ratio of TANK/WSHED is extremely small.
-------
The volume of water stored, not the volume occupied by the -water-
saturated part of the aquifer, is represented by TANK times WSHED. The
height of water, HEAD, which provides the driving force for FLOW, also
depends on the void fraction and shape of the aquifer. The relationship
between TANK and HEAD can be determined from experimental data as shown
in Appendix E. If experimental data are not available, a linear rela-
tionship between TANK and HEAD may be assumed.
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SECTION VII
DEVELOPMENT OF DRIFT MINE MODEL
Several approaches are possible in developing a model of a pyrite system.
The major source of variations arises in the choice of the bases to be
used. The choice of a coordinate system depends on factors such as
computational facility, spatial visualization, and physical reality.
The easiest choice is to list all possible variables with a tabulation
of data and feed the mass of numbers to a computerized multiple regres-
sion analysis. This statistical approach offers computational facility,
but sometimes at the sacrifice of physical reality. Since the goal of
this research is to maintain physical meaning so that different sites
can be compared, a statistical approach must be ruled out.
For the sake of generality and physical significance, the best approach
is to work with Cartesian coordinates. The physical orientation of the
system can be easily described in these coordinates. Physical and
chemical variables such as water flow, oxygen gradients, and the water
table are also easily defined in rectangular coordinates.
Computational neatness can be assured by the careful definition of the
variables. For example, a technique to calculate the oxygen gradient
in terms of the distance from the air-solid interface has already been
explained.
DESOKIIT10N OF MICRO-SYSTEM
Let us begin development of the computational model by examining a
sketch of a pyrite-containing coal seam as shown in Fig. 8. Generally,
the coo.1 seam is divided into a number of layers of coal and shale.
The water table may intercept the coal seam, which extends a relatively
great distance from the air-solid interface.
One of the layers is shown in expanded form in Fig. 9- The stratum is
of such size that oxidation and removal conditions can vary widely over
the stratum. Therefore, the stratum is subdivided into several layers,
and thfcfje layers are then divided into blocks. The basic assumption of
whole model must now be stated: An average set of conditions exists
over e;jch volume and can be used in any calculations for that block.
The system behavior is then the linear sum of the behavior of all these
sino.l 1 reaction volumes.
The block marked "A" in Fig. 9 is further expanded in Fig. 10. A
material balance has been developed about the block to relate the oxi-
dation product formation and removal rates. Oxidation is the chemical
reaction of oxygen and pyrite. Gravity diffusion is the very slow
downward movement of highly concentrated product solutions. Leaching
is the removal of products by ground water trickling through the oxidized
vo.luem. Flooding is the removal of products when a volume is inundated.
-------
CF\
SANDSTONE
OVERBURDEN
WORKING FACE
HIGH WATER TABLE
*-
LOW WATER TABLE
Figure 8 - Sketch of Underground Pyrite System from
Smith and Shumate (37)
-------
J
I
4.
-L J
Figure 9 - Stratum in Seam Divided into Micro-Volumes
Trickling
Water
Gravity
Diffusion
I
\ I /
OXIDATION
' t X
i
i
Leaching
Gravity
Diffusion
Figure 10 - Storage Volume Material Balance
-------
All of these terms have been described so now they need only be slightly
expanded or altered to give a single expression to describe the events
in volume "A . "
Oxidation rate is a function of the oxygen concentration, the pyrite
surface available for oxidation, and the reaction rate constant. The
oxygen concentration gradient can be calculated using Eq_. (?)• The
pyrite available and the reaction rate constant can be estimated from
data such as that described by Larez,.18
Previously, a rate constant was calculated by assuming that the reactivity
of a gram of pulverized pyrite was distributed along the walls of some
void volume. Larez, however, reported rates based on a volume of binder
material rather than on the basis of pyrite weight or surface area. In
this case, the void fraction, e, of the binder must be used in calculating
the rate constant. For shale, e is in the range 0.2 to 0.3-35 For
coal, the only data on porosity are of the micro-structure measured by
nitrogen adsorption and other such techniques. Therefore, it has been
necessary to make a rough estimate of e for coal. Dr. K. S. Shumate,
of the Civil Engineering Department of The Ohio State University, has
suggested that e probably has a relatively low value for coal — in the
range 0.005 to 0.02.32 For computational purposes a value of 0.005
void fraction will be used for coal.
Larez1 oxygen uptake rates and the void fraction may be used to estimate
a rate constant for the naturally occurring pyrite. We may write the
general first -order rate equation as
Rate (moles/hour /volume gas) = kR(l/hour) Cox(mol-es oxygen/volume gas).
The experimental rate, Rategxp, was reported as oxygen uptake per total
volume of solid per hour. Since the gas volume equals the void fraction
times the total volume,
pe = kR C0x.
This may be rearranged to give
kR = RateExp/(e CQX)-
If an oxygen level of 21 per cent is assumed in the bulk air phase, and
Larez' oxygen uptake rates of 3 US O2'hr~1-cm"3 solid for shale and
1 ng'hr"1'cm"3 for coal are used, kR has a value of 0.06? per day for
shale and 0.80 per day for coal. The higher value for coal arises be-
cause the rate constant is inversely proportional to the void fraction.
In the following pages, a number of variables will be introduced. The
model terminology is summarized in Table 2. The basic notation used
-------
TABLE 2
NOMENCLATURE FOR THE PROGRAM
ADD Water entering TANK from soil layer water balance
AFLAG Parameter denoting the month being executed
AG Identifies the month being executed
AGO Dummy variable for AG
ALEFT Product storage after flooding
ALK Factor converting acid load from oxygen consumption basis to
equivalent alkalinity basis
ALKALI Ground water alkalinity (ppm)
ALT Elevation of stratum relative to datum plant (ft)
AMONTH Month
AOUT Daily acid removal by leaching (ib)
CCPRFT Constant for calculating rate constant
CONA Constant for calculating rate constant
CONFH Constant relating FLOW and aquifer storage (TANK)
CON5 Conversion factor for WSHED
DEFICT Deficiency of water in root storage (inches)
DEHK Distance in K-direction that is flooded (ft)
DI Length of air-solid interface increments (ft)
DIF Base gravity diffusion constant
DIFF Gas diffusivity (ft^/day)
DIFFG Gravity diffusion rate constant for a layer
DK Length of depth increments (ft)
DSLV Fraction of stored products removed each day by leaching
DTHETA Time increment length (days)
-------
DVOL Volume of each micro-block (ft')
EFF Efficiency factor for evapotranspiration
EMKNF Excess water content minus runoff (inches)
EXCS Excess water (inches)
FADD Temperature factor for water entering storage
FJ Ratio of stored products to equilibrium storage level
FLOOD Acid removed during inundation (ib)
FLOW Drainage outflow rate (gallon/day)
FLOWMI Minimum flow rate to cause acid removal by flooding (gallons)
FLSUM Total acid removal by inundation (lb)
FRAG Fraction of stored products removed daily during flooding
FSUM Monthly accumulation of FLOW (gallon/month)
FSUMA Annual accumulation of FLOW (gallon/year)
FTGMOL Volume occupied by gm. mole gas (ft3)
GASC Gas concentration under mine conditions
GRAVIN Gravity diffusion into a volume (lb)
GRAVOT Gravity diffusion out of a volume (lb)
GSUM Monthly acid removal by gravity diffusion (lb/month)
HEAD Head of water stored in aquifer (inches)
HEADMI Minimum flow rate to cause acid removal by leaching
KITE Height of the layers being executed (ft)
IDAY Date
IN Input channel equals to unit 5
10 Output channel equals to unit 6
IP Punched output channel equals to unit 7
-------
IY Identification of year
IYEAR Year
KAT Control device in programming
KEEP Length of month
LAST Date of previous data input
LTHETA Days since preceding data input
NDEPTH Number of depth increments in model
NFEET Number of air-solid interface increments
NL Top layer of strata
NLAYER Number of layers in coal seam model
NPUNCH Punched output control
OXIDN Oxidation in a volume (ib)
OXX Oxygen concentration (mole fraction)
OXY Oxygen concentration (mole fraction)
PER Constant value to determine the distance that is inundated
PEVAP Potential evapotranspiration of each month (inches)
PWATER Current water storage in root structure (inches)
PWHC Provisional water holding capacity of root structure (inches)
PYCON Void fraction of the stratum
RAIN Rainfall precipitation (inches)
RATE RAIN/RTIME
RATEK Reaction rate constants of strata
REACT Oxygen consumption rate of pyritic material
(lag 02-cm~3 solid-hr"1)
RKEEP Parameter to stand for RAIN
ROCK Literal description of strata
-------
RSUM Monthly accumulation of water entering storage (inches)
RSUMA Annual accumulation of water entering storage (inches)
KTIME Dioration of rainfall (hr)
RUNOFF Water runoff from over-burden (inches)
SNOW Precipitation as snow (inches water)
SOX Total initial acid storage (ib)
STORE Oxidation product storage arrays
SWMELT Amount of melted snow (inches)
TACID Total acid output based on the three removal mechanisms (ib)
TANK Aquifer storage (inches)
TEMP Mine temperature correction factor
THICK Thickness of strata (ft)
TMEAN Average daily temperature (°F)
TOP Datum plane for top of coal seam
TSUM Accumulation of total acid load (ib)
TYPE Literal description of strata
UP Difference in height between layer and water level (ft)
VAP Monthly potential evapotranspiration value (inches)
WASH Equilibrium product storage in layer
WATER Water level relative to the strata (inches)
WOVERW Fractional saturation of soil, PWATER/PWHC
WSHED Watershed area of mine (ft?)
WSLOPE Slope of the water level during inundation
WSUM Total acid removed by leaching (ib)
XMAX Total distance in K-direction (ft)
-------
XMIN Distance in K-direction that is not flooded (ft)
YSU Monthly accumulation of acid load (lb/month)
YSUMA Annual accumulation of acid load (ib/year)
in the computation model is "J" for the layer number counting upwards
from the bottom layer, and "K" for the block number counting in a hori-
zontal direction from the air-solid interface. In addition, the program
provides "I" notation for increments along the interface for situations
where conditions may vary horizontally along the exposed face.
The quantity of oxidation, which increases the amount of products stored
in volume "A" (3TGRE(l,J,K) in our notation) can be expressed as follows:
OXIDK(I,J,K) - kR(j)cox(i,J,K)DvoL(i,j,K) (17)
OXIDN(l,J,K) is the oxygen consumed per day in a block of volume DVOL
(l,J,K). Cox(l>JjK) is the oxygen concentration in the void volume,
and kft(j) is the rate constant for layer J.
A gravity diffusion function which includes a dependence on the quantity
of stored products and which assumes no horizontal motion of products is:
GRAVOT(I,J,K) = DIFFG(J)STORE(I,J,K) (18)
GRAVIN(I,J,K) = DIFFG(J+I)STORE(I,J+I,K) (19)
GRAVIN and GRAVOT are the gravity diffusion in and out of a volume,
STORE (l,J,K) is the pounds of oxidation products, reported as oxygen
consumed, stored in the volume, and "J+l" refers to the volume above.
DIFFG(j) is the fraction of products stored in layer J which moves by
gravity diffusion each day. For different strata, DIFFG(j) is calcu-
lated as a constant fraction, DIF, of the oxidation rate constant.
This dependence is based on the assumption that gravity diffusion de-
pends on how fast oxidation products form, and inversely depends on the
void volume available for product storage. Both of these factors are
included in the rate constant. The magnitude of DIF, 0.01, is chosen
to give a net monthly removal rate of about two pounds of acid as
described in Section VI. Calculated values of DIFFG(j) are in the
range 0.005 to 0.001.
Removal by leaching and flooding are both functions of underground water
flows. The leaching occurs as water trickles through channels in the
oxidized volume. The trickling water picks up oxidation products and
enters the receiving stream. The products which are removed may have
been formed either along the flow channel walls or have diffused from
53
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adjacent "dry" channels. The basic assumption of the leaching model is
that most of the water observed as drainage has not contacted the reactive
pyrite volume, but merely dilutes the acid. The reasoning is that if
the reactive area were continually washed by large volumes of water, the
fine channels in the binder would be filled with water. The water then
would block the transport of oxygen to the pyrite, and oxidation would
virtually cease.
The quantity of products leached depends both on the amount of products
present and on the number of flow channels being utilized for flow. The
utilization of flow channels is largely controlled by how much liquid is
moving. Therefore, AOUT, the quantity of material leached from a volume
may be expressed as a function of the storage contents and the rate of
water trickling vertically from the surface:
AOUT(I,J,K) = STQRE(I,J,K) • FJ • DSLV. (20)
DSLV is the fraction of stored products removed each day by water trick-
ling downward through the binder and pyrite. The value of DSLV has been
obtained by correlating the calculated water infiltration rates with
observed variations in acid load at the McDaniels Mine. The best match
of observed and predicted acid load was obtained for
DSLV = 0.0002*(FLOW-HEADMI), (2l)
where HEAHMI is value of FLOW below which no leaching occurs. The term
FJ is the ratio of the quantity of stored products to the equilibrium
product storage level. The equilibrium storage is the amount of products
that would be maintained in an open system where oxidation and removal
rates were equal. The equilibrium conditions were estimated by allowing
the simulation program to run under conditions of 21 per cent oxygen
atmosphere for a three-year period. The quantities of product stored
at the end of this period were used as the equilibrium storage.
Acid removal by flushing is mainly due to the rise or movement of the
water table. In order to evaluate the flushing mechanism, the water
table must first be determined. One method is actual measurement by
digging test wells into the hill. Morth2s obtained an equation to
describe the water level of the McDaniels Test Mine by this method.
However, this information is not usually available. Furthermore, "the
true shape of the water table is not critical for model studies but
some form must be selected for computational purposes."25 For the
general case, a different approach can be used.
The water table may intersect the system as shown in Fig. 11. In
this table, WSLOPE is the slope of the water level and DEHK is the dis-
tance on the bottom layer of the system which is inundated. If the
acid removed by flooding is assumed to vary little with WSLOPE, a fixed
-------
SLOPE OF WATER TABLE
(WSLOPE)
Figure 11 - Location of Water Table
value for WSLOPE can be used and the value of PER selected to match the
acid removal contributed ty flooding. DEHK is assumed to be a function
of FLOW minus a base flow (FLOWMI). This relation is shown in Eq.. (22).
DEHK = PER*S QRT(FLOW-FLOWMI).
(22)
The mean DEHK for a hydrologic year is selected so as to provide enough
exposed pyrite to generate the required yearly acid production. If
field data are not available, DEHK must be determined by estimating the
shape and location of the water table during high and low flow periods.
Procedures for evaluating the constants in Eq. (22) are given in
Appendix E.
After finding the number of blocks in the system that will be flooded
during inundation, the fraction (FRAC) of the acid stored in each block
that will be removed each day by this mechanism is calculated. Similar
to the leaching mechanism, daily acid removal by flushing can be calcu-
lated as the product of STORE and FRAC.
When a storage volume is inundated, the oxidation products gradually
dissolve and flow away. The amount of products removed per day is
FLOOD(I,J,K) = FRAC.STORE(I,J,K).
(23)
55
-------
FRAC is the fraction of products stored in a volume which are dissolved
each day that the volume is inundated. A value of 0.002 per day has
been found most appropriate for FRAC. This is a higher value than that
of DIFFG (0.0005 to 0.001 range) and that of DSLV (0.0005 to 0.0015
range) since inundation supersedes and includes gravity diffusion and
leaching. An upper limit on the rate of removal during inundation
arises because of product solubility limitations, and because of the
fact that products must still diffuse out of capillary size channels
in the inundated volume.
At this point, it is appropriate to discuss in more detail how "suitable"
values were obtained for the constants DIF, DSLV, and FRAC. The basis
for the evaluation of the constants was the annual acid loads measured
at McDaniels Test Mine.
While the three removal mechanisms, leaching, gravity diffusion, and
inundation, have been considered as parallel and independent, the total
removal must fit the constraints of the observed data. Hence, if one
rate is increased, the other two removal rates must be reduced.
In light of the preceding discussion, the general technique for evaluating
DIF, DSLV, and FRAC was to pick a value for each and determine how well
the annual predictions of acid loads matched the annual loads observed at
McDaniels Mine. The key for the initial estimate of the constants was
the experimental knowledge that gravity diffusion removed two to four
pounds of acid per month combined with an estimate of the total product
storage obtained by allowing the program to run for a simulated period
of three or four years. The total initial storage was about 150 pounds
of acid, and assuming 30 pounds of removal by gravity diffusion per year,
a gravity diffusion removal rate of 0.1 pound per day was used. As an
order of magnitude estimate, this gave 0.1/150, or about 0.000? per day
for DIF. To get what was essentially a "trial and error" approach
started, initial guesses of FRAC and DSLV were set equal to DIF. These
values were the right magnitude, but gave low predictions.
The values of the three constants were raised to bring the annual predic-
tions of acid load in line with observed values. Once the annual loads
were in line, the "fine tuning" or matching of short-term acid loads was
undertaken. The inundation removal term was the most sensitive of the
three rates during the first three months of the year. It is, in process
control terminology, a derivative function which responds rapidly to
changes in the water table. Hence, the inundation constant FRAC could
be used to match early year increases in acid load. The leaching con-
stant DSLV is most important in times of high flow so it could be varied
to produce the best acid load predictions in April, May, and June.
As each constant was varied, the other two also had to be adjusted.
During the general trial and error evaluation, it was observed that any
constant could be varied by 30 or UO per cent of its value without great
damage to the annual prediction capability of the model. However such
-------
variations in FRA.C or DSLV could shift short-term prediction peaks by
as much as 3 or k weeks.
Once all the events probable in a given volume have been defined, the
appropriate terms are summed to give the new storage contents in the
volume. Under normal circumstances (no flooding) the new product
storage in a volume is the sum of the rates in Eqs. (17-20) plus the
previous storage:
STORE(I,J,K) - STORE(I,J,K) + OXIDN(l,J,K) + GRAVIN(l,J+l,K)
-GRAVOT(I,J,K) - ADUT(I,J,K). (2k)
During inundation, the water forms an oxygen diffusion barrier so that
oxidation virtually ceases, and
STORE(I,J,K) - STORE(I,J,K) - FLOOD(l,J,K). (25)
The total acid removed from the system is the sum of all AOUT(ljJjK),
and FLOOD(l,J,K) where appropriate, terms plus the GRAVOT terms from
storage volumes immediately above the water table. The calculation of
acid load as the sum of aj.1 acid removal rates assumes that oxidation
products leave the mine as soon as they enter the ground water. The
summation of all these removal terms plus the calculation of new storage
quantities are performed by a digital computer. The computer program
which does these calculations iteratively to simulate the passage of
time will be described in the following section.
COMPUTER PROGRAMMING OF MODEL
The programming of this or any other model is the restatement of regular
mathematical equations in the particular form required by a digital com-
puter. This language of the computer has already been introduced with
the I,J,K notation at the beginning of this section. The computational
model of the drift mine will be described in terms of one main program
and three sub-routines. The main program maintains generality with
regard to most pyritic systems, but the subroutines include special
provisions for a specific mine site. A flow chart for the main program
is shown in Fig. 12, and flow charts for the subroutines are shown in
Figs. 13, 1^, and 15.
The main program has two principal sections. The first section handles
bookeeping such as defining variables, establishing computational arrays,
and setting initial values. The arrays are the subscripted variables
which represent incremental changes in distances or conditions in
different locations. The initial conditions to be established include
a base datum plane, a minimum water level datum, dimensions of the coal
and shale strata, alkalinity of ground water, the "water shed" area
drained by the mine, experimental or estimated oxidation rates, and
conversion factors. The most critical set of initial values is the
57
-------
Establish
C ompu t a t i on al
Arrays
Define Input/
Output Channels
Read in and
Echo Initial
Conditions
Define Data
Storage
Constants
Read in
Daily Weather
Data
RKEEP - RAIN
Call DAYS
Call REMOVE
Return FLOW
Determine Water
Table
Compute Oxygen
Gradient for
Each Stratum
No
No
4—
Print Out
Daily
Results
Yes
Maintain Monthly
and Annual Totals
of Flow and Acid
Load
Have All
Layers Been
Computed
Yes
Stop If "END"
Card Is
Reached
Have All
Volumes
Been Computed
TAGID = AOUT
STORE = STORE -
AOUT - GRAVOT
+ OXIDN + GRAVIN
Calculate GRAVIN,
GRAVOT, OXIDN,
and AOUT
TAGID = FLOOD
STORE = STORE
- FLOOD
FLOOD = FRAC
* STORE
Yes
Is the Volume
Inundated?
