EPA-600/2-76-112
November 1976
Environmental Protection Technology Series
RESOURCES ALLOCATION TO
OPTIMIZE MINING POLLUTION CONTROL
Industrial Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL PROTECTION
TECHNOLOGY series. This series describes research performed to develop and
demonstrate instrumentation, equipment, and methodology to repair or prevent
environmental degradation from point and non-point sources of pollution. This
work provides the new or improved technology required for the control and
treatment of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-76-112
November 1976
RESOURCES ALLOCATION TO
OPTIMIZE MINING POLLUTION CONTROL
by
Kenesaw S. Shumate, E. E. Smith,
Vincent T. Ricca, Gordon M, Clark
The Ohio State University Research Foundation
Columbus, Ohio 43212
Contract No. 68-01-0724
Project Officer
Eugene F. Harris
Extraction Technology Branch
Industrial Environmental Research Laboratory
Cincinnati, Ohio 45268
INDUSTRIAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This report has been reviewed by the Industrial Environmental
Research Laboratory-Cincinnati, U.S. Environmental Protection Agency,
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the U.S. Environ-
mental Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
11
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FOREWORD
When energy and material resources are extracted, processed, con-
verted, and used, the pollution to our environment and to our aesthetic
and physical well-being requires corrective approaches that recognize
the complex environmental impact these operations have.
The Industrial Environmental Research Laboratory - Cincinnati uses
a multidisciplinary approach to develop and demonstrate technologies
what will rectify the pollutional aspects of these operations. The
Laboratory assesses the environmental and socio-economic impact of
industrial and energy-related activities and identifies, evaluates and
demonstrates control alternatives.
This report presents a comprehensive model for mine drainage simu-
lation. The model predicts pollution loads for given situations and
then recommends optimum allocation of resources for treatment of abate-
ment procedures. The work presented in this report is the first of
several projects aimed at computer analysis of mine sites.
The model described herein has not been fully tested against a
real situation. Other contracts are planned to continue this type of
research. The product of this study, and following studies, will be of
use to planning agencies and the mining industry. Through use of tools
such as this, we may be able to increase production of vital energy
resources while continuing to improve the environment.
David G. Stephan, Director
Industrial Environmental
Research Laboratory
Cincinnati
111
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ABSTRACT
A comprehensive model for mine drainage simulation and optimization of
resource allocation to control mine acid pollution in a watershed has
been developed.
The model is capable of: (a) producing a time trace of acid load and
flow from acid drainage sources as a function of climatic conditions;
(b) generating continuous receiving stream flow data from precipitation
data; (c) predicting acid load and flow from mine drainage sources using
precipitation patterns and watershed status typical of "worst case" con-
ditions that might be expected, e.g., once every 10 or 100 years; and
(d) predicting optimum resource allocation using alternative methods of
treatment and/or abatement for "worst case" conditions during both wet
and dry portions of the hydrologic year.
The model is comprehensive and may, therefore, be more detailed than
required. This attention to detail was given in the belief that it will
be easier to simplify the model than to modify it to increase detail.
Because of the detail incorporated in the model as now constituted, a
large amount of field data is required as input. In most cases, the
desired field data are not now available.
The model has not been fully tested or compared to real systems, nor has
sensitivity to input data been determined. Therefore reliability of the
model, and the necessity of detailed field data, have not been established.
Comparisons with real systems are necessary to determine the level of
simplification that can be permitted before the validity or usefulness
of the model is impaired.
This report was submitted in fulfillment of Contract Number 68-01-0724
by The Ohio State University Research Foundation under the sponsorship
of the Environmental Protection Agency.
KEY WORDS:
Mine Drainage, Computer Models, Watershed Models, Deep Mines, Refuse
Piles, Stripmines, Coal Mine Drainage, Acid Generation, Acid Drainage
Treatment
IV
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CONTENTS
Page
Disclaimer ii
Foreword ill
Abstract iv
List of Figures vii
List of Tables xi
Acknowledgments xiii
Section
I CONCLUSIONS 1
II RECOMMENDATIONS 2
III INTRODUCTION 3
IV SHORT DISCUSSION OF THE PROJECT MODEL CONTENT AND
OPERATION 5
Basic Physical Phenomena 5
Hydrologic Model 5
Hydrologic Cycle and Its Model 6
History of the Hydrologic Model Development 6
Model Operation 8
Polluted Water Generated by Mining Activities 8
Acid Generation Model 10
Pyrite Oxidation 10
Removal of Oxidation Products 12
Pollutant Source Models lU
Deep Mine Source Model 19
Combined Refuse. Pile-Strip Mine Source Model 19
Basin Model 19
v
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CONTENTS (continued)
Section Page
Cost-Effectiveness Model 21
Acid Control Alternatives 22
Socio-Political-Economic Considerations 2U
Basin Optimization Models 2U
V ILLUSTRATIVE EXAMPLES 33
Source Models 33
Input Requirements 3^
Basin Information 3^
Climatic Data 3^
Deep Mine Information 3^
Refuse Pile-Strip Mine Information 3^-
Discharge Data 35
Examples of Output 35
Deep Mine Source Model 35
Combined Refuse Pile-Strip Mine Source Model 37
Other Information ^0
Basin Optimization ^0
VI EVALUATION OF OVERALL TECHNIQUE ^9
Source Model 50
Optimization Model 5^-
VII PUBLICATIONS 56
VIII APPENDICES 57
Appendix A - Deep Mine Pollutant Source Model 58
Appendix B - The Refuse Pile and Strip Mine Pollutant
Source Models 10^-
Appendix C - Optimization Model for Resource Allo-
cation to Abate Mine Drainage Pollution 183
Appendix D - Cost of Drainage Treatment 459
VI
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LIST OF FIGURES
Figure Ho. Page
1 Schematic of hydrologic cycle 7
2 Moisture accounting in Stanford Watershed Model 9
3 Idealized deep mine element 12
k Schematic of Deep Mine Drainage Model 15
5 Schematic of Combined Refuse Pile-Strip Mine Model l6
6 The Deep Mine Source Model 17
7 Total acid load and acid load from each source
area 18
8 Schematic diagram of subdivided "basin 20
9 Input-output diagram for Basin Optimization Models 2.k
10 Stream network 25
11 Illustration of stream network with potential
instream treatment facilities 27
12 Single stream with adjoining land uses 31
13 Streamflow hydrograph at the Big Four Watershed
Outlet 35
l^f- Daily minewater discharge from McDaniels' Mine 36
15 Daily acid load discharge from McDaniels' Mine 36
l6 Acid load nonuniform short duration rain 37
17 Stream flow hydrograph at the basin outlet 38
18 Daily flows from acid producing areas 38
19 Daily acid loads from acid producing areas 39
VII
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LIST OF FIGURES (continued)
Figure Ho. Page
20 Flow and acid load from acid producing areas -
short duration rain 39
21 Stream network lj-1
A.I Schematic of hydrologic cycle 6l
A.2 Underground pyritic system 62
A.3 Moisture accounting in Stanford Watershed Model 65
A.4 Schematic of Acid Mine Drainage Model 68
A.5 Infiltration from UZS that is held in LZS 69
A.6 Logic diagram of The Ohio State University version
of the Stanford Watershed Model 72
A.7 Logic diagram of the Acid Mine Drainage Model 75
A.8 The test watershed site 77
A.9 Double mass plot of precipitation data 78
A. 10 Streamflow hydrograph at the Big Four Hollow
watershed outlet 8l
A. 11 Daily minewater discharge from McDaniels' Mine 84
A.12 Daily acid load discharge from McDaniels1 Mine 85
B.I Hydrologic cycle on a refuse pile 108
B.2 Step diagram of the Refuse Pile Model 112
B.3 Acid load for continuous rain 135
E.h Acid load short interval continuous rain 137
B.5 Acid load nonuniform short duration rain 138
B.6 Soil column 152
B.7 ACDPRO Program listing 157
B.8 ACDPRO flow chart 158
Vlll
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LIST OF FIGURES (continued)
Figure Ho. Page
B.9 The ACDSEC Subroutine Program 162
B.10 The ACDSTR Subroutine Program l64
B.ll CRPSMM (Combined Refuse Pile - Strip Mine Model)
block diagram iyo
C.I Single-stream watershed L&4-
C.2 Effect of instream treatment facilities 186
C.3 Single stream with adjoining land uses 192
C.4 Illustration of stream and node designation 197
C.5 Program MAXEF 259
C.6 Function CABAT 297
C.7 Function CSAV
C.8 Function EFFECT
C.9 Subroutine ERROR 509
C.10 Subroutine HEFESE J10
C.ll Subroutine TOFE 521
C.12 Subroutine TOME J24
C.13 Subroutine ZOE 529
C.l4 Program ALCOT J40
C.15 Subroutine COM) J82
C.l6 Subroutine ERROR 589
C.17 Subroutine NEXFES 590
C.l8 Function NON 402
C.19 Subroutine PTMAX 4o4
IX
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LIST OF FIGURES (continued)
Figure No. Page
C.20 Subroutine PTMX
C.21 Subroutine STORE
C.22 Function TCOST
C.23 Subroutine TOFF
C.24 Subroutine TON
C.25 Subroutine ZO
D.I A plot of acidity concentration vs. lime cost
D.2 A plot of acidity concentration vs. lime cost
1967 West Virginia University data '^
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LIST OF TABLES
Table No. Page
1 Illustrative variation of basic value with
maximum pollution concentration 30
2 Mine sources and pollution control costs ^3
3 Average annual pollutant loads kk
k Pollutant and stream flows spring rates ^5
5 Pollutant and stream flows summer rates k6
6 Minimum cost (DWMC) model results ^7
7 Maximum effectiveness (DWME) model results kj
8 Minimum annual pollution control costs from
the DWC model k8
A.I S₯M parameters 6k
A. 2 AMD parameters 67
A.3 Basin and mine characteristics 79
A.^l- Daily infiltrating water reaching the mine
aquifer 80
A. 5 Synthesized daily minewater discharge 82
A.6 Synthesized daily acid load 83
A.7 Synthesized monthly and annual minewater discharge
and acid load 86
B.I Input variables obtained from the Stanford Water-
shed Model 113
B.2 Input variables into the refuse pile
B.3 Internal variables of the refuse pile model 115
XI
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LIST OF TABLES (continued)
Table No. Page
B.4 Daily acid load in direct runoff 125
B.5 Daily acid load in interflow 126
B.6 Daily acid load in baseflow 127
B.7 Daily acid load 128
B.8 Daily direct runoff reaching receiving stream 129
B.9 Daily interflow reaching receiving stream 130
B.10 Daily baseflow reaching receiving stream 131
B.ll Daily flow reaching receiving stream 132
B.12 Monthly summary of acid loads and flows 133
B.13 Specific day output 13^
B.lU ACDERO Program input and output l60
B.15 CRPSMM internal variables 165
B.l6 CRPSMM input variables l66
C.I Illustrative variation of basic value with
maximum pollution concentration 192
D.I Cost and effectiveness of various techniques for
controlling acid mine drainage 460
D.2 Estimation of capital investment cost 46l
D.3 Estimation of total production costs 462
Drk Estimated costs of lime neutralization of acid
mine drainage 464
D.5 Estimated costs of lime neutralization of acid
mine drainage based on equation (D.4) 466
D.6 Estimated costs of lime neutralization of acid
mine drainage based on equation (D.4) 46?
XI1
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LIST OF TABLES (continued)
Table Ho. Page
D.7 Estimated costs of lime neutralization of acid
mine drainage based on equation (D.5)
D.8 Estimated costs of lime neutralization of acid
mine drainage based on equation (D.5)
Xlll
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ACKNOWLEDGMENTS
The authors are grateful for the assistance of Dr. John T. Heibel,
Assistant Professor of Chemical Engineering, The Ohio State University,
for his efforts in assembling cost functions information used in the
optimization model.
The following graduate students have made significant qontributions in
the research project and much of their writing has been incorporated
into this report:
Kurtis Chow, Post Masters, Department of Chemical Engineering,
The Ohio State University.
Stanley Johnson, Master of Science, Department of Civil
Engineering, The Ohio State University.
Arthur Maupin, Master of Science, Department of Chemical
Engineering, The Ohio State University.
Richard K. Law, Master of Science, Department of Chemical
Engineering, The Ohio State University.
David Bitters, Ph. D. candidate and Graduate Research
Associate, Department of Industrial and Systems Engineering,
The Ohio State University.
Marilyn Vaughn, Master of Science, Department of Industrial
and Systems Engineering, The Ohio State University.
The following personnel of the Environmental Protection Agency have
contributed much effort in technical assistance and administration
of this project.
Eugene F. Harris, Project Officer, Mining Pollution Control
Branch, National Environmental Protection Agency, Cincinnati,
Ohio.
Ronald D. Hill, Mining Pollution Control Branch, National
Environmental Protection Agency, Cincinnati, Ohio.
xiv
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The project investigators are grateful to The Ohio State University
Research Foundation personnel for their administrative assistance and
coordination with the sponsor.
Finally, a special thanks to Chet Ball and his staff for their fine
job of typing and drafting performed in the writing of this report.
xv
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SECTION I
CONCLUSIONS
1. Source models for predicting the time dependent acid production
from deep (underground) mines, refuse piles, and spoil banks hE&v^j
been developed. '»
2. The source models simulate flow and acid load data from the prin-
cipal sources of mine acid.
3. In the deep mine and combined refuse pile-spoil bank model, over-
land as well as subsurface flows are determined by the Ohio State
University Version of the Stanford Watershed Model. Stream flows and
acid concentrations< are calculated from the watershed model output'.
4. The deep mine source model has been validated, but the refuse
pile-spoil bank model has yet to be compared to suitable field data.
5. In general, sufficient field data is not now available to fuLJ-y
utilize the present models; additional hydrologic data is usually
needed.
6. The optimization models provide a compact and efficient cost
optimization algorithm capable of determining the least cost set
of pollution control decisions for a branching array of acid sources.
7. The optimization model can also determine the distribution of
pollution control decisions over the total array of acid sources
which will produce the most desirable water quality for a fixed upper
limit on dollars for pollution control.
8. The optimum resource allocation may vary with the "worst case"
situation: (a) high flow, high acid load, or (b) low flow, high acid
concentration.
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SECTION II
RECOMMENDATION'S
The validity of the unit source models as related to "real world"
situations should be established. The performance of the acid genera-
tion models should be evaluated by comparing predicted acid loads and
in-streani concentrations with actual field data.
A sensitivity study of the key parameters in the models should be made;
the degree of precision needed for these parameters, and methods for
simplifying the amount and type of required, input data need to be
evaluated in relation to the degree of simulation success wanted.
Deficiencies in (normally) available field data should be described
ajad guidelines for future acquisition and collection methodology
developed.
Prepare readily usable models for EPA personnel, including instruc-
tional material for potential users with both detailed guidelines,
card decks, tapes, as well as short courses when desired.
A predictive model should be developed for analyzing unmined areas
to predict level of pollution to be expected as a function of the
type and scale of mining anticipated, and to provide a basis for
selecting mining and abatement methods to minimize pollution and cost
of abatement.
The Optimization Model should be applied to analyze an existing water-
shed to assess the model's utility, ease of application, and potential
results.
The effect of a reservoir as a component part of a watershed should
be included in the Optimization Model so it could be evaluated as an
alternative abatement method.
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SECTION III
INTRODUCTION
The purpose of the work reported herein was to develop a planning and
management tool for use in determining cost-effective actions to elimi-
nate or abate acid mine drainage from coal mining operations. Specifi-
cally, computer based modeling techniques have been developed for the
description and/or prediction of acidity levels in the drainage from
deep and surface mines, and from coal refuse piles. Using these source
models, the acid load from a given acid source or grouping of related
sources can be predicted for any desired time period, with geological
conditions and rainfall variation accounted for in the models. Knowing
the acid load from each source, as a function of time, alternative mine
drainage treatment and at-source abatement techniques can be identified
and their costs estimated, together with their effectiveness in terms
of reduction of the unabated acid loads. Alternative cost and effec-
tiveness estimates for the individual acid sources are then used as
input to an optimization model, which can be used to calculate the
minimum cost for a given level of abatement in the basin, or, alterna-
tively, the maximum water quality attainable for a given cost.
The approach used in the development of the computerized models out-
lined above was dictated by the current level of knowledge concerning
the formation of acid in mines and refuse piles, the transport of acid
to the receiving streams via ground and surface water runoff, and the
cost and effectiveness of possible abatement and treatment alterna-
tives. Due to the extremely short-term and seasonal variability in
mine drainage quality and quantity from a given source, which is
closely associated with local hydrology and precipitation patterns, and
due to the extreme differences in the behavior of different mine types
with regard to acid drainage production, caused by widely differing
geologies and physical characteristics of the disturbed areas, empiri-
cal techniques for the description and prediction of acid load and
drainage quantity have met with little success. Just as modern hydro-
logic models have developed into relatively detailed simulations of the
actual physical processes occurring during rainfall and runoff, so must
realistic acid mine drainage models simulate in some detail the physi-
cal and chemical processes known to occur. Thus, the source models
developed in this work are mathematical simulations of the chemical
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reactions and water movements occurring in the actual sources as con-
trasted with empirical relationships derived by the fitting of curves
to water quality data collected in the field. The use of determinis-
tic, predictive models to describe the acid output from sources in a
basin for a selected annual or multi-year precipitation sequence leads
to the capability of being able to identify "worst cases" for each
source, in terms of acid concentration or acid discharge rate. These
worst cases often correspond to the spring flush from a deep mine, or
an intense summer thunder storm on a refuse pile. By selecting feasi-
ble treatment or at-source abatement techniques, designed on the basis
of "worst case" acid loads and total flows, corresponding alternative
costs for abating and controlling mine drainage pollution can be opti-
mized across the basin by a suitable optimization technique. The
nature of the input cost and acid load data generated by the above
techniques makes a partial enumeration algorithm for solving nonlinear
integer programming problems the most suitable optimization technique.
The project approach outlined above led to the advisability of dividing
project activities into four major subject areas. These were the
hydrologic sub-model, the acid generation sub-model, abatement and
treatment cost and effectiveness data accumulation, and the resource
allocation optimization model. Work in these four major areas over-
lapped to a high degree, and frequent meetings of all project person-
nel, together with periodic meetings with the Project Officer were
utilized to maintain coordination of effort. In the following sec-
tions, the theory and structure of the overall model are presented on
a step-by-step basis, covering each component of the model, in turn.
Illustrative examples of each of the model components follows, together
with critical evaluation of the technique, and comments on the future
development of this approach.
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SECTION IV
SHORT DISCUSSION OF THE PROJECT MODEL CONTENT
AND OPERATION
This section presents an overview of the various components or sub-
programs of the total project model, in a low key technical format, to
provide the reader with a general understanding of its content and
operation. Detailed technical discussions are given and are referred
to in the Appendices. Hopefully, this method of presentation will per-
mit the reader to understand the overall picture of the report contents
without unnecessarily, at this phase of the reading, being burdened
with highly technical, mathematical, and computer language passages.