No
Describe Each
Event Probable
in Volume
Figure 12 - Main Program Flow Chart
-------
IDAY,
AMDNTH
No
Does Amonth
= AGO
Yes
LTHETA =
IDAY - LAST
LAST = IDAY
Return
Determine KEEP,
Length of Previous
Month
LTHETA = KEEP
- LAST + IDAY
AGO = AMONTH
LAST = IDAY
I
Return
Figure 13 - Flow Chart of Subroutine DAYS
-------
AMONTH
Identify
AMONTH
Compare
AMONTH with
Internal Table
Obtain PEVAP
from Data
Table
Return
Figure lU - Flow Chart of Subroutine EVAP
60
-------
First Call
Establish
Initial
Values
Return
Calculate Water
Deficiency of
soil, DEPICT
Is TMEAN
greater than 32°F?
No
RAIN is treated
as SNOW and
stays on ground
Yes
92$ EXCS as RUNOFF
8i EXCS as EMRNF
Normal Entry
RUNOFF, SWMELT,
EMRNF equal to
zero
Enter Data
RAIN, TMEAN
RTIME, PWHC
FADD = f(TMEAN)
WOVERW = PWATER/PWHC
EFF =
PWATER/PWHC
±
ADD = f(FADD, WOVERW)
Can EVAP
PEVAP =
(PEVAP/30)*EFF
If TMEAN is greater than 32°F
0.1 inch of SWMELT for every
degree day
T
Soil Layer Water Balance:
PWATER = PWATER + RAIN + SWMELT + EMRNF - ADD - PEVAP - RUNOFF
Transfer ADD to TANK
Relate HEAD to TANK:
HEAD = f (TANK)
FLOW = CONFH * HEAD
±
DSLV = f(FLOW)
Return to MAIN program
Figure 15 - Flow Chart of Subroutine REMOVE
61
-------
estimate of oxidation products stored in the system from previous oxi-
dation. That is to say, we are breaking into a "steady state" system,
and the steady state point is nonzero in value.
To obtain initial storage values, the computer program was allowed to
run for a simulated period of three years of oxidation and removal.
The oxidation rates were based on 21 per cent oxygen level in the mined-
out volume since prior to the start of the observation period, McDaniels
Mine had been open to the atmosphere. The final storage values,
STORE(l,J,K), were then punched out on standard computer cards in a
format suitable for reading-in as data. Once the initial conditions
have been established, the simulated daily mine behavior can be calcu-
lated.
The second section of the program, which does the day-to-day simulation,
will be described in terms of a typical run. The first step in the
simulation is the reading of meteorological data. The date, the inches
of precipitation, hours of duration of precipitation, mean daily temper-
ature, and oxygen concentration at the air-solid interface are the input
data. The program is written in such a manner that only positive infor-
mation such as precipitation or changes in the temperature or oxygen
level need be read in. The input data are examined to determine if any
conditions have changed, and the amount of precipitation is recorded.
The subroutine "DAYS" is called to determine the number of days, LTHETA,
since the previous data input. The program is run on the condition that
precipitation occurs only on the LTHETA day--whether this is one day or
one month from the previous precipitation. The program performs the
following set of calculations for each day. The computer variables
introduced in this section are summarized in Table 2.
1. The subroutine "REMOVE" is called. This routine, de-
scribed later in more detail, calculates the ground flow
and the quantity of water in underground storage. The
factor DSLV, the fraction of stored products removed
each day by leaching, is also returned by "REMOVE."
2. The position of the water table in relation to the coal
seam is calculated from Eq. (22).
Steps 1 and 2 have furnished numerical information for calculating
product removal rates. The next steps are performed iteratively over
the computer, array of oxidation storage volumes, STORE(l,J,K), for all
volumes above the water table. For inundated volumes, the program
skips to Step 7.
3- The oxygen mole fraction, XNN, in the void volume is
determined using the oxygen gradient equation [Eq. (?)]•
The total volume of the block, DVOL, is calculated.
The oxidation, as pounds of oxygen consumed per day, is
determined.
62
-------
U. The quantity of products removed by leaching, AOUT, is
calculated using Eq. (20).
5. The gravity diffusion in, GRAVIN, and out, GRAVOT, are
computed using Eqs. (18) and (19).
6. The terms calculated in Steps 3? ^» and 5 are summed to
obtain the change in product storage. The program then
skips to Step 8.
7. The quantity of products removed from an inundated
volume is obtained from Eq. (23). Since there is no
oxidation in inundated volumes, the new storage quan-
tity is calculated simply by subtracting the quantity
removed from the product storage value.
8. The quantity of acid removed from each storage volume
is added to the running total, TACID, of acid removed.
In addition, sub-totals of the amount of acid removed by
each mechanism are also kept.
After the calculations have been performed for all of the volumes of
the STORE(l,J,K) array, the results are prepared for output.
9. The acid load, TACID, is converted from an oxygen consump-
tion to a "total acid" basis by multiplying by 200/112.
This is the stoichiometric ratio of 2 H2S04 to 7/2 02
when acidity is expressed as the calcium carbonate
(CaC03) equivalent.
10. The acid load is then corrected for the influence of
alkalinity in the entering ground water. A value of
20 ppm alkalinity has been used for the McDaniels Mine.
11. The daily acid load is added to the cumulative monthly,
YSUMA, and annual YSUM, acid load totals. Similarly,
monthly totals of removal by gravity diffusion, GSUM,
inundation, FSUM, and leaching, ASUM, are also accumulated.
12. The daily flow, acid load, and precipitation are printed.
At the end of each month, a summary including flow, total
acid load, inches of water entering underground storage,
and the acid removed by each mechanism is printed.
13- Similarly, annual or quarterly summaries may be printed.
The sample program in Appendix C shows monthly and
annual summaries.
Once the calculations have been performed for one day, the program
repeats Steps 1 through 12 LTHETA times. On the LTHETA day, the call
63
-------
of the "REMOVE" subroutine includes the amount of precipitation.
"REMOVE" performs all calculations involving rainfall and ground water
flows.
Several subroutines have been written to assist the main program. The
subprograms were written for either of two reasons. First, some routines
are of general use so it is convenient to be able to move them from one
main program to another. Second, each subroutine is compiled independ-
ently. This feature can greatly simplify "debugging" and identification
of errors in the program. Errors can be corrected immediately rather
than propagating and giving false error messages in unrelated portions
of the program.
The subroutine "DAYS" determines the number of days between two consecu-
tive data inputs. The name of the month and the date are read into the
routine which compares the name of the month with the name of the month
from the preceding input. If the names of the months are the same, the
routine obtains the difference of the two dates and returns this as the
elapsed time, LTHETA. If the months are different, the routine deter-
mines the number of days in the preceding month from an internal data
table. The old date is subtracted from the month length. The difference
is added to the new date to give LTHETA. The "DAYS" subroutine simpli-
fies data input since only positive information or changes in conditions
need be read because the time between changes can be computed. "DAYS"
is a general routine that can be transferred from program to program.
The subroutine "EVAP" determines the potential evapotranspiration at
the McDaniels Test Mine. Monthly evapotranspiration rates have been
calculated according to the Thornthwaite and Mather^ technique. These
values are read into the main program as data and transferred to the
subroutine through a common statement. The call to the subroutine
includes the name of the month. "EVAP" finds the evapotranspiration
rate corresponding to the month from an internal data table, and re-
turns this value to the calling program. This routine can be used for
other sites if the appropriate evapotranspiration rates are calculated
or measured and supplied to the program.
Subroutine REMOVE
The major subroutine is "REMOVE," which has been written to calculate
drainage flow rates. The program also determines the fraction of stored
products to be removed each day by leaching.
On the first call of "REMOVE," initial conditions are established. An
estimate of TANK is made and the program allowed to run for 3 to 5 years
to obtain an initial value of TANK. On each succeeding call, the
following operations are performed:
1. Daily potential evapotranspiration is determined. The
monthly maximum evapotranspiration is obtained by calling
-------
"EVAP." This value is converted to a daily value by
dividing by the days per month. The daily value is
reduced according to the moisture content of the soil
layer.
2. The water deficiency in root storage, DEFICIT = PWHC - FWATER,
is calculated.
3- The Soil Layer Water Balance is made:
A. If there has been rainfall or snow melting for the
day, the precipitation (RAIN) is compared to DEFICT.
If RAIN is greater than DEFICT, 92$ of the excess
rain (EXCESS) goes to runoff; the remainder to the
soil layer (EMRNF). If RAIN is less than DEFICT,
all precipitation enters soil layer.
B. The mobility of water in the soil layer, as denoted
by FADD, is determined from the mean temperature for
the day (see Appendix E).
C. The ratio of water in the soil layer to the saturated
water content (PWATER/PWHC = WOVERW) is calculated.
D. ADD, the water leaving the soil layer to aquifer
storage (TANK), is calculated as a function of FADD
and WOVERW [Eq. (2?a) and (27b), Appendix E].
E. The new value for PWATER is calculated from the
water balance on the soil layer [Eq. (l6)].
k. The new daily value for aquifer storage (TANK) is deter-
mined as the addition of ADD minus the loss from storage
due to flow from the mine (FLOW).
5. DSLV, the fraction of stored products removed by leaching
is then calculated using Eq. (21).
-------
SECTION VIII
VERIFICATION OF MODEL
The validity of the model can be evaluated by using the model to simu-
late mine drainage behavior for a period during which there are natural
data. Such a comparison has been made for the McDaniels Test Mine, the
auger holes, and the Decker No. 3 mine.5'2'
The computer program was run using the physical description of the mines
and meteorological data as inputs. The experimental variations of
oxygen in the mine atmosphere were also included in the data. The out-
put from the program was the daily drainage, in gallons, and the acid
load, in pounds. In addition, monthly and annual totals of drainage
and acid load were printed.
The day-by-day predictions of the model have been graphically compared
with the natural observations. The drainage flow rates are shown in
Figs. 16-22, and the acid loads are compared in Figs. 23-29- A hydro-
logic year beginning with the October dry season has been used as the
time basis. This choice simplifies visualization of the cyclic nature
of acid mine drainage rates.
The data in Figs. 16-29 show the capability of the model to predict the
sharp peaks of drainage and acid load in the spring of each year. Like-
wise, the figures show the steady decline of flow rates through the
summer and fall. The success of the model in predicting short-term
variations has fulfilled a major objective of this investigation. Such
a short-term response is necessary if the model is to be used to predict
peak loads for use in the design of treatment facilities. Similarly,
the operation of existing treatment plants may require knowledge of
when peak acid loads will occur.
While the agreement of predicted and observed short-term data is desir-
able, the validity of the model in the general case may depend more on
the long range predictions. Tables 3-8 summarize the monthly and annual
(on a calendar year basis) drainage flows and acid loads. In these
tables it can be seen that monthly predictions are generally within 20
per cent of the measured rates, and that annual values agree within 5
per cent. The goodness of fit of long-term data is important since
there were large year-to-year variations in acid load because of the
variation of oxygen levels in the mine atmosphere.
The practical significance of the agreement of long-range predictions
and observations is that for unmanned treatment facilities in isolated
areas, the model could be used to estimate the quantity of treatment
chemicals which must be available. The model can also estimate how
often the chemicals must be replenished.
67
-------
ON
CD
Figure 16 - Drainage Flow for McDaniels Test Mine
-------
:97i
1969
Figure 17 - Drainage Flow for Auger Hole #1
-------
-
a PR
OCT
1969
1970
OCT
Figure 18 - Drainage Flow for Auger Hole #3
-------
70Or
•<
600
500
300
aoo
x
LEGEND
MEASURED
PREDICTED
Figure 19 - Drainage Flow for Auger Hole
-------
TOO
600
I 50°
g «00
I
i joo
20O -
IOO -
LEGEND
• MEASURED
• PREDICTED
1969
it
APS
OCT
JJLY
OCT
1970
Figure 20 - Drainage Flow for Auger Hole #5
-------
70O,-
600
- 500
g400
S 300
j
E
200
ICO
LEGEND
MEASURED
PREDICTED
J 1 1 L
J L
OCT
JAN
APR
1969
JULY
1970
OCT
JAN
APR
1971
JULY
OCT
JAN
Figure 21 - Drainage Flow for Auger Hole
-------
g 400
o
*
LEGEND
— MEASURED
— PREDICTED
JAN
APR
JULY
OCT
Figure 22 - Drainage Flow for Decker #3 Mine (196k)
-------
Figure 23 - Acid Load for McDaniels Test Mine
-------
2.0,
LEGEND
MFIAiuREO
\A'WA - •'' /.
vv^ Kjy..^
1970
APR
JULY
1970
• -^ J
OCT
JAN
t
APR JULY
1971
OC"
JAfi
Figure 2k - Acid Load for Auger Hole
-------
2.0 r
•:
o
8 08
0.4
OC7
1969
LEGEND
MEASURED
PREDICTED
JAN
Figure 25 - Acid Load for Auger Hole #3
-------
-
16
I
CO 1.2
_J
.
o 0.8
c
0.4
OCT
1969
LEGEND
-MEASURED
• PREDICTED
JAN
- -
JULY
1970
OCT
JAN
APR
JULY
OCT
JAN
1971
Figure 26 - Acid Load for Auger Hole
-------
2.0
-
;
:
: e
1969
LEGEND
MEASURED
PREDICTED
Figure 27 - Acid Load for Auger Hole #5
-------
20 r
.
LEGCMD
I96S
Figure 28 - Acid Load for Auger Hole
-------
LEGEND
•MEASURED
PREDICTED
JAN
APR
JULY
OCT
Figure 29 - Acid. Load for Decker #3 Mine (1964)
-------
TAHLE 3
DRAINAGE FLOW RATES FOR i-KBANIELS TEST
1967
January
February
March
April
CO
ro
June
July
August
September
October
November
December
Total
Actual
6,510
6,300
8,700
11,250
13,800
12,150
7,500
6,150
5,700
5,400
5,250
5,400
94,110
Predicted
6
4
8
11
12
11
7
6
4
5
6
5
90
,473
,910
,049
,766
,506
,857
,953
,004
,264
,163
,163
,181
,289
1968
Actual
7,560
6,090
7,510
10,350
16,300
8,610
8,700
8,500
7,000
6,360
5,670
6,550
99,000
Predicted
5,256
6,685
7,986
12,077
15,673
16,982
10,1*5
9,03^
7,679
6,931
6,488
7,095
112,031
1969 1
Actual
6,780
7,200
6,920
11,250
12,000
9,030
8,100
7,240
5,730
5,680
5,520
5,400
89,000
Predicted
6,669
6,500
6,602
8,1^5-5
9,493
8,763
8,253
6,477
5,101
5,816
5,443
88,397
Actual
5,850
6,100
9,000
9,570
11,730
9,500
8,740
7,690
7,290
6,940
8,100
9,300
99,000
970
Predicted
4,921
4,734
6,5^4
9,819
10,371
9,600
8,628
8,cC6
7,556
8,o5o
9,850
9,219
98,9:5
1971
Actual
8;250
10,500
12,450
10 , 500
13 , 500
9,900
G QQQ
8,250
7,500
6,900
7,200*
7,3CO
97,550
Predicted
9-09-i
7,834
10,592
9,905
8,266
7,757
i" f~-1' \
' ) >"- ^
3,05:
7,lv°
-
-
86,505
* Not included in the annual total.
-------
TABLE It
DRAINAGE FLOW RATES FOR AUGER HOLES 1, 3, ^, 5, 6
1970
January
February
March
April
Kay
June
CD
CO
July
August
September
October
November
December
Total
Aueer
Actual
6,oii+
5,376
10,912
10,050
8,71+2
3,690
3,069
l*,06l
2,970
i+,876
5^30
10,509
75,690
Hole #1
Predicted
U,32l+
7,262
9,975
13,535
6,507
U,ll*8
3,263
l*,8l*8
2,29!+
3,762
6,039
12,73^
78,690
Auger Hole #3
Actual Predicted
2,325
5,208
9,556
10,11+0
-
3,750
2,139,
2,9LU
1,290
1,1*51+
3,570
It, 526
1+6,875
3,071+
p.039
8,023
10,097
1+.622*
3,010
1,932
2,555
1,676
2,829
^05
k,55k
1*7,255
Aurer Hole //U
Actual Predicted
2,211 2,
*+,890 U,
6,060 5
8,130 7
3
1,350 1
2,1*1*9 2
1,1+10 1
1,550 2
2,1+60 3
3,689 3
38,309 36
,217
,326
,822
,781
,2U1*
,580
,505
,M5
,188
,1*05
,521
,981*
Auger Hole /f;5
Actual
775
810
1,115
1,200
-
1,235
868
930
750
1,21*0
865
1,155
10,9^3
Predicted
1,156
1,021*
1,613
2,100
1,132*
686
1*12
729
301
6oU
91+1
938
10,502
Auger
Ac-
2
5
10
11
9
5
9
3
k
i*
1*
Lusl
,601*
,208
,788
,1*30
-
,690
,177
,393
,5^0
,1+33
,020
,260
70,5^3
Hole £6
Predicted
3,952
6,392
10,81*8
l1*, 139
7,700*
6,523
3,500
1+.251+
2,925
3,31*1
6,095
6,3H
68,276
-------
TABLE k - (Continued)
Auner Hole #1
1971
January
February
March
April
May
June
July
August
September
October
Kov caber
Decer-ber
Total
Actual
- 7,099
10,892
8,184
4,020
11,556
2,670
2,278
3,450
2,550
2,250
2,250*
3,780*
56,379
Predicted
4,479
10,407
13,301
4,583
9,077
2,126
2,449
3,991
4,688
2,480
-
-
57,582
Auger Hole =3
Actual Predicted
7,595
9,300
15,640
4,440
8,928
1,950
11519
1,612
1,200
900
930*
1,950*
53,08.':
3,132
8,933
8,767
3,014
6,753
1,534
1,578
1,822
2,499
1,915
-
-
39,964
Auger 1
iiole #4
Actual Predicted
6,107
8,624
5,208
3,150
6,913
2,760
1,426
1,395
1,050
1,110
750*
1,200*
37,743
2,415
6,965
6,7^5
2,376
5,159
1,256
1,257
1,852
1,892
1,567
-
-
31,481
Auger Hole #5
Actual Predicted
1,630
1,180
1,366
1,080
1,085
960
750
735
750
720
600*
450*
10,256
1,265
1,3&9
2,149
807
1,370
342
3r r
OO
601
555
394
-
-
9,219
Auger 1
Hole £6
Actual Predicted
11,191
9,100
11,191
10,500
11,501
7,920
4,154
3,534
2,520
2,100
1,650*
2,250*
63,711
5,208
9,533
14,652
5,839
8,849
3,387
2,996
3,594
3,608
3,120
-
-
60,786
* Not included in the anr.uaQ. total; units are in gallons.
-------
TABLE 5
DRAINAGE FLOW FOR DECKER #3 MINE
1964
January
February
March
April
May
June
July
August
September
October
November
December
Total
Actual
(gal/1440)
1,856
1,305
6,591
5,39^
2,588
901
706
642
1+38
293
24l
1,547
22,502
Actual
(gal/1440)
1,626
1,761
8,248
5,642
2,099
1,279
1,558
1,597
519
287
346
1,974
29,287
85
-------
TABLE 6
ACID LOAD FOR MCDANIELS TEST MINE*
1Q67
January
February
March
April
Kay
June
July
August
September
October
TJov ember
December
Total
Actual
4.5
7.6
13.8
12.6
11.2
7-5
4.2
2.U
2.3
3-0
4.2
4.3
77-6
Predicted
4.0
5.2
8.6
13-7
15-0
8.5
U.U
4.2
4.5
5.7
5-9
5-2
8^.9
1968
Actual
5-7
9-5
12.6
23.0
39.5
16.8
12.4
11. U
7-2
5.5
4.8
5.4
154.0
Predicted
6.3
9.9
15-6
28.9
39-8
42.7
11.3
10. U
6.6
6.4
5-4
4. 6
187.9
1969
Actual
7.9
12.7
9-7
25.4
20.7
10.2
6.7
5-0
3.2
3-4
2.8
2.5
112. 0
Predicted
6'.0
8.8
12. U
18.3
23-9
1^.7
12.1
9-8
5.8
U.9
U.I
3.U
12U.2
1970
Actual
3-1
5-2
8.5
12.5
lU.9
7.7
5-1
5-0
3-7
3-9
lt.1
6-9
80.6
Predicted
U.2
5.4
8.7
14.9
17.2
9-3
7.5
6.5
3.7
3.8
3.9
2.5
88.0
1971
Actual
6.1
7.0
8.7
5.4
11.4
5-3
5-7
4.1
2.4
2.1
1.5**
1.1**
58.2
Predicted
3--0
4.3
8.3
9-2
9.8
5-6
4.8
4.9
3-1
2.8
-
-
56.0
* Units are in pounds.
t included in the annual total.
-------
oo
TABLE 7
ACID LOAD FOR AUGER HOLES 1, 3, U, 5, 6*
1970
January
February
March
April
May .
June
July
August
September
October
November
December
Total
Auger
Actual
5.1
6.3
12.0
12.1
16.2
8.3:
3.7
6.3
5-1
U.5
U.8
lU.l
98.5
Hole gL
Predicted
2.6
6.9
10.3
12.1
5.1'
2.7
2.6
U.I
3-0
U.I
7.U
2UVB
85.0
Auger
Actual
U.2
22.9
19-5
11.1
-
3-3
1.6 .
5.U
1.5
1.5
5.U
8.U
8U.8
Hole ,#3
Predicted
5-9
8-3
17-3
22. U
5.U**
2.8
1.6
2.7
1.7
3.1
5.1
U.8
75.3
Aus-er
Actual
2.1
lU.9
9-0
11.2
-
2.U
1.5
3.0
1.8
1.5
3.0
6.0
56. U
Hole Jih
Predicted
2.7
7-0
9-3
10.9
3.8**
2.1
1-7
2.8
1.8
2.6
U.U
U.8
50. 1
Auger
Actual
1.2
1.8
2.7
3-3
-
2.7
1.5
2.U
2.2
2.U
1.5
2.7
2UA .
Kcle -;~5
^red^cted
2.0
1.5
1-5
1.6
1.1**
1.0
1.0
1-5
1.2
1.7
2.0
1.7
16,5
A^p-
Actual
U.5
21.0
39-5
-
-
-
10.5
20.3
11-7
9.6
11.7
17.1
155-9
Hole 4J6
•pT-p^-; fc^d
15.8
lU.3
2U.1
25.2**
17.0**
13-7**
8.5
ll.l
8.8
10.6
17.9
17-3
128.9
-------
TABLE 7 - (Continued)
Auger Hole #1
1971
January
February
March
April
May
CD
CD
June
July
August
September
October
November
December
Total
Actual Predicted
9-0
11.7
7.8
3.0
7-8
2.0
2.0
3-0
2.7
2.1
1.9**
3.0**
51.1
6.4
10.5
22.0
6.4
16.6
3-9
3-6
5-9
6.7
4.9
-
-
87.0
Auger Hole #3
Actual Predicted
13.8
18.3
24.0
3-6
15.6
1.5
1.2
2.4
1.5
0.6
0.5**
4.2**
82.5
3-4
17.1
22.7
3.5
15-5
2.2
1.8
2.3
4.5
2-9
-
-
76.0
Auger
Actual
10.5
6.9
5.1
3.0
5-4
1.5
0.8
0-9
0.8
0.7
0.9**
3.0**
35.6
Hole #4
Predicted
3.5
13-7
17-3
4.3
11-3
2.5
2.2
3-2
3.4
3-0 .
-
-
64.0
Auger
Actual
5-7
3-9
3-0
1.9
2.7
1-9
1.5
2.1
4.0
2.1
2.1**
2.2**
28.8
Hole #5
Predicted
2.0
2.3
4.0
2.0
2.7
1.8
1-9
2.6
2.7
2-3
-
-
24.0
Auger r
Actual ]
33-6
27.6
23-3
16.0
27-9
17.1
12.6
12.0
9-0
6.3
3.2**
5.4**
187.4
tele £6
/redic.ed
15.6
19-5
36.0
18.6
24.6
11.9
10.0
14.1
13-5
11.5
-
-
175-0
x Units are in pounds.
**Not included in the annual total.
-------
TABLE 8
ACID LOAD FOR DECKER #3 MINE
196^
January
February
March
April
May
June
July
August
September
October
November
December
Total
Actual
(Ib)
10,793
H,kk2
58,360
39,672
15,300
5,076
3,802
3,5^5
2,797
1,973
1,800
3,399
167,959
Predicted
(Ib)
7,^28
10, 21k
111,036
U6,298
15,^85
33,181
^,373
5,^2
2,933
2,389
2,6UO
8,5^6
219,900
-------
A word of warning should, be issued before the model is strongly praised
or condemned for the level of agreement with the natural data. The
natural measurements are based on flow samples collected once or twice
each week. Obviously, the reliability or the comparison would be
improved if sampling frequency were increased.
When the acid removal was discussed in Section VI, the description of
three different removal mechanisms was emphasized. The importance of
each of these mechanisms in the actual simulation is shown in Table 9«
The annual acid loads are compared with the quantity of acid removed
by each method. (The annual totals in Table 9 are less than the sums
of the three separate rates since only the total includes the influence
of alkalinity in the ground water. For the case of 20 ppm alkalinity
in the water, the acid reduction is about 1? Ib/year for 100,000 gallons
of flow.)
TABLE 9
COMPARISON OF ACID REMOVAL RATES
McDaniels
Test Mine
Auger Hole #1
Auger Hole #3
Auger Hole #U
Auger Hole #5
Auger Hole #6
Acid
Leaching
(lb/yr)
65.7
Ul.2
38. If
33-9
11.1
158.8
Removal Mechanism
Gravity
Flooding Diffusion
(lb/yr) (lb/yr)
6.3
Il7.il
U9.8
2^.1
6.1
26.6
31-9
11.9
1.5
3.1
2,7
13-7
Leaching removal is the most important mechanism, contributing about
50 per cent of the acid load. Inundation removal is responsible for
20 per cent of the acid, and the remainder is removed by gravity
diffusion. As would be expected from the description of the mechanisms,
gravity diffusion fluctuated less from year to year than did the leaching
and inundation removal rates. The diffusion is independent of the
quantity and frequency of precipitation which serves as the driving
force for the other mechanisms. The relative uniformity, or lack
thereof, may be seen in more detail by examining the sample output for
90
-------
1970 shown in Appendix C. For all months, gravity diffusion is always
two or three pounds while leaching and inundation removal have sharp
peaks in the spring. The rest of the year inundation removal virtually
ceases, and leaching removal is at about the same level as gravity
diffusion with occasional peaks corresponding to rainy periods. Simu-
lation data for other years also show this pattern. There are even
greater peaks in the inundation and leaching rates for the very high
acid load year, 1968.
-------
SECTION IX
UTILIZATION OF MODEL
Although a model capable of describing past events at a drift mine has
been developed, the actual objective of this investigation, namely to
make predictions, must still be accomplished. The use of the model of
a drift mine for prognosticating falls into two areas; i.e.,
1. prediction of what will happen under different conditions
at McDaniels Test Mine, and
2. showing how the model may be generalized for use with
other pyritic systems.
PREDICTIONS
The best test of any model is how well it can foretell what will happen
when perturbations are imposed on the system in question. For a drift
mine, the perturbation of most interest is the exclusion of oxygen from
the atmosphere. McDaniels Test Mine has been under a positive pressure
of nitrogen for more than two years. The oxygen level in the mined-out
volume has been reduced to less than one per cent, and the acid loads
from the mine have started to decrease. The question to be answered,
or predicted, is how long flow from the mine will remain acidic. The
answer is "probably a very long time" if one considers that oxygen
dissolved in water will continue to enter the mine. Practically speak-
ing, there is very little oxidation occurring, so the real prediction
is how rapidly stored products will be removed.
The product removal rate in the model has been related to the infiltra-
tion of water from the surface of the ground. The rate of infiltration
in turn is dependent on the level of precipitation. Therefore, a number
of predictions are possible depending on the estimate of precipitation.
The best source of precipitation data is meteorological records from
previous years. During the 1965 - 1970 period, the rainfall in south-
eastern Ohio ranged from 30 to 1+5 inches per year. In 1968 there were
1*5 inches of rain including nearly 13 inches in May. In 196? and 1969*
precipitation totaled only 30 inches. Since the annual average rainfall
is about 38 inches in the region, the 30- and ^5-inch years probably
represent extremes. Therefore, duplicates of 1968 and 1969 will be
used as sample data for wet and dry years. The prime reason for using
existing rainfall data for generating predictions is to ensure that the
natural pattern of storms and dry spells is included. Another reason
for using the existing data is that the program requires temperature
data, and these are already available in the data decks for preceding
years.
Two sets of predictions have been undertaken. The more important one
is determining what will happen if the low oxygen level is maintained
93
-------
in McDaniels Mine. The second set investigates the effect of imposing
changes on the system at different points in the hydrological year.
The initial product storage and hydrologic conditions for the predic-
tions were established by allowing the program to run through the normal
196? - 1970 simulation.
The prediction of what will happen if the current low oxygen level is
maintained will be useful in evaluating the nitrogen addition experiment
of Smith and Shumate.37 On the basis of an observed decrease in acid
load of 30 per cent during 1970, acid loads should be reaching a very
low level within two years. To check this hypothesis, the simulation
of two years at McDaniels Mine has been run for cases of above and
below average rainfall. These cases bracket the expected precipitation
and removal rates and give the range of times that will be required to
achieve a desired minimum acid load level.
The results for the two cases are remarkably similar. About 35 pounds
of acid removal were predicted for 1971 and about 20 pounds for 1972
in each case. Since the results are identical, only the predictions
for the high rainfall case are shown in Pig. 20. The expectation of
a substantially higher rate for the wet year was based on the high acid
loads in 1968, which included a period when oxygen was being injected
into McDaniels Mine.
The breaks in the curve in Fig. 20 indicate periods when the program
predicts alkaline drainage from McDaniels Mine. The actual fulfillment
of this predictions depend on the validity of the estimate that ground
water entering the mine contains 20 ppm alkalinity. Also to be verified
at some point in the future is the tacit assumption that no acid is
diffusing into or otherwise entering the drainage from outside the
stated boundaries of the system. Whether or not the observed drainage
ever becomes alkaline at McDaniels Mine, the acid load should be down
to 20 or 25 Ib/year by 1972. On a concentration basis, this is about
20 ppm acidity in the drainage.
In the second simulation experiment the effects of the timing of changes
in the concentration of oxygen in the mine atmosphere were studied.
The situation that has been studied assumes that the oxygen level at
the McDaniels Mine was returned to 21 per cent as in normal air. Two
cases have been examined:
1. The oxygen level was raised on January 1, 1971. In this
case the change immediately precedes the wettest part of
the year.
2. The oxygen level was raised on July 1, 1971. In this
case the change follows the rainy season.
For this experiment, the average rainfall year, 1970, was used as the
data source.
-------
vo
VJl
1.6
o
Q
T3
C
O
Q.
TJ
O
O
0.8
T3
"o 0.4
Oct.
1970
End of Rainfall Data
Essentially Alkaline
Jan
Apr.
July
Oct
Jan
Apr
July
1971
1972
Figure 20 - Acid Load Predictions for 1971 and 1972 Using 1968 Rainfall Data
-------
The results of this experiment are shown in Fig. 21. For Case 1, where
the oxygen level was changed in January, there is a rapid system re-
sponse in terms of increased acid load. The curve plotted for Case 2
during the first half of 1971 represents the acid load if the nitrogen
addition had been continued during that period. For Case 2, the re-
sponse to increased oxygen levels appears more slowly. However, if the
Case 2 curve in Fig. 21 is compared with the continued addition curve
in Fig. 20, it is apparent that there are slight increases in acid load
even when the reintroduction of oxygen into the mine was done during
the dry season. Significant increases in acid load for Case 2 do not
appear until the wet spell in late December.
In the second year of the simulation, differences in acid load for the
two cases become smaller. However, the fact that differences in acid
load still exist a year after oxygen was restored to the mine atmosphere
can be taken as evidence of the slowness of the time response of the
system. This delay in change of drainage composition is in accord with
the observations of Smith and Shumate37 in the natural laboratory study.
They had estimated lag times for McDaniels Mine in the range from six
months to one year.
The simulation experiments that have been run are examples of tests
that can be performed with this model. Other investigations could in-
clude the use of zero-order oxidation rate (oxygen concentration inde-
pendent) or evaluating the effects of "leakages" of oxygen into the
mine through the over-burden. The most important use of the model still
to be described is the application to other pyritic systems. This topic
will be discussed in the following section.
GENERALIZATION OF MODEL
A model has been developed which well describes the flow of acidic mine
drainage from a specific drift mine. This model includes physical,
chemical, hydrological, and meteorological features of the mine environs.
To convert this specific model to a general model of pyritic systems,
two levels of generality must be considered. The first level is that
of geometric similarity to other drift mines. At this level, our model
is virtually a general model. The second level of generality is chemi-
cal similarity to any other system containing oxidizable pyrite, such
as refuse piles or auger holes. At this level, the spatial configura-
tion is different and limits the use of coordinate based features of
the drift mine model, to say nothing of possible mechanistic differences.
Geometric Similarity
The utilization of the model in cases of geometric similarity can be
considered in terms of the underlying assumptions and input data re-
quirements for the two parts of the model—oxidation and product removal.
The oxidation model requires physical and chemical information about the*
mine. Physical data include the length of the exposed coal face, the
96
-------
2.0
1.6
1.2
*
§
T3
c
r>
o
Q_
"g 0.8
o
0.4
LEGEND
Jan I, 1971
July I, 1971
Jan
May
Aug
Oct.
Jan.
1971
April July
1972
Oct.
Figure 21 - Effect of Tim-ing of Increase of Oxygen Level on Acid Load
Predictions for 1971 and 1972
-------
number and thickness of coal and shale layers in the seam, and the
porosity of the pyrite-containing strata. Chemical data include pyrite
reactivity and oxygen concentration in the mined-out volume. If the
required information is not available, certain approximations can be
made. For example, in a mine containing only open rooms, the perimeter
of the mine cavity can be used to estimate the length of exposed coal
face. If the mine contains pillars or passageways, the surfaces of
these must be considered as part of the exposed area. The perimeter
of a pillar could be used as a measure of the exposed length, but it
must be remembered that the volume-to-surface ratio is lower for a
pillar than for a wall. Hence, there will be fewer oxidation products
formed per unit area of pillar than for the same area of regular wall.
Using the length of exposed coal face is based on the assumption of a
uniform atmosphere in the mined-out volume. The computer program has
been written to handle varying conditions along the exposed surface
(this is the "I" direction), but the time required for computer calcu-
lations increases linearly with each increment of change in conditions
along the surface.
In the absence of porosity and reactivity data, oxidation rate data of
the type that Larez18 reported may be used. In fact, the computer pro-
gram for this model has been written under the assumption that such
data will be used.
Actual data are required to describe the number and thickness of coal
and shale layers in the seam. Finally, there must be an estimate of
the bulk oxygen concentration in the mine. Starting with the bulk
oxygen level and reactivity data, the oxygen gradients within the
strata can be calculated using Eq. (?)•
The rate of removal is determined as the sum of the rates of removal by
three mechanisms. The usefulness of this part of the model in the
general case must be evaluated in terms of the suitability of each
mechanism.
The dependence of the gravity diffusion rate on the concentration of
stored products is fundamental to the definition of diffusion. The
value, DIFFG(J), used for the fraction of products moved daily by
gravity diffusion, was chosen on the basis of experimental observation
and by correlation of acid loads under low water flow conditions at
McDaniels Mine. The fact that two independent evaluation techniques
yielding similar values of the gravity diffusion coefficient indicate
that the value could have general applicability.
The leaching removal mechanism has been related to the trickling of
water downward from the surface after precipitation. The validity of
this mechanism in the general case depends largely on the strata over-
laying the coal seam. If there is an impervious layer which blocks the
percolation, no water is available for leaching. Where there is a
highly fractured sandstone overburden, as at McDaniels Mine, percolation
98
-------
is rapid, and leaching is an important removal mechanism. Since there
are very few totally impermeable formations, leaching removal will
occur in most mines. The overburden will influence the time delay
between precipitation and observed changes in the leaching rate. The
constants in the model derived from McDaniels data represent a time
delay of two to four days depending on the wetness of the soil. For
overburden less permeable than fractured sandstone, the time delay will
be greater and the observed response will be flatter; that is, there
will be no sharp increases in acid load after a storm.
Products can be removed only by inundation if the coal seam lies in the
range of movement of the water table. Evaluation of this removal mecha-
nism for different sites requires information about the location of the
pyritic material relative to the water table.
In general, the removal rates depend on underground water movement.
The calculation of water flow variations in our model is based on
fundamental information such as infiltration capacity, potential evapo-
transpiration, and meteorological data. A number of techniques have
been described for determining infiltration capacity.11 Thornthwaite
and Mather42 have presented a method to estimate potential evapotrans-
piration if the latitude and vegetative cover are known for the site
in question. Monthly summaries of weather data are published by the
Environmental Data Service.9 From the fundamental information, the
day-to-day flow variations can be predicted.
Precipitation falling as snow is treated as being delayed until tempera-
tures above freezing occur. The rate at which the snow melts is propor-
tional to the number of degrees above freezing.44 The melted snow is
treated as an equivalent amount of rainfall as far as flow rate calcu-
lations are concerned. This way of computing snow melt is based on the
assumption that in the McDaniels Mine area, southeastern Ohio, snow
melts throughout the winter rather than accumulating to great depth,
and then melting in the spring. Depending on the type of winter, other
techniques have been described for calculating snow melt runoff rates.
However, the actual estimate of water flow is usually obtained by cor-
relation of data for each site.44
Finally to use this model, the investigator must obtain an estimate of
the "water shed" area of the mine being studied, as described in Appendix
E. This value controls the magnitude of flow predictions, but has no
influence on the rate of product removal or formation. The area does
influence the concentration of acidity in the drainage. The concentra-
tion of acid is an important biological consideration.
Summary of Data Requirements
The basic information required to use our oxidation and removal model
for another drift mine includes the following items:
99
-------
1. Prevailing oxygen concentration in mined-out volume
2. Number and thickness of coal and shale layers in seam
3. Rate constants and porosity of each layer
h. Area of air-solid interface
5. Meteorological data
6. "Water shed" area of mine
7. Position of mine relative to water table; or preferably,
flow and acid load data during high and low flow periods.
These data can be plugged into the model and calculations made using
the procedures described in Appendix E. It is not unreasonable to
expect the model to estimate annual acid loads to within ± 15$ of the
true value when flow and acid load data are available. The monthly
predictions would be less reliable on a percentage basis.
Refuse Pile
The following discussion of a refuse pile draws extensively on the work
of Good13 at the New Kathleen pile of Truax-Traer. The oxidation in
the refuse pile occurs in a zone about 10 inches thick at the surface
of the pile instead of extending as much as 50 feet into the binder as
in a coal seam.35 A clay mantle which blocks oxygen transport is the
stated reason for the limited reaction zone. However, the concentration
of pyrite is so great in the refuse that it is entirely possible that
the oxygen gradient goes to zero in this short distance. If data on
the bulk porosity of the refuse and the pyritic content were known, the
oxygen gradient could be calculated using the exponential expression,
XGO = Xconexp[-(kR/D)'/2Z], developed for coal and shale binders. However,
Good has presented rate information on the basis of pounds of acid
formed per day per acre of refuse pile area. On a smaller scale, Brown115
took samples from the New Kathleen pile and obtained laboratory scale
oxidation rates. Since the laboratory conditions are well defined,
Brown's data can be used to estimate a rate constant for the exponential
gradient calculation. Brown's laboratory rates check Good's field data
quite well.
While there is a similarity in the area of oxidation between refuse
piles and drift mines, major differences arise in the removal mechanisms.
In drift mines, underground water flows are responsible for continuous
removal of oxidation products. In refuse piles, oxidation occurs, for
the most part, above the level of ground water flows. A fourth removal
mechanism, physically impossible underground, becomes dominant. This
is the direct washing by precipitation on the refuse pile. This is
analogous to the underground leaching by trickling water. The rain
100
-------
water washing mechanism is efficient since the water, uncontaminated
by acid, contacts a region of high product concentration, and the
resultant acidic solution quickly flows away by gravity. The key
point brought out by Good13 and Corbett10 is that not all of this
acidic solution immediately runs off into receiving streams. Instead,
a fraction of from 15 to 30 per cent of the drainage flows into the
pile and is temporarily stored. This stored water is gradually re-
leased as flow or springs at the base of the pile.
The drainage flow behavior of a refuse pile can be modeled by starting
with a material balance, as was done for the drift mine. Similar
factors must be considered, including rate and frequency of precipita-
tion, infiltration capacity, temperature, and evaporation. Transpira-
tion will not be very important since the acidic conditions at the
surface of a refuse pile are not conducive to plant growth. A storage
tank model could be used to describe the head or driving force available
for flow from the pile. If a storage tank model were used, the tanks
could only be assigned limited volumes. In other words, like a sponge,
the pile can only hold so much water. Any additional water runs off
immediately. This immediate acid runoff is of major importance since
it is the sudden shock of acidity which causes much damage to the
receiving stream.
The storage tank concept has physical validity since Good, using test
well measurements, observed distinct water storage volumes in the New
Kathleen refuse pile. The number and capacity of storage tanks in a
model could be determined empirically for a specific pile. This infor-
mation might be generalized for refuse piles on the basis of a storage
volume per unit area of refuse pile. To summarize, Good13 and Brown5
have presented sufficient information for the development of a model
of drainage flow and acid load from a refuse pile. Such a model could
give a very good estimate of the quick runoff and acid release during
or immediately after a storm. The daily flows from internal storage
could be estimated to within a factor of two or three.
Strip Mine System
Another type of pyrite system geometrically dissimilar to a drift mine
is a strip mine. Development of a strip mine model requires an exten-
sive background in hydrology. In this type of raining, the cuts taken
and the spoil banks left behind distort natural water flow patterns.