The total model consists of rather distinct sub-parts and, therefore,
for readability, these components are first discussed separately and
then the complete project model can be seen by their integration. The
discussion at this point will be limited to the basic composition of
the sub models. Section v presents illustrative examples of the
application of the model.
Component discussions will trace the project model development from
basic physical phenomena through its cost effectiveness stage to the
final phase of optimization of resource allocations.
BASIC PHYSICAL PHENOMENA
There are two basic physical phenomena associated with acid mine drain-
age. The first is the determination of the amount and movement of
water associated with the various mine types; the second is the de-
scription of the rates of pollutant generation in these mines.
Hydrologic Model
The quantities of minewater flow or drainage are closely related to the
concept of the hydrologic cycle. Hence, by modeling the hydrology of a
watershed, the water activities in the various mine types can readily
be accounted for by observing the respective portions of the hydrologic
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cycle model that apply to the waters involved in the mines. Discus-
sions herein will now be limited, more or less, to the actual hydro-
logic model used in this project.
Hydrologic Cycle and its Model -
Three zones of hydrologic events can be assigned to describe a hydro-
logic cycle. Figure 1 shows a schematic diagram of the cycle as used
by the model.
Upper Zone--This zone is above the soil surface. It is used to
describe the activities at and after precipitation above the soil
surface. The activities include interception, transpiration,
evaporation, overland flow, surface detention and depression
storage.
Lower Zone--This zone is the soil between the water table and
land surface. It is used to describe the activities of infiltra-
tion from the upper zone, percolation, interflow, and the degree
of soil moisture saturation.
Deep Lower Zone--This zone is the soil below the water table. It
is used to determine groundwater flow to the stream, and to deep
storage (or aquifer). Because moisture percolates through the
cracks and crevices of the aquifer, a time delay occurs between
moisture entering the aquifer and leaving the aquifer as mine-
water flow.
The hydrologic cycle is a continuous process. Precipitation falls on
the upper zone and some of it will enter into the lower zone and deep
lower zone. The balance will enter the upper zone (interception plus
depression storage). To complete the cycle, evaporation and transpir-
ation occur from all three zones.
History of the Hydrologic Model Development -
The various components of the hydrologic cycle can be described by
mathematical expressions which can then be integrated to produce a
total hydrologic model. These models, programmed for the high-speed
digital computer, simulate the hydrologic cycle behavior in a basin.
Several such models have been developed over the past decade. A very
versatile and successful one, the Ohio State University version of the
Stanford Watershed Model (SWM), was used, with slight modifications, in
this project to calculate the quantities of water generated at the mine
sites. A brief review of the history of this particular model follows.
The basic Stanford Watershed Model (SWM) was developed by Professors
Crawford and Linsley at Stanford University in the early sixties.
Dr. James, while at the University of Kentucky, modified the model
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INTERCEPTIONS
TRANSPIRATION
PRECIPITATION
tIPPFR 70MF
UPPER ZONE
./INTERCEPTION PLUS
*tDEpRESS|ON STORAGE
DEPRESSION
WATER TABLE'
LOWER ZONE STORAGE
SURFACE DETENTION
EVAPORATION
GROUNDWATER FLOW TO STREAM
TO
DEEP
STORAGE
Figure 1. Schematic of Hydrologic cycle
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slightly and translated it into FORTRAN computer language in the mid-
sixties. Various researchers at universities, governmental agencies,
and consulting firms have worked with and proven the acceptabilities of
the model over the years. Since 1968, researchers at The Ohio State
University have made modifications to progress the model along these
lines: the model was flow-diagrammed and a detailed expose''on the
mechanics of its operation was written; computer plotted hydrograph and
hyetograph programs were developed; key parameter sensitivity studies
were performed; multiple groundwater recession phenomena were included;
swamp and excessive soil shrinkage crack storage routines were created;
snowmelt considerations for the Midwest areas were included; modifica-
tions for handling small watersheds were made; and finally, a User's
Manual for the total modified model was written. The complete model
and detailed evolution is presented in Appendix A.
Model Operation -
The basic scheme for the model's operation, that is, moisture account-
ing in a watershed, can be seen quickly in the logic block diagram of
Figure 2.
In addition to the climatological data (precipitation, evaporation,
wind, solar radiation, and temperature), 21 input parameters related to
the physical aspects of the basin (12 measurable, 11 trial and adjust-
ment, and 8 assigned or selected parameters), are required for the
model. Tables in Appendix A describe these inputs and detailed
explanations are given to determine their values. The mathematical
formulations of the hydrologic concepts involved and the technical
aspects of the computer programs to simulate these, along with their
linking mechanisms represented by the various blocks in the logic dia-
gram, are of little interest at this point. Full explanations are
given in Appendix A.
Of particular interest at this time are the blocks in the diagram
flagged by asterisks to indicate points in the total hydrologic model
where specific water quantity information is accessed for individual
mine water generation information.
Polluted Water Generated by Mining Activities -
The overall discharge from a basin containing mining activity can be
considered as a composite of natural unpolluted flow emanating from the
unmined portions of the basins plus the various polluted discharges
associated with the mines in the basin. The mining activities could
produce polluted water discharges from deep mines, strip mines, or
associated refuse piles.
The modeling procedure for quantitizing these discharges is basically
the same in all cases, that is, the use of a hydrologic model to
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MAJOR INPUT
Precipitation
Pan Evaporation and Coefficients
Physical Watershed Parameters
Initial Soil Moisture Conditions
Initial Groundwater Storage Conditions
MAJOR OUTPUT
Synthesized Streamflow
Synthesized Evapotranspiration
Evaporation from Exposed Water Surfaces
Runoff from Impervious Surfaces
Upper Zone Soil Moisture Storage
Interception
Upper Zone Soil Moisture
Overland Flow Surface Detention
Overland Flow
Interflow Storage
Lower Zone Moisture Storage
Groundwater Flow
out of Basin
Evapotranspiration
Groundwater Storage
Groundwater Flow
LEGEND
Operations performed
in 15 minute intervals
(or smaller if specified)
.Operations performed
in 60 minute intervals
Figure 2. Moisture accounting in Stanford Watershed Model
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predict the quantities of water involved and application of the
appropriate pollution generation model to ascertain the quality of
these waters.
The nature of the various mining activities dictates that the water
generation will originate at different locations both in the earth's
crust and in their counterparts in the model.
Referring to Figure 2, water for the deep mine situation is obtained
from the model component of Groundwater Storage (point * on Figure 2).
In the case of a strip mine or refuse pile, wherein acid products may
accumulate at or near the soil surface, water may be obtained from the
Upper Zone Soil Moisture and Overland Flow Surface Detention blocks
(points ** on Figure 2), and from Interflow Storage and Lower Zone
Moisture Storage (points *** on Figure 2). Details of just how this
water quantity information is obtained and how it is further processed
through the models are briefly described later in the source model por-
tion of this section, and are technically explained in Appendix A.
Acid Generation Model
For purposes of this report^ the term "acid generation" will be defined
as the removal of acid from a mine or refuse pile via the drainage from
the system. The acid materials so removed are provided by the oxida-
tion of pyritic materials in the mine by oxygen, leading to the forma-
tion of the predominant products, sulfuric acid and ferrous or ferric
iron. The acid generation rate or acid load from a pyritic system such
as a deep or strip mine, or a refuse pile, is determined by the amount
of acidity picked up by the flowing water. The net acid concentration
in the discharge will be the acid generation rate, in weight per unit
time, divided by the drainage flow rate.
The hydrologic model described above provides a definition of the
amounts of water flowing through the system. It is the task, then, of
the Acid Generation Model to describe two additional processes which
are, for practical purposes, largely independent of one another. These
are (l) the rate of pyrite oxidation (or acid formation), and (2) the
rate of transfer of oxidation products (acidity) to the drainage water.
The linking of the Hydrologic Model and the Acid Generation Model will
then provide the Source Model, described later in this section.
Pyrite Oxidation -
There are two factors which may determine oxidation rate, depending on
which is controlling: (l) the chemical reaction, and/or (2) rate of
transport of reactant (oxygen) to the reaction site. Before this con-
cept can be explained, the "reaction site" must be defined. Basically,
it is an exposed pyrite surface together with the gas, liquid, and
solid interfaces at this surface. Its characteristics are described by
10
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the interfacial area per unit volume of pyritic material and the
conditions at this surface, particularly oxygen concentration. For
practical purposes, bacterial catalysis of pyrite oxidation is in-
significant, and, under conditions encountered in the field, the
reaction can be considered first order with respect to oxygen (i.e.,
the rate varies in direct proportion to the oxygen concentration),,
A finite concentration of oxygen must be present at the pyrite sur-
face before the surface can be termed a "reaction site".
A deep mine element, as shown in Figure 3 is a typical example of a
pyritic system. Assuming the mined-out volume of a mine has an oxygen
concentration of 21 percent, reaction sites will be exposed to oxygen
concentrations varying from 21 percent at the working face to 0 percent
back into the coal strata. The oxygen concentration profile and the
net oxidation rate in a particular pyritic system depends on the void
volume (porosity) and the exposed surface area of pyrite per unit
volume. The calculation of the oxygen concentration profile is simply
a problem of diffusion plus chemical reaction for which quantitative
mathematical solutions are available. Specific examples are given in
Appendix B.
Note that "reaction sites" extend as far into the porous media as
oxygen diffuses. The greater the void volume, or porosity, of a
pyrite-containing stratum, the greater the rate of oxygen diffusion
because of the larger gas flow cross-sectional area available for dif-
fusion. At the same time, more pyrite surfaces are exposed in a porous
material simply because of the larger void space available for diffu-
sion and because of the greater total surface exposed to the vapor
phase. Conversely, the tighter the formation, the lower the quantity
of oxygen which will diffuse through it, and the less oxygen which is
available for oxidation per unit volume of material.
Since oxygen diffusivity in water is 1 x 10~4 that in air, essentially
all oxygen must be transported to the reaction site as a vapor. Diffu-
sion through water is insignificant, and the quantity of dissolved
oxygen in water entering an underground mine is too small in itself to
produce a significant acid load. This leads to the important fact that
pyrite submerged under a pool of stagnant water, or enclosed in a
porous medium which is saturated with water, will not be oxidized to
any significant degree.
The general principles of Figure 3 still apply, in the case of a strip
mine or refuse pile, except that oxygen diffusion would be from the
soil-air interface down through the soil.
Another fact brought out by the conceptual model that must be kept in
mind when interpreting discharge data is that the quality of effluent
water is not directly related to- the quality of water at reaction
sites, that is, discharged water does not describe the aqueous
-------
environment at reaction sites in terms of concentration of oxygen,
oxidation products, ferric/ferrous ratio, or other factors influenc-
ing the oxidation rate.
sandstone
Mined-out Volume
21% 02
Working »-
Face
y/^ / * / ,..>..... '
,'
1
Coa 1 i
1
i
\%':^v?.-::-:-:-'-'-'.-.v'::-V-<-/:--.vv>
'V:/;':-':: Shale _;!';: \V:-V::.-VvVj
Coal {
i ,
i *
a>
in
H-
^ S
2 e
° § &
S 8 x
i: o o
C/) Q.
O> O o
f" ._
b-i"!
03 "c
t. CX *-
>i
-------
3. Diffusion or "weeping" of saturated solutions of reaction
products caused by water condensing on reaction sites due
to the lowered vapor pressure of the highly concentrated
solutions at these locations.
The particular removal mechanism (or mechanisms) involved at a specific
reaction site depends on its location in respect to the water table
and/or flow channels through which ground water percolates. If a re-
action site is isolated from these sources of direct removal, oxidation
products will build up until the degree of saturation at the site and
surrounding area is high enough that the rate of transport to points
of direct removal by percolation or flushing is equal to the oxidation
rate. Hote that the build-up of oxidation products has no effect on
the oxidation rate.
Obviously, the instantaneous rate of oxidation product removal, or acid
generation rates, is a complex resultant of both pyrite oxidation rate
and water movement in the system. Over a long term (measured, at the
minimum, in years) the total amount of oxidation products removed may
be equal to the total amount of oxidation product formed, but the
daily or weekly acid loads, as measured from the discharge, cannot be
related directly to the rate Of pyrite oxidation.
All three of the above removal mechanisms have been observed either in
the laboratory or in the mines. The flushing and percolation mechan-
isms are self-evident. The diffusion, or "weeping" process is too slow
to be observed directly, but has been measured in the laboratory.
In the case of a refuse pile, pyritic material will generally be dis-
tributed throughout the pile, with only pyrite at and near the surface
being exposed to oxygen. Spoil banks in a strip mine complex, on the
other hand, may contain pyritic materials near the surface, or may be
buried under a layer of nonpyritic, and hence, nonacid producing soil.
In either case, the same basic oxidation product removal processes can
be active as in the case of the deep mine. However, due to the forma-
tion of acid at or near the surface, significant amounts of acid may
appear in direct runoff and/or interflow, as well as in the base flow
from the system. The direct runoff component is more of a "surface
rinse" than a percolation or infiltration induced action, while the
interflow is closely related to the percolation mechanism in a deep mine.
The differing physical structure of a deep mine, as contrasted with
spoil banks and refuse piles, makes it impractical to develop a com-
pletely generalized Acid Generation Model applicable to both. Rather,
separate models have been developed; namely, the Deep Mine Model, and
13
-------
the Combined Refuse Pile and Strip Mine Model. Both operate in accord-
ance with the same principles in that they calculate both the rate of
acid formation in the system and the release of acid to the system
drainage in accordance with the predominant oxidation product removal
mechanisms; both are linked with the Stanford Watershed Model to pro-
vide overall Source models. Block diagrams of the essential mechan-
isms of the two Acid Generation Models are shown in Figures U and 5.
Detailed descriptions are given in Appendices A and B.
Pollutant Source Models
An acid source is defined, for purposes of this report, as a deep mine,
strip mine, or refuse pile in which pyrite oxidation occurs. Depend-
ing on the scale of the system being simulated, a source might be a
single mine or refuse pile, or a grouping of individual mines or piles
having similar characteristics and treated, in aggregate, as a single
source. All sources, regardless of type, have three basic characteris-
tics which must be adequately simulated; the rate and physical location
of pyrite oxidation in the source system, the transport of acid products
from reactive sites to the effluent drainage from the source, and the
dilution of this concentrated drainage by water in the receiving stream.
As indicated previously, the net pyrite oxidation rate for a source is
the solution to one or more sets of equations describing the diffusion
of oxygen to the reactive sites and the consequent oxidation of the
pyrite. The Acid Generation Models perform this calculation, giving
the amount of acid produced in specific reaction zones. Transfer of
this acid to the mine or pile drainage depends on the flow of water
through or near the zones where the acid is formed, as reflected in the
transport mechanisms. While it is computationally convenient to in-
clude in the Acid Generation Models the calculation of acid movement
within the source and into the source drainage, these calculations re-
quire input from the Hydrologic Model to define the location and extent
of water movement through the source. The Stanford Watershed Model,
through its capacity to separately account for water storage and move-
ment in the upper zone, lower zone, and deep lower zone, provides this
input data. To the extent that water movement in the system will affect
pyrite oxidation rates, this information must also be supplied by the
Hydrologic Model. Lastly, the identifiable source drainage, together
with its acid load, must be mixed with surface water flowing from non-
acid portions of the basin under consideration, and a continuous
accounting must be made of all water and acid in the basin. Thus,
three requirements must be satisfied in the linking of the Hydrologic
Model to the Acid Generation Models; the determination of acid movement
and acid flow as a ^unction of pyrite oxidation rate and a mass balance
on both acid and water for the entire source-basin system.
Two source models have been constructed by linking the Hydrologic Model
with the respective Acid Generation Models, yielding the Deep Mine
Source Model, and the Combined Refuse Pile-Strip Mine Source Model.
-------
MAJOR INPUT
Mine Descriptions
Oxidation Rate Parameters
Initial Acid Storage
Flow and Acid Load
Coefficients
Calculation of Infiltration
Water Reaching Ground-
water by SWM
I
MAJOR OUTPUT
Synthesized:
Minewater Flow
Acid Load
Aquifer Storage
Minewater
Flow
Calculation of Oxidation
Rate Constants
Oxidation of Pyritic
Material
Comparison of Water
Level Relative to
the Strata
Oxidation
Products
Inundation Does Not
Occur in the
System
Acid Removal by
Leaching
Acid Removal by
Gravity
Diffusion
Inundation Occurs
in the System
±
Acid Removal by
Inundation
Figure k. Schematic of Deep Mine Drainage Model
-------
MAJOR INPUT
Soil Column Descriptions
Oxidation Rate Parameters
Initial Acid Storages
Direct Acid Runoff Parameters
Calculation of Acid
Production Rate for
each Representative Area
Compartmentalized Formation
and Storage of Acid Products
between Areas and between
Zones within each Area
Calculation of Surface
and Underground Water
Movement and Storages
by SWM
F
Acid Removal by
Direct Runoff
Acid Removal by
Interflow
Acid Removal by
Base Flow
MAJOR OUTPUT
Synthesized:
Sub-basin flow
Acid Load
Acid Transfer to
Deep Storage
Figure 5. Schematic of Combined Refuse Pile-Strip Mine Model
-------
These models are presented through the use of block diagrams paral-
leling the actual sequence of the mathematical and computer processes
(Figs. 6 and ?). Appendices A and B give detailed technical informa-
tion on the model linking.
Precipitation
Climatic Input
I
Watershed Characteristics
Data
Overland Flow
Deep Storage
HYDROLOGIC
MODEL
Mine
*>- Mlnewater
Discharge
Becomes Input
to Acid Model
Portion of
Water in mine
Aquifer Trickling
Through Channels
in the Pyritic
System
STREAMFLOW
at
Basin Outlet
Amount and Timing
of Water Quantity
Percolating to the
Groundwater Storage
in the Basin
Aquifer
Storage Around
Coal Mine
ACID
GENERATION
MODEL
Mine Characteristics Data
Pyrite Oxidation Parameters
Pollutant Product Removal Parameters
{MINEWATER DISCHARGE RATE AND ASSOCIATED WATER QUALITY]
Figure 6. The Deep Mine Source Model
17
-------
Precipitation
Refuse Pile Option
Water Table
Strip Mine Option
Spoil Bank or Pile Drainage
Climatic Input
Watershed
Characteristic Data
t
HYDROLOGIC MODEL
Applied to Watershed
Having One or More
Strip Mine or Refuse
Pile
f Stream Flow
~*\ at Basin Outlet
Amount and Timing of Precipitation and of
Quantities of Overland Flow, and
Groundwater Flow
Combined Flows
Preserving Time
Relationships
Acid in Overland Flow, Each Area
Acid in Inter Flow, Each Area
Acid in Base Flow, Each Area
r
ACID
GENERATION
MODEL
^Refuse and/or Spoil Characteristics
Acid Production Rate Parameters
for Each Source Area
Acid Transport Characteristic for
Each Source Area
JMINEWATER DISCHARGE RATE AND ASSOCIATED WATER QUALITY
Fig-ure 7. Total acid load and acid load from each source area
18
-------
Deep Mine Source Model -
In the case of the deep mine, the major point of linkage between the
Hydrologic Model and the Acid Generation Model is associated with sub-
surface flow and water storage in the region of the mine. Since the
deep mine generates acid in regions not directly affected by overland
flow or interflow, these components are not involved with the transport
of acid, or the inundation of reactive sites which influences both
acid transport and pyrite oxidation rate. Because of the frequent
occurrence of relatively impermeable clays underlying coal strata, the
acid formed in the mine, if not flushed out in the drainage, tends to
stay 'in the reactive zone. While exceptions to this reaction do occur,
the present model has not been extended to cover such cases.