The oxidation or acid load can still be estimated by the techniques
described in Section VI.
Sternberg and Agnew40 have undertaken the development of a model of
drainage in a surface-mined area. They obtained solutions for changes
in ground water elevation and ground water flow that would occur in
response to a uniform rate of deep percolation over the spoil bank.
The solution for ground water flow can be used to predict maximum and
minimum flows from the spoil bank to the last cut.
101
-------
SECTION X
STATUS OF MODEL DEVELOPMENT
It should be emphasized that the capability of the mathematical model
to predict flow and acid load has not been thoroughly explored. For
example, there has been no attempt to optimize the value of TANK for
the auger holes to obtain a better match of field data. A larger value
of TANK would have decreased the fluctuations in predicted flows shown
in Figs. 17-21. But rather than optimize by trial-and-error procedures,
the value of TANK, calculated as described in Appendix E, was used to
test the generality of procedures found to be successful for the
McDaniels Mine. It is now apparent that the calculated values of TANK
for the auger holes are too small. Better values would have been
obtained by assuming TANK numerically equal to that used for the
McDaniels Mine (see Table 1^, Appendix E).
Alternative forms of an equation for calculating ADD were never checked.
For example, it would seem more logical to describe the relationship
between ADD and WOVERW by an exponential rather than a linear function.
As the soil layer approaches saturation the ADD should increase more
rapidly than proportional to WOVERW. Expressing ADD as an exponential
function of WOVERW would also result in a more rational relationship as
derived from field data, between TANK and HEAD.
The more underground mine systems that are modeled and checked with
field data, the more general and reliable the model can be made.
Ideally, the constants of the flow and acid load equations can be
related to the geologic-hydrologic features of the system in terms of
the physical model on which the mathematical model is based. At the
present time, however, the reliability of this relationship is not
known. Comparison of constants such as presented in Table lU would
be very informative if a wider range of pyritic systems were modeled.
The acid load data for the Decker No. 3 Mine was estimated without
using any information on the geology of the area in which the mine is
found. The pyrite-bearing zone was assumed to be coal having the same
sulfur content and void fraction as the coal found at the McDaniels
site. This could account for the relatively poor agreement between
predicted and observed acid load data for a mine model which predicted
flow data quite well.
On the other hand, the fact that acid loads can be predicted by a model
based almost entirely on field data poses the question, "How critical
is the location and concentration of pyritic material in the coal and
shale strata to the definition of a good model?" If no field data are
available, as would be the case if one were to develop a model for a
proposed mine site, geologic and hydrologic data must be used to esti-
mate the amount of pyritic material that would be exposed to air (i.e.,
not submerged) over most of the hydrologic year. The actual effect of
103
-------
assuming different strata and pyrite concentrations on acid load pre-
diction vas not studied.
IQk
-------
SECTION XI
ACKNOWLEDGEMENTS
The majority of the work in translating the conceptual model of an under-
ground pyritic system to a useable calculational mode was performed by
Dr. A. H. Morth as part of his Ph.D. dissertation in Chemical Engineering.
The subroutine REMOVE included in this report is a modification of
Dr. North's subroutine. The modification was made by Mr. Kurtis Chow as
part of his research toward a Master of Science degree in Chemical
Engineering. Professor Edwin E. Smith, Department of Chemical Engineer-
ing, was research advisor for both graduate students. Dr. Morth is now
with the Ohio Geological Survey.
Professor Harry Hershey, also of the Department of Chemical Engineering,
contributed to the writing and debugging of the computer programs.
Professor K. S. Shumate, Department of Civil Engineering, provided
guidance in the areas of hydrology and geology as well as being respon-
sible for much of the experimental data used in formulating the model.
Detailed data on the Decker No. 3 Mine were furnished by Noel N. Moebs.
105
-------
SECTION XII
APPENDIXES
10?
-------
APPENDIX A
GRADIENT COMPUTER PROGRAM
During the investigation of the influence of "breathing" on pyrite oxi
dation, a complicated differential equation was derived. This second-
order, variable-coefficient, unsteady-state equation is shown here
again :
AP(0)(L-Z)
- . — ATS - . i ii T - i - ' '
d9 •a±i dZ^ RT
Since there are no straightforward analytical solutions to this equation,
it has been solved using finite difference approximations and digital
computation. Crank-Nicolson implicit finite differences have been used
to estimate all derivatives. Using the notation "I" for steps in the
Z(distance) domain, and "J" for steps in the 0(time) domain, the follow-
ing approximations are obtained:
, j+i) - x(i, j+i))
and
\/\Ll
+ X(l+l, J) - 2X(I,J)
The next step is the collection of coefficients of each time and dis-
tance term. The collection of constants for the equation is shown in
Table 10. The six sets of coefficients are general and are equally
valid for a point X(M,N). To evaluate an X(l,J) means that the five
surrounding X values must be known. However, this evaluation can not
be done directly since the J+1 terms are in the next time step. There-
fore, it is necessary to solve for all the J+1 terras first, and then
back substitute. This may be easily done since the matrix in Table 10
is tridiagonal having nonzero elements only on the main diagonal and
on the diagonals immediately above and below the main diagonal. The
solution of this matrix is obtained using the "TRIDAG" subroutine of
the Ohio State University Chemical Engineering package. To use "TRIDAG,"
boundary conditions must be known, and a standard setup followed. Since
the solution to the matrix is implicit, the (I, J+l) terms are defined
as the main diagonal.
109
-------
TABLE 10
FINITE DIFFERENCE COEFFICIENT MATRIX
Terms X(l-l, — ) X(l, --) X(l+l, --)
x(--, J)
X(--, J+l)
0.5 CDAB
0.5 CDAB
(AZ)-'
+ AP(L-Z)
RT
CDAB .
TZzF
- CDAB +
(AZ)2
-kpC + ^
R RT
C
AS
C
A0
0.5 CDAB
0.5 CDAB
_ AP(L-Z)
RT
The setup of "TRIDAG" for our system is as follows:
Boundary Conditions
1. For J = 1, X(l) = XQ exp[-(kR/D)'A'W.]. This is a re-
statement of the analytical oxygen gradient, a good
initial approximation.
2. For J = 1, 2,...N, X(l) = X0. The first concentration
increment is the bulk concentration for all time steps.
3. For I = N, where N is much greater than 1, X(N) = X(N+l).
In other words, at a great distance from the air-solid
interface, the oxygen concentration gradient is zero.
Column Vectors
1. A(N) = coefficients in lower diagonal (l-l, J+l).
2. R(N) = coefficients in main diagonal (I, J+l).
3. C(N) = coefficients in upper diagonal (l+l, J+l).
k. D(N) = coefficients of known values such as
X(0,J), X(N,1), X(l,J), and so forth.
The "GRADIENT" program functions by calculating the vectors A, R, C,
and D. Once these vectors are evaluated, the subroutine "TRIDAG" is
called. "TRIDAG" solves the matrix described by A, R, C, and D and
returns the solution vector X(N), the oxygen mole fraction gradient.
The program prints the values of X(N) and then repeats the calculations
for as many time steps as are desired.
110
-------
The program includes provision for varying the channel length, L, and
for using different size time and distance increments. A printout of
the program and samples of the output are shown on the following pages
111
-------
GRADIENT Program
MAIN
~C ~THIS PROGRAM EST I MAT ES " "OXYGEN MUL E FRACTION" .....
_C_ _IN A LONG CHANNEL. CRA_NK MCCLSCK FINITE
C ....... niVFERENCE APPRnX IMTTIONS "AK£" USED Y'UR THF
C _DERIVATI VF.5. THE RESULTING SERIES OF EQUATIONS
_. -__„ - SQL VED us ! NG- THE- • TR j -L-j AG i SUB ROUTINE
C
C "THE "ECU ATI C\ BEING SOLVED IS ........
C __ C*DX/OT = 9*P^_QJ!: tD2X/D7.2> ~ K*X*C + X*DELP/ ( RT
"c -" DEL PVTkf y"^TL-zT * (0x7077) .....
C
i orr^A ( looo) TR uooorr c ( looo) 7~ oriooo
I X(LOOO), XSTURE( lOOf 4), TS'JM( IOC)
c "" "" ..... ...... """"
P.-JM l * !NP_.UT_ Ml1 .! NUMOER. _ _
"c" ""t'Hi's "i's WiT "NUMBER "~5" AT "OHTO""STATE '
= 5
C THIS IS UNIT NUMBER 6 AT OHIO STATE_ UN I VERJII T Y
„..___.._. ...... . ......... ..... .....
c"
C READ INITIAL CCNHITICNS AND OTHER DATA
"C" ClS'LENGTH OF CHANNEL ...... " .......
C _N I S NUMBER CE INCREMENTS^ PER FCCT _
~C~ ""NCiR'nEP" 'l"S" CRDFP." OF ""Rg'AC tfON " ............... "
c
___ RFAOt I N»_LOOl) L. _Ni_Mj WIN t
NSTORE"^ NORDER
C
___ _ __
c" "OTHE"TA i s Ti NE TNCPE^E'NT IN" "HOURS
_C_ __ P IS AMBIEMT_PRESSURE, MM. HG. _ ____ _
C f" " IS ~ A M B I'E N'T T E M P ' E R A YD R ET" C E GR'F'ES TA~H R E N HE 'ft
C RATEK JS REACTION RATE CONSTANT _
T "DAB "IS OXYGcN IN AIR DIFFUSIVITT
N,lOOTI1ETA, P» T , RATEK DAB
•
GAS C ONS T AM M M . H G . FT ** 3 / GM. M 0 L E D EG RE E RA NK I NE
_ _ __ _ _ _
E" = "760. "*""359. 7 K5^^""*~492 .T
C ___ ___ ___ _
NRTf ETlO, 200"2 r~DtHETA7EVP» T, RATEK.NORDER ,L
WR TE UC, 2005 }
C CALCULATED CELT A Z_
~'"~DI'- r.o /~ZN ""
C__S_AWTGQ CAUSES DEL TA_ P J0_ CHANGE SIGN DAILY
NHOURS j= _48
COUNT = 16.0
112
-------
C ASSUME A DAILY DE L TA~"P OF " B! GO P NM. ~HGT
__ VOL = 8.?3 ____ _ ____
BI'GDP ^TzT^ '
OF.LTAP = BIGDP / NHGLRS
NHQURS =""NkiURS""+~"l ......... " ......
.C ___________________________
c E s f A B'L i S"H "IN i fi A L~ E'XPONE'N T i AT G R AD i ¥NT'~
c
ROOT f_s _
NNi = "fvjL "V 2
DO 110 I = 2» NN
Z = DZ * ( I - 1 ) _
~XTfr~= ~ ."21" * (EXP '(-ROUT * Z") I"
IF (XU) .LT. l.E-40) GO TO 111
GO TO 113
1H ""DO 112 'I "=" Kt "NN
112 Xt I ) = 0.0
- _ _ . T1_
"c ..... "" ...... ~ "" " '"" ~" " —
_C ST_ARf A SERIES OF CYCLES _
c " ...... ...... ~"
j)o 30 'MM = it M
SUM "= ..... o".~o ..... ...... .....
______ DELTAf _ = DELTAP * SAWTGO
""tTM'E" ="~OVO
CTART A 24 HOUR CYCLE
— _ _ _P = P + _PELTAP
R'ttfj'a~T.3"4""*TP7~ 760. ) * "C4<52frO""/~S»'I"5ri"OT
CTOTAL = P/ (F.*T)
~C '""CAlTULA TE"" §rcT]ND"~ORD"lTR""C"CrN"S"T"AlfT
CCNl = 3 .5*CTOTAL*DAB / (CZ**2)
"C CALCULATE TRANSPCRT""CiCNST"ANT r~
_ CON 2 =_ j)ELTAP /(E*Tj
C " CALCULATE TI>E CCNSTANT "
CDN3 = CTOTAL / DTHETA
C __ C At Cll I L AT F. _CCNS .T ANT FOR JN FL U EN C E_ 0 F R EAC T ION ORO_ER
"C"aN"4" *" . 2T* RATEK"* 'C"Td'tAL*"< T - "NOPDER "") "
C. __CiALC_u_!:A.TE T^_.
"C" Af""R, A"ND"C""ARFCOEF'FICiENTS
C 0 IS SOLUT ION TERM
DO 1 I - I, NL
C( I ) = CON1 - CON2MNL - I)
113
-------
A(T) = " "CLNl " "> 'CON2*•(x"(NL~"-l)~~- 2"."* X (NL ) )
_____ _ _ _ ______ ____ __
C ESCAPE f-'Rijfi CC" LCCP" AT END "OF 21 "HOUR" "C"YCL E ...... "
______ IF_(^ NTIVE .F.C. NHOIJRS ) GG 1C 30
C PR INt INIT I'AL "AND' FINAL " SF TS" OF C'OlMCE M'TRA TI ON "DATA"
__ __ JF{ MM VEG_. I ) GO TO 21 __ __ __
-.- ~|"F~<"~MM .LT^ ""MINTGC "tGTo "" " "" ......... "~
__ 21 ___ CpNjr_INjJE ___ ______ ___ ______
miifiPF - i "T"9 , 9, 15"
° E u f vt R Y B TH T ! - NC RE M E NT
_ . . . ____
"is "•FfMf=~ "j" "NT" fME"- T > "7" COUNT" "
N.FJrAG__= FLAG_ _ ____ _ ______
FLArT= "FLAG '-~NF LAG
_J_F_ ( __A8S £FL AG ) ,GT . _ 0 .0 1 _) GO TO _ 20
9"' WRITE (Tc"f2"oooT~wfi"T"T i>"ET P"
-------
__y^ UF P. UT_1LR§L_?L9.
"be"Vo" i = i~, 20
___P.f. S.J = pz * n j: l > __ _
W'FUT ~E(7o, 2601") bi'sTi x( i: jVATI ) .RUT ,cu
10 CONTINUE
C WRITE OUT EVERY FCURTH DISTANCE INCREMENT
._.
is= oi *( r - i
P*.1 ^JL^LY NCN ZE_RC R_ _ _
IF( X("rr"".rE". 0.0001) "GO "fO"20
U .JL^ITEJ !Q,'JL°_9JU OJ_SJ_fX< IJ ,A(_I )»R
20 CONTIii'CiE" " " ' " ......... "
5T_nRE_CA!LY CAT* FOR_LATEr< PR_INTOUT
""i'Fc "" N'TI KE VNE. ""NHRS") GC TC so
. _ _
XSTCRE"'(>Mf 2l = XT15)
XST)[JRC _ ( ^M.t__3^_ =__XJ_3 5 )
"x STORE" ("MM, AJ"= x"( loo)'
an
_ _____ ____ ___ ___ _____ _
CALL TRIDAGl A T~R f "C'7 CT X~i"NK")
_C _ TRIOAGJS AN 0_HJCJ J5TATE SUBROUJINE _FOR SOL_yij^G_
C " TR I D I AGO IN AT" N A'Tk I C ES SUCH "AS" t hCS E " A"R "IS "IN~(T 'FROM"
C .IMPLICIT SOLUTIONS OF ^A SS TRANS PORT EQUATIONS
"DO is b ~"i "= i, NN"
IF( X( I )_.LT. 0.0 )_ X (I ) _= 0 .0 ____ ____ ___
..... T*50"" C'CNtTNUE """' ."
TIME = TIME + DTHE TA
TSUM(MM) = SUM * 120. / 112. * VOL
\1 CONTINUE _
"30 CONTINUE" " "
__ __ _ __
"00" 31 K>~= V, M
31 WRITF (10,2004) MM, XSTDRE(MM, 1), XSTOREtMM,
I~ 2 ) ," X S'T'C R E"(' M M73" ft" ~X"S"rO'R R MTTTOT" T5 "0 M f Mfi 1
__ STOP _ _ _
"lOO'O "F'O'RM'AT T "5F10.6") ~
100 I FORMAT ( 5 15 )
"2CCTO ""'FORMA TT"////""1~"TH"r5~l"5~D"A"7~»"71"5";""r"~"ffFT"ER~~"*T
___ 2__F8 .3,_ « HOURJ •, _/_/ 12X,_ • THE PRE SSURE I S *j
~2 F7.3", "•" 'MMHG."f"~f //7l5X , "' DEPT h' ,* 1 OX", ""
3 l02_FRACTIDN_t!_l8x' 'A(I) S ISXf'RtU ' f 13X,
"«V ' • CTI )"'" , "15X ,~ "lift I") '")
2001 FCRMAT( IHOflCX, F10.3, 1 OX T F 10.6, AE17.8)
"200~2 FDRMATTiHiT^DT i~T7F^T2r"r""'WRV'r"7r"t""13faS'"'1T"
. 1 « CONST ANT =', F6.4,// • INITIAL PRESSURE =»,
3 ' DECREES R.J;// '_ RATE _CONSTANT =', F 1C. 8, //
4' I' QRDTPrcF REACrrGN"IS""r", r2",//"»"TENGT"H !Sr, ""
5 13, • FEET* )
115
-------
"2003 FORMAT { 1 H1, ' X(I) VALUES ARE TABULATED •,
1 • B EL CW F£R THE. LAST',// ' (3AILY TIME INCRb_M^,__
2~*ENT~"A~r~THE 2ND","""T3TH7 ~35TH ,~PlD "FOC TH " •", "
3 'DISTANCE INCREMENTS1, // ' A FORM OF STEADY',
„._ i.._^__T_E j-s--R^-rHEo'"'hHE"N" VALUES" FOR ALT ERNAT E ' 7
5i • DAYS ARE THE SAME', //' HU S IS USUALLY ',
6"»~OCCURS AFTER 20""TU 30^ DAYS «,//"' THE FINAL "•,"
_7_ _'COLUMN_ I S THE_P_YRITE_ OXI OI ZE.D IN HG_y]S/^Y' • __
1 "//"/ i^X , ~«OAY"«';6Xf" rC2 FRACT ION ',"6"CXV 'OX"ID"ArrON ' J"
2004
2005
FORMAT
FORMAT
END
{
(16
LH1
X,
'
I
3,-
b(
8X,
FQ
.6
) )
116
-------
XI) VALUES APE TARDLATFD KFLO«,-i FOR THF LAST DAH.Y
TIME INC RE MEM AT THF. 2hfQ AND 15TH DISTANCE INCPEWCNTS.
A FORM OF STEADY STATE IS REACHED WHEN VALUFS FOR
ALTERNATE HAYS ARE THF SAME. THIS USUALLY HCCUfS AFTEP
15 TO 20 DAYS. THE FIiMAL COLUMN IS THE PYRTIE OXIDATION
IN MILLIGRAMS OXYGEN' CONSUMED PER DAY
DAY"
P
?
4
b
6
7 "
8
9 '
10
11
12
""• 1?
14
15
16
•" 17
18
is '
20
TABLE
OXYGEN HOLE
0.113937
0. 1 85306
0.1 13768
0. 1 8529R
0.113781
0. 1 85298
0.113779
0.185298
0.113779
0. ] 85298
0.113779
0.185298
0.113779
0.185298
'0,113779
0.185298
0. 1 13779
0.185298
0.1 13779
0.185298
11
FRACT ION
0.002585
0.007099
0.001R57
0.007087
" 0.001784
0.007075
0.001774
0.007072
0.001772
0.007071
"0.001771
0.007071
0.001771
0.007071
0.001771
0.007071.
"0.001771
0.007071
'0.001771
0.007071
..........
OXIDATION
" 9.899684
12.941030
9.^87527
12.830006
9". "47 53 57"""
12.«25077
" - - o.A7?S85
12.8237QR
C. 47 19 57
12.823528
9.471822
12.823472
; 9. ^7 177 4
12.82346^
9.^71774 "
12.823457
" 9.471774' '"""
12,823457
9.471774
12.823457
OT = 0.50 HOUR
•- • " •" *""• - . .- .. -i
GAS CONSTANT =
INITIAL PRESSUR
TEMPERATURE = 5
RATE CONSTANT '=
OROEP OF REACT]
LENGTH IS .400 F
1.2215
E = 745.0
'•!•». DEGREE
0.0300
ON" IS'O
EFT
MM HG
S PANKINF
117
-------
THI_S_IS _DAY_ l_'AfTER 3V000
THE PRESSURE IS 740.750 MMhG,
DtPTH C2 FRACTION
~ o .6 " 6.2 i oooo
r~l70(30 0 . 1 3 l?94
~~27ooo 67 c 82"? 61'
"T7000 " " 6\0508'97
"~Vro60 '"0.0305VO
~ "5TO 0 0 6T617995"
~T."000 O'.'O 12 Tb'2"
_. -?- -Q^-fj- OTOT2 830"
""8"."00 0 670T23T 6"
'97600 6.0 TT6Tf
10.000 0.010808
11.000 0.009877
12.000 0.003842
13.000 O.OC7755
14.000 0.006675
15.000 0.005651
16.000 0.004721
17.000 0.003904
18.000 O.CC32C5
19.000 0.002620
20.000 0.002135
118
-------
APPENDIX B
ESTIMATION OF POTENTIAL EVAPOTRANSPIRATION
The use of the Thornthwaite and Mather4? method for estimation of poten-
tial evapotranspiration (PE) requires monthly average temperatures and
the latitude for the site. Information on the type of soil and vegeta-
tive cover in the region are also required. The PE technique was devel-
oped by an analysis of data from all over the United States. The
correlations which were developed have been published in the form of
a manual of tables.