Combined Refuse Pile-Strip Mine Source Model -
In the case of the Refuse Pile-Strip Mine Source Model, the linkage
between the Hydrologic Model and the Acid Generation Model is neces-
sarily more complex than in the case of the Deep Mine Source Model.
Since, in this case, acid is generated at or near the ground surface,
the reactive sites may be flushed directly by direct run-off and by
interflow, as well as by percolation going to groundwater storage and
base flow. Further, acid formed at or near the soil surface may be
temporarily stored at intermediate depths, and carried deep into the
refuse pile or spoil bank, to remain there until released by under-
ground flow at a much later time. Therefore, all of the flow compo-
nents of the Hydrologic Model, as well as precipitation itself, are
required input in this case since pyrite oxidation is assumed to cease
during periods of rainfall, due to direct blockage of oxygen diffusion.
The primary difference between the strip mine option and refuse pile
option is the presence of an inert layer overlying the reactive pyrite
in the former, and direct exposure of reactive pyrite in the latter.
The option names are for convenience only, since some spoil banks would
require the "refuse pile" option, and a covered refuse pile would re-
quire the "strip mine" option. Both options can be used simultaneously
in the Acid Generation Model, and the linking mechanism to the Hydro-
logic Model is common to both.
Basin Model
In the application of the source models described above to a large
drainage basin, the overall basin would normally be divided into sub-
basins, each of which may or may not have one or more acid sources
within its boundaries. The sub-basin size definition would be deter-
mined by the variability of hydrologic characteristics across the total
basin in question, the degree of resolution required with regard to
both water and acid discharge rate predictions, or both. (The factors
underlying such decisions are discussed in more detail elsewhere in
this report.)
19
-------
Figure 8 is a schematic diagram of a basin subdivided into three sub-
basins, two of which have acid sources.
Basin Outlet
Figure 8. Schematic diagram of subdivided basin
Sub-basin A includes a deep mine, strip mine, and refuse pile, while
Sub-basin B has only a deep mine. In the application of the Source
Models to this example, both the Deep Mine Source Model and the
Combined Refuse Pile-Strip Mine Source Model would be applied to Sub-
basin A, with the latter model including both the strip mine and refuse
pile in the same application. The Hydrologic Model would be applied
only once over Sub-basin A, as it is common to both Source Models. The
20
-------
dual Source Model application would give the acid source drainage flow
and acid loading rates at points 1, 2, and 3, and the flow rate at the
basin outlet, point 5, all as a function of time for any time period
(e.g., one year) and precipitation sequence desired. The source models
identify the drainage flow rates and acid loading rates at the indi-
vidual sources, but identifies the sub-basin flow only at the sub-basin
outlet. Further, flow times in the stream above the sub-basin outlet
are not calculated by the model, and water quantity upstream from point
5 can not be directly computed. In most applications, the simplifying
approximation that all acid sources discharge into the stream at the
sub-basin mouth will yield satisfactory results. If required, stream
routing techniques could be applied within the sub-basin, but this is
now considered to be an unwarranted refinement, and has not been built
into the model.
The application of the Deep Mine Source Model to Sub-basin B would
yield the mine drainage flow and acid load rates at point U, and the
sub-basin outflow at point 5. Again, the mine acid load would normally
be assumed to discharge into the stream at point 5 for purposes of cal-
culating the acid concentration at point 5 as a function of time.
Having estimated the flow and concentration at point 5 from both Sub-
basins A and B, the flows can be added, normally with the assumption of
complete mixing, to calculate an average acidity concentration.
Between points 5 and 6, there are no acid sources tributary to the
stream, and acid from above point 5 is diluted further by flow from
Sub-basin C, and may be neutralized in some degree by alkalinity pre-
sent in this flow. Stream routing times from point 5 to point 6 may or
may not be taken into account, depending on the degree of accuracy re-
quired in estimating acid concentrations at point 6. The most appro-
priate method of combining sub-basin flows into the basin model varies
with the individual case, and has not been included in the computer
programs presented here. While decisions as to the degree of refine-
ment required in accumulating sub-basin flows and acid loads depends
heavily on field data available and judgment of the analyst, it is
anticipated that stream routing requirements can be held to a minimum,
particularly in the application of the "worst case" optimization pro-
cedure .
COST-EFFECTIVENESS MDDEL
It is appropriate at this point to recapitulate the overall structure
of the acid mine drainage abatement resource allocation procedure which
has been developed on this project, to put cost and effectiveness
determinations in the proper perspective.
The first step in the sequence is to define the nature and extent of
the problem, which requires an estimate of the acid load from each
21
-------
source, as a function of tame. This step, together with an estimate of
the stream flow throughout the basin, provides a basis for the calcu-
lation of acid concentrations throughout the basin, again as a function
of time. The Source Models described are designed to supply the acid
loading information from each source and to provide the individual
characteristics of each source.
The second step is the selection of alternative treatment and/or at-
source abatement procedures which may be feasibly applied at the indi-
vidual sources. The associated costs of each control alternative at
each source, together with the effectiveness of each alternative in
terms of acid reduction, becomes the basic input data for the selection
of the optimum mix of treatment or at-source abatement efforts at each
source. Further, the application of a uniform quality standard over
the entire basin may be unrealistic, since existing or proposed land
and water use may vary widely from point to point in the basin. Thus,
some mechanism is necessary for varying the required water quality, or
for weighting the value of good quality at different points throughout
the basin. Considerations concerning these questions of cost, effec-
tiveness, and valuation are discussed.
The third step is to determine the optimum distribution of resources to
the control of acid drainage within the basin, using input from both
Source Models, which define the pre-abatement condition of the basin,
and the cost-effectiveness estimates for the various acid control
alternatives.
Acid Control Alternatives
There 'are basically two approaches to acid mine drainage control, at-
source abatement, and chemical or physical treatment of the drainage.
Examples of at-source abatement include the sealing and flooding of
deep mines, the inert gas blanketing of deep mines, and the regrading
and covering of spoil banks and refuse piles, with or without lime or
limestone application to the soil. All at-source abatement procedures
have the common aim of eliminating, by some means, the exposure of
pyritic materials to atmospheric oxygen. The primary advantage of at-
source abatement is that, once accomplished, maintenance costs are low,
or are eliminated altogether. The primary disadvantage is that the
effectiveness of at-source abatement procedures in terms of acid load
reductions are not very spectacular, or require long periods of time to
reach maximum apparent effectiveness, due to the slow bleed-out of acid
accumulated in the system prior to abatement activities.
Chemical or physical-chemical treatment, as opposed to at-source abate-
ment, has the advantage of being quite positive in its effect. All of
the acid can be neutralized and the soluble metals removed by appro-
priate chemical neutralization and precipitation. Even the anions,
particularly sulfate, can be removed by such processes as reverse
22
-------
osmosis. However, operating costs can be quite high, sludge or brine
disposal problems may be extremely difficult and expensive, and, the
most sobering prospect of all, the required period of treatment may be,
for all practical purposes, interminable. The "natural" burn-out of
pyrite in mines, refuse piles, and spoil banks is measured not in
years, but in decades or centuries.
The problem of estimating the cost and effectiveness of at-source
abatement techniques is a difficult one, and procedures cannot be
generalized. Field demonstration project results available at this
time are disappointing, primarily because pre- and post-abatement
drainage monitoring efforts have been generally inadequate for a defin-
itive evaluation of the techniques applied. While the cost of sealing
a mine or covering a refuse pile can be estimated by conventional pro-
cedures, the anticipated effectiveness of a given technique is diffi-
cult to predict. The effectiveness values estimated and reported for
existing cases can not, in general, be taken at face value, and the
judgment and experience of the analyst is an important factor in evalu-
ating existing data.
As an alternative to the prediction of the effectiveness of proposed
at-source abatement procedures on the basis of existing data, the use
of the Source Models as predictive models for the evaluation of at-
source abatement alternatives is strongly encouraged. These models are
designed to respond to changes in oxygen availability to the pyrite in
the system, and to changes in the hydrologic regimes affecting the
system, all of which can be estimated for a given at-source abatement
technique.
The costs and effectiveness of chemical and physical-chemical treatment
alternatives can be closely estimated by conventional techniques once
the drainage flow and acid loading characteristics of a given source
are known. A review of reported costs of treatment by alternative
methods was made, and is included in Appendix D. In general, cost will
be a function of flow and loading, with unit costs decreasing with in-
creasing scale of the treatment system. Details of the formulation of
such functions are also given in Appendix D. Plant size is determined
largely by the flow rate of the drainage to be treated, while the cost
of treatment chemicals required is determined by the average annual
acid load to the plant; both flows and loadings are provided by the
Source Models. Identification of the capital cost of the treatment
system, together with the estimated annual maintenance and operation
costs, and appropriate amortization rates, provides the basis for cal-
culation of an effective annual cost estimate for use in the optimiza-
tion model. Here again, the wide variety of treatment alternatives
available and the importance of taking the characteristics of the
individual source into account in selecting feasible alternatives make
a generalized computer program for this cost estimation step impracti-
cal.
23
-------
Socio-Political-Economic Considerations
The decision to implement pollution control measures at mine sources in
abater shed is influenced by socio-economic and political considera-
tions . The importance associated with maintaining stream quality
varies throughout a watershed. In particular, the land use in the
vicinity of the stream should influence the requirement and importance
of achieving desirable stream quality levels. Accordintly, the basin
effectiveness measure defined in the following section provides for the
influence of socio-political-economic considerations on the relative
importance of individual stream reaches.
BASIN OPTIMIZATION MODELS
The Source Models can predict the acid load emitted from a particular
site as a function of time; moreover, the acid load can be predicted
for situations resulting from the application of pollution control
measures taken to improve environmental quality. In addition, the
Source Models can predict stream flows, and cost estimates can be
generated for chemical treatment control measures at each pollution
source. The Basin Optimization Models take these pollution loadings,
control measures, and costs to determine optimal allocations of pollu-
tion control effort at each source with respect to the following
criteria: (l) least cost allocation to achieve a specified quality
level, and (2) most effective allocation for a specified cost. Rela-
tionships among these models are shown in Figure 9- The structure and
use of the optimization models developed during this study follows.
Control Measure
Alternatives at
Acid
Generation
Model
Source Model
Hydrologic
Model
\<
^\i
Stream Flows
^
Each S<
jurce
Basin
Optimization
Models
Preferred Set of
Control Measures
Overall Stream
Quality. Total _
System Cost *"~
Cost
Estimation
Figure 9. Input-output diagram for Basin Optimization Models
-------
The Basin Optimization Models represent the basin as a network of
streams and a set of individual pollution or mine sources feeding these
streams. Deep mines, strip mines, or refuse piles are all referred to
as mine sources in the optimization model. The effluent from a mine
source is assumed to enter one of these streams at a single point on
the stream called a node. A single basin outlet stream is assumed to
exist, and this basin outlet stream may have tributaries, and these
tributaries may have tributaries. This network of streams creates a
hierarchy among the streams which has, at most, a level of three. That
is, the basin outlet is a third-level stream being fed by second-level
streams, and the second-level streams are fed by first-level streams.
A typical stream network is shown in Figure 10.
Level I
Stream
Level 2
Stream
D Pollution Source
Q Stream Node
Figure 10. Stream network
Each mine source, noted as a small square in Figure 10, is represented
as providing pollutant influent to the stream at a node point, and
values for these pollutant flow rates in kilograms per hour are pre-
dicted by the Source Model as input data to the Basin Optimization Models.
For example, the pollutant might be acid, and the pollutant flow rates
25
-------
would specify the total acidity of the effluent from each mine source.
Also the stream carries a fluid flow, exclusive of pollutant, and the
stream flow rates in cubic meters per second are predicted by the Unit
Source Model as input data to the Basin Optimization Models at each
node point. Values of these stream flow rates are assumed to be
unaffected by actions to control stream pollution levels.
In addition to pollutant inputs from mine sources, the streams have
natural pollutant inputs occurring throughout the network. These
natural inputs are assumed to be distributed continuously between
nodes, but the stream reach between each pair of nodes may have its own
unique input rate. Thus, the natural pollutant input rate in kilograms
per hour occurring between each pair of nodes is specified as input,
and these natural pollutant inputs may have either positive or negative
values. For example, a natural acid input rate of ^0.05 kilograms per
hour between two nodes would indicate an alkaline condition alleviating
part of any potential acid mine drainage.
The nodes in the stream network are convenient points for specifying
alternative pollution control decisions. A survey of possible methods
for controlling mine drainage pollution indicated three general cate-
gories of pollution control methods as far as the optimization model
is concerned: (l) Abatement at the mine source, (2) treatment at the
mine source, and (3) treatment in the stream channel. Abatement is
assumed to reduce pollutant flow but not necessarily eliminate it. A
mine source produces pollutant flows, specified by input data to the
optimization model, where the flow with abatement is less than the flow
without the benefit of control measures. Examples of abatement are
flooding or sealing of deep mines; covering, leveling, compacting,
burying or grading of gob piles; and grading, covering, or replanting
of strip mines. All of these methods have the potential for reducing
pollutant flows, but their effectiveness varies from site to site.
Treatment, whether in the stream channel or at a site, is assumed to
reduce pollutant flow to zero (without affecting the stream flow exclu-
sive of pollutant), but treatment will not affect a condition where the
stream pollutant measure is already negative. Using our acid mine
drainage example again, the treatment facility will neutralize an acid
stream until it has no total acidity, but it will not affect an alka-
line stream. The assumption is being made here that once the decision
is made to install a treatment facility, the most economical solution
is to remove all acid conditions but do not change alkaline conditions.
Treatment facilities may be either at a mine source or in the stream
channel. Source or site treatment is an option which is assumed to be
available at any source, and site treatment is regarded as being able
to treat all pollutant effluent before it reaches the stream. Only
certain nodes, designated by input data, are capable of being locations
for instream treatment facilities. These facilities, if implemented,
26
-------
will treat all fluid passing through a node; moreover, an instream
treatment facility would treat the effluent from its local mine source
before its effluent enters the stream channel. A typical stream net-
work with potential instream treatment sites is shown in Figure 11.
Stream Node
D Mine Source
H Stream Node with
Potential Instream
Treatment Facility
Figure 11. Illustration of stream network with potential
instream treatment facilities
In addition to stream quality, pollution control costs are explicitly
considered by the optimization algorithms. All costs incurred by these
pollution control measures are assumed to be average annual costs which
include recovery of capital, operating and maintenance costs. The cost
to perform abatement at each site is specified by input data from the
cost estimation step. Annual treatment costs involve two cost compo-
nents, i.e., a variable cost that is directly proportional to the
average annual amount of pollutant processed and the average annual
cost exclusive of the variable cost component. An example of the
variable cost component would be the cost of chemicals for neutraliza-
tion of acid. The Cost Model provides as input data the variable cost
to treat one unit of pollution in dollars per kilogram, and this value
2?
-------
is assumed to be constant for ail treatment processors. To calculate
costs for treatment processors, the following cost data are specified
by input for each mine or instream treatment site.
(l) Average annual cost of a treatment processor exclusive of
variable cost for both instream processors and mine sources
($).
(2) Average annual pollutant load in kilograms emitted from mine
sources without site abatement.
(3) Average annual pollutant load in kilograms emitted from mine
sources with site abatement.
(U) Average annual natural pollutant input in kilograms between
each pair of stream nodes (maybe either positive or nega-
tive).
Note that the optimization model must consider the fact that the in-
stream treatment processors will experience an annual pollutant load
that is a function of upstream abatement and treatment pollution con-
trol decisions.
A mathematical analysis of the optimization problem formulated to find
a set of decisions at each node that constitute either a minimum cost
of maximum effectiveness solution is described in Appendix C. This
analysis revealed the following characteristics of the optimization
problem: (a) the set of possible decisions is discrete, (b) the number
of possible decisions increase very rapidly with the number of mine
sources and instream treatment facilities considered; for example, two
instream treatment facilities and fourteen mine sources imply over one
billion uniquely different possible decisions, and (c) the constraint
equations and criteria functions are nonlinear functions of the deci-
sion variables. For the above reasons, standard optimization methods
such as linear programming and linear integer programming are inappro-
priate algorithms. Thus, an efficient nonlinear discrete optimization
method had to be devised as a part of this research effort.
Another factor complicating any solution procedure is the dynamic
stochastic nature of pollutant and stream flows; i.e., the pollutant
flow rates and stream flows as predicted by the Pollutant Source and
Hydrologic Models are time varying functions. Moreover, since these
functions are strongly influenced by precipitation patterns, they are,
in fact, stochastic. One way of handling their stochastic nature is to
adopt a conservative approach by selecting very long time traces from
the Source Models and analyzing these traces. Preferably, analyses of
the Source Models can be conducted to indicate which precipitation
patterns give the maximum pollution concentrations. Optimizing, using
these precipitation patterns, will generate confidence that quality
28
-------
constraints will be maintained and that effective decisions will be
generated. The basic assumption being made is that optimizing in this
manner will yield a solution that provides quality and/or effectiveness
measures at least as good as the worst case analyzed so frequently that
any violations can be ignored.
Going one step further, a useful optimization algorithm can be
obtained by completely suppressing the dynamic stochastic nature of the
pollutant and stream flows. This approach will be called the
"deterministic worst-case analysis." The basic idea inherent in this
approach is to select a set of single values for pollutant and stream
flows that represents the most adverse situation from a quality view-
point. Then, an optimal solution using these values should almost
always give better quality or more effectiveness in actual practice
than considered in the solution procedure.
Two deterministic "worst case" Basin Optimization Models have been
developed as a result of this research effort. They are defined below
along with their identifying mnemonics:
1. Deterministic "worst-case" minimum cost (D₯MC) model.
2. Deterministic "worst-case" maximum effectiveness (DWME) model.
The D₯MC model takes a specified quality standard expressed in parts
per million (ppm) that must be maintained throughout the stream network
and determines a least-cost set of decisions achieving this standard.
This set of decisions amounts to a specification of the treatment and
abatement decisions at each mine site and treatment processor. There
may be more than one set of decisions that give the same overall mini-
mum cost; however, the DWMC model only provides one of these decisions
as output.
The purpose of the maximum effectiveness (DWME) model is to allocate a
fixed budget in the most effective manner. The maximum pollution con-
trol budget is specified as input data. The effectiveness measure also
requires input data, but these inputs must be consistent with the
measures used in the DWME.