The best way to use the PE tables is to construct a table of data as
they are read. The data shown in Table 12 are listed in six columns.
TABLE 12
ESTIMATION OF POTENTIAL EVAPOTRANSPIRATION
Tmean Calculation Constants* Inches Potential
Month (°F) A B C Evapotranspiration
January
February
March
April
May
June
July
August
September
October
November
December
33.5
3^.7
U2.1
53.3
62.8
71. k
7^.7
73.3
66.9
55.6
^3-3
3^.2
0.06
0.16
1.19
3.68
6.¥i
9.3^
10.56
10. OU
7.78
i*. 30
i.ifl
0.11
0.0
0.0
0.02
0.06
0.10
O.lU
0.15
0.15
0.12
0.07
0.03
0.0
25.^
25.1
30.9
33.3
37.0
37-3
37.9
35.5
31.2
28.8
25.2
2U.8
0.0
0.0
0.62
2.00
3-70
5.22
5.69
5.3^
3.7^
2.02
0.75
0.0
* Calculation constants are explained in the following paragraphs.
The first two columns in Table 12 contain the name of the month and
the monthly average temperature in degrees Fahrenheit. The second,
third, and fourth columns contain calculational constants. The sig-
nificance of these columns, labeled A, B, and C, is as follows:
Column A—Intensity of incident sunlight. This is a function
of the temperature and is read from Table 1 in
Section I of the PE manual. In physical terms,
this variable is an estimate of the energy avail-
able to evaporate water.
119
-------
Column B—Daily unadjusted PE. This term is read from Table
3 in Section II of the manual. It is a function of
the sunlight intensity, type of soil, and vegetation.
Column C—Correction factor to convert daily unadjusted PE
to monthly values. This factor is based on the
latitude and represents the number of 12-hour days
of sunlight per month. The correction is based on
the fact that plant growth, and transpiration, re-
quire sunlight. This term is obtained from Table
6 in Section III of the manual.
The sixth column is the adjusted PE in units of inches of water per
month. This value is obtained by multiplying Columns B and C. The
values in the sixth column are those which are used in any further
calculations. These are the values •which have been read into the
"PEVAP" subroutine as data.
Thronthwaite and Mather have also presented tables for scaling down the
potential evapotranspiration for cases where the soil is less than
saturated, as is the assumption in the initial calculation. These
scaling factors have been written into the "PEVAP" subroutine.
120
-------
APPENDIX C
DRIFT MINE PROGRAMMING
and
SAMPLE OUTPUT FOR 1970
OF AUGER HOLE NO. 1
121
-------
MAIN Program
O*
C THIS IS THE MAIN PROGRAM FOR THE CALCULATION OF ACID MINE
C D9.AIW.GE FROM DRIFT MINKS. THr: STRUCTURE OF THE PROGRAM IS
C BASSO ON THFI MATHEMATICAL MOD^L BY MGRTH. THE MCDANIELS
C RESEARCH COMPLEX WHICH IS ACNTNI$TE<>?P BY THE OHIO STATE
C UMIV=PSITY HAVE REfrN US"D TO DEVELOP THIS MODEL.
C**
C ESTABLISH APRAYS FOR TH2 SYSTEM:
C THE SYSTCM CAN B- SUBDIVIDED INTO 5 SECTIONS IN I-DIRFCTION, 15
C LAYERS IN J-DIR5CTIDN» AND 30 INCREMENTS IN K-DIRECTION.
C**
DIMENSION ALT(5,.\5>, OT C 5 ) t DIFFG(5,15J, PYCON(5,15), RAT£K(5,15),
1REACT(5,!«5) , ROCK(5,15), STC«E ( 5 , I 5 , 30) , THICK(5,15>, TOP(5)r
2TYPE(5,J5), WASM15,15), WATER(5»3Q)
C**
REAL BLANK, END, YEAR, JAN, FFP, f-'AR, APP, MAY, JUNE, JULY, AUG,
1SEPT, OCT, NPV, DEC
C**
INTEGEP COMTOL
C**
COMMON/C*./ BLANK, END, YEAR, JAN, FEB, MAR, APR, MAY, JUNE, JULY,
J*UG, SEPT, nCT, NOV, DEC
C**
COMMON/CO/ ADD, AFL4G, AG, AGO, AMONTHt CONTOL, FLAG, IDAY, KEEP,
1LAST, LTHETA, PWATEP, PWHC , RAIN, RSUM, RSUMA, RTIMF., TANK,
2TMEAN,
COMMON /CC/ VA'P <12)
C**
C OPERATIONAL CONSTANTS:
C IN IS INPUT CHANNEL. AT OHIO STATE UNIVERSITY, IN IS UNIT 5.
C 10 IS PRINTED OUTPUT CHANNEL. IT IS EQUAL TO 6.
C IP IS PUNCHED OUTPUT CHANNEL. IT IS EQUAL TO 7.
C**
IN * 5
10 « 6
IP * 7
C**
C INITIALIZATION:
C AG AMD AGO APF IDENTIFICATION OF THE MONTH BEING EXECUTED.
C IY IS IDENTIFICATION OF YF.AR.
C**
AGO = BLANK
AG * BLANK
IY » 0
123
-------
c**
c
r
C
C
C
C
ESTABLISH
I P
IF
IF
CONTGL
CHNMJL
tf ?00 ) .
CHNTOL
( S TA T.c.
100
c**
c
c
c
c
c
c**
c
c
200
c
c
c
c
c
300
C**
c
c
c
c
c
c
c
c
c
c
c
c
c
CONTROLLING
IS EQUAL TO
IS FQUAL TO
IS
ECU.iL TO
#300).
CrVICE FOR THE PROGRAM:
1, ONLY ADD IS CALCULATED (STATEMENT f»5 00).
2, ADD, AND TANK ftRE CALCULATED (STATEMENT
3, ADD, FLOW, AND ACID LOAD APE CALCULATED
READ (IN,
CONTINUE
5100) CO.NTOL
CONTOL * 1
READ IN DATA FOR CALCULATING ADD:
PWAT5". IS CURPFNT WATER STORAGE IN ROOT STRUCTURE IN INCHES.
PWHC IS PROVT-S1CNAL WATER HOLDING CAPACITY IN INCHES.
VAP IS MONTHLY POTENTIAL EVAPPTRANSP I RAH ON VALUES.
READ (IN, 5MO) PWATER, PWHC
READ (IN, 5?20) (VAP (!), I = 1,12)
WRITE < 10, 6380)
IF ONLY ADD IS DESIRED,
ADO (STATEMENT
IF (CONTOL
CONTINUE
SKIP THE FOLLOWING, AND CALCULATE DAILY
.LE. T)GO TO 400
CONTOL = 2
PE»D IN DATA FOR CALCULATING TANK:
WSHED IS WATERSHED ARSA OF MINE.
TANK IS AOUIFER STORAGE OF WATER
CDNFH IS CONSTANT RELATING AIJGIFER STORAGE AND FLOW.
READ (TN, 5210) WSHED, TANK, CCNFH
WRITE < 10, 638i.)
IF (CONTOL .LF. 2) GO TO 400
CONTINUE
ACID LOAD:
INTERFACE INCREMENTS
COMTOL = 3
PEAD IM DATA FOR CALCULATING
NFEFT IS NUMBER OF AIR-SOLID
NI.AYFR IS NUMBER OF LAYc»S IN COAL SEAM MODEL
NDcPTH IS NUM^cR OF DEPTH INf.REMC-NTS IN MODEL
NPUNCH IS PUNCHED OUTPUT CONTROL
DK IS LENGTH QP D2PTH IMCERMjNTS
ALKALI IS GROUND WATER ALKALINITY. IT HAS A VALUE EQUAL TO 20 IN
THIS MOOEL.
FLQW1I IS MINIMUM FLOW TO CAUSE ACID REMOVAL BY FLOODING.
H^ADMI IS TNI MUM FLOW T0 CAUSE ACID RCVOVAL BY LEECHING.
PER IS A CONSTANT VALUE TO DETERMINE THE DISTANCE THAT IS
iriUN
-------
C WSLOPE IS HYPOTHETICAL SLOPE OF WATER TABLE.
C DI IS LENGTH OF AIR-SOLID INTERFACE INCREMENTS
C TOP IS DATUM PLANE FOR TOP Op CC/L SEAM
C KOCK AND TYPE ARE LITERAL OE^CR IPT] ON T= STRATA
C ALT IS ELEVATION OF STRATUM RELATIVE TO DATUM PLANS
C RFA.CT IS OXYGEN CONSUMPTION PATE 0^ PYRITF. IT HAS VALUES EQUAL
C TO 0.5 FOR COAL AND 2.5 FTP. SHALE.
C PYCON IS VOID FRACTION OF TH? STRATUM
C**
RFAD (IN, 5MO) NFEET, NLAYER, NDfcPTH, NPUNCH
RTAD (INt 53?0) DK, ALKALI, FLGWMI, HEADMI, PER, WSLOPE
PO i:io I = I, NFEET
RFAD (IN, 5330) 01 (I), TOP (I)
00 ?.200 J = 1, NLAYER
PT-AD (IN, 5340) ROCK (I,J), TYPE (ItJ), ALT (ItJIt REACT t!tJ)»
IPYCOM tI,J)
1200 COriTINU?
1119 CONTINUE
C**
C INITIALI/ATIOM;
C D1FFG IS GRAVITY DIFFUSION RATE CONSTANT FOR A LAYER
C STQRF IS OXIDATION PRODUCT STORAGE A9RAYS
• C**
NL = NLAY6R + 1
00 1!10 I = ) , NFEET
niFFP, ( I,NL) » 0.0
ALT ( ! , .NL) = TOP (I)
DO 1X17 K = lt NDbfPTH
STORE (It NL, K) = 0.0
3 117 CONTINUE
7.118 CONTtf.'UE
C CALCULATE RATE CONSTANT (THEORY BASED ON THE MODEL BY MORTH(6M
C TF^P IS MINE TEMPERATURE CORRECTION1 FACTOR
C FTGMOL IS VCLUM? OCCUPIEO BY GM. MOLF. GAS
C CCPRFT IS CONSTANT FOR CALCULATING PATE CONSTANT
C CTNA IS CONSTANT FOR CALCULATING RATE CONSTANT
C RAUK jc REACTION RATE CONSTANTS Cc STRATA
C THICK IS THICKMFSS OF STRATA
C DIFFG IS GRAVITY DIFFUSION RATE CONSTANT FOR A LAYER.
C OIF IS BASE GRAVITY DIFFUSION CONSTANT.
C**
TEMP a 0.15
FTGMOL = 359. / ^54.
CCPRPT * (2.54 ** 3) * 3.72S.
COMA = CCPPFT * FTGMOL / (0.21 * 32.) * TEMP
OTF = 0.0\
WFITE (10, 6300)
DO J20? I = )., rjFEET
DO !?02 J = I, MAYER
REACT (T,J1 * REACT (IVJ) * i .f-6 * 24.
125
-------
PATfK (ItJ) * R = ACT (IfJ) * CONA / PYCON (I»J)
THICK U,J) - ALT (I, J+-M - ALT (I,J)
DIFFG U,J) « DIP * RATEK (IfJ)
C**
c ECHO INPUT DATA:
c**
waiTC (IOt 6201) It Jf P-OCK, (IfJ)f TYPE (ItJ)t ALT (IfJ)f
IO/STE (i, j), PYCON (11 J)
1202 CONTINUE
1203 CONTINUE
c**
c
c
c
c
c
c
c
c
1205
1496
1 498
7.500
400
c**
C
C
C
C
r
INITIAL IZ4TIONJ
P IS PRESSURE IN MINE
DIFF IS GAS DIFFUSIVITY IN
SQUARE FEET PER DAY
GASC IS GAS CONCENTRATION UNDER MINE CONDITIONS
DTHETA IS TIME INCREMENT Lf
SOX !S TOTAL INITIAL ACID S
WASH IS EQUILIBRIUM PRODUCT
PRftC IS FRACTION OF STORED
P = 4 5 i. .
DIFF = 0.692 * ?4. <• 0.6
GftSC = 32. / 359. * 492. /
DTHETA = I .0
SOX = 0.0
FRflC = 0.0?
DO !?OS I = 1, NFEET
DO 1?05 J = If NLAYER
R5A" (IN, 7000) (STORE (I,J
CONTINUE
DO 1500 I = If NFEET
DO 149f> J = 1, NLAYER
DO 14- -56 K = 1, ,NDEPTH
SOX = SOX * STORE ( I, J,K)
CONTINUE
WRITE ( 10, 6305) (STORE (I,
WaSH ( I ,J) = STORE (U Jf 1)
CONTINUE
CONTINUE
WRITF. ( IOt 6302) SOX
CONTINUE
INITIAL NATION:
K?TP IS LFNGTH OF MONTH
LTHETA IS DAYS SINCE PRECED
NGTH
TOR AGE
STORAGE IN LAYER
PRODUCTS REMOVED DAILY
515.
fK), K « If NDEPTH)
JfK), K * 1, NDEPTH)
IMG DATA INPUT
KAT !S CONTROL DF.VlCF IN PRCGRAMVING
PSltM TS HP'JTHI Y Arr.UMUlATTn
M OF WATFR FNTFR1NK ST
DURING FLOODING,
STORAGE
C RSUMA IS ANNUAL ftCClJ^ULATI?^ OF WATF.P ENTERING STORAGE
C TSUM ISACCUMULATION OF TOTAL ACID I GAD.
C WSUM IS TOTAL ACID RJMOViD BY LEACHING.
C FLSD^ IS TOT4L ACID REMOV4L ^Y FLOODING.
C G«UM IS MONTHLY TOTAL ACID Rr-MOVAL RY GRAVITY DIFFUSION,
126
-------
C YS'JM IS MOMT^LY *CCUKULf.T I CN OF ACTO LOftP.
C YSUMA IS ANNUAL ACCUMULATION OF ACID LOAD.
C Pr>'JM !S aCCUMULATIQN fjF FLOW Pf-R MONTH.
C FSUMA IS AN\'UAL ACCUMULATION OF FLOW.
= 30
TA ~ 1
KftT - 0
1605 CONTINUE
QSUM = 0.0
RSUMA = 0.0
IF (CONTOL .NF.. 3) GO TO 1501
TSUM 3 0.0
WS'JM = 0.0
FLSt,M = 0.0
GSUM » 0.0
YSUM = 0.0
YSUMA = 0.0
FSUM = 0.0
FSUM* = 0.0
1501 CONTINUE:
C RFAO IN DAILY WITHER DATA. THERE IS NQ-LIMIT ON THE NUMBER OF
C " Yf=A
-------
C CALL SUBROUTINE DAYS TO DETERMINE THE DATE BEING EXECUTED.
C**
CALL DAYS
C**
c INITIALIZATION:
C RKE = P IS VARIABLE TO STAND FOR RAIN.
C**
RKEEP =
RMN = 0.0
C PERFORM TH= FOLLOWING CALCULATIONS BASED ON THE INFORMATION
C R'TWE'M THE LAST AND THE NEXT INPUT WEATHER DATi
C**
DO 3005 M = 1 , LTHETA
IF (M ,CQ. LTH^TA) RAIN = RKEEP
IP (KAT .ME. o) GO TO 2305
C**
C CALL W.'TBAL TO CALCULATE ADD, TANK, OR FLOW AS INDICATED BY
C CONTOL.
C VMTfU IS USED TO INITIALIZE VALUES USED IN SUBROUTINE WATBAL.
C AF^?R INITIALIZATION! PERFORM CALCULATIONS FOR THE NEXT DAY,
CALL WATRA (DSLV, FLOW, 1* )
GO TO TOO 5
2305 CALL WATBAL (CSLV, FLOW, M)
IF ONLY *DD IS DESIRED (CONTOL = ?)t PRINT OUT THE RESULTS
IF (CONTOL ,NE. 1) GO TO 500
IF (1C - AGO ) 1020, 1010, 1020
1010 WRIT^ ( I0t 6100) AGO, IDAY, PAIN, ADD
GO TO i:.00
1020 IF (ID*Y ,GT. KEEP) GO TO 1030
1025 WPITC (10, 6100) AG, IDVf, PAIN, ADD
GO TO :',iJO
1030 IDAY = I^AY - K5FP
WRTTF (10, 6100) AGO, IDAY, RAIN, ADD
1100 CONTINUr
IF (IDAY .NE. K<=EP) GO TO 2005
WRIT= ( 10, 6110) RSUM
WR1TF ( TO, 6380)
P.SUM = .0.0
GO TO 3005
500 CONTINUE
IF (CONTOL .GT. 2) GO TO 600
C IF T&t« IS DESIRED (CONTOL =2), PROCEED WITH THE FOLLOWING
C INITIALIZATION AND PRINT OUT RESULTS:
128
-------
IF (AG - AGO) ?020, 2010t 2020
2010 WRITE (10, 6200) AGO, IDAY, TANK
GO TO 2 LOO
2020 IF UDAY .GT. KEcP) GO TO 2030
2025 WRIT? < 10, 6200) *G, IDAY, TANK
GO TO 2100
2030 IDAY = IDAY - KE=P
WP!T« < 10, 6200) AGO, IOAY, TANK
2! 00 CONTINUE
GO TO 3005
600 CONTINUE
C*'-
C IF FLOW AND ACID LOAD ARE DESIRED, PROCEED WITH TH6 FOLLOWING:
•C FROM WATfUL, FLOW OF A CtRTAIN DSY HAS BEEN OBTAINED.
C DETEKMIN1: POSITION DF WATER TABLE BY RELATING FLOW TO THE
C INCREMENTS IN K-DIR?CTION WHICH IS INUNDATED.
C DEHK IS TH<= DISTANCE IN K-D1RECTIQN THAT IS INUNDATED. SEE
C CHAPTPR V FOR ESTABLISHING THE DELATION.
IF (FLOW .LT. FLDWMI) GO TO 3114
D=HK = PF.R * SQRT (FLOW - FLOWMI)
GO TO 3115
3114 DEHK = 0.0
3115 CONTINUE
C**
C XMAX IS TOTAL DISTANCE IN K-DIRECTION
C XMIN IS DISTANCE IN K-DIRECTION THAT IS NOT INUNDATED.
C**
XMAX = NDEPTH * DK
XMIN = Xl'AX - 05HK
IF (XMIN) 3307, 3307, 3317
WATER IS WATF.R LEVEL RELATIVF TO THE STRATA.
330^ CONTINUE
DO 331'. I = 1» NFEET
WATER (1,1) = ABS (XMIN) * WSLCPE * ALT (1,1)
KB = 2
00 3?- 15 KA * KB, NDEPTH
WATPR (I, KA ) - WATER (I, KA-1 ) + WSLOPE * DK
IF (WATfiR (I,KA) .GT. TOP (I)) WAT=R (I,KA) = TOP (II
3315 CONTINUE
331* CONTINUE
GO TO -»316
332.7 CONTINUE
00 331.? I = 1 , MFcST
IF (I .GT, 1) XMIN - XMIN «• (ALT (1,1) - ALT (i,lM / WSLOPE
DO 3310 KA = 1,
DF = KA * DK
KB = KA
129
-------
IF (XMIN .LT. OF .AND. KA .EO. 1) GO TO 3309
IF (OF - XMIN) 3309, 3309, 3308
3309 CONTINUE
WATF« ( ItKA) = ALT (I,1)
3310 CONTINUE
GO TO 337.2
3308 CONTINUE
DO 3319 KKA = KA, NDOPTH
WATF? (!, KKA) = WATFR (I, KKA-1) + WSLOPE * QK
IF (WATFR (I, KKA) .GT. TOP (I))- WATER U,KKA) = TOP (I)
3318 nr)NTINUf:
3312 COMTINUF
3316 C0 K * l'i NDEPTH
TNN » K
DNK = (TNN - 0.5) * DK
XNN = OXX * EXP (-SORT (RATEK (I,J) / DIFF) * DNK )
C**
c THE FOLLOWING CALCULATIONS DESCRIBE EACH EVENT PROBABLE IN THE
c BLOCKS
C UNIFORM MINE STRUCTURE IN K-DIRECTION IS ASSUMED
C BY C™PA9ING THE WATER LFV'L TO 'I HL HEIGHT (HITS) WITH RESPECT TO
C THE.PATUM PLANE, WHETHER TH: BLOCK IS INUNDATED CAN BE
C**
HITE - ALT U,J)
IF (HITF - W-".T5R
-------
c**
C IF THE BLOCK IS FLOODED, FOLLOWING EVENTS OCCUR.
C ALFFT IS PRODUCT STORAGE AFTER FLOODING
C DTHFTA IS TIME INC^-McNT LENGTH IN DAYS
C FLOOD IS ACID REMOVCD OU»!NG INUNDATION.
ALEFT - STORE (I,J,K) * (1. - FRAC) ** DTHETA
•=• STORE (ItJfK) - ALEFT
FLOCD
(I,J,K) r STORF U,J,K) - FLOOD
C**
C MAINTAIN RUNNING TOTAL OF REMOVAL BY INUNDATION
FLSUM = FLSUM + FLOOD * 196. / 112.
IF (FLSUM .LT. 1.5-10) FLSUM * 0.0
GO Trj 3939
3655 CONTINUE
C**
C IF THE BLOCK IS NOT FLOODED, OXIDATION OCCURS AND ACID REMOVAL
C BY LEACHING, AMD GRAVITY DIFFUSION DOMINATED.
C OXIDN IS OXIDATION IN A VOLUME
C GASC IS GAS CONCENTRATION UNDER MINE CONDITIONS
C GRAVDT IS GRAVITY DIFFUSION OUT OF A VOLUME
C GRAVIN IS GRAVITY DIFFUSION INTO A VCLLWE
OXIDN = RATEK (I,J) * G^SC * XMN * DVOL * PYCON U,J) * DTHETA
GRAVOT » DTFFG (I,J) * STORF (I,J,K) * DTHETA * FJ
GRAVU1 = DIFFC (I,J*l) * STOP? (ItJ«-t,K) * O^HETA * FJ
C**
C AOUT IS DAILY ACID REMOVAL BY LEACHING.
C THE NEW AC!0 STORAGE IN A BLOCK IS THE SUMMATION OF ^EWLY
C OXIDIZED MATERIAL AMD THE ACID REMOVFO BY FLOODING, LEACHINGt
C : AND GRAVITY DIFFUSION.
C**
AOUT = STORE (I.JrK) * DSLV * FJ
STOR£ (I,J,K) = STORE U,J,K) + OXDIN + GRAVIN - GRAVOT - AOUT
C**
C KEEP RUNNING TOT&.L OF ACID REMOVAL BY LEACHING
C**
WSUM = WSUM * AOUT * 196. /1!2.
C**
C DFTERMINE AGIO LOAD IN THE BOTTOM LAYER OF THE SYSTEM WHICH
C -WILL BE REMOVED BY GRAVITY DIFFUSION.
C UP IS DIFFERENCE IN HEIGHT BETWEEN LAYER AND WATER LEVEL
C«*
UP = HITF - WATER (I,K)
IF (J .GT. 1) GT TO 3939
IF (UP .GT. 0.) GO TO B989
AOUT = AOUT *• GRAVOT
C**
C KEEP RUNNING TOTAL OF REMOVAL BY GRAVITY DIFFUSION
131
-------
GSUM * GSUM t GRAVOT * 196. / 112.
3939 CONTINUE
C TOTAL OATLY ACID REMOVAL
C**
TACIO = TACID + AOUT
CONTINUE
CONTINUE
3000 CONTINUE
C COMV'RT ACID LOAD FROM AN OXYGEN CONSUMPTION BASIS TO EQUIVALENT
C ALKALINITY BASIS.
C ALK IS FACTOR CONVERTING ACID LOAD FROM PXYGEN CONSUMPTION! BASIS
C TO EQUIVALENT ALKALINITY BASIS.
ALK = FLOW * ALKALI * 6.33F-6
TACID = TACIO + .196. / l\2. - ALK
TSUM = TSUM + TACID
TACID = TSUM / ".
TSUM = TSIJM - TACID
FSUM = FSUM + FLOW
FSUMA = FSUMA * FLOW
YSUM = YSUM + TAT. ID
YSUMA - YSUMA *• TACID
IDAY = LAST *• M
C**
C PRINT OUT SUMMARY OF DAILY RESULTS
IF (AG - AGO) 3020, 3010, 3020
3030 WRITE ( 10, 6350) AGO, IDAY, FLOW, TACID, RAIN
GO TO 3001.
3020 IF (IDAY .GT. KEEP) GO TO 3030
WRITr (IP, 6350) AG, IDAY, FLOW, TACID, RAIN
GO TO 3001
3030 IDAY = IDAY - KEEP
WRITE (in, 6350) AGO, IDAY, FLOW, TACIO, PAIN
3001 CONTINUE
IF (IDAY .NE. KEEP) GO TO 3005
WRITE (10, 6341) FSUM, YSUM, RSUM
WRITE (10, 6345) WSUM, FLSUM, GSUM
WUT= ( 10, 6382 )
WSUM =' 0.0
FLSUM = 0.0
GSUM = 0.0
FSUM = 0.0
YSUM = 0.0
RSUM » 0.0
3005 CONTINUE
LAST « IHAY
KAT = L
132
-------
2*^00 CONTINUE
3050 CONTINUE
IY = IYFAR
C*-'*
C WRIT^ OUT ANNUAL SUMMARY:
IF (CONTOL ,N5. 1) GO TO 3060
WPIT5 ( IT, 6340) IYCAR, RSUM
GC TO 3 <>06
3060 CONTINUE
IF (CONTOL .NE. 2) GO TO 3070
WRITr (In, 6355) IYEAR
3070 CONTINUE
WRIT' (TO, 6370) IYEAR, FSUM, YSUM, RSUM
C PRINT OUT ACID STORAGE IN cACH SLOCK OF THE SYSTEM
C**
00 3?(n I = It NFFET
DO 320; J = :, NLAYER
W«MT = ( I0t £350) (ST03F (I,J,K), K - 1, NDEPTH)
3201 CONTINUE
GO TH ".606
C WRITE OUT MESSAGE TO DENOTE END OF PROGRAM EVALUATION
C**
2200 CONTINUE
WPITP (10, 6360)
C**
C IF INITIAL ACID STORAGE IS NEEDED TO PREDICT ACID LOAD REMOVALf
C PUNrH OUT DATA CARDS, OTHFRWISF. STOP THE PROGRAM.
C**
IF (CONTOL .LT. 3) GO TO 321.7
IF (NPU'ICH .EC. 0) GO TO 3217
OH 3?17 I = lt NF5ET
DO 3?1? J = 1 t MAYER
WRITE (IP, 7000) (STORE (I,J«K)t K = It NDEPTH)
3217 CONTINUE
STOP
5100 FTRMAT (15)
5.110 FORMAT (8F^0.5)
5120 FORMAT H2F5.2)
5210 FORMAT (FIO.O, 2F10.5)
5310 FORMAT (4151
5??0 roOM^T (TF5.2, F15.5, 3FJ0.5)
5 = 30 CORMAT ('-F15.5I
5340 FORMAT (?t4t 2X, 3F10.4)
5J30 FORMAT CX, A4, .'.X, 121 2X, 4Fi0.5t 14)
6300 FORMAT CHI, f THE FOLLOWING IS A DESCRIPTION OF THE MINE',/
133
-------
1' BEING MODELED.
2' SECTION LAYER
THE LAYERS ARE COUNTED FROM THE BOTTOM.',//
MATERIAL ELEVATION MRATE)', 3X,«VOID',/
6301
6 ^05
6302
6JOO
M 10
6200
6350
6341
(3X, 12,
CO (3X, F8.
(//FIO.?///)
(3X, A4, 15,
5X,
A4,
7X, 12, 3X, ?A4, ?Xt F5.2, 4X, F8.6, 2Xf F7.3)
FORMAT
FORMAT
FORMAT
FORMAT (3X, A4, 15, BX, 2F1
FORMAT (//,
FOUMAT (3X,
FORMAT <3X, A4,
FORMAT (//, 5X
I/ ?X, MCIO REMOVAL -DURING MONTH IS'
2 ENTERING
i FORMAT (5X,
•INCHES CF WATPR ENTERING STORAGE
15 i 3X, FIO.2)
15, 3X, F6.0, 4(3X, FIO.5))
•DRAINAGE FLOW DURING MONTH IS',
IS',F6.2//J
F10.0, 'GALLONS',
? IS', F6.?,
'ACID REMOVED BY
, F10.0,
• ,//)
'POUNDS',/ 5X, 'WATER
LEACHING IS'» F10.0, 'POUNDS',/ 5X ,
I 'ACID REMOVED BY FLOODING IS', F!0.0, 'POUNDS',/ 5X, 'ACID REMOVED
2 PY GRAVITY DIFFUSION IS', F10.0, 'POUNDS',///)
6340
6?55
6370
I
FORMAT
-------
Subroutine - DAYS
SUiiK'OI.; Tl !\E UAVS
REAL BLANK, E M!> , YfAR,
2 MAY, JUKE , " JULY , AUC, S
COMi-MN /CA/ riLAi\K ,E MO ,YF.
2 MAY , JLJKF, JULY, AUG, S
C. nMKQM/Ci'J/ APC.NTH, AG,R
1 1ANKC, KSIV'it KSUMA, FLA
2 PKATER, LAST, KELP, LTH
C Cl
221 0
2214
221 r>
2218
2 2 VI
2 20 1
220^
2 2 i 5
2 2 ',0
IF{ AGO .E
Jf'CK ] CJ $ f [: I
IF( AGC
KELP = 28
GCJ TO 2230
IF(AGO .FC
i"".'ro . APK .
KFFP = 31
GO TO 2230
Kf EP ~- 30
C CM IINiUE
IF( AMCATH
1. 1 Ht-T A =" I
GO T(] 2233
I IHL'TA "=
CONT IMUF
CUM INLE-
AG = AGO
A"GO"=" AMD'S!
FLAG = 0.0
AFLAG = 0 .
IF (AGO .FC
IF"( AGO . FC
If (AGO .EO
IF (AGO .FC
IF(AoO .FC
IF (AGO .EC
IF (AGO . FO
PETUKN
ENH
t). BLANK ) GO
F XU\T h HAS C
- ff-:rt» 2215 ,
JAN, FEB, MRi APR,
\ IT , CCT , "MOV, DEC
AR, JAN,FFB,MAR,APR,
EPT, OCT, MOV, DFC
AIN, RTIMF. , TKEANijAGG,
G," AFLAC-V WSHEO» PWIC ,'
ETA, I CAY
TC 22'tO
HANGED
2214, 2211>
. SI PT .CR. AGC .EC. NCV .OR. />GO
OR . AGO ".EO.
- -
- AGC ) 2205
DAY -"LAST
KFfcP - LAS1 .+
TH ~ •'••'
o "
. CCT AFLAG
. NCV AFLAG
. OF.C AFLAG
. JAN AFLAG
. FF. B AFI. AC
. P-'AR AFI. AG
. APR ) AFLAG
JCIME » 'GO TO '2218
" "' " " " " "
, 2201 , 2205
IOAY ' ' "'
= 1.
= 1 .
= 1.
= 1 .
= I .
- 3'.
= 2.
135
-------
Subroutine- F- VAP
SUcWnjT Pit: ' EVAP (PEVAP)
C . SimP.OUT IfJl:: ESTIMATES PCTENTIAL KV fl I'd HANS P I K A \ ION
C. US IM"G""THIKNTHV.A'I TE" ME THOD ..........
REAL HLANK, END, YEAR, JAN, PFB, MAR, APR,
2 "fMYi JUNE, JULY, AUG , SEPT, CCT , Nt)V', DEC .....
CIHMUN/CA/ BLANK, FNO, YrAR, JAN ,f-E B ,MAR , A PR ,
2 N'AY, JLINF:, JULY, AUG. SEPT, OCT, NOV. DEC
CLIH''!nM /CR/ AMCJNTH, AG,RA|N, PTlfTr, TKEAN,AGCi
1 TANKC, RSU'-I, RSUMA, FLAG, AFLAG, "WSHt 1) , ' P WHC ,
2 PWATF.K, LAST, KEEP, LTHFTA, fCAY
CUMMUN /CC/ VAP( 12) ............. " .............
IF< AMO^TH - JAN ) ?, I, 2
"T" Pf-VAP = VAP( I)"
RETURN
..... 2 IF~< " A-'.ONtH '- >"EB "") '"'A,' '"3," "A
3 PEVAP = VAP( ?)
" .......... RETURN ........... ..... " ....... ' .......
f\ IE( AMO'^TH - IV A P. ) 6, 5, 6
5
RETURN
6 I'F'C "A'Md'i-jTH"-" APR )" 0',"7, "8
7 Pf VAP - VAP ( A >
" P.L-'TJjRM
8 !F( A MONTH - MAY ) 1C, 9, 1C
"9 PtVAP" = V API" 5 )
RF TURN
"10 " IF-('"A"MOr\(TH""-"""JU"NF:y""l2t""'l"l"i '"l"2"
11 PEVAP = V/Pl 6)
RETURN ....... "" "" ...... .......... ""
12 1F( AMONTH - JULY) 1 4 , 1 2 , 1 '1
1'3 " PEVAV = VAP ( 7)" ............ ............
RETURN
'\i* ...... IF( ..... A-1GM1H" -"AUG ) 16, "1'5V" 1'6"
15 PEVAP = VAP( 8 J
RETURN "' ...... " ......... ""
16 IF< AMUNTH - SEPT) 18t Hi 18
17 PEVAP = VAPl O) " ........ "
PETUKN
^... ---j-pj -^^Q^yH - OCT"")" 2"C, "19"," "20"
1Q . PEVAP = VAP( 10 )
....... RE TURN ................
20 l*( A'l'HTH - NOV ) 22, 21, 22
21 "PEVAP '= V'AP(ll)"
RHTURN
??_ pr'VAP =" "VAP( \2\ ................
RLTURN
" ..... r f\0 " .......... " ........ ...................
136
-------
Subroutine REMOVE
SUPRCITINE REVCV (CSLV, FLGkv, V)
C**
C THIS SIRRCUTINE IS TC CALCULATE THE DAILY WATER BALANCE, ADC,
C FLCVi PATES, AND FRACTION CF PRCDUCTS REMOVED EACH CAY BY
C LEACHING.
RFAL BLANK, ENO, YEAR, JAN. FEB, MAR, APR, MAY, JUNE, JULY, ACG,
1SFPT, CCT, NCV, DEC
INTEGER CCNTGL
C + *
CQMMCN/CA/ BLANK, EMC, YEAR, JAN, FEB, MAR, APR, KAY, JUNK, JLLY,
1AUG, SFPT, GCT, NCV, UEC
C**
CQMMON/CB/ ADC, AFLAG, AG, AGC, AfQNTH, CONTOL, FLAG, IT«Y, KEEP,
1LAST, LTHETA, PWATEH, PV«HC, RAIN, RSUK, PSU^A, PTI^E, TANK,
2, fcSHEC
C**
EXTERNAL EVAP
C**
C CFFINF INITIAL CCNCITICNS AND REMOVE OLD VALUES FRC* COMPUTER
C STCRAGE.
C SNCU IS PRECEPITAT ICN IN THE FCP!" OF SNCV*
C CON5 AhC A ARE CALCULAT ICNAL CONSTANTS
C**
SNCW = 0.0
CCN5 * USHEO * 7.5 / 12. C
A = 42C3. / 528.
RETURN
ENTRY REMOVE (DSLV, FLCW, M)
C**
C CALCULATE DAILY POTENTIAL EVAPCTHANSPIRAT ICN.
C SURRCUTINE EVAP IS TC CALCULATE POTENTIAL FVAPCRATICN ANC IT
C RETURNS A MONTHLY AVERAGE PCTKNTIAL VALUE.
c**-
CALL EVAP (PEVAP)
C SUBTRACT EVAPORATICN FRCM RCCT STCRAGE.
C D6FICT IS DFFICIENCY CF fcATE* IN PLOT STCRAGE.
C**
OEFICT = PWHC - PLATER
IF (DFFICT ,LT. 0.0) DEPICT * 0.0
C**
C POTENTIAL EVAPCTRANSP IRATION DEPENDS CN *CISTURE CCNTENT OF
C GROUND. THE fcFFICIENCY FACTOR (EFF) IS FOUND TO BE ECUAL
C TC PLATER / P*HC. THE DAILY PEVAP IS ECUAL TO PEVAP / 30 *EFF«,
137
-------
c**
EFP = PWATEP / PUHC
PEVAP = PEVAP / 30.
PEVAP = PFVAP * EFF
C**
C SCIL LAYER WATER BALANCE:
C INPUT: PAIN OR SNOV,
C OUTPUT: RUNOFF, PEVAPt AND ADD
C ADC IS HATER ENTERING STORAGE (TANK) AND IT IS A FUNCT1CN OF
C TfFAN AND WOVERU.
PATF. = RAIN / RTIPE
IF («AT£ .GE. 0.25) RAIN = 0.25 * PTIME
C**
C IF TMEAN IS BELCW FKEbZINGi ANY PREC EP I T AT I CN IS TREATEC AS SNOW
C SWMELT IS AMOUNT CF MELTED SNCW
C RUNCFF IS WATER RLNCFF FKCN CVFR-RURCEN
C EMRNF IS EXCESS WATER CONTENT MINLS
C FACC IS TEMPERATURE FACTOR FCR WATER ENTERING STCRAGE
C**
IF (TPEAN .GT. 32.) GC TC 3092
SNCW = PAIN * SNCW
RAIN = 0.0
SWPFLT = 0.0
RUNGFF = 0.0
EVRNF = 0.0
FACC = 0.075
GH TC 30S7
30<32 CCNTINLE
C**
C IF TfFAN IS ABOVE FftFEZINGt PRCCEF.O WITH THE FCLLCMNG:
C IF RAINFALL IS GREATER THAN HEFICT, THE DIFFERENCE IS EXCS. 92
C PERCENT GF THE EXCS IS ASSUMED TO BE RUNCFF ANC THE RFST
C (E^PNF) IS ADDED TC THE BALANCE.
C**
FXCS = RAIN - CEFICT
IF (EXCS) 3093, 30<53, 3094
3003 EXCS = 0.0
3094 PUNCFF = 0.92 * EXCS
EMPNF = EXCS - RUNOFF
C**
C CALCLLATE FADO AS A FUNCTION CF TEMPERATURE. FOR DESCRIPTION OF
C THE DEVELOPMENT, SEE CHAPTER V OF THE TEXT.
C**
IF (TfFAN .GE. 45.) FACC = 0.6
IF (TVEAN .LT. 45. .AND. TVEAN .GT. 32.) FADD = O.C557 * T^EAN
I- 1.707
C**
C IF SKCW FPCM PREVICUS CAYS MELTS DURING TMF/.N AbCVE FRFE.7ING
C CNE TENTH OF AN INCH IS MALTED FOR EVERY DEGREE DAY.
138
-------
c**
IF (SNCVx) 3095, 3CS5, 3056
3095 SW^ELT = 0.0
GC Tf 3C97
300fc SrtNELT = O.I *
-------
c**
TANK = TANK f ADC
IF (TANK .LT. 0.55) HEAD = TANK
IF (TANK ,GE. 0.55) HFAC = 32.1 * TANK - 17.1
FLCH = CCNFH * H£AC
TANK = TANK - FLC*
DSLV ~ 0.0002 * (HLC^ - HEADVI)
3077 CCNTIKUE
FLC^ = FLOW * CCN5
C**
C RETURN TC THt ^AIN PRCCRAN WITH APPROPRIATE VALLES,
C**
RETURN
EMC
140
-------
Sample Output - Auger Hole #1
Date
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
JAN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
2**
25
26
27
28
29
30
31
Flow
(gal/day)
103.
107.
109.
128.
169.
194.
185.
175.
166.
157.
14-8.
1
-------
Date
FtB
FEB
FEB
FEB
FEB
FEB
PER
FER
FEB
FF.B
FCB
FEB
FEB
FEB
F«=B
FFB
FFB
FFB
FEB
FFP
FEB
FFB
FEB
FEP
F6B
Fffl
FEB
FFB
1
2
3
4
5
6
7
9
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Flow
(gal/day)
1*9.
2^»2.
2)9.
1*9.
173.
177.
182.
248.
320.
300.
265.
236.
212.
191.
328.
288.
2^5.
344.
409.
352.
305.
306.
305.
302.
29B.
259.
226.
1^9.
Acid Load
(Ibs/day)
0.07820
0. 106^7
0.12262
0. 12598
0. 12499
O.L2435
0.12675
0. 15362
0.2103^
0. 23747
0.2'i679
0.2384"
0. 2? 5 75
0.20714
0.260.? 4
0.26705
0.2618P
0.3J5PO
0. 371^9
0.39157
0.331R8
0.3731 5
0.36510
0.35193
0. 34030
0.316?7
0.2R908
0.25P40
Rain
(in.)
0 .0
0. 60GOO
0.0
0.0 ..
0.0
0.0
0.02000
0.2 7COO
0.54000
0.040.00
0.0
0.0
0.0
0.0
0.28000
0.0 .