The effectiveness measure has been designed to indicate the relation-
ships between pollution levels, environmental impact, and land use in
the vicinity of the watershed. These relationships are reflected in
the effectiveness measure using two concepts:
1. The basic value of a stream based upon maximum pollution
concentration level.
2. The relative importance of the stream between two nodes based
upon its land use.
29
-------
The above concepts are applied to individual stream reaches between
adjacent stream nodes to compute a reach effectiveness measure which is
the product of its relative importance and its basic value. Total
watershed effectiveness is assumed to be the sum of the individual
reach effectiveness measures. These concepts are described in more
detail below and illustrated by examples.
The basic value of a stream reach is a number between zero and ten that
indicates the reach's value based on observable effects from pollution
concentrations. These effects include phenomena such as aquatic life,
aesthetics, and water supply processing, which are assumed to be
related to the maximum pollution concentration experienced. To portray
the variation in basic value, maximum pollution concentrations are
classified into intervals within which the observable effects are
assumed to be constant. Table 1 illustrates the variation of basic
value with pollution concentration.
Table 1. ILLUSTRATIVE VARIATION OF BASIC VALUE WITH
MAXIMUM POLLUTION CONCENTRATION
(ppm)
Maximum pollution
concentration
Observable effects
Basic value
> 10
8-10
6-8
h-6
< k
Fish cannot survive, noticeable
odor, strong discoloration, water
treatment costs increased by 100$.
Game fish cannot survive, high
scavenger fish mortality, notice-
able odor, water treatment costs
increased by
High game fish mortality, scavenger
fish will not reproduce, water
treatment costs increased by 25fo.
Game fish will not reproduce.
Aquatic life unaffected.
0
7.5
10
For each stream reach between two nodes, the basic value is determined
and is weighted by the relative importance of the stream reach to give
the effectiveness measure for this same stream reach. Relative
30
-------
importance is a quantity varying between zero and ten that specifies
the importance of controlling pollution levels in each stream reach
between adjacent nodes, land use in the vicinity of the stream reach,
the impact of pollution on this land use, and the length of the reach
to be considered in assigning relative importance values. The distri-
bution of relative importance values throughout the watershed is deter-
mined in several steps. The first step is to select the most important
stream reach (as defined by the stream between two adjacent nodes)
which is given a relative importance value of ten. Then all other
stream reaches are assigned values consistent with the difference be-
tween their importance and that of the most important stream reach.
The application of the above concepts is illustrated by the stream por-
trayed in Figure 12. The predominant land uses are noted in the
figure. The most important reach, with respect to the impact of pollu-
tion, is the reach between nodes 1 and 2; thus, this reach is assigned
a relative importance of 10.0. The other reaches are evaluated to have
relative importances of 7-0 downstream of node U, 5.0 between nodes
2 and 3, and 2.0 between nodes 3 and h. Using these relative impor-
tances, the effectiveness measures for each stream reach can be
obtained by determining basic values for each reach and multiplying
these basic values by their respective relative importances. For
specified abatement and treatment decisions, let the maximum pollution
concentrations be 6.8, 5-9j 5-5j and 6.1 ppm, starting at the head of
the stream (node l) and preceding downstream. Using Table 1, the basic
values for each reach are 4, 7*5? 7*53 3-nd ^, respectively. Multiply-
ing by the reach relative importances, the individual reach effective-
ness measures are hO.O, 37-55 15.0, and 28.0, respectively. Summing
these reach effectiveness measures, the stream effectiveness measure
is 120.5.
Figure 12. Single stream with adjoining land uses
-------
Thus, to use the DWME model, a maximum annual cost budget, basic
values, and relative importances must be specified as input data. It
is possible, perhaps even likely, that there are many possible solu-
tions that yield the maximum effectiveness solution. When additional
solutions are encountered in the solution procedure giving maximum
effectiveness within the budget constraint, the least-cost solution is
recorded as optimal; however, the DWME algorithm was not explicitly
designed to find the maximum effectiveness solution and then to deter-
mine the least costly way this solution was obtained. Thus, lower cost
solutions for maximum effectiveness may exist. If the maximum effec-
tiveness solution has the same basic value on all reaches, then the
DWMC algorithm can be used to determine the least costly solution for
maximum effectiveness.
Several other suggestions are offered to assist in the application of
these models.
1. When a potential instream treatment site is not colocated
with a mine source, then a dummy mine source can be created.
This dummy source should have no pollutant effluent, and the
cost to perform site abatement or site treatment should be a
very large number.
2. Mines may exist that can not be controlled for technical
reasons or because of legal or political constraints. When
this case occurs, then the effluent from these mines may be
regarded as a natural pollutant avoiding the use of nodes or
decision variables.
32
-------
SECTION V
ILLUSTEATIVE EXAMPLES
Since the basic composition and operation of the component project
models have been discussed, we will show in this section, by sample
applications, the operation of the models. The procedure will be to
indicate what types of inputs are required and what typical results or
outputs can be expected.
Critical discussions, on the rather limited applications to date, will
be given later. Details on parameter value determinations, various
types and format of data inputed, and the modeled results are given in
the appendices.
For ease of reading, the two basic types of computer based sub-models
developed on this project, the Source Models and the Optimization
Model, are presented individually.
SOURCE MODELS
As seen earlier, the two types of source models, deep mine and combined
refuse pile-strip mine, are basically of the same structurea hydro-
logic model coupled to an acid generation model. Examples are given
below of applications of both Source Models.
Finding suitable test sites poses great difficulty in that complete
data on simultaneous hydrologic and acid minewater discharge are non-
existent or unknown to us. However, for a test of the Deep Mine Source
Model, we were able to utilize a mine site where good mine drainage
data were available, partial hydrologic data had been collected, and
enough climatological data was available in the immediate region to
reasonably assemble the remaining data. In a preliminary test of the
Combined Refuse Pile-Strip Mine Source Model, field data were much less
complete than in the case of the deep mine, and it was necessary to
superimpose hypothetical strip mine and refuse pile areas on a real
watershed for which hydrologic data were available.
33
-------
Input Requirements
Given below is a descriptive list of the major information items
required to operate the models:
Basin Information -
Watershed drainage area
Land use and distribution
Flow capacity of main channel
Mean overland flow path length
Retardance coefficient for surface flows
Average ground surface slopes
Interflow and baseflow recession constants
Channel routing parameters
Index parameters reflecting interception, depression storage,
infiltration, soil moisture storage, interflow movement, and
groundwater movement
Climatic Data -
Precipitation records
Streamflow records
Evaporation rates and coefficients
Meteorological information for snowmelt
Deep Mine Information -
Mine area
Coal seam descriptors, materials, thickness
Pyrite oxidation rate parameters reflecting diffusion, reac-
tion, and temperature
Acid transport parameters reflecting gravity diffusion,
inundation, and leaching
Initial acid storages
Alkalinity conversion factors
Refuse File-Strip Mine Information -
Strip mine and refuse pile areas
Representative soil profiles of acid producing areas
Pyrite oxidation rate parameters reflecting diffusion, reac-
tion, and temperature
Initial acid storages
Acid transport mechanism parameters reflecting depth leached
by direct runoff, leaching parameters, effective acid
solubilities
-------
Discharge Data -
Drainage flow records
Drainage quality records
Detailed descriptions of the information requirements, as applied to
the examples shown, are given in Appendices A and B.
Examples of Output
Deep Mine Source Model -
A small drift mine (McDaniels) in Southern Ohio was chosen for a test
application of the Deep Mine Source Model. Details of the history of
this mine site and sources of data are given in Appendix A.
Simulation outputs are obtained both in tabular and graphical form.
All of the following sample output is shown in expanded form in
Appendix A. The figures (13,1^,15) below are not actual ones but,
rather, condensations to show what a typical plotted output of a
computer run gives. The plots are labeled and what they represent
is self evident.
CO
^
E
tu
§
a:
UJ
o
Stream Flow Rate
at the Basin Outlet
for a Particular
WaterYear
DAYS
Figure 13. Streamflow hydrograph at the Big Four Watershed Outlet
35
-------
(A
1
li-
ar
UJ
I
UJ
b
Daily Minewater Flow
Big Four Hollow
Water Year 1970-1971
-Simulated
DAYS
Figure ih. Daily minewater discharge from McDaniels1 Mine
O>
Q
O
Drift Mine Acid
Load at the
Mine Opening
Observed
Simulated
DAYS
Figure 15- Daily acid load discharge from McDaniels' Mine
36
-------
If the model is to be used to evaluate a proposed at-source abatement
technique such as mine sealing, the specific deep mine input informa-
tion is modified to reflect the effects of sealing, and the model is
run as above. In this manner, both the short and long term effect of
at-source abatement alternatives may be tested. The analyst so engaged
is referred to Appendix A, and to the report by Morth et al. entitled,
"Pyritic Systems: A Mathematical Model."
Combined Refuse Pile-Strip Mine Source Model =
Since an adequate test site for this Source Model was not available,
hypothetical strip mine and refuse pile areas were superimposed on
Watershed 9^ of the Worth Appalachian Experimental Watershed near
Coshocton, Ohio. The strip mine and refuse pile area of this water-
shed were assumed to be 10$ and 2%, respectively. Details of the
sources of data, site history, and assumed acid producing character-
istics are given in Appendix B.
For this model, simulation outputs are obtained only in tabular form
and may be plotted by machine. The figures (l6 through 20) shown
below are graphical representations of the output. The plots are
labeled, and what they represent is self evident from their titles.
Note that only simulated data are shown, since there was no recorded
data for this hypothetical example.
o>
3
O
O
Flow
Jt. in
m3/s
Refuse Pile or
Stripmine Acid
Load Rate
Acid Flow Rate
at the site.
HOURS
Figure 16. Acid load nonuniform short duration rain
37
-------
6
*»
O
Stream Flow Rate at
the Basin Outlet for
a 9 Month Period
DAYS
Figure 17- Stream flow hydrograph at the basin outlet
KV-
£
co"
1
LL
a
Refuse Pile
Strip Mine
Daily Flows from Acid Producing
Areas for a 9 Month Period
DAYS
Figure 18. Daily flows from acid producing areas
-------
o
^
CP
J£
a"
<
3
O
O
Refuse Pile
Strip Mine
Daily Acid Loads from Acid
Producing Areas for a 9
Month Period
O
<
DAYS
Figure 19. Daily acid loads ft-om acid producing areas
Flow
~^ Acid Load
Flow and Acid Load from Acid
Producing Areas Individual
Rainfall Event
-Total Flow and Load
Flow and Load in Direct Runoff
CO
1
HOURS
Figure 20. Flow and acid load from acid producing
areas - short duration rain
39
-------
As in the case of the Deep Mine Source Model, the Combined Refuse Pile-
Strip Mine Source Model can be readily applied to the prediction of the
effectiveness of at-source abatement techniques. For example, regrad-
ing and covering of a refuse pile effectively changes the location of
the pyritic material with respect to the soil surface. This will have
the effect of decreasing oxygen availability to the pyrite, and making
the acid produced inaccessible by direct runoff. When these changes
are made in the input parameters describing the system, the model can
be used to predict both short and long term effects of the proposed at-
source abatement procedure. An example of such a predictive run is
shown in Appendix B.
Other Information -
Both of the Source Models are programmed to produce many aspects of the
details of the process as well as final outputs. Tabular output is
available for items such as:
(i) Daily infiltration water reaching the mine aquifer.
(ii) Average daily streamflow rates leaving the watershed.
(iii) Average daily flow rates from drift mine opening.
(iv) Average daily acid load (by origin component and total)
issuing from drift mine.
(v) Daily acid load from a refuse pile direct runoff, inter-
flow, baseflow, and then total contribution.
(vi) Portions of the above that eventually reach the receiving
stream.
(vii) Monthly and annual sum of the above quantities.
(viii) Specific details of the above items on a 15-minute basis
for any specified period
Basin Optimization
To illustrate the application of the basin optimization models, a
stream network with a variety of pollution sources was constructed.
These models were applied, answers computed, and the results described
in this section. The stream network is shown in Figure 21. The basin
outlet stream has three tributaries, and four additional streams feed
these tributaries. Thus, there are four level one streams, three level
two streams, and one level three .stream. Note the three potential in-
stream processor sites, and also observe that the third instream
-------
Level
Stream
No.
Level 2
Stream
No.
Level I
Stream
No. 2
Level 2
Stream
No. 2
Instream Treat
ment Site No. 2
Level 2
Stream
No. 3
Level
Stream
No. 3
Instream Treat-
ment Site No. I
Level 3
Stream
No.
Instream Treat-
ment Site No. 3
Level I
Stream
No.4
Stream Node with an
Adjacent Mine Source
Q Instream Treatment Site
Figure 21. Stream network
-------
processor site is not colocated with a mine source. Thus, a dummy mine
source will be used at the fifth node on level three stream number 1.
Tables 2 through 5 present the input data for this basin required by
the optimization models. Table 2 presents a short description of the
mine sources represented and the abatement and treatment costs. The
variable chemical cost to treat one kilogram of total acid is $0.264.
Table 3 gives the average annual pollution loads in kilograms for each
source for calculating treatment variable costs. Two different condi-
tions were selected as "worst-cases" and analyzed. Spring pollutant
and stream flow rates are used to represent a situation where early
spring rains axe releasing winter pollutant accumulations. Summer flow
rates depict a low stream flow situation where pollutant concentrations
are severe. Tables h and 5 present the spring and summer flow rates,
respectively. These values are estimates selected to illustrate the
basin optimization models and are not based upon actual cost predic-
tions or predictions from the Pollutant Source Models.
The results from the minimum cost and maximum effectiveness models are
shown in Tables 6 and 7, respectively. Two cases are depicted where
the eight stream case is the entire basin as shown in Figure 21 and the
three stream case is a subsystem consisting of level-one streams three
and four and level-two stream three. The minimum cost model was oper-
ated with a specified quality standard of five parts per million.
Total pollution control costs for the minimum cost model results are
shown in Table 8. The maximum effectiveness model was operated with
the effectiveness measure given in the example of Section IV. Each
stream reach was assigned a relative importance of 10 with the excep-
tion of the basin outlet stream where each reach was given a relative
importance of 1. An annual pollution control budget of $300,000 was
allowed for the entire basin, and the three stream network was allowed
$85,000 per year. In each case, the maximum effectiveness model
stopped calculating when it determined that the solution shown in
Table 7 gave the maximum possible effectiveness measure. Thus, a
minimum-cost maximum-effectiveness solution would have to be obtained
by operating the minimum cost model with a four parts per million
quality standard.
Although the input data are hypothetical, several observations concern-
ing the results in Tables 6 and 7 are instructive. There is a marked
difference between the solutions obtained from the D₯MC and the D₯ME
models; however, this difference should be discounted because the DWME
solutions are not necessarily least-cost solutions. After running the
D₯1C model for the higher quality standard, these differences should be
reduced.
Another comparison can be made between the optimal solutions for the
three stream subsystem and the complete eight-stream basin. The solu-
tions are identical in all cases for the minimum cost model;
-------
Table 2. MINE SOURCES AND POLLUTION CONTROL COSTS
Node
Level 1 streams
Number 1
1
2
3
Number 2
1
2
Number 3
1
Number U
1
2
3
Level 2 streams
Number 1
1
2
Number 2
1
2
3
Number 3
1
2
3
Level 3 streams
Number 1
1
2
3
it
5
6
7
Description
Small drift mine
Small gob pile
Small drift mine
Large underground mine
Large gob pile
Large drift mine
Large drift mine
Large gob pile
Small drift mine
Large underground mine
Spoil banks
Large underground mine
Large gob pile
Spoil banks
Small drift mine
Large gob pile
Large underground mine
Small drift mine
Spoil banks
Small drift mine
Small drift mine
Dummy source
Large gob pile
Large underground mine
Abatement cost
($i/yr)
3000
2250
3000
30000
15000
22500
30000
22500
3750
15000
15000
30000
22500
15000
6000
30000
22500
3000
7500
3750
1*500
9999999
22500
22500
Treatment pro-
cessor cost
($i/yr)
2500
2000
1800
15000
5000
11000
10000
6000
2500
2200
2000
17000
1*000
5000
1*000
1*000
12000
3000
2500
7000
2000
9999999
2200
10000
-------
Table 3. AVERAGE ANNUAL POLLUTANT LOADS
(kg)
Level 1 streams
Number 1
1
2
3
Number 2
1
2
Number 3
1
Number 4
1
2
3
Level 2 streams
Number 1
1
2
Number 2
1
2
3
Number 3
1
2
3
Level 3 streams
Number 1
1
2
3
1+
5
s
6
7
Annual pollutant
no abatement
2041
2041
2041
163292
49895
30617
20412
6804
3084
14968
6123
76657
113398
183M
4536
113398
254-01
998
3084
3084
6123
0
49895
12247
Annual pollutant
abatement
680
227
680
54431
4536
2268
9979
3402
1361
2268
36287
4536
1361
907
3629
11340
454
454
1361
2722
0
2268
4082
Annual natural
pollutant
-181
-181
-181
-181
-227
+45
0
-45
-45
+45
+45
-91
-136
-181
-227
-227
-181
-91
-91
-91
-91
0
-181
-272
-------
Table 1+. POLLUTANT AND STREAM FLOWS SPRING RATES
Node
Level 1 streams
Number 1
1
2
3
Number 2
1
2
Number 3
1
Number 1+
1
2
3
Level 2 streams
Number 1
1
2
Number 2
1
2
3
Number 3
1
2
3
Level 3 streams
Number 1
1
2
3
k
5
6
7
Pollutant flow
no abatement
(kg/hr)
0.91
0.009
1.00
68.0^
0.91
36.29
20. Ill
1.36
1.81
18.11+
0.91
^5.36
1.81
2.2?