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
GALLONS OF FLO
POUNDS OF ACID
INCHES OF RAIN
DURING MONTH IS
DURING MONTH IS
ENTERING STORAGE
7262
6.c
IS 1.91
ACID REMOVED BY TNUNPATICN 5.477
ACID REMOVED BY GRAVITY DIFFUSION 0.549
ACID REMOVED BY LEACHING 2.774
-------
MAP
MAR
MAR
MAR
MAP
MAR
MAP
MAP
MAP
MAR
MAR
MAP
MAR
MAR
MAP,
MAR
MAR
MAR
MAR
MAR
MAP
MAP
MAP
MAR
MAR
MAR
MAR
MAR
MAP
MAR
MAP
Date
1
2
3
4
5
6
7
8
9
10
il
12
13
14
15
16
17
18
19
20
21
?2
23
?4
25
?6
27
28
29
30
31
Flow
(gal/day)
?73.
3? 5.
361.
393.
401 .
378.
358.
3
-------
Date
APR
APP
APfi
APR
APP
APR
APR
APP
APR
APR
APR
APR
APR
APP
APR
APP,
APR
APR
APR
APR
APR
APR
APR
APR
APR
APR
APR
APR
APR
APR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
IP
20
21
22
23
24
25
26
27
2fl
29
30
Flow
(gal/day)
420.
434.
450.
458.
458.
452.
517.
557.
576.
577.
567.
547.
521.
500.
478.
451.
422.
392.
361.
3^9.
367.
372.
368.
3SO.
415.
432.
435.
429.
430.
420.
Acid Load
(Ibs/day)
0. 3'3743
0.43801
0.47699
0.50781
0.53044
0.54526
0.48593
0.44264
0.41175
0. 38707
0.36602
0.34605
0.32665
0.30760
0.37526
0.41475
0.43157
0. 41769
0.39546
0.37320
0.35947
0.34R06
0.33793
0.33500
0. 34890
0.37725
0.39951
0.41457
0.42545
0.42750
Rain
(in.)
0.15000
1.76000
0.0
0.0
0.0
0.16000
0.05000
0.0
Q.O
0.0
0.0
0.0
0.14000
0.06000
0.0
0.0
0.0
0.0
0.30000
0.54000
0.0
0.0
0.37000
0.54000
0.0
0.0
0.0
0.25000
0.0
0.0
GALLONS OF FLOW DURING MONTH IS 13535
POUNDS OF ACID DURING MONTH IS 12.2
INCHES OF RAIN ENTERING STORAGE IS 3.42
ACID REMOVED BY
ACID REMOVED 8Y
ACID R EMOVEO BY
INUNDATION 9.351
GRAVITY DIFFUSION 0.0
LEACHING 5.346
-------
D"»te
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MA Y
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
MAY
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Flow
(gal/day)
402.
378.
361.
338.
313.
285.
257.
229.
202.
176.
151.
127.
124.
141.
151.
153.
179.
192.
198.
196.
139.
177.
162.
146.
170.
132.
187.
184.
176.
183.
193.
Acid Load
(Ibs/day)
0.41281
0.38864
0.36277
0.33610
0.30870
0.274*3
0.24715
0.22132
0.19665
0.17413
0.15404
0. 13621
0.12187
0.11175
0.10458
0.09906
0.09718
0.09722
0.09858
0.09959
0.09912
0.09746
0. 09489
0.09140
0.09120
0.09254
0.09397
0.09500
0.09475
0.09606
0.09753
Rain
(in.)
0.0
0.16000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.30000
0.37000
0.05000
0.0
0.48000
0.0
0.04000
0.0
0.0
0.0
0 .0
0.0
0.65000
0.0
0.03000
0.0
0.0
1.48000
0.0
0.0
GALLONS OF FLOW DURING MONTH IS 6507,
POUMDS OF ACID DURING MONTH IS 5.1
INCHES OF RAIN ENTERING STORAGE IS 1.34
ACID REMOVED BY
AGIO REMOVED BY
AGIO REMOVED BY
INUNDATION 1.149
GRAVITY DIFFUSION
LEACHING 3.029
0.669
-------
Date
JUNF
JUNc
JUNti
JUK'E
JUNF
JUN^
JUNF
JUNE
JUNF
JUN«E
JUNE
JUNF
JUNE
JUNE
JUNE
JUNF
JUN£
JJNE
JUNE
JUNE
JUNF
JUNE
JUNF
JUNE
JUNF
JUNE
JUNE
JUNF
JUNE
JUNE
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Flow
(gal/day)
193.
190.
1 87.
191.
193.
1«1.
185.
1 78.
168.
158.
146.
135.
123.
117.
1!3.
126.
134.
137.
136.
H2.
126.
119.
111.
102.
93.
83.
BO.
94.
102.
106.
Acid Load
(Ibs/day)
0.09986
0.10052
0.10088
0. 10154
0.10229
0.10292
0.10293
0.10205
0.10046
0.09832
0.0-5576
0.09291
0.0898 i.
0.08696
0.03448
0.03363
0.09367
0.08399
0.08428
0.08433
0.08397
0.08320
0.08204
0.03052
0.07868
0.07656
0.07471
0.07439
0.07489
0.07566
Rain
(in.)
0.0
0.12000
0.45000
0.10000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.25000
0.15000
0. 80000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.27000
0.78000
0.0
0.0
0.0
GALLONS OF FLOW DURING MONTH IS 4143.
POUNDS DP ACID DURING MONTH IS 2.7
INCHES OF RAIN ENTERING STORAGE IS 0.92
ACID REMOVED HY INUNDATION 0.092
ACID REMOVED BY GRAVITY DIFFUSION 1.023
ACID REMOVED BY LEACHING 2.152
-------
Date
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
JULY
1
2
3
4
5
6
7
8
9
10
11
12
13
14-
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Flow
(gal/day)
106.
104.
105.
105.
121.
130.
134.
133.
130.
1?4.
117.
110.
102.
93.
84.
81.
92.
98.
100.
, 99.
102.
102.
100.
95.
97.
95.
91.
98.
100.
102.
112.
Acid Load
(Lbs/day)
0. 07638
0.07685
0.07738
0. 07794
0.07985
0.03229
0.08481
0.08688
0.08818
0.08885
0.08877
0.08816
0. 08704
O.OB547
0.08352
0.08184
0.08151.
0.08183
0.09231
0.03267
0.08340
0.08407
0.08442
0.08440
0.08458
0.08468
0.08450
0.09502
0.08571
0.08655
0.08833
Rain
(in.)
0.0
0.23000
0.12000
0.75000
0.0
0.0
0.0
0.0
0.0
0.0
0.06000
0.0
0.0
0.0
0.30000
0.64000
0.0
0.0
0.0
0.31000
0.0
0.0
0.0
0.32000
0.0
0.0
0.50000
0.0
0.10000
0.50000
0.0
GALLONS OF FLOW DURING MONTH IS 3263.
POUNDS OF ACID DURING MONTH IS 2.6
INCHES OF RAIN ENTERING STORAGE IS 0.82
ACID REMOVED BY
ACID REMOVED BY
AGIO REMOVED BY
INUNDATION 0.022
GRAVITY DIFFUSION
LEACHING 1.868
1.299
-------
Date
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AUG
AJG
AUG
AUG
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Flow
(gal/day);
117.
118.
117.
117.
115.
111.
105.
98.
90.
117.
158.
187,
205.
215.
218.
217.
211.
203.
194.
1*3.
171.
161.
171.
175.
175.
171.
165.
156.
147.
136.
125.
Acid Load
(Ibs/day)
0. 09046
0.09235
0.09377
0.09505
0.09596
0.09621
0.09583
0.09490
0.09348
0.09530
0.10260
0.11478
0.12867
0.14404
0.15649
0.15616
0. 17319
0.17483
0.17516
0.17220
0.16734
0.16159
0. 15895
0.15724
0. 15586
0.15441
0.15177
0. 14824
0. 14405
0.13936
0.13435
Rain
(in.)
0.0
0.0
0.21000
0.0
0.0
0.0
0.0
0.0
1.50000
1 .00000
0 .0
0.0
0.0
0.0
0.0
0 .0
0.0
0.03000
0.0
0.0
0.12000
O.B8000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
GALLONS OF FLOW DURING MONTH IS 4848.
POUNDS OF AGIO DUPING MONTH IS 4.1
INCHES OF RAIN ENTERING STORAGE IS 1.22
ACID REMOVED BY
AC 10 REMOVED BY
ACID REMOVED BY
INUNDATION 0.605
GRAVITY DIFFUSION
LEACHING 3.018
I .490
148
-------
Date
SEPT
SEPT
SEPT
SEPT
S=PT
SEPT
SEPT
SFPT
SEPT
SFPT
SEPT
SEPT
SEPT
SFPT
SEPT
SFPT
SEPT
SEPT
SEPT
SFPT
StPT
SEPT
SEPT
SEPT
SEPT
SEPT
SEPT
StPT
SEPT
SEPT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Flow
(gal/day)
114.
133.
93.
34.
37.
R9.
89.
87.
93.
79*
78.
77.
76.
75.
74.
73.
71.
70.
69.
68.
68.
67.
66.
66.
64.
63.
62.
65.
66.
67.
Acid Load
(Ibs/day)
0.12900
0.12367
O.HB41
0.11341
0.10982
0.10722
0.10518
0.10342
0.10174
0.10003
0.09865
0.09753
0.09660
0.0*5580
0.09511
0.09450
0.09394
0. 09340
0.09294
0.0^256
0.09229
0.09208
0.0
-------
Date
OCT
OCT
OCT
OCT
OCT
OCT
OCT
HCT
DCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
OCT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
10
20
21
22
23
24
25
26
21
26
29
30
31
Flow
(gal/day)
63.
69.
69.
70.
71.
72.
72.
73.
73.
73.
74.
76.
78.
83.
105.
123.
136.
145.
151.
154.
158.
168.
174.
178.
180.
180.
178.
175.
171.
176.
190.
Acid Load
(Ibs/day)
0.0426?.
0.09316
0.09370
0.05431
0.09496
0.09565
0.0^632
0.09697
0.0=>758
0.09819
0. QQ998
0.09978
0.130S4
0.10238
0.10676
0.11346
0. 12096
0.12P34
0.13686
0. 1^368
0. 1*948
0.15653
0.16497
0.17189
0.17763
0. 18214
0.18549
0.18775
0.18907
0.19070
0. 19627
Rain
(in.)
0.0
0.0
0. 30030
0.0
0.0
0.0
0.0
0.0
0.0
0.55000
0.45000
0.0
0.0
0.81000
0.10000
0.0
0.0
0.0
0.0
0.11000
0.56000
0.02000
0.0
0.0
0.0
0.0
0.0
0.0
0.60000
0.73000
0.0
GALLONS Oc FLOW DURING MONTH IS 37.62
POUNDS OF AGIO DURING MONTH IS 4.1
INCHES OF RAIN ENTERING STORAGE IS 1.18
ACID REMOVED
ACID REMOVED
ACID REMOVED
BY INUNDATION 0.480
BY GRAVITY DIFFUSION
BY LEACHING 2.725
1.893
150
-------
Date
NOV
MOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
NOV
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Flow
(gal/day)
200.
206.
216.
219.
2?5.
2?. 9.
211.
233.
233.
232.
232.
231.
229.
227.
219.
1 98.
131.
185.
1«5.
203.
198.
198.
174.
160.
148.
146.
161.
172.
130.
1^0.
Acid Load
(Ibs/day)
0.20550
0.21355
0.226^6
0.23685
0.25311
0.26637
0.27683
0.28492
O.?3099
0.29538
0.29845
0.30042
0.30138
0.30153
0.29401
0. 29102
0.26377
0.25236
0.24731
0.24413
0.24070
0.23428
0.22554
0.21592
0.20563
0.19717
0.19350
0.19297
0.19356
0.10712
Rain
(in.)
0.0
0.60000
0.10000
0.03000
0.03000
0.03000
0.03000
0.03000
0.03000
0.09000
0.04000
0.0
0.04000
0.48000
0.32000
0.0
0.0
0.0
0.0
0.40000
0.0
0.04000
0.0
0.0
0.0
0.0
0.0
0.0
0.25000
0.0
GALLONS OF FLOW DURING MONTH IS 6039,
POUNDS OF ACID DURING MONTH IS 7.4
INCHES OF RAIN EMTERING STORAGE IS 1.50
ACID REMOVED
ACID REMOVED
ACID REMOVED
BY INUNDATION 2.015
BY GRAVITY DIFFUSION
BY LEACHING 4.550
1.871
151
-------
Date
OEC
DFC
OEC
DEC
OEC
DFC
OEC,
DEC
DEC
DEC
DEC
DEC
DEC
DEC
DEC
DEC
DEC
DEC
OEC
DEC
DEC
OEC
DEC
DEC
DEC
DFC
DEC
DEC
DEC
DEC
DEC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Flow
(gal/day)
313.
401.
461.
505.
430.
368.
316.
2°9.
366.
373.
410.
431.
432.
449.
334.
358.
3^0.
389.
466.
453.
387.
444.
688.
638.
545.
468.
404.
351.
307.
270.
239.
Acid Load
(Ibs/day)
0. 29693
0.45491
0.64256
0.61660
0.74705
0.76763
0.74345
0.69445
0.71970
0.73876
0.79631
0.87441
0.93447
0.99303
0.95938
0.91320
0.89517
0.87829
0.94354
0.98499
0.94276
0.96832
0.91687
0.86089
0.73382
0.86658
0.85846
0.80769
0.73306
0. 64038
0.56915
Rain
(in.)
0.0
0.0
0.10000
0.20000
0.0
0 .0
0.0
0.0
0.0
0.0
0.0
1.00000
0.0
0.0
0.0
0.26000
0.24000
0.0
0.0
0.0
0.0
0.88000
1.04000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
GALLONS OF FLOW DURING MONTH IS 12734.
POUNDS OF ACID DURING MONTH IS 24.6
INCHES OF RAIN ENTERING STORAGE IS 3.22
ACID REMOVED BY INUNDATION 19.437
ACID REMOVED BY GRAVITY DIFFUSION 0.044
ACID REMOVED BY LEACHING 8.665
SUMMARY OF DATA FOR 1970
GALLONS OF FLOW DURING YEAR IS 79690.
POUNDS OF ACID DJRING YEAR IS 85.
INCHES OF RAIN ENTERING STORAGE IS 19.69
152
-------
APPENDIX D
INSTRUCTIONS FOR USE OF MA.IN PROGRAM
The use of this program for predicting flow rates and acid loads at
other sites is described in this appendix. The discussion presumes
that the reader is familiar with the technical content of the model
and needs only "nuts and bolts" information to use the computer program
for his system.
The application of this program requires that the user furnish three
kinds of information; i.e.,
1. specific program statements as described below,
2. data describing system, and
3. meteorological data.
The user must furnish statements identifying the input and output
channels of his computer installation. These statements have the form
IN = Input channel number,
10 = Printed output channel number, and
IP = Punched output channel number.
The statements replace the IN, 10, and IP identities at the beginning
of the program. These are channels 5> 6, and 7> respectively, in the
Ohio State University computer system.
Since only portions of the total program are used in the process of
developing the model, an integer control is used to select that portion
of the program that is wanted. If only ADD is to be calculated, as is
the case when Watershed is being evaluated, control (CONTOL) is 1. To
calculate ADD and TANK, control = 2. For ADD, FLOW, and Acid Load,
control = 3-
Description of the Input data cards are listed in Table 13.
153
-------
TABLE 13
INPUT DATA FOR COMPUTER PROGRAM
Control Card, Columns 1 -
Card 1
Columns 1-10
11 - 20
Card 2
Columns
6 - 10,
etc.
I. To Generate ADD
Variable
5 CONTOL
Variable
PWHC
PWATER
VAP
Card 3 "to end of weather data*
Columns 2
7
10
21
31
- 5
- 8
- 20
- 30
- Ho
- 50
Final Card
Columns 2 - h
AMONTH
IDAY
RAIN
RTIME
TMEAN
OXY
"END"
Format
I 5
Format
F10.5
F10.5
F 5-2
A k
I 2
F10.5
F10.5
F10.5
F10.5
A 3
II. To Generate TANK
Card 1 to Card 2 are the same as in I, Control Card integer
= 2
Card 3
Columns 1-10
11 - 20
21 - 30
WSHED
TANK
CONFH
F10.0
HO.5
no. 5
Card k is the same as Card 3 in I.
Final Card is the same as Final Card in I.
III. To Calculate FLOW and Acid Load
Card 1 to Card 3 are the same as in II, Control Card integer
= 3
Card U
Column 1-5
NFEET
I 5
-------
TABLE 13 - (Continued)
Variable Format
Columns 6 - 10 NLAYER I 5
11 - 15 NDEPTH I 5
16 - 20 NPUNCH I 5
Card 5
Columns 1-5 DK F 5-2
6-10 ALKALI F 5.2
11 - 25 FLOWMI F15.5
26 - 35 HEADMI F10.5
36 - k5 PER F10.5
U6 - 55 WSLOPE F10.5
Card 6
Columns 1-15 DI F15.5
16 - 30 TOP F15.5
Card 7 to NLAYER + 7
Columns 1-8 ROCK TYPE 2 A k
11 - 20 ALT F10.1*
21 - 30 REACT F10.14
31 - 1*0 PYCON F10.5
Repeat Card 6 and Card 7 to Card NLAYER + 7 for NFEET - 1 times,
The Cards following Card NLAYER + 7 are the same as Card 3 in I.
Final Card is the same as Final Card in I.
* Summary card can be placed between the daily weather cards as
frequently as desired. Their Format are:
Columns 2-5 "YEAR" A U
51 - 5^ The year number I U
155
-------
A set of HLAYER cards, one for each stratum or substratum, follows the
initial data. In addition to the natural division between coal and
shale layers, it is desirable to subdivide thick binder layers into
thinner layers for computational purposes. In our test case, the coal
layers were divided into sections of no greater than six-inch thickness,
The natural shale layers were one to four inches thick so no division
was necessary. Each card contains a brief alphameric description of
the stratum, the elevation of the bottom of the stratum relative to a
datum plane, the oxygen consumption in the material p.g C^-hr"1 'cm'3,
and the void fraction of the binder.
The final batch of descriptive input data is the initial quantity of
oxidation products stored in each incremental volume. If initial
values are not known, they may be estimated by assuming they are zero
(by inserting an appropriate number of blank data cards) and allowing
the program to run for a simulated period of three to five years.
Storage values will be built up in the STORE (l,J,K) array in this
simulation. These values may be obtained as punched output by reading
a positive value of NPUNCH on the first data card. The punched data
may then be recycled as initial conditions.
Once the system has been described, day-to-day weather data are read
into the program. Each daily data card contains the month and day,
(MONTH and IDAY), the inches of precipitation (RAIN), the hours of
duration of the precipitation (RTIME), the mean temperature (TMEAN),
and the oxygen mole fraction (OXY). Each of these data, except OXY,
must be included on every card. OXY need only appear on the first
card, and thereafter only when its value changes. The remaining data
need only be read for positive changes (i.e., precipitation or tempera-
ture changes), otherwise, the program will assume zero rainfall and
constant temperature. During warmer weather, it is adequate to assume
the monthly average temperature since the chief program use of the
temperature data is the calculation of freeze-thaw information.
The month must be read in as standard three- or four-letter notation:
Jan, Feb, Mar, Apr, May, June, July, Aug, Sept, Oct, Nov, Dec. No
periods are to be used in these abbreviations.
In addition to the weather cards, output control cards may be included
in the data deck. On these cards the word "Year" is punched instead.
of the month, and the year number of the preceding year may be punched.
Placing 'a "Year" card at the end of a block of data will give a print-
out of the summary for total flow and acid load since the previous
"Year" card. Monthly reviews are always printed, so the "Year" card
permits quarterly or annual totals to be printed. The final data card
must contain the word "End" in the month slot to terminate calculations.
The first output from the program is an echo of the descriptive data.
The normal output from the program is the daily flow rate, acid load,
and the quantity of precipitation. In addition, monthly totals of flow
156
-------
and acid load are printed. The monthly acid load is also divided into
the amount removed by each of the three removal mechanisms. The total
reflects the alkalinity of the ground water so it is less than the sum
of the three subtotals. As was mentioned above, provision has been
made for printing longer-term summaries of flow and acid load data if
such are desired.
157
-------
APPENDIX E
EVALUATION OF PARAMETERS AND CONSTANTS FOR SUBROUTINE "REMOVE"
Based on the general principles stated in Section VI, daily drainage
flow and acid load from an underground mine can be calculated with the
help of a digital computer. Calculation of some of the important
parameters and constants are illustrated below. Others are either self-
explanatory or were outlined when describing the program itself.
PWHG: Provisional water holding capacity, or simply, the ability of
the root structure in the soil alyer to hold water. A value of 10
inches for PWHC was used in the Morth model.25 For the McDaniel's model
of this report, a value of k inches was selected after a number of
values were tried. PWHC's larger than k inches gave low levels of
saturation for the winter months. On the other hand, PWHC values
smaller than k inches gave excessive runoff. As a result, a PWHC of
k inches was chosen for the model of the McDaniels complex.
PWATER: Moisture content in the soil layer in inches. This value
varies with the soil layer water balance according to Eq. (16). During
the winter months, the soil layer at the test site is usually close to
saturation (with water) and PWATER should have a value close to PWHC.
On the other hand, in the summer months PWATER will have its lowest
value. In this model, soil layer water balance was started during the
highly saturated period. PWHC values equal to U inches were used as
the initial values.
PEVAP: Potential evaporation. Monthly PEVAP was estimated by the
method of Thornthwaite and Mather.42 SUBROUTINE EVAP chooses the
appropriate value for a given month, which is divided by 30 to become
the dally value. PEVAP is also proportional to the efficiency factor
(EFF), which is the ratio of PWATER to PWHC.
FADD; Temperature factor for determining ADD. When temperatures are
above ^5°F, predominantly during June to October, a constant value for
FADD of 0.8 is assumed. For temperatures below the freezing mark,
occurring mostly in the months of November to March, water in the soil
layer is frozen and less mobility results. A small fraction (FADD = 0.075)
of the water content was assumed to go to storage. When temperatures
are between 32 and ^5°F, a linear relationship given by Eq. (26), was
assumed between the mean temperature (TMEAN) and FADD.
FADD = 0.0557 * TMEAN - 1.707 (32-U5°F). (26)
WOVERW; ratio of PWATER to PWHC. The amount of water leaving the soil
layer as ADD was assumed to be a linear function of WOVERW as expressed
by the equation
159
-------
ADD - FADD * (0.^58 * WOVERW - 0.128) (2?A)
ADD = FADD * (1.38 * WOVERW - 0.38), (2?B)
where Eq. (27A) applies to the mine and auger holes in the McDaniels
complex, and Eq. (27B) was used for the Decker No. 3- Constants for
the ADD equation selected to either increase or decrease RUNOFF during
the "wet" periods of the hydrologic year. The greater the amount of
water removed from the soil layer per day, the more water that can be
taken into the soil layer before it becomes saturated. In the case of
mines with large watersheds or those with relatively level terrain
above the mine, more of the precipitation will enter the soil layer
and Eq. (27B) should be tried first.
WSHED ; Watershed area in square feet through which water passes through
the soil to provide drainage flow water. This is determined by the
observed annual flow (or monthly flow during steady flow period) and
the calculated water entering the aquifer over the same period. Since
FLOW is in gallons and ADD is in inches, a conversion factor of 12/7.5
is used to give WSHED in square feet units. Before a predicted value
for FLOW can be calculated, WSHED must be known. Therefore, the first
step in applying the model must be the calculation of the annual ADD
total. The values of WSHED used for the McDaniels Test Mine, auger
holes, and Decker #3 Mine are listed in Table lU. Sample calculations
using annual flow data and data points during a steady flow period are
illustrated below using data from Auger Hole #1.
A. WSHED by annual flow data:
Annual ADD for 1970 = 19.69 inches
Observed 1970 total flow from Auger Hole #1 = 75.690 gallons
WSHED = P008 x „ - x = 6180 ft*
19.69 inches 7.5 gallons ft.
B. WSHED by data during steady flow period:
Monthly ADD for July, 1970 =0.82 inch
Observed total outflow in July, 1970 from Auger Hole #1 = 3069
• gallons
WSHED = 3069 gallons x ftg x 12 in. = 6ooo ft?
0.82 inch 7.5 gallons ft.
TANK; Aquifer storage for drainage flow. The concept of TANK is
hypothetical; therefore, a value representing aquifer storage, which
is the source of drainage flow, cannot be determined by field measure-
ments. The base value of TANK is not the most critical factor in the
160
-------
TABLE 14
LIST OF CONSTANTS AND PARAMETERS
WSHED (ft2)
Base TANK (in.)
CONIH
HEADMI (in.)
WSLOPE
PER
FLOWMI (gal)
McDaniels
Test Mine
7,920
2.13
0.0200
1.510
(150 gal)
0.15
1.8
300
Auger Hole
6,180
1.10
0.0236
0,931
(85 gal)
0.08
1.5
115
Auger Hole
#3
4,710
1.18
0.0207
0.491
(30 gal)
0.12
1.6
60
Auger Hole
#4
3,640
1.07
0.0240
0.550
(30 gal)
0.07
1.4
80
Auger Hole
#5
1,010
0.51
0.1120
0.
(0 gal)
0.10
1.7
0
Auger Hole
#6
6,800
0.86
0.0392
0.420
(70 gal)
0.16
2.0
95
Decker #3
Mine
2,750,000
0.50
0.0300
0.660
(34,000 gal)
0.10
2.5
290,000
-------
relation for predicting FLOW, but the relationship of TANK - HEAL is
most important. Certainly, the better the base value for TANK, the
"better the TANK - HEAD relationship can be described. The procedures
for estimating TANK from experimental data are outlined in the following
steps:
1. During a steady flow period, values of TANK are compara-
tively constant. In light of this, the generation of the
base value of TANK is best started in this period.
2. The program (i.e., SUBROUTINE REMOVE) was run for a
period of four years. Auger Hole #1 will be used to
illustrate how the values for constants used in FLOW
calculations were obtained.
a. assume TANK = 0.82
This is a hypothetical value, not the base value
discussed in the above paragraphs. The actual
value is not critical, but some value must be
assumed. For reference purposes, 0.82, which was
the total monthly ADD in July, 1970, was chosen
to be the value of TANK.
b. Temperature and rainfall data used for the period
were a repetition of 1970 data.
c. The relation: FLOW = CONIH * TANK was used. The
value of CONFH was determined by
FLOW _ 0.026 _
TANK 0.82 ~
where 0.026 is the July, 1970, average daily flow
in inches obtained from
3960 gallons month ft3 1 12 in.
month 30 days 7.5 gallons 61bO ft" ft.
= 0.026 inches.
d. After the first two years of program running period,
values of TANK in July, 1969, and 1970, became
"steady" values, ranging between 1.15 and 1.06. An
average value equal to 1.1 was used as the assumed
base value of TANK during the steady flow period.
3. CONFH; Constant relating flow and aquifer storage.
During steady flow period, TANK (l.l) and the average
162
-------
daily flow (0.026) are known. Then, CONFH is the
quotient of 0.026/1.1 = 0.0236 for Auger Hole #1. Other
CONFH values are listed in Table ±k.
HEAD; Head of water stored in the aquifer. Auger Hole #1 is used for
the purpose of illustration. The procedures to establish the relation-
ship between TANK and HEAD are listed as follows:
1. Up to this point, values for WSHED (6l80 ft2), base TANK
(l.l inches), and CONFH (0.0236) are known. With these
parameters and constants, FLOW in gallons per day and
daily TANK in inches can be obtained from the output of
the program.
2. Outputs for the steady flow period were examined. The
examination was conducted in the following manner.
a. Convert the observed flow data from gallons per day
to inches of water per day by the relation
WSHED * ^jr * CONFH;
for example, the observed FLOW was 350 gallons per
day on March 8, 1970. The corresponding HEAD to
give this FLOW will be
350 gallons x 1 x 12 in. -. ft3 x 1 ,. -, dav
day 6180 fty ft. 7.5 gal. 0.0236
=3-84 inches.
b. From the output of the program, the value of TANK
•was found to be 1.2 inches on March 8,1970.
c. The values from steps a and b above were located on
HEAD vs. TANK plot as one point to establish the
relationship between HEAD and TANK.
d. Several other points were obtained by repeating
steps a through c; then a diagram (as shown in
Fig. 30) was constructed.
3- Based on the data shown in Fig. 30, two intersecting
straight lines were used to represent the curve for the
sake of ease in formulating the equations which were
used in the computer program.
163
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6r
a
UJ
x
I 2
TANK (in.)
Figure 30 - HEAD vs TANK from Experimental Data
161*
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DSLV; Fraction of products removed each day by leaching. At and below
the minimvim flow rate, the amount of acid removed by leaching was
assumed to be negligible. Above this minimum flow (HEADMl), leaching
is an important contribution to the acid output and the following re-
lation was assumed:
DSLV = CONDH x (HEAD - HEADMl). (28)
CONDH is a constant. By trial and error methods, a value for CONDH
equal to 0.0002 was found to give satisfactory DSLV values. To deter-
mine HEADMl, flow and acid data for a given period were compared.
During flow periods that give a low and steady acid load, acid load
was assumed to be due to diffusion only. The average flow (in inches)
during these periods is HEADMl. For Auger Hole #1, such a period
occurred between June and July of 1970, and HEADMl = 0.931 inch (or
85 gal/day) was used. The values of HEADMl for the other mines being
modeled are listed in Table 14.
WSLOPE: Hypothetical slope of water table. From the point in the
K-direction that is flooded, the water table is assumed to rise with
slope (WSLOPE). A fixed value for WSLOPE can be assumed and the value
of DEHK (described in the next paragraph) can be determined so as to
provide enough exposed pyrite material to meet the yearly (or monthly)
acid load required. After different values (listed in Table 1^) of
WSLOPE were used in the development of the model, a fixed value of 0.1
was found to be adequate for use in the models evaluated to date. This
is because the variation of WSLOPE has little effect on the acid load
removed by inundation.
DEHK; The distance in the K-direction that is flooded. DEHK is calcu-
lated by using Eq. (22). In the equation, PER is a constant value so
determined that DEHK will have enough exposed pyrite to generate the
required yearly acid production. After several trials, a value for PER
equal to 1.5 was selected for Auger Hole #1. FLOWMI in Eq. (22) is a
constant value which was determined by comparing flow and acid load for
a given period. During flow periods that give high acid loads, flooding
was assumed to be the major contribution to acid removal. The average
flow (in gal/day) during these periods is FLOWMI. For Auger Hole #1,
such a period occurred between March and April of 1970, and FLOWMI =
115 gal/day was used.
To summarize; the procedure for modeling a mine by methods proposed
in this report may be outlined as follows:
A. Evaluation of Basic Constants and Parameters
1. Generate daily, monthly, and annual ADD from SUBROUTINE
REMOVE
2. Calculate WSHED and base TANK values
165
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3. Generate daily values of TANK from SUBROUTINE REMOVE
k. Establish relationship between TANK and HEAD
5. Estimate location of water table (i.e., evaluate DEHK).
B. Calculate FLOW and Acid Loads
The required input data are listed as follows:
1. To generate ADD:
PWHC, PWATER, VAP, and daily weather conditions (AMONTH,
IDAY, RAIN, RTIME, TMEAN)
2. To generate TANK:
In addition to the data required in 1, WSHED, TANK, and
CONFH are required
3. To calculate FLOW and acid loads:
In addition to the data in 1, and 2, NFEET, NLAYER,
NDEPTH, NFUNCH, DK, ALKALI, FLOWMI/HEADMI, PER, WSLOPE,
DI, TOP, ROCK, TYPE, ALT, REACT, and PYCON are needed.
166
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SECTION XIII
REFERENCES
1. Agnew, A. F., and Corbett, D. M., "Hydrology and Chemistry of Coal
Mine Drainage in Indiana," 157th National Meeting, Am. Chem. Soc.,
Division of Fuel Chemistry, Minneapolis, (1969).
2. Bailey, J. R., "Biological Oxidation of Pyrite," M.S. Thesis, The
Ohio State University, (1968).
3. Bird, R. B.; Stewart, W. E.; and Lightfoot, E. N., Transport
Phenomena, John Wiley and Sons, New York, (1960).
k. Birle, J. D., "Sulfide to Sulfate Reaction Mechanism in Pyritic
Materials," M.S. Thesis, The Ohio State University, (1963).
5. Brown, W. E., "The Control of Acid Mine Drainage Using an Oxygen
Diffusion Barrier," M.S. Thesis, The Ohio State University, (1970).
6. Burke, S. P., and Downs, R., "Oxidation of Pyritic Sulfur in Coal
Mines," AIMME Transactions, 130 (1938), 1*25.
7. Caruccio, F. T., "The Quantification of Reactive Pyrite by Grain
Size Distribution," Proc. Thrid Symposium on Coal Mine Drainage
Research, Pittsburgh, Pa., (1968).
8. Caruccio, F. T., and Parizek, R. R., "An Evaluation of Factors
Affecting Acid Mine Drainage Production in Western Pennsylvania,"
Proc. Second Symposium on Coal Mine Drainage Research, Pittsburgh,
Pa., (1968).
9. "Climatological Data, "Environmental Data Service, United States
Department of Commerce, (1895- ).
10. Corbett, D. M., "Ground Water Hydrology Pertaining to Surface
Mining for Coal—Southeastern Indiana," Proc. Second Symposium on
Coal Mine Drainage Research, Pittsburgh, Pa., (1968).
11. Davis, S. M., and DeWiest, R. J., Hydrogeology, John Wiley and
Sons. New York, (1968).
12. Dugan, P. R., and Lundgren, D. G., "Energy Supply for the Chemauto-
troph Ferrobacillus Ferrooxidans," J. Bact., 89:9 (1965), 825.
13. Good, D. M., "The Relation of Refuse Pile Hydrology to Acid Pro-
duction," M.S. Thesis, The Ohio State University, (1970).
Ik. Grove, D. R., "Ferric Ion Oxidation of Pyrite," M.S. Thesis, The
Ohio State University, (1970).
167
-------
15. Jutte 3 R. B., Jr., "Effect of Oxygen and Nitrogen in Aqueous
Solution on the Kinetics of the Sulfide to Sulfate Reaction,"
M.S. Thesis, The Ohio State University, (1966).
16. Kim, H. W.., "Vapor Phase Oxidation of Pyrite," M.S. Thesis, The
Ohio State University, (196*0.
17. Konicek, M. G., "The Biological Oxidation of Pyrite," M.S. Thesis,
The Ohio State University, (1966).
18. Larez, A. L., "Kinetics of Pyrite Oxidation," M.S. Thesis, The
Ohio State University, (1970).
19. Lau, C. M.; Shumate, K. S.; and Smith, E. E., "The Role of Bacteria
in Pyrite Oxidation Kinetics," Proc. Third Symposium on Coal Mine
Drainage Research, Pittsburgh, Pa., (1970]7
20. Lorenz, W. C., and Tarpley, E. C., "Oxidation of Coal Mine Pyrites,"
United States Bureau of Mines Report of Investigations No. 62k7,
21. "Mine Drainage Abstracts; A Bibliography," Coal Research Board,
Pennsylvania Department of Mines and Mineral Industries, Bituminous
Coal Research, Inc. (1965- ).
22. Moeb, N. N., "Mine Air Sealing: A Progress Report" Proc. Second
Symposium on Coal Mine Drainage, Mellon Inst. Pittsburgh, Pa.,
(1968).
23. Morth, A. H., "Reaction Mechanism of the Oxidation of Iron Pyrite,"
M.S. Thesis, The Ohio State University, (1965).
2k. Morth, A. H., and Smith, E. E., "Kinetics of the Sulfide-to-Sulfate
Reaction," 151st National Meeting, Am. Chem. Soc., Pittsburgh, Pa.,
(1966).
25. Morth, A. H., "Acid Mine Drainage: A Mathematical Model" Ph.D.
Dissertation, The Ohio State University, (1971).
26. Moulton, E. Q,., "The Acid Mine Drainage Problem in Ohio," Engi-
neering Experiment Station, Bulletin 166, The Ohio State University,
(1957).
27. Ohio State University Research Foundation, "Sulfide to Sulfate
Reaction Mechanism," Water Pollution Control Research Series 1^010
FPS--02/70, Federal Water Quality Administration, Department of
Interior, (1970).
28. Nelson, H. W.; Snow, R. D.j and Keyes, D. B., "Oxidation of Pyritic
Sulfur in Bituminous Coal," IEC, 25 (1933), 1355.
168
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29. Sasmcgo, S., "Oxidation Kinetics of Pyritic Materials in Aqueous
Media," Ph.D. Dissertation, The Ohio State University, (1969).
30. Scott, R. B.; Hill, R. D.; and Wilmoth, R.'D., "Cost of Reclamation
and Mine Drainage Abatement-Elkins Demonstration Project,"
lUOlO—10-70, Water Quality Office, Environmental Protection Agency,
(1970).
31. Shumate, K. S., and Smith, E. E., "Development of a Natural Labora-
tory for the Study of Acid Mine Drainage Production," Proc. Second
Symposium on Coal Mine Drainage Research, Pittsburgh, Pa., (1968).
32. Shumate, K. S., Associate Professor, The Ohio State University,
Personal Communication.
33- Shumate, K. S.; Smith, E. E.; and Brant, R. A., "A Model for Pyritic
Systems," 157th National Meeting, Am. Chem. Soc., Division of Fuel
Chemistry, Minneapolis, Minn., (1969).
3^. Singer, P. C., and Stumm, W., "Oxygenation of Ferrous Iron in Mine
Drainage Waters," 157th National Meeting, Am. Chem. Soc., Division
of Fuel Chemistry, Minneapolis, Minn., (1969).
35. Smith, E. E., Professor, The Ohio State University, Personal
Communication.
36. Smith, E. E., "Engineering Aspects of Acid Mine Drainage," Proc.
Second Annual Symposium, Water Resources Research, The Ohio State
University, (1966).
37. Smith, E. E., and Shumate, K. S., "Pilot Scale Study of Acid Mine
Drainage," Water Pollution Control Research Series lAOlO EXA
03/71.
38. Smith, E. E.; Svanks, K.; and Halko, E., "Aerobic-Anaerobic Oxida-
tion of Pyrite," 157th National Meeting, Am. Chem. Soc., Division
of Fuel Chemistry, Minneapolis, Minn., (1969).
39- Smith, E. E.; Svanks, K.; and Shumate, K. S., "Sulfide to Sulfate
Reaction Studies," Proc. Second Symposium on Coal Mine Drainage
Research, Pittsburgh, Pa., (1968).
kO. Sternberg, Y. M. and Agnew, A. F., "Hydrology of Surface Mining—A
Case Study," Water Resources Res., 1*:2, (1968), 363-8.
Ul. Stiles, D., Unpublished Data, The Ohio State University.
169
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Thornthwaite, C. W., and Mather, J. R., "Instructions and Tables for
Computing Potential Evapotranspiration and the Water Balance,"
Publications in Climatology, Volume X, Number 3> Drexel Institute of
Technology Laboratory of Climatology, Centerton, New Jersey (1957).
Vimmerstedt, J. P., and Struthers, P. H., "Influence of Time and
Precipitation of Chemical Composition of Spoil Drainage," Proc.
Second Symposium on Coal Mine Drainage Research, Pittsburgh, Pa.,
(1968).
Wisler, C. 0., and Brater, E. F., Hydrology, John Wiley and Sons,
New York (1959).
170
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SECTION XIV
LIST OF PUBLICATIONS
1. Morth, A. H.; Smith, E. E.; and Shumate, K. S., "Pyritic Systems:
A Mathematical Model," 3rd Symposium on Coal Mine Drainage, Mellon
Inst., Pittsburgh, Pa., May 1920, 1970,
2. Morth, A. H., "Acid Mine Drainage: A Mathematical Model," Ph.D.
Dissertation, The Ohio State University (1971).
3. Chow, K. Y. "Computer Stimulation of Acid Mine Drainage," M.S.
Thesis, The Ohio State University (1972).
*U.S. GOVERNMENT PRINTING OFFICE:1972 514-149/94 1-3
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SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
The Ohio State University Research Foundation, Columbus, Ohio
Title
Pyritic Systems: A Mathematical Model
JQ Authors)
Movth Arthur H
Smith, Edwin E.
Shumate, Kenesaw S.
16
21
Project Designation
1U010 EAH
Contract No. 1^-12-589
Note
22
Citation
Environmental Protection Agency report
number EPA-R2-72-002, November 1972.
23
Descriptors (Starred First)
Mine Drainage; Computer Models; Coal Mine Drainage; Pyrite; Pollution Abatement;
Industrial Wastes
25
Identifiers (Starred First)
27
Abstract
A mathematical model of an acid mine drainage system has been developed for under-
ground mines. The model relates the rate of acid formation to the rate of pollution
discharge from the system.
The calculational model was developed using a digital computer to simulate an exist-
ing mine as the sum of many micro scale mines, each representing a small reactive
volume in the system being modeled. The input to the model is a physical and chemi-
cal description of the system. Day-to-day simulation requires data on temperature,
rainfall, and oxygen concentration at the exposed coal face. The output of the
model is estimates of daily acid load and drainage flow, plus monthly and yearly
summaries.
The calculational model was based on a carefully described physical model so that a
predictive model can be constructed with little or no experimental data. However,
methods for constructing the computational model are given which can utilize the
field data available to increase the reliability of the model.
Abstractor
Dr. Edwin E. Smith
Institution
The Ohio State University Research Foundation
WR:I02 (REV JULY 18691
WRSIC
SEND TO;
WATER RESOURCE! SCIENTIFIC INFORMATION CENTER
US. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
• GPO: 1S69-3S9-339
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