3.63
0.91
25.140
1.81
0.36
0.91
k.5k
0
0.91
18.11+
Pollutant flow
abatement
(kg/hr)
0.27
0.005
0.32
22.68
0.1+5
2.27
9-07
0.91
0-91
6.80
O.U5
22.68
1.36
0.1+5
0.91
0.68
11. 3^
0.68
0.09
0.1+5
2.27
0
0.68
6.80
Natural
pollutant
flow
(kg/hr)
-0.009
-0.009
-0.009
-0.009
-0.011+
-0.005
-0.011+
-0.011+
-0.011+
-0.009
-0.009
-0.011+
-O.OlU
-0.011+
-0.018
-0.018
-0.018
-0.009
-0.009
-0.009
-0.009
0
-0.011+
-0.018
Stream
Flow
(m3/sec)
0.15
0.18
0.20
0.30
0.70
0.18
o.U6
0.70
0.79
0.30
0.82
0.21+
1.52
1.65
0.37
i.Uo
2.07
^+.57
5.^9
5-52
7-^+7
10.21
10.21
10.36
-------
Table 5. POLLUTANT AND STREAM FLOWS SUMMER RATES
Node
Level 1 streams
Number 1
1
2
3
Number 2
1
2
Number 3
1
Number 4
1
2
3
Level 2 streams
Number 1
1
2
Number 2
1
2
3
Number 3
1
2
3
Level 3 streams
Number 1
1
2
3
4
5
6
7
Pollutant flow
no abatement
(kg/hr)
0.23
2.04
0.045
0.91
54-43
0.544
0.227
68.01*
0.036
0.36
0.36
1.81
68.04
1.36
0.023
56.70
0.27
0.023
0.18
0.023
0.068
0
68. ok
0.36
Pollutant flow
abatement
(kg/hr)
0.009
0.227
0.01k
0.32
0.45
0.023
0.18
1.81
0.027
Q.Ik
o.ik
0.91
2.27
0.09
o.oo4
18.14
o.ik
0.009
0.0*15
0.009
0.036
0
1.81
0. Ill-
Natural
pollutant
flow
(kg/hr)
+0.005
+0.005
+0.005
+0.009
+0.009
+0.014
+0.005
+0.005
+0.005
+0.005
+0.005
0
0
-0.005
-0.005
-0.005
-0.009
0
0
0
0
0
-0.005
-0.009
Stream
flow
(m3/sec)
0.02
0.02
0.06
0.09
0.12
0.09
0.21
0.24
0.46
0.06
Ool8
0.09
0.36
0.55
0.12
0.76
1.10
1.83
2.59
2.71
3-66
5.33
5-33
5.52
-------
Table 6. MINIMUM COST (DWMC)
MODEL RESULTS
Table 7. MAXIMUM EFFECTIVENESS (DWME)
MODEL RESULTS
Node
Level 1 streams
Number 1
1
2
3
Number 2
1
2
Number 3
1
Number h
1
2
3
INSTa No. 1
Level 2 streams
Number 1
1
2
Number 2
1
2
3
INST No. 2
Number 3
1
2
3
Level 3 streams
Number 1
1
2
3
It
5
INST No. 3
6
7
Spring rates
8 streams
Treat
-_b
Treat
Treat
Abate
Treat
Treat
Abate
Treat
--
Treat
Treat
Treat
.-
Treat
--
Treat
__
Treat
3 streams
Treat
Treat
Abate
Treat
Treat
Treat
Summer rates
8 streams
Abate
Treat
Treat
Treat
Treat
Treat
Treat
Treat
Treat
Treat and
abate
Treat
Treat
--
__
Treat
3 streams
Treat
--
Treat
Treat
Spring rates
8 streams
Treat
Treat
Treat
Treat
Treat
Treat
Abate
Treat
Treat
--
Treat
Treat
--
Treat
Treat
Treat
Treat
Treat
Treat
Treat
Treat
Treat
3 streams
Treat
Treat
Abate
Treat
--
Treat
Treat
Summer rates
8 streams
Treat
Treat
Treat
Treat
Treat
Treat
Treat
--
Treat
Treat
Treat
Treat and
abate
Treat
._
Treat
Treat
--
Treat
Treat
Treat
Treat
__
Treat
Treat
3 streams
Treat
Treat
__
Treat
Treat
--
aDTST = Instream treatment site
b = No action
-------
Table 8. MINIMUM ANNUAL POLLUTION CONTROL
COSTS FROM THE DWMC MODEL
Spring rates
8 streams
3 streams
Summer rates
8 streams
3 streams
Annual Cost
$229,000
84,000
259,000
77,000
however, there is a different solution at two nodes for the maximum
effectiveness model. Thus, the subsystem or sub-basin results and
basin results are similar, but different solutions can occur. It
should be noted that the case chosen would 'not be as sensitive to
changes from a sub-basin to a basin because there are no upstream
inputs to the sub-basin.
The differences between the results for spring and summer rates
obtained from the DWMC model will present more problems in actual
application. An examination of the DWMC computer runs indicates that
the optimal solution based on the summer flow rates would not satisfy
the five ppm quality standard using spring flow rates. The opposite
comparison cannot be made without rerunning the computer program. This
comparison would imply that "worst cases" are somewhat unique and a
solution for one "worst case" is not necessarily adequate for another.
This problem in applying the models needs further investigation.
The computer times from these runs indicates that the algorithms devel-
oped can be operated for systems of this size economically. The long-
est computer times were required by the maximum effectiveness model to
solve the complete basin problem with summer flow rates. For that
case, approximately two minutes of CPU time was used on Ohio State's
IBM 370 Model 165 computer for a cost of thirty dollars. The computer
times required by the DWMC model were about one-half of the DWME times.
Thus, computer costs for these optimization models will be inexpensive
for problems of this magnitude.
ij-8
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SECTION VI
EVALUATION OF OVERALL TECHNIQUE
The major contribution which has been made in the development of the
overall resource allocation model described in the preceding sections
lies in the specific capabilities of the two major sub-model types
incorporated in the overall model; the source models, and the optimiza-
tion models. The source models provide a rational means of describing
and predicting the complex time dependent acid production phenomena
which occur in the predominant types of mining environments. Until
now, no such analytical tool has been available for simulating acid
flow and load data. The optimization models, utilizing flow and load
data, together with appropriate cost information, provide a compact
and efficient cost optimization algorithm capable of determining the
least-cost set of pollution control decisions for a branching array of
acid sources, with the option of either drainage treatment or at-source
abatement at each acid source and a given specific water quality
standard. Alternatively, the optimization sub-model can determine the
distribution of pollution control decisions over the total array of
acid sources which will result in the most desirable water quality
obtainable, given an upper limit on dollars available for pollution
control. This sub-model also represents an analytical tool which has
not been heretofore available.
Of the two sub-models, the source models will be the most difficult to
apply realistically to field situations. The complexities inherent in
the natural phenomena of pyrite oxidation and mine drainage formation
are reflected in the multitude of parameters required for even a mar-
ginally accurate description of acid flows and loads by the source
models, and the calibration of the source models to field conditions
will never be an easy task. However, this should in no way be used as
an excuse to rely on more simplistic approaches for the estimation of
acid flows and loads, as such methods have consistently demonstrated
their inability to provide useful answers. The output of the optimi-
zation models may be severely limited by inadequate acid flow and load
data used as input to this model, and attempts to use the optimization
model without high quality input data will have questionable value
until the sensitivity of optimization model results to input data vari-
ations is clarified. The value of the resources being mined and of the
-------
resources being threatened by the effects of mining justify and demand
a high degree of sophistication in the analysis and solution of mine
drainage problems.
Although the optimization model structure is simpler, thus making it
appear easier to apply, most field situations will be difficult to
evaluate realistically because of this simpler structure. Situations
are likely to be encountered that are unlike the set of assumptions
selected in formulating this model. Many of the requirements for
extending and enriching the optimization model will only become appar-
ent when they are actually used; thus, further development should be
coupled with actual use rather than attempting to cover every contin-
gency .
The following discussions are intended to give a realistic evaluation
of the strengths and weakness of the overall resource allocation model.
Since the source models are coupled in series to the optimization
model, with no feedback from the latter to the former, the two sub-
models will be evaluated separately.
SOURCE MDDEL
The deep mine and the Combined Refuse Pile-Strip Mine (CRPSMM) Source
Models have been specifically designed to provide a means of predicting
time traces of the drainage flow and acid load from a given acid
source, for any period of time desired, and under any presumed precipi-
tation sequence.
At present, advances in the basic understanding of pyrite oxidation and
acid transport mechanisms over the past decade, together with an
already well developed science of hydrologic modeling, have made it
possible to frame the source models in rational, mechanistic terms,
thus avoiding the inherent and proven inadequacies of empirical or
statistical predictions of mine drainage behaviors. The model param-
eters which have been used to describe acid formation, and water/acid
movement are subject to rational interpretation. Many of these param-
eters are, to varying degrees, open to independent determination in the
laboratory or in the field. Others can be determined only by calibra-
tion of the models to field data.
The source models are themselves composed of a hydrologic model coupled
to an acid generation-acid transport model. In the interest of keeping
the acid generation/transport sub-models as simple as possible, it was
necessary to develop the two separate models, deep mine, and CRPSMM.
While both describe the same phenomena, the physical differences be-
tween deep and surface mines made dual model development preferable to
a highly complex generalized model. Of the two source models, only the
Deep Mine Source Model has been tested in the field. Realistic testing
50
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of the CRPSMM model awaits the availability of more complete field data
than were available during the course of this study. While the ability
of the deep mine model to describe field observations with reasonable
accuracy has been demonstrated, the CRPSMM model is offered only as a
first generation model and it may require significant modification
before it can be used as a practical tool.
Recalling that both source models utilize the same hydrologic model
(the OSU version of the Stanford Watershed Model), remarks as to the
strengths and weaknesses of this hydrologic model are in order. Many
hydrologic models are currently in use for purposes ranging from flood
plain delineation to low-flow water quantity prediction. When water
quality is not a consideration, it is often possible to utilize a
special purpose model of relatively simple form. For example, in flood
studies a model specifically designed to reflect flood flows might be
used. Such a special purpose model would normally have little or no
capabilities for the accurate prediction of subsurface flows and low-
flow conditions. In the analysis of mine drainage, however, critical
acid concentrations may occur under either high- or low-flow condi-
tions, and in all cases, acid concentrations and loads are determined
by both subsurface and overland flow components. Even in refuse piles,
much of the acid load is transported in subsurface flow at extremely
high concentrations, and this transport requires accurate accounting of
subsurface flows by the hydrologic model. Upon the appearance of
highly acidic subsurface flow components at the ground surface, dilu-
tion by overland flow may provide a major moderating influence on acid
concentrations in the stream, and accurate accounting of overland flow
is a necessary characteristic of the hydrologic mode. Of the hydro-
logic models available, few are designed to provide a high degree of
capability for both surface and subsurface component accounting. The
Stanford model has demonstrated such capability, and was chosen for
this reason. However, it must be recognized that this complex hydro-
logic model, together with its formidable array of descriptive param-
eters and input data requirements, also demands careful calibration to
specific field conditions, with the availability of three years of
stream flow data being considered necessary for optimum calibration of
the model. While the possibility of hydrologic model simplification
exists, only experience in application of the current form of the model
to mine drainage situations will tell whether, and to what degree, such
simplifications may be possible.
The acid generation and transport portion of the Deep Mine Source Model
is described in detail in Appendix A of this report. In the simpli-
fied description of a mine according to this model, the coal seam is
divided into discrete elements by using a three-dimensional rectangular
coordinate system, and acid production, storage, and removal are calcu-
lated for all elements in a manner which ensures a complete mass
balance for oxygen, oxidation products, and water moving within the
system and its surroundings. To avoid unnecessary complexity in the
51
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model, many of the constants used in the mathematical description of
oxidation rate, product transport, etc., are assumed to be constant
for the entire system, or for an entire layer in the multilayer coal
seam. For example, the coefficient DIP, used to calculate product
removal from each element by gravity diffusion, is assumed to be a
constant for the entire mine. Since DIF is defined as the fraction of
acid formed in an element which is transferred each day to the next
lower element, the application of the same value of DIF to all ele-
ments is an obvious but necessary simplification. Data simply do not
exist to justify estimation of individual values of DIF to each ele-
ment in the mine.
A second example is the assignment of the same value of reaction rate
constant to all elements in a given layer or slice of the strata being
modeled. While this is approximately correct, it cannot be expected
to hold true except as an average effective value for the layer.
While numerous other examples of the assignment of "average effective"
values to model parameters can be cited, the above is sufficient to
make the point that the highly complex nature of the mine system is
idealized to a high degree. As long as the model simulates historical
records to an acceptable degree, a higher degree of sophistication is
unwarranted. The validity or fallacy of the degree of simplification
currently used in the model can be determined only by future experi-
ences in applying the model to a range of geographical locations and a
range of mine sizes. The model as it now stands has a sufficiently
large number of constants, factors, etc., so that it is possible to
fit the model to any set of field data which is reasonably complete.
Whether this will be an empirical exercise in curve fitting, or cali-
bration of a basically valid model reflecting the fundamental mecha-
nisms controlling water movement and pyrite oxidation remains to be
determined. Indications to date, are that the Deep Mine Source Model
is indeed valid, and that the various factors and coefficients used do
reflect the basic phenomena they are intended to describe. It, thus,
holds the promise of being a useful tool not only in the prediction of
future acid loads from an existing mine, based on model calibration
using historical data, but also in the prediction of acid loads after
specific at-source abatement programs are carried out, such as partial
flooding, mine sealing of various types, etc. Such predictions are
possible only on the presumption that the intended abatement technique
will affect various model parameters in a predictable way. Experience
to date at the McDaniels Test Mine in Southeastern Ohio has indicated
that the model has this capability, but further testing is desired.
A constraint on the current model is the fact that it is written for a
single mine, having a given set of descriptive parameters. When the
Deep Mine Source Model is to be applied to a complex of mines, the
analyst has the choice of applying the model separately to each mine,
-------
or of aggregating the individual mines into a single effective mine,
and handling the effluent from this effective mine as if it discharged
at a single point. Alternately, the total discharge from an effective
mine might be reallocated to the individual mine locations on the basis
of individual mine areas, with or without consideration given to other
factors.
The manner in which a complex of mines should be approached will depend
largely on the degree of uniformity of characteristics expected among
the mines in a given area, and the use to which the model is being put.
For a basin study, it is likely that the aggregation scheme outlined
above would provide sufficient simulation, with the exception that
mines in different seams would probably require separate handling due
to large probable differences in the hydrologic characteristics of the
different seams. However, for at-source abatement design and simula-
tion for specific mines, the individual mines would almost certainly
have to be modeled separately.
The complexity of the system being modeled, together with the number of
input parameters which must be determined or estimated for the calibra-
tion and operation of the Deep Mine Source Model, make it necessary
that the analyst be closely familiar with mine drainage systems. The
model in its present form cannot be approached as a black box system,
and is not amenable to operation by personnel who are not well versed
in the subject.
Many of the above comments relating to the acid production and trans-
port component of the Deep Mine Source Model also apply to the corre-
sponding component of the combined Refuse Pile-Strip Mine (CEPSMM)
Source Model, described in detail in Appendix B. The major difference
between the deep mine and refuse pile-spoil bank simulations is that
the former utilizes only the underground flow components of the
Stanford model in the simulation of acid transport, while the latter
uses both surface and underground flow components in this capacity.
The fact that the acid is produced at or near the surface in the strip
mine-refuse pile case, rather than in a deep cavity, makes the problem
of simulation simpler in some respects, but more difficult in others.
In the strip mine-refuse pile models, consideration must be given to
underground flow phenomena. A large percentage of the total acid load
leaving these sources of acid drainage come from, or are carried by,
the underground water flow. This flow tends to dampen the effects of
storm runoff from refuse piles unless the slopes are unexceptionally
steep or the surface unusually compact.
In strip mined areas, over half the acid load (over an extended period)
is carried by underground flow. This chronic flow from strip mines has
a major effect on acid concentration in receiving streams during low
flow periods.
53
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A major difficulty in estimating input parameters for the CRPSMM model
is that while coal seam characteristics are relatively constant
throughout a given deep mine, the actively oxidizing pyrite in a strip
mine or refuse pile represents disturbed material, at or near the sur-
face, in which pyritic material is mixed to varying degrees with rela-
tively inert materials from the overburden. A careful study of the
area, including physical and chemical analysis of both surface and sub-
surface samples, is necessary to give a basis
pyrite location and reactivity.
OPTIMIZATION MODEL
Given cost estimates and inputs from the source models, the Optimiza-
tion Models were formulated to determine the optimal resource allocation
to different point sources involving treatment and abatement alterna-
tives. The initial formulation of the optimization problem showed that
it is discrete, nonlinear, and stochastic. Moreover, pollution and
stream flows vary as a function of time and are inherently stochastic
principally due to precipitation patterns. To simplify the mathe-
matics, the problem was solved by assuming that a single worst case
could be identified. That is, a single condition could be identified
where any resource allocation giving a particular stream quality for
the worst case flows would never give lower quality at other points in
time. With this assumption, a nonlinear discrete optimization algo-
rithm has been derived and is ready for use for a complex of mines and
streams as described in Section IV
Problems are likely to be encountered in using this Optimization Model
in several areas as outlined below:
1. The single worst case assumption has been shown to be false
as shown by the example presented in Section V.
2. Pollution and stream flows are known to be stochastic.
3. The sensitivity of resource allocation to input data vari-
ations needs definition.
h. Situations are likely to be encountered which are unlike the
mine and stream complex depicted in Section IV.
These problems are discussed in the following paragraphs.
The example in Section V involved two worst case flow situations where
one situation was identified as a high flow situation during the spring
and another was a low flow situation representing summer conditions.
If the resource allocation deduced from spring flows would satisfy
quality standards in the summer or vice versa, the existence of a worst
-------
case would be confirmed and the decision problem would be to decide
which situation to use as the input to the model. However, the results
show that a spring least cost solution may not meet quality standards
in the summer and vice versa. Moreover, other "worst cases" may exist.
Possibly year A may produce a worst case that gives a poor quality
solution in year B. To ignore this problem invites the possibility of
introducing pollution control action that is thought to guarantee good
stream quality but does not exist in actuality.
The stochastic nature of stream flows and pollution flows introduces
additional problems in the analysis, but recognition of the stochastic
nature of flows may lead to increased understanding and efficiency in
the pollution control process. For example, assume that the planner
knows the cost of meeting quality standards with a 0.8 probability in
a given year as well as the added cost to give a 0.95 probability;
then the search for the absolute worst case may be regarded as unneces-
sary.
The facts that multiple "worst cases" exist and the flows are sto-
chastic generate questions concerning the resolution and accuracy of
input data required by the Optimization Models. The model has been
shown to be sensitive to changes in input data values but little is
known concerning the degree of sensitivity. How accurate do the input
values from the pollution source models need to be to result in good
decisions concerning pollution control actions? Can rough actual data
values be and somehow give "ballpark" estimates of the effectiveness of
pollution control actions?
Even with all of the above questions answered, actual situations will
present new problems in applying the Optimization Models. For example,
the Lake Hope area in Ohio has underground mines with multiple open-
ings. Control costs vary with the number of openings sealed and these
openings must be sealed in a particular order since the elevations of
the openings vary. This decision concerning which openings to seal
cannot be handled by the existing model. In addition, individual mines
in the vicinity of the Clarion River in Pennsylvania drain into several
different streams with different quality characteristics. What if
mines drain into a lake or reservoir? These real situations may pre-
sent problems in the application of the Optimization Model.
Although the above discussion indicates the existence of problems, the
current Optimization Models represent a significant advance in the
capability of analyzing mine drainage pollution problems. The current
algorithm is efficient and presents a challenge to construct since the
discrete nonlinear nature of the equations involved eliminates the use
of available algorithms such as linear programming and integer linear
programming.
55
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SECTION VII
PUBLICATIONS
The following publications have resulted from research conducted under
this project:
Ricca, V. and Chow, K. , "Acid Mine Drainage Quantity and Quality
Generation Model," presented at the Annual Meeting of the Ameri-
can Institute of Mining, Metallurgical and Petroleum Engineers,
Chicago, 111., Feb., 1973. Accepted for publication in the
Transactions, Society of Mining Engineers of AIME, Salt Lake City,
Utah, December, 197^.
Johnson, S., "Computer Simulation of Acid Mine Drainage from a
Refuse Pile," Master of Science Thesis, Department of Civil
Engineering, The Ohio State University, March, 1973.
Maupin, A., "Computer Simulation of Acid Mine Drainage from a
Watershed Containing Refuse Pile and/ or Surface Mines," Master
of Science Thesis, Department of Chemical Engineering, The
Ohio State University, August, 1973.
The following presentations were conducted using material derived from
this research project:
Clark, G. , Ricca, V., Smith, E. , "Presentation of Project Results
to EPA Personnel and Guests," Washington, D. C., Feb.,
Ricca, V., "Hydrologic Modeling," guest lecture presented at the
Third Short Course on the Hierarchical Approach in the Planning,
Operation and Management of Water Resources Systems, Case West-
ern Reserve University, Cleveland, Ohio, May, 1974.
Ricca, V., "Acid Mine Drainage Modeling," Environmental Engineer-
ing Seminar, The Water Resources Center, The Ohio State University,
May,
Ricca, V. , CE 820 Advance Hydrology, course lectures on modeling,
The Department of Civil Engineering, The Ohio State University,
Jan., 1971*-.
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SECTION VIII
APPENDICES
Page
A. Deep Mine Pollutant Source Model 58
B. Refuse Pile-Strip Mine Pollutant
Source Model 104
C. Optimization Model 183
D. Cost of Drainage Treatment
57
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APPENDIX A
DEEP MINE POLLUTANT SOURCE MODEL
TECHNICAL DETAILS AND COMPUTER PROGRAMS
This appendix contains details on the pollutant source model as to its
history, modifications, and linking mechanisms.
An in-depth discussion of their application, showing input parameter
values and selection methodology, data assembly, and typical graphical
and tabular outputs is included.
The section concludes with a set of procedures to operate the deep mine
pollutant source model.
The material presented herein was taken as much as possible from publi-
cations (papers presented and Master of Science Theses) written as part
of this project during the research period.
INTRODUCTION
Acid mine drainage is a serious water pollution problem, for its con-
taminants will eventually affect the quality of the receiving streams.
According to the Appalachian Regional Commission (1969)*, 10,500 miles
of streams have been polluted by mine drainage, and 70 percent of this
acid pollution is accounted for by underground mines. Due to the severe
damage to aquatic life, to recreational and industrial use, and to
domestic water supply, more stringent mining and anti-pollution laws
have been legislated and coal mine operators are required to treat the
mine water discharges to meet the standards. For years now, abatement
and treatment methods have been extensively studied. Progress reports
presented in the Fourth Symposium on Coal Mine Drainage Research, 19721
suggest that a thorough investigation and understanding of the basin
discharge is necessary in order to cope with the mine drainage problem.
The extent of mine water discharge contamination can be considered as
^References listed at the end of this unit pollutant source model.
58
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a function of the basin streamflow and acid generation load. A conserv-
ative treatment cost estimation these days is $0.^0 per 1,000 gallons
for water with 100 ppm iron, 500 ppm acidity. These figures need not
include collection and pumping costs nor the cost of dispersing of
chemical waste by-products. To achieve optimal abatement and treatment
of mine drainage, predictions of the quantity and quality of mine water
discharges are needed.
Basin discharge is a continuous process and it can be considered as a
macro-system. This system can be subdivided into micro-systems to
describe the various mine discharge types in the basin. The mining
activities could produce acid water discharges from deep mines, strip-
mines, or associated gob piles.
In this appendix we will discuss only one micro-system, the drift
(deep) mine type by looking at a single mine and its watershed. The
total research project considers a multiple mining complex in an exten-
sive stream basin.
The system (a mine and its watershed) will be studied and described by
mathematical relationships which will be processed with the aid of a
digital computer. Once the mine discharge is formulated as functions
of mine water and acid generation within, continuous output of mine
drainage to the receiving stream flow can be simulated. From these
the watershed discharge and quality can be predicted.
Mine drainage simulation models can be useful in: predicting mine
water quantity and quality, quantitizing the cost for treatment prior
to discharge, evaluating the effects of abatements efforts, and above
all, helping to cope with mine drainage pollution problems.
The model that is presented herein is a hybrid of computer programs
for the hydrologic behavior of a watershed and for the generation of
acid mine water. The former is structured on hydrologic cycle concepts
and the latter on pyrite oxidation kinetics and oxidation product re-
moval. The total model is programmed for the high speed digital com-
puter (IBM 370/165).
The major inputs to the model are: climatological, watershed charac-
teristics, and mine characteristics data. By the use of the hydrologic
portion of the model the amount and timing of water that flows through
the pyritic system is determined. From this information, the acid pro-
duction portion of the model predicts acid load generation due to
leaching, inundation, and gravity diffusion. The outputs from the
total model include: average daily minewater discharge, the associated
acid concentration or load, plus the average daily flow in the receiving
streams or at basin outlets.
59
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CONCEPTS OF THE SIMULATION MODEL
The simulation model consists of two major components: minewater flow
and acid load. The former is related closely to the concept of hydro-
logic cycle, whereas the latter is based on the concept of pyrite oxi-
dation kinetics and oxidation product removal. A clear understanding
of these concepts is needed in formulating the mathematical models.
To study the workings of the total model we will look at the two major
portions separately then show how they are joined. Before getting^into
the model components a brief review of the hydrologic cycle, reaction
kinetics, and oxidation product removal may be helpful.
Hydrologic Cycle
Three zones of hydrologic events can be assigned to describe a hydro-
logic cycle. Figure A.I shows a schematic diagram of the cycle as
used by the model.
1. Upper Zone - This zone is above the soil surface. It is
used to describe the activities at and after precipitation
above the soil surface. The activities include intercep-
tion, transpiration, evaporation, overland flow, surface
detention and depression storage.
2. Lower Zone - This zone is the soil between the water table
and land surface. It is used to describe the activities
of infiltration from the upper zone, percolation, inter-
flow, and the degree of soil moisture saturation.
3. Deep Lower Zone - This zone is the soil below the water
table.It is used to determine groundwater flow to the
stream, and to deep storage (or aquifer). Because mois-
ture percolates through the cracks and crevices of the
aquifer, a time delay occurs between moisture entering
the aquifer and leaving the aquifer as minewater flow.
The hydrologic cycle is a continuous process. Precipitation falls on
the upper zone and some of it will enter into the lower zone and deep
lower zone. The balance will enter the upper zone (interception plus
depression storage). To complete the cycle, evaporation and transpira-
tion occur from all three zones.
60
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GROUNDWATER FLOW TO STREAM-
LOWER ZONE STORAGE -"'' \
TO
DEEP
STORAGE
Figure A.I. Schematic of hydrologic cycle
Pyrite Oxidation Kinetics
Acid mine drainage is caused by the natural formation of acid by the
oxidation of iron pyrites (FeS2 in the coal seams) in the presence of
water and air. The reaction in its simplest form can be represented
by equation A.I.
FeS2 + 7/2 02 + H20 = H2S04 + FeS0
(A.I)
The oxidation kinetics of pyrites have been thoroughly investigated.2~5
Lau et al.s have reported that bacterial catalysis is not likely in
underground environments. Smith and Shumate7 have also shown that zero
order reaction kinetics enhanced by microbial activity are not signifi-
cant in underground pyritic systems. Morth and Smith have stated that
the oxidation rate can be satisfactorily approximated as first order
with respect to oxygen concentrations between the range of zero to 21
percent in mines. Equation A.2 shows the rate of oxidation:
61
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r - krCo
(A.2)
where r is the rate of oxidation, kr is the reaction rate constant, and
C0 is oxygen concentration. Because pyrite oxidations occur along the
small channels in coal or shale, the reaction rate depends on the avail-
ability of oxygen at exposed reaction sites.
Oxidation Product Removal
Oxidation product removal is a function of the hydrogeologic character-
istics including porosity and permeability of the overburden, sizes of
cracks and crevices, position of the oxidizing material and fluctuations
of the water table.7 Three removal mechanisms (see Figure A.2) have
been proposed and tested by laboratory observations and physical con-
siderations.8 These three mechanisms are:
1. direct leaching by ground water which percolates through
channels and fractures and removes oxidation products
formed at tJunes when the channel was not full of water,
2. flooding of products from an inundated volume by a rising
water table, and
3. gravity diffusion of saturated solutions of reaction
products.
Tricking
Water
Leaching
Gravity
Diffusion
Oxidation
Inundation
w
Gravity
Diffusion
Figure A.2. Underground pyritic system
62
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The first two mechanisms which cannot be readily determined experimen-
tally are closely related to underground water flow patterns, whereas
the third mechanism which has been observed in laboratory studies is
independent of water flow. Data of a high and a steady period of mine-
water flow and acid load are needed to evaluate the parameters for the
determination of the amount of acid removal by various mechanisms.
EVOLUTION OF THE MODEL
Once the concepts of the simulation have been established, mathematical
models can be formulated to simulate the hydrologic cycle. The Ohio
State University version of the Stanford Watershed Model with slight
modifications is used to calculate the amount of moisture reaching the
mine aquifer. A model described by Morth, Smith, and Shumate9 can be
used to simulate the pyrite oxidation kinetics and oxidation product
removal. Evolution of these models are briefly described as:
Stanford Watershed Model (SWM)
The Stanford Watershed Model was developed by Crawford and Linsley in
the early sixties.10 James11 modified the model and translated it into
FORTRAN language in the late mid sixties. Various researchers12'13
have worked with and proved the acceptability of the model in the late
sixties. Since 1968 researchers at The Ohio State University have made
modifications to progress the model along these lines: Balk14 flow-
diagrammed the model in detail and wrote an expose on the mechanics of
its operation. Briggs15 developed a computer plotted hydrograph pro-
gram and made a sensitivity study of the key parameters. Owen16 added
multiple recession constants and a swamp and soil crack storage rou-
tines to the model. Mease17 developed a snowmelt subroutine for the
Midwest. Valentine18 made modifications to make the model applicable
to small watersheds. Warns19 compiled a user's manual. The completed
model in its present form has been summarized by Ricca and presented
in a three-part report.20 All programs can be executed by an IBM
370/165 time sharing computer system.
The original model consists of 15 input-output control options. The
Ohio State University version has been extended to 20. Besides the
climatological data (precipitation, pan evaporation, wind speed, solar
radiation, and temperature) 31 input parameters (12 measurable param-
eters, 11 trial and adjustment parameters, and 8 assigned or selected
parameters) are required by the model. Table A.I lists the definitions,
names, and sample values (see Case Study later in this appendix) of
these variables. A detailed explanation to determine these variables
is provided by Ricca.20 The SWM is formulated by using these variables
together with the concept of hydrologic cycle discussed in the previous
section. A block diagram of the program for the model is shown in
Figure A.3°
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Table A.I. SWM PARAMETERS
Model
Parameters
A
AREA
CHCAP
COE
ETL
IRC
Kl
KK24
KSC
KSF
L
SS
CB
CX
CY
EDF
EF
EMIN
GWS
KV24
LZS
LZSN
SOW
EPXM
K3
K24L
K24EL
NN
NNU
RFC
UZS
Parameter Definitions
Measurable Parameters
Impervious area that drains directly into the stream channel
Watershed drainage area in square miles
Index capacity of the existing channel incubic feet per second
Empirical constant for convection
Estimate of the stream and lake surface area as a fraction of AREA
Daily interflow recession constant
Long term ratio of average basin rainfall to average watershed ppt.
Daily baseflow recession constant
Streamf low routing parameter for low flows
Stream routing parameter for flood flows
Mean overland flow path length in feet
Average ground slope in feet/foot of the overland flow surfaces
Trail and Adjustment Parameters
Index controlling the rate of infiltration
Index to estimate interception, depression storage capacity of
the soil surface
Index controlling time distribution, quantities of moisture
entering interflow
Index for estimating soil surface moisture storage capacity
Factor relating infiltration rates to evaporation rates for
seasonal adjustment
Minimum value of EN
Current value of groundwater slope index in inches
Daily baseflow recession adjustment factor
Current soil moisture storage in inches
Soil profile moisture storage index, in inches
Groundwater storage increment, in inches
Assigned or Selected Parameters
Maximum interception rate for dry watershed
Soil evaporation parameter
Index for groundwater flow leaving basin
Groundwater evaporation parameter
Manning's n for overland flow on soil area
Manning's n for overland flow on impervious area
Index for routing
Current soil moisture storage
Sample Value
0.00
1.01
39.
0.00177
0.001
0.0313
1.0
0. 0226
0.966
0.737
1120.
0.0122
2.2
0.7
3.0
0.4
4.0
0.1
0.100
0.75
4.5
6.0
0.100
0.2
0.3
0.0
0.0
0.400
0.10
1.0
0.0
-------
Os
MAJOR INPUT
Precipitation
Pan Evaporation and Coefficients
Physical Watershed Parameters
Initial Soil Moisture Conditions
Initial Groundwater Storage Conditions
MAJOR OUTPUT
Synthesized Streamflow
Synthesized Evapotranspiration
Evaporation from Exposed Water Surfaces
->| Runoff from Impervious Surfaces I-
Interception
Upper Zone Soil Mositure
Upper Zone Soil Moisture Storage
frj Overland Flow Surface Detention
-W Overland Flow |-
Interflow Storage
S> Lower Zone Moisture Storage
Groundwater Flow
out of Basin
Groundwater Storage
Routing
Evapotranspi ration
Groundwater Flow
LEGEND
Operations performed
in 15 minute intervals
(or smaller if specified)
Operations performed
in 60 minute intervals
Figure A.3. Moisture accounting in Stanford Watershed Model
-------
Acid Mine Drainage Model (AMD)
The Acid Mine Drainage Model was based on the conceptual model of an
underground pyritic system by Shumate and Smith.21 Chow8 formulated
the conceptual model to produce a mathematical model for a drift (deep;
mine. Chow22 utilized field data to progress and test the^model. A
more recent description of the model is given by Morth, Smith, and
Shumate.9
The mine system can be divided into many micro-volumes and equations
can be written to describe the events (oxidation and its product re-
moval mechanisms) occurring in each micro-volume. The total mine
behavior is then the sum of events in each micro-volume. Figure A.d
can be used to illustrate this.
In addition to the daily climatological data, twenty three parameters
are to be determined to run the model. Nine are used to describe^the
mine system, five to describe the pyrite oxidation kinetics and^nine to
describe the oxidation product removal mechanisms. Table A.2 lists the
definitions, names, and sample values of these variables. A block dia-
gram of the model's oxidation kinetics and product removal mechanisms
is shown in Figure A.U.
TOTAL MODEL (SWM-AMD)
In this section we will attempt to present only the basic modifications
made to link the two aforementioned models. Readers who will be study-
ing the combined model in detail are urged to study the individual
models by reviewing the pertinent references mentioned for we will not
backtrack unnecessarily over this material in this discussion.
The SWM involves calculations of hydrologic phenomena to describe the
events that occur in the hydrologic cycle. From the lower zone, mois-
ture percolates to the groundwater. The relationships for the fraction
of moisture that percolates to groundwater (l-PRE)* and the degree of
saturation (LZS/LZSN) in the lower zone can be shown in Figure A.5-
Mathematically, infiltration moisture reaching groundwater (Fl) can be
expressed by equations A. 3 and A A.
Fl = (l.O-PRE)*(plf-SHKD)*(l.O-K2l4-L)*PA (A.3)
for infiltration reaching groundwater from the lower zone storage, and
*These quantities are the actual computer program variable names and for
the sake of consistency we will retain these names in this discussion.
66
-------
Table A.2. AMD PARAMETERS
Model
Parameters
Parameter Definitions
Sample Value
Mine System
WSHED
NFEET
NLAYER
NDEPTH
DK
DI
TOP
ROCK, TYPE
ALT
Watershed area of mine in square miles
Number of air-solid waterface increments
Number of layers in coal seam
Number of depth increments in model
Length of depth increments in feet
Length of air-solid interface increments in feet
Datum plane for top of coal seam in feet
Literal description of stratums
Elevation of stratum relative to datum plane in feet
0. 00168
1
10
25
1
100.
13.8
COAL
10.0-13.8
Pyrite Oxidation Kinetics
REACT
PYCON
TEMP
FTGMOL
CCPRFT
Oxygen consumption rate of pyrite
Void fraction of the stratum
Mine temperature correction factor
Volume occupied by gram mole gas in cubic feet
Constant for calculating rate constant
2.55, 0.55
0.30; 0.005
0.15
0.79
28287. 36
Oxidation Product Removal
TANK
CONFH
ALKALI
FLOWMI
HEADMI
PER
WSLOPE
FRACT
DIF
Aquifer storage in inches
Constant relating mine water flow and aquifer storage
Alkalinity conversion factor
Minimum flow rate to cause acid removal by flooding
Minimum flow rate to cause acid removal by leaching
Constant to determine the inundated distance
Hypothetical slope of the water level
Fraction of stored products removed daily by inundation
Base gravity diffusion constant
0.5
0. 0165
20.
260.
0. 00010
1.1
0.08
0.02
0.001
6?
-------
CO
MAJOR INPUT
Mine Descriptors
Oxidation Rate Parameters
Initial Acid Storage
Flow And Acid Load
Coefficients
Calculation of Infiltration
Water Reaching Ground-
water (Being Replaced By
SWM)
Aquifer Storage
Calculation of Oxidation
Rate Constants
Oxidation of Pyritic
Material
Comparison of Water
Level Relative To
The Strata
I
Inundation Does Not
Occur In The
System
Inundation Occurs
In The System
MAJOR OUTPUT
Synthesized:
Minewater Flow
Acid Load
Minewater
Flow
Oxidation
Product
I
Acid Removal By
Leaching
Acid Removal By
Gravity
Diffusion
Acid Removal By
Inundation
Figure A.4. Schematic of Acid Mine Drainage Model
-------
I.O
0.0
o PRE = FRACTION OF INCOMING
MOISTURE RETAINED IN LZS.
0,8
0.2
ON
CD
111
cr
CL
0.6
0.4
0.4
O.6
UJ
cr
QL
I.
0.2
0.8
0.0
0.0
0.2 0.4
0.6 0.8 1.0 1.2
LZS/LZSN RATIO
1.4
1.6
1.8
1.0
2.0
Figure A.5. Infiltration from UZS that is held in LZS
-------
Fl = (l.O-PKE)*RECE*(l.O-K2UL)*PA
for infiltration reaching groundwater from the upper zone, where
PRE is the fraction of incoming moisture retained in the soil
surface or soil storage,
PU is the residual rainfall after soil surface moisture
depletion,
SHED is the sum of current moisture entering surface runoff
plus interflows,
is a parameter indicating groundwater flow leaving the
basin,
PA is the pervious fraction of the watershed, and
KECE is the current rate of soil surface moisture infiltration.
Values of Fl in equations A. 3 and A.J+ are calculated in 15 minute inter-
vals. The sum of equations A. 3 and A.h is the total infiltration water
reaching the groundwater in a period of 15 minutes. As shown in
Figure A.I, the groundwater will either leave the basin as streamflow
or it will go to deep storage (aquifer). It is the latter that enters
the mine aquifer and trickles through channels in the pyritic system.
These 15 minute interval Fl values can be summed up to provide the
daily infiltration moisture reaching the groundwater (SADD). The
reason for using daily values of SADD is that the time lag or delay
between the groundwater entering an aquifer and the outflow of mine-
water from the aquifer is quite long and therefore the minewater flow
varies slowly on a daily basis. These daily values of SADD can be
punched out on IBM cards or written on magnetic tapes and then fed into
the AMD model. These procedures can be summarized by the following
formulations :
Hourly infiltration moisture reaching groundwater:
u
ADD = £ Fl
1
for four 15-minute intervals .
70
-------
Daily infiltration moisture reaching ground-water:
2k
SADD = £ ADD
1
for 2k one-hour periods.
There are 365 (or 366) SADD values in a water year. Once the daily
SADD values can be determined by the SWM, daily aquifer moisture storage
(TANK) and daily minewater flow (FLOW) can be calculated by using the
AMD model.22 The relationships are:
TANK = TANK + SADD(l) where I = 1,2 365
HEAD = f (TANK)
FLOW = f (HEAD)
TANK = TANK - FLOW
Once the amount of water that flows through the pyritic system can be
determined, acid loads removed by leaching, inundation, and gravity
diffusion can be obtained. The sequence of input parameters for the
AMD has been modified due to the changes employed in linking the indi-
vidual models. Subroutine MINE is added to read the input parameters
to describe the mine and subroutine ACID is used to calculate the oxi-
dation and removal of the pyritic materials. The MAIN program of AMD
is to coordinate the linking of SADD and TANK, to calculate FLOW, and
to write the outputs in tabulated form. A complete logic diagram to
describe the SWM-AMD model is shown in Figure A.6 and Figure A.7.
APPLICATION TO A DEEP MINE
To determine the success of the simulation, the capability of the model
must be tested. This suggests comparing the predictions from the model
against existing data.
Finding a suitable test site poses great difficulty in that complete
data on simultaneous hydrologic and acid minewater discharge are non-
existent or unknown to us. However, we were able to utilize a mine
site where good mine drainage data was available, partial hydrologic
data had been collected and enough climatological data was available
in the immediate region to reasonably assemble the remaining data.
A small drift mine (McDaniels) in Southern Ohio was chosen for testing
the model. The following will include a description of the mine water-
shed, a listing of the model input parameters developed for this site,
the simulation output, and a disqussion of the results obtained.
71
-------
A
Initialization
REAL
INTEGER
DIMENSION
LOGICAL
COMMON
1
r
Read Input
Including:
Options, WS Parameters,
Soil Moisture Parameters,
Overland and Interflow
Parameters, Channel Routing
and Groundwater Parameters,
Hydrograph axis data
i
Calculate Recession
Constants
i
r
Read and Write Detail
Storm Data *
1
Read Detail
Storm Hydrograph
axis data
1
Call Subroutine RTVARY
1
i
t
Calculate Groundwater
Flow
<
t
Calculate Overland
Flow
1
Initialization of
Snow Variables
*
Plotting the Detail
Storm hydrograph
axis
Labeling ordinate of
Runoff Hydrograph
Calculate Infiltration
Parameters
Calculate Soil Surface
Moisture Storage
Index
Plotting of Rainfall
Distribution as used
in the model
Call Subroutine DYLOOP
2
Plotting on the IBM
1627 or 1130
Call Subroutine LOGPLT
if DKN (16) = 1 3
Call Subroutine LOGPL
if DKN (16) = 1
Call Subroutine ARITHP
if DKN (17) = 1
Call Subroutine ARITH
if DKN (17) = 1
6
Call Subroutine DAYOUT
7
Call Subroutine DAYPUN
(See Figure 7) 8
Write results
Subroutine RTVARY j.
Dummy Subroutine in the
OSU Version. Used in the
Kentucky Version to vary
streamflow routing time
according to streamflow
magnitude
(Continued next page)
Figure A.6.
Logic diagram of The Ohio State University version
of the Stanford Watershed Model
-------
Subroutine DYLOOP 2
Performs most of the
hydrologic computations
1
Initialization
REAL
INTEGER
DIMENSION
LOGICAL
COMMON
i
Compute Lake
Evaporation
i
r
Compute Variable
Groundwater Recession
Constants
1
r
Make Evapotranspiration
Adjustments
1
Call Subroutine SNOWMELT
9
1
Begin Variable Time
Accounting and
Routing
i
t
Rainfall Upper Zone
Interaction
i
Lower Zone and
Groundwater
Infiltration
Calculations
i
Calculate Amount of Water
Entering Aquifer From
Lower Zone
i
Calculate Amount of Water
Entering Aquifer From
Upper Zone
1
t
Routing Calculations
i
t
Storm Output
1
Plotting of Storm
Output
i
t
Hourly Overland Flow
and Rainfall Sorting
1
Adding of
Groundwater Flow
i
t
Draining of Upper
Zone Storage
Calculate Total Amount
of Water in Aquifer
(Lower and Upper Zones)
Group 15 Minute Intervals
into Hourly Interval
4 P.M. Adjustment
of Values
Infiltration Correction
Calculations
Calculation of Evapo-
transpiration Loss
from Groundwater
Daily, Monthly, Yearly
Summary Storage of Ground-
water Reaching Aquifer to
Be Used by S_
I
Store Errors and
Flow Durations
Monthly Summary
Storage
(continued next page)
Figure A.6. Continued
73
-------
Subi
online
SNOW
MI-;I,
r 9
I
Determination of
Vapor Pressure
T
Determination of
Temperature
Rain or Snow
Test
Snow Details are
Stored
I
Criteria for Re frozen
Melt water
I
Subroutine DAY PUN S
Set-up and Punch-out data
for output for one
particular day
Subroutine PAYOUT
Set-up data for
output for one
particular day
Subroutine TEST
Tests the value
of C2
*
Subroutine Head
Dummy Subroutine in
the OSU Version to
replace 360 Subroutine
for a compilation
check
Subroutine LOGPLT 3
Plots Recorded Flows on a
5 cycle log scale from
0.01 to 1000. 0 cfs
Subroutine LOGPL 4
Plots Synthesized Flow in
cfs with a dashed curve
same scale as L.OGPLT
Call Subroutine DASHC
1
Subroutine ARITHP 5
Plots Hecorded Flows on
arithmetic scale of the
user's choice in cfs
*
an
Subroutine ARITH 6
Plots Synthesized Flow
in cfs with a dashed
arithmetic curve of the
same scale as ARITHP
* Not used in the SWM-AMD
x Details of Corresponding Subroutines
if: Subroutines not called from the MAIN
program
Figure A.6. Concluded
-------
Initialization
REAL
INTEGER
DIMENSION
COMMON
Read Headings of Program
Call Subroutine MINE 1
Read Groundwater Reaching
Aquifer From SWM
(See 8, Figure A.6)
Read Recorded Minewater
Flow and Acid Load
Echo Check Inputs
Calculate Minewater Flow
Call Subroutine ACID 2
Call DAYOUT
1
r
Call GRAPH
_3
4
Write Results
Subroutine MINE 1
Read in Last of the
Parameters to Describe
The Mine, to Calculate
Oxidation Reaction Rate,
Minewater Flow, and
Acid Load
Subroutine ACID 2
Calculation of Oxidation
Reaction Rate
Initialization
REAL
INTEGER
DIMENSION
COMMON
Enter ACIDIC
To Determine Water Table
and to Calculate Acid
Removal
Calculate Water Level
Calculate Acid Removal
by Inundation
Calculate Acid Removal
by Leaching
Calculate Acid Removal
by Gravity Diffusion
Subroutine DAYOUT
Set-up Data
For One Particular Day
Subroutine GRAPH 4.
Punch-out Cards to Plot
the Minewater Flow and
Acid Load (Simulated vs.
Recorded) on a IBM 1627
x Details of Corresponding Subroutines
Figure A.7. Logic diagram of the Acid Mine Drainage Model
75
-------
Description of the Study Area and Data Available
The Site -
The watershed under study is located in Southern Ohio, about 10 miles
northwest of McArthur, Ohio. It has an area of about one square mile
and a relief of 800 to IQl+O feet mean sea level. The main stream in
the basin is Big Four Hollow which drains into Lake Hope k miles down-
stream. The flow in this stream has been monitored for the last two
years and will be the basic hydrologic data collected. Within the
site, numerous deep mining activities were conducted. One of these
deep mines, McDaniels Mine, is of particular interest in this study
because Smith and Shumate7 have developed this mine into a 'natural
laboratory'. Through many years of continuous effort, flow and acidity
data for the mine have been collected and reported. It is the purpose
of this case study to apply the SWM-AMD and test its simulated values
against the existing data. Figure A.8 shows the location of the study
area in Ohio and the Big Four Hollow watershed area.
The Climate -
Precipitation in this area follows the general pattern of Ohio River
Valley. Long duration, low intensity rainfall covering large areas
occurs in the winter, whereas short duration, high intensity storms
covering a small area dominate in the summer. Since the SWM requires
precipitation data of hourly intervals and these data are not avail-
able for the exact location of McDaniels Mine, data from McArthur is
used. Figure A.9 shows double mass plotting analysis used to test this
data against three surrounding station's data. The McArthur record was
judged to be representative of the precipitation at the mine site.
Evaporation data for the study of this watershed were computed by using
the meteorological data from nearby stations and processing it via the
Penman method.23 This method had been proven to work well in other
Ohio areas therefore it was deemed adequate for this application.
The Geology -
The area consists of shales, clays, coal, sandstones and limestones.
The mine is in the Middle Kittanning ($6) coal bed. The sandstone over
the coal bed is about UO feet thick. On the top of this is a thin
layer of the Lower Freeport zone. The remaining upper part of the
geologic section is of sandstone or silt composition with minor occur-
rences of shale, and thin coal seams.
Physical and Hydrologic Characteristics of the Watershed -
These characteristics are listed in Table A.3.
76
-------
--t/ ;(; A - \?^
Figure A.8. The test watershed site
77
-------
i 5
c
o
O 4
o
O)
CL
c
o
o
WATER YEAR 1971 - 1972
A = Athens
J = Jackson
L = Laureiville
M = McArthur
I
12345
3 Station Average Precipitation, inches/month
Figure A.9. Double mass plot of precipitation data
78
-------
Table A.3. BASIN AND MINE CHARACTERISTICS
The
Basin
Characteristics
Drainage area, sq. miles
Length of principal water course,
Average slope percent
Peak discharge of record, cfs
Land use
feet
1.01
1120.
0.0122
27 (2/22/70)
heavy forest cover
The
Mine
Area, sq. ft.
Average height, ft.
Peak minewater flow recorded, gallons per day
Peak acid load recorded, Ibs per day
Principal materials in coal seam
600.
3.
788 (5/27/68)
1. 9 (5/27/68)
Coal, shale
Mine Characteristics -
Also shown in Table A.3.
Program Input -
1. For Groundwater and Streamflow--Input parameters to calculate the
groundwater reaching the mine aquifer and the streamflow are listed
in Table A.I according to their actual program name. See reference
20 for a detailed description of the variable names, their dimen-
sions, and the methodology for obtaining their value.
2. For Minewater and Acid Load--Input parameters to calculate the
minewater flow and acid load are listed in Table A. 2 according to
their actual program name. See reference 9 for a detailed descrip-
tion of the variable names, their dimensions, and the methodology
for obtaining their values.
Program Output -
Simulation outputs are obtained both in tabular and graphical forms.
1. Daily infiltration water reaching the mine aquifer is listed in
Table A..k. A hydrograph of the streamflow at the watershed outlet
is shown in Figure A.10.
2. Daily minewater discharge and its acid load are listed in Tables
A. 5 and A.6 respectively. Their graphical output are shown in
Figures A.11 and A.12. Monthly and annual summaries of minewater
flow and acid load by component source generation are tabulated in
Table A.?.
79
-------
Table A.U. DAILY INFILTRATING WATER REACHING THE MINE AQUIFER
CAILY INFILTRATION WATER REACHING GRCUNDWATER, BIG FOUR HOLLOW
V.ATFR YEAR 1970-1971 UNIT IN INCHES
CD
O
GAY
1
2
3
4
5
6
7
8
q
10
11
l?-
13
14
15
16
17 ~
18
19
20
?1
22
23
?4
25
26
_ 2T...
28
29
30
31
ncT
0.0
0.007100
0.0
0.0
0.0
0.0
0.0 ' '
c.o
0.0
0.006300
0.002500
C. 000100
0.0
0.1 70800
0.007900
0.004600
0.001600
0.000300
0.000100
O.C36700
0.043200
O.OC1900
0.001100
0.000100
0.0
0.0
0.0
0.0
0.089600
0.077800
0.010800
NCV
0.00250C
O.C67600
O.OC8900
C.OC5900
0.004700
O.OC3600
O.C021CO
C. 000600
0.000100
O.C00100
0.0
0.0
0.0
0.051700
0.015000
0.004200
0.003300
0.002700
O.C02100
0.038300
0.004400
0.013400
0.004300
0.002500
0.002000
0.001700
0.001300
O.OulOOO
0.016700
0.003700
CEC
O.CC3100
0.002200
0.018500
0.002700
0.001700
O.OC1500
O.OC1200
O.OC0900
O.OOC70C
0.000300
0.038000
0.045700
0.004200
O.CC3100
0.001800
0.045200
0.01570C
O.OC4500
O.CC3600
0.00260C
0.048100
0.053900
0.057800
0.007500
C.0103CO
O.OC6800
O.C05300
0.004400
O.OC3800
C.CC3300
0.0
JAN
0.002500
0. 002COO
0.007COO
0.054400
0.004800
0.0025CO
0.0021CO
0.00190C
0.0015CO
0.001100
0.001000
0.000900
0.031300
0.042300
0.005300
0.003900
0.009500
0.004500
0.003800
0.013500
0.003100
0.009500
0.003800
0.006300
0.0033CO
0.018600
0.003000
0.002700
0.032000
0.0126CO
0.0
FEB
0.003400
O.OC3000
0.002700
O.OC2400
0.054300
O.OC6300
0.010900
0.051500
C. 010100
O.OC5000
0.004200
O.CC3400
O.C19400
O.OC3800
O.OC3300
0.002800
0.018700
O.OC3900
O.OC7900
0.010300
O.OC7000
0.065900
0.008000
0.003000
O.OC2100
O.OC1100
0.000500
0.0
MAR
0.0
0.0
0.0
0.0
0.0
0.031800
0. 009300
0.003500
0.031800
0.043600
0.004000
0.003000
0.001700
O.OOC6CO
0. 012600
0.000500
C.0001CC
0.0
0.016200
0.007100
0.000500
0.0
0.004900
0.000100
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
c.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
APR
MAY
JUN
JUL
AUG
SEPT
0.
0.
0.
0.
0.
0.
0.
0.
C.
0.
0
0
0
0
0
0
0
0
0
0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
009200
0
0
0
092100
157200
051500
006300
000700
0.
0.
0.
0.
0.
0.
0.
0,
0.
0.
0
0
0
0
0
0
0
0
0
0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
0
0
0
036600
000300
0
0
0
112100
0.
0.
0.
0.
0.
0.
0.
0,
0.
0.
0
0
027900
030800
007400
001000
0
0
0
0
0.
0.
0.
0.
0.
0.
0.
0.
C.
0.
0
0
056500
000300
0
0
0
0
0
0
0.
0.
0.
0.
0.
0.
C.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
004000
003000
001700
OOC6CO
012600
000500
0001CC
0
016200
007100
000500
0
004900
000100
0
0
0
0.0
0.
0.
0.
0
0
0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.0
0.
,0
0.
0.
0.
C .
0.
0.
0.
0.
0.
0.
0.
0.
0
066900
085500
OC2500
000100
014000
0
0
0
0
0
0
0.0
0.
,0
o.c
0.
0.
0,
0,
0,
0.
,0
,0
.0
.0
.0
.0
0.0
0.0
0.043000
0.078600
0.004600
0.001200
0.000100
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.088000
0.001900
0.007500
0.000100
0.0
0.053100
0.003900
0.000500
0.0
0.024900
0.000100
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.003500
0.0070OO
0.0
0.0
0.0
0.0
0.0
0.0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
0,
0.
0,
0,
0
0
0
0
0
0
0
0
0
0
0
,0
,0
.0
.102400
0.120400
0.002500
0
0
0
0
.000500
.0
.0
.0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
005900
005700
0
0
081100
000900
000500
000200
036100
002400
000300
0.0
0.
0.
,0
.0
0.056500
0
0
0
0
.000800
.000400
.0
.0
-------
GO
Simulated -
Observed -
Tabulated daily values
are also outputted for
the program run. (Not
shown in this paper)
Correlation coefficient for this plot = 0.85
OCT
NOV
FES
JUN
JUL
RUG
SEP
Figure A.10. Streamflow hydrograph at the Big Four Hollow watershed outlet
-------
oo
Table A. 5. SYNTHESIZED DAILY MINEWATER DISCHARGE
SYN MiNEWATER FLOW IN GALLONS FOR MINE * 1
WATER YEAR 1970- 1971
OCT ~ NOV CEC JAN FEB MAR APR MAY JUN JUL AUG SEPT
I
2
3
^
5
6
7
B
9
" 10
11
12
13
14
"15""
16
17
18
19
20
21
22
73
24
25 -
26
27
28
29
"Ta
31
220.
219.
216.
213.
210.
206.
203.
200.
197.
107.
195.
192.
190.
262.
261.
259.
256.
252.
249.
261.
276.
273.
269.
265.
261.
257.
253.
250.
285.
"" 315.
315.
310.
333.
331.
327.
322.
317.
312.
306.
300.
294.
288.
282.
277.
294.
294.
290.
286.
282.
277.
238.
284.
284.
281.
276.
272.
267.
262.
257.
260.
256.
252.
248.
251.
247.
243.
239.
735.
231.
226.
222.
234.
249.
246.
243.
239.
254.
255.
252.
249.
245.
261.
280.
299.
297.
295.
292.
289.
285.
281.
?77.
271.
267.
262.
26C.
279.
275.
271.
266.
262.
257.
253.
248.
244.
252.'
266.
2£3.
259.
258.
255.
252.
253.
249.
248.
247.
245.
241.
245.
241.
238.
247.
247.
242.
239.
236.
232.
229.
248.
246.
245.
263.
262.
259.
256.
252.
256.
252.
391.
386.
389.
385.
382.
381.
378.
402.
399.
395.
390.
384.
379.
373.
367.
362.
356.
351.
346.
355.
353.
350.
345.
359.
355.
351.
347.
342.
342.
337.
332.
327.
330.
328.
323.
318.
316.
311.
306.
302.
297,
293.
288.
284.
280.
276.
271.
267.
263.
25°.
256.
252.
248.
244.
241.
237.
233.
230.
226,
223.
220.
216.
213.
210.
207.
204.
201.
198.
195.
192.
189.
186.
183.
180.
178.
175.
177.
174.
171.
169.
207.
305.
390.
383.
365.
345.
461.
612.
594.
571.
576.
553.
531.
509.
487.
465.
444.
423.
403.
382.
362.
343.
323.
304.
286.
267.
260.
256.
253.
249.
245.
241.
238.
234.
231.
227.
224.
220.
236.
267.
265.
262.
258.
254.
250.
246.
243.
239.
235.
232.
228.
264.
260.
260.
256.
252.
248.
245.
241.
237.
250.
246.
243.
239.
235.
281.
300.
297.
293.
289.
295.
291.
287.
282.
278.
274.
270.
266.
262.
259.
258.
255.
251.
247.
243.
240.
236.
233.
229.
238.
248.
247.
244.
240.
237.
233.
230.
226.
223.
220.
216.
213.
210.
207.
204.
201.
198.
195.
192.
189.
186.
228.
278.
274.
271.
267.
263.
259.
255.
251.
272.
268.
264.
260.
256.
252.
248.
245.
241.
240.
239.
235.
232.
264.
260.
257.
253.
265.
262.
258.
254.
251.
247.
268.
264.
260.
257.
253.
-------
Table A.6. SYNTHESIZED DAILY ACID LOAD
SYN TOTAL ACID LOAD IN FCUNDS/DAY FOR MINE #
WATER YFAR 1C70- 1971
" paY
"T3CT"
NOV
DEC
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEPT
CD
1
?
3
4
5
6
7
8
9
to -
11
12
13
14
15
16
17
Ifl
10
"20
?l
22
23
24
25
26
27
28
29
30 ~
31
0.013
0,074
0.032
0.03B
0.044
0.048
0.051
0.053
0.055
0.056
0.058
0.059
0.059
0.065
" 0.070
0.073
0.076
0.078
0.079
0.082
0.086
0.089
0.091
0.092
~~~0.0<3T
0.092
0.092
0.092
0.097
0.105
0.113
0.117
0.125
0.131
0.134
C.136
C.138
0. 138
0.138
0.136
0.135
0.132
0.130
0'. 12 7
0.128
0.12B
C. 129
0. 128
0.127
0.125
0.126
0.126
0.126
0.126
0.125
0.124
0.122
0.120
0.1 18
0.117
0.115
0. 114
0.113
0.112
0. 112
0. Ill
C. 110
C. 109
0. 108
0.107
0.106
0, 106
C. 108
0. 109
0. 110
0.110
C. 112
0.113
0. 115
0.115
0. 116
0. 118
0. 124
0.133
C.140
0.145
C.150
0.151
0.153
0. 153
C.152
0. 150
0. 148
0.146
0. 143
0. 145
0. 146
0. 146
0. 146
0. 144
0.142
0.140
0. 138
0. 136
0. 136
0. 138
0. 139
0. 139
0. 139
0. 139
0. 133
0. 138
0.138
0. 138
0. 137
0.137
0.137
0.137
0. 137
0.136
0. 137
0. 138
0. 138
0. 138
0.138
C.137
0.136
0. 138
0.139
C.140
C.144
0. 148
0. 149
C. 150
C. 150
C. 151
0.151
0.208
0.252
0.288
0.316
0.338
0.355
0. 359
0.357
0.372
0.383
0.391
C.397
0.393
0.388
0.384
0.380
0.368
0.358
0.349
0.343
0.338
0.333
0.329
0.328
0.326
0.324
0.321
0.314
0.308
0.3C2
0.297
0.293
0.289
0.286
0.281
0.276
0.272
0.266
0.261
0.256
0.250
0.244
0.238
0.232
0.225
0.220
0.214
0.209
0.204
0. 198
0.194
0.189
0.186
0. 182
0.179
C.176
0. 174
C.171
0.169
0.167
C.164
0.162
0. 160
0.158
0.157
0.155
0.153
0.151
0.150
0.148
0.146
0.145
0.143
0.141
0.140
0. 138
0.137
0.136
0.135
0.134
0.139
0. 168
0.238
0.294
0.324
0.334
0.368
0.446
0.507
0.545
0.575
0.589
0.597
0.594
0.584
0.567
0.546
0.526
0.5C4
0.504
0.490
0.466
0.434
0.403
0.371
0.340
0.313
0.290
0.272
0.256
0.244
0.233
0.224
0.216
0.210
0.204
0.199
0.195
0.194
0.200
Q.205
0.208
0.208
0.208
0.207
0.206
0.205
0.203
0.202
0.200
0.198
0.205
0.208
0.210
0.211
0.211
0.211
0.210
0.209
0.208
0.2C9
0.209
0.209
0.209
0.208
0.222
0.239
0.252
0.262
0.267
0.274
0.280
0.281
0.281
0.278
0.275
0.271
0.266
0.261
0.255
0.250
0.246
0.242
0.238
0.234
0.231
0.228
0.225
0.222
0.221
0.222
0.223
0.224
0.223
0.223
0.222
0.220
0.219
0.217
0.215
0.213
0.211
0.209
0.206
0.204
0.202
0.200
0.197
0.195
0.193
0.191
0.197
o.2ir
0.232
0.242
0.249
0.252
0.252
0.252
0.251
0.258
0.264
0.266
0.265
0.263
0.260
0.258
0.255
0.253
0.250
0.249
0.246
0.244
0.252
0.255
0.256
0.257
0.263
0.266
0.265
0.265
0.263
0.262
0.269
0.274
0.274
0.272
0.271
-------
CO
-p-
_o
U-
D
o
Q
Simulated
Observed
DRILY MINEWflTER FLOW
SIMULflTED VS. OBSERVED
BIG FOUR HOLLOW
WflTER TERR 1970-1971
°. I 10 20 I 10 20 I 10 20 I 10 20 I 10 201 10 20 I 10 20 I 10 20 I 10 20 I 10 20 I 10 20 I 10 20
0 Oct. Nov. Dec. Jan. Feb. Mar. Apr. May. Jun. Jui. Aug. Sep.
Figure A.11. Daily minewater discharge from McDaniel's Mine
-------
00
o
Q
T>
O
O
o
Q
DRILY RCID LORD
SIMULRTED VS. OBSERVED
BIG FOUR HdLLGH
MRTER TERR 1970-1971
Simulated
Observed
O | 10 £0 | 10 20 I 10 20 [ 10 20 | 10 20j id 20 | 10 20 | 10 20 | 10 20 | !0 20 [ 10 20 j 10 20 |
Oct. Nov. Dec. Jan. Feb. Mar Apr. May. Jun. Jul. Aug. Sep.
Figure A.12. Daily acid load discharge from McDaniel's Mine
-------
Table A.?. SUTHESIZED MONTHLY AND ANNUAL MTNEWATER DISCHARGE AND ACID LOAD
ANNUAL SUMMARY FOR VcATER YFAR 1970-1971 MINE # I
rrcT~" " NOV cec ""'JAN" FEB MAR " APR MAY JUN " JUL AUG SF.P
"SYN. INFILTRATION HATER REACHING GROUNDWATER " ' . -- - - -
0.462 0.264 0.398 0.296 0.315 0.141 0.0 0.486 0.225 0.242 0.293 0.248
3.371 INCHES
SYN. MINE WATER FLOW
0.0115 0.0134 0.0123 0.0122 0.0137 0.0158 0.0103 0.0181 0.0114 0.0126 0.0109 0.0118 0.1542" ~CF$0
SYN. MINE HATER FLOW .
7480. 8708. 7987. 7895. 8888. 10256. 6697. 11757. 7383. 8136. 7093. 7631.
*»*********#****#***************#
****
99910. GALLONS
******»*>**
SYN. TOTAL ACID LCAD
2.2 3.8 3.8 4.3 6.8 9.4 5.1 12.1 6.5 7.5 6.7 7.8
76.1 LBS
*»**»>***"***£***************************#******»***********»***
"* SYN. ACID LOAD BY LEACHING *
SYN. ACID LOAD BY LEACHING
2.8 3.8 3.7 4.0 5.2 6.4 4.0 8.6 5.2 6.2 5.4
************************************************
6.4
61.8 LBS
* SYN. ACID LOAD RY GRAVITY DIFFUSION
1.0 l.C 1.3 1.5 1.3 1.5 1.8 1.5 2.0 2.2 2.4 2.5
v«**************************************
20.2 LBS
***************
SYN. ACIO LOAD BY INUNDATION
0.1 0.4 0.2 0.1 2.8 2.5 0.0 4.8 0.1 0.5 0.1 0.2
11.9 LBS
***************************************
-------
Discussion of Results
The general trends for the streamflow, minewater flow and acid load for
the single water year tested are reasonably well simulated. Because
streamflow and minewater flow are based on hydrologic cycle concepts
and acid load generation is based on the concept of oxidation and pro-
duct removal mechanisms, the first two outputs are discussed together
and the latter one separately.
Groundwater is the source of moisture supply to the minewater flow and
a contributing source to the streamflow. The amount of groundwater
available is determined by the hydrologic cycle modeling of S₯M.
Climatological data (extensive if snowmelt is involved) are needed to
use the model. Generally speaking, these data are important to decide
the accuracy of the simulation and they are usually scarce in isolated
mining sites. In order to utilize the model, it is suggested that the
availability of data should be checked. If it is not readily at hand,
efforts should be made to collect these data a priori, if reliable
predictions of mine drainage are to be obtained. In the present case
study, the climatological data were for the most part approximated.
For example, precipitation was estimated by utilizing three nearby
stations' data. Furthermore, pan evaporation data are important to
determine the evapotranspiration of the area, and again, these data
were synthesized in this case study.
Besides climatological data, model parameters such as EF, EMIN, CB,
EDF, are very sensitive to the values of groundwater. Numerous trials
and adjustments are performed to choose their best values as judged by
comparing simulation results to flow records. It is essential to note
that all these parameters are interrelated so that it is necessary to
adjust each one separately and check the effects on the groundwater
behavior. A general guideline is to produce sufficient SADD which is
required to simulate the minewater flow (as a function of aquifer
storage) while at the same time match the recorded streamflow as
closely as possible.
In the present case study only one year of data was used. This presents
a problem in achieving equilibrium in the soil moisture balance in the
watershed. The reports on the model state that at least three years of
modeling are recommended for the adjustment period. Hence our single
year of data falls short of this requirement.
The results of streamflow indicate a trend of undersynthesis in spring
and oversynthesis in summer and fall. The under/or oversynthesis can
be modified by adjusting the parameters such as EF, EMIN, CB, EDF to
improve the simulation of streamflow. However, on the other hand,
values of SADD will be too small or too large due to the adjustments.
No definite explanation will be attempted at this time for these be-
haviors since the data used is too limited. A possible explanation
8?
-------
to the undersynthesis is that snowfall during winter is unable to
infiltrate into the frozen soil so that the modeled groundwater soil
moisture in spring will not be representative of the actual watershed
conditions. Again, the model is capable of handling the snowmelt prob-
lem but the data was not available. Possible explanations to the over-
synthesis are: local rain storms occur in summer and fall seasons whic
are not represented correctly by the approximated precipitation data;
evapotranspiration values are not large enough for the two seasons; and
actual soil moisture may be considerably lower than the modeled volume
during these seasons due to dry summer conditions.
The simulation of minewater flow is mainly based on values of SAW and
TANK. These two values were optimized to give the best simulated re-
sults. However, in the spring the hydrologic model appears to be Bunder-
synthesizing the amount of water reaching the mine aquifer, that is,
groundwater allocation, and this in turn causes the minewater discharge
to be correspondingly undersynthesized. This adding of small or zero
increments of SADD in the spring causes a reduction in the aquifer
storage value, the effects of which propagate undersynthesis of mine
flow into the early summer months.
The trend for acid load closely follows that for the minewater discharge
because two of the removal mechanisms (leaching and inundation) are
functions of the minewater flow. On the other hand, the gravity dif-
fusion mechanism is relatively constant throughout the year. The major
contribution to the sustained acid load removal is the leaching. Inun-
dation accounts for the peak loads.
Generally speaking, the results obtained in this limited data study can
not be used to justifiably evaluate the model' s ability. Both of the
individual models have been shown to work well with the proper quantity
of data. At least two more years of data are needed to permit the model
to reach equilibrium status. Also better climatological data including
snow conditions should also improve the simulation.
In conclusion, taking all of the above discussion into consideration
it is strongly felt that the model will be capable of predicting the
minewater discharge quantity and quality.
88
-------
PROCEDURES TO ROT THE DEEP MIKE POLLUTANT
SOURCE MODEL COMPUTER PROGRAM
Since this model was created by linking two previously established and
published models, the program listing of both of these models will not
be duplicated herein. They are available in the references (20) for
the hydrology and (22) for the acid generation.
The following will be details on using the two models along with needed
modifications, etc., to form the deep mine pollutant source model.
Sample values of parameters used for the examples discussed in Chapter
V, as they were listed on the computed cards, will toe included in these
instructions.
Basic Requirements
1. The computer programs for: "The Ohio State University Version
of the Stanford Streamflow Simulation Model" (herein referred
to as the Stanford Watershed Model - SWM) ref. 20 and "Com-
puter Simulation of Acid Mine Drainage - AMD) ref. 22.
2. Digital Computer - this model was run on an IBM 370/165 at
the Instruction and Research Computer Center (IRCC) at the
Ohio State University (OSU).
3. Plotter facilities - either an IBM 1130 or IBM 1620 computer
is used to drive an IBM 1627 plotter at the IRCC at OSU.
/
Operating Steps
1. Part One - To generate SADD toy using SWM.
a. Determine the watershed parameters. See ref. 20 for
methods of evaluating the parameters and suggested values.
to. Transfer these values onto IBM cards. See ref. 20 for
details.
c. Run the SWM program. Class I Job at IRCC, OSU.
d. Along with the normal SWM output optioned, punched output
cards of SADD values are to toe obtained (31 cards/water
year). One may also obtain punched cards to plot the
watershed hydrographs if this option has been requested
in SWM.
2. Part Two - To calculate Minewater flow and Acid Load toy AMD.
a. Determine the parameters. These will be listed below,
their definitions given, and sample values shown. Methods
to determine these parameters are explained in ref. 22
and/or 8. The Sample values here are toased on McDaniels1
Mine, Big Four Hollow, Vinton County, Ohio.
89
-------
Card #1 IMINE - number of mines being considered in the
basin. This program is designed to handle up to 3 mines at a
time. FORMAT (13)
i
* alO 0 0 0 8
n . a, n 13 -i -s .6 n -3 .1 jj
Zl 3
oooo oia 0800
11 17 0 14 is];? 11 IB 19 73
' " 1 1 1 I
D 0 0 0 010 C 0 0 0
71 7773 21 ?'!.>; 2? .'3:3 ;c
1 1 1 1 111 1 1 1 1
4
ooaoolooooo
:i 32 33 U 3a|ln 37 31 33 40
11 1 1 ill 1 1 1 '
fil 1 " 8
n o olio o o o'o'O o n M' »U M dlii o o o o f a o o oiu o u a o
* ' TQ n ~-1 73 i* R-|'S '' 7B T3 '"
,,.:««««- -'111111
Card #2 N - the parameter to control the number of cards
to be read in to label the title of the printed output. For
example: if it takes only 1 card to label the title, N = 20;
if 2 cards, N = 1+0, etc. FORMAT (13)
113411719 IQJl! 12 13 14 IS IE 17 li '3 70
1 2
« n o o o o o o c olo o o o o
"sow ii|:s i? is is 73
"1111
3
0000fl!90n0li
21 222324 2:|7i 27 232330
1 1 1 nil i < 1 1
l
4
000 0 010 00 0 0
3> X 33 3* 3SJ3E 31 3$ 35 43
i n nil 1 1 11
5
1) 0000)00 000
11'"
6| 7
o o o o ni" " " n "I" i n n olo o o o o
8
0 0 0 0 010 0 0 0 0
^ n 73 74 75J7S 77 13 75 f.
'' 1 1 1 1
Cards #3 to 'j WWW - alphanumeric input to label the
title of the output. Here we have 3 cards, therefore N - 60
FORMAT
THIS IS' THE AMD HGUei UITH VALUCS Or INFILTRATION HATER CALCULftTEP FROM SUM.
[l J ___ »_«_ I » IQJ n "p ,_ll»;l l| 227324 .26 ' :~ i)il32 !>1*_X_ U_ _40J '434445 41 I4jsi)|;ii; S4 .SCSI : 1MJ t7 a Si~^ IB lc|il
~'"~
__ _ _
ELS MINE IS SUPtKifl^GSeO OH TO U/S94* LITTLE H{U.~Crh:'E£KfTD"~TE₯T THE SUM-
;« 55 S6 '58
536? 78 H 74 1373 77 n '1 W
J -A 4 It
1
r<1 n 0 0 010 0 0 0 0
' i i u
0 0 0 0 010 0 0 0
II i? o 14 '!>{:; 17 li °,3
in i i i
21
0
"
1
3 00 OOlO
T! I73J!t ?j|2S
M 1 1 111
3!
000 OiOODO Old
:; ;8;930J3! 320334?^'
1 1 * *
4
0000
5l
0 0 0 0 010 n n n nln
6|
n n n nln o 0 0 0|0 0 0 0
-.
olo a
«*»«
7i
00 OjO 0
Gl 63 7QJ/! 7?
1. ,
0 0 010 00
13 7i 5!j?o 77 73
i 1 HI 1 1
a
00
1 1
90
-------
Card #6 CONTOL
FORMAT (12)
- program controlling device set = 3
1
100000100 o o s
s|« i i 1 10
- « 1
31 72 23 24 25 26 2! 2S :s 33
2
a oooaio o o o o
11 12 !3 14 ISJI5 !7 19 19 7':
1 II 1 1)111 11
1
a o o o BIO o o a a
: 22 23 24 2'-!2B 27 :3 23 3D
1 11 1 lilt 1 1 1
1
3! 32 33 34 35 36 37 38 39 4C
4
0 00 0 010 0 0 0 0
31 32 33 34 «|;s 37 31 39 K
1 1 1 111! 1 1! 1
I
4! 43 43 *4 45 46 4? 48 43 50J5! « SJ i* « i5 57 b8 5i £0
£1 G2 S3 64 65 56 S7 63 69 70
5| 6| 7
0 0 0 0 0!0 0 0 8 OiO 0 0 0 0)0 0 0 0 0
11 42 43 44 .i:-|40 47 IS 49 50 51 52 S3 54 55|M 57 M S9 60
i 1 1 1 in 1 1 '
0 0 0 0 DID 0 0 0 0
SI t2 £3 M 6SJE6 67 68 69 70
1
71 72 73 74 75 76 77 78 ;> f>0
8
3 0 0 S Old 0 0 0 0
T. 7: 13 u Jij:; n '8 '3 Ea
1 1 n in 1 1 1 1
Card #7 {between As and Ae, i.e., cards #7 to #6l is a
DO LOOP from 1 to I mine times}
WSHED - watershed area of mine in square miles.
TANK - aquifer storage in inches.
CONFH - constant relating minewater and HEAD.
CONM - program constant see reference 22
CONB - program constant see reference 22
FORiMAT (F20.10, lfFlO.3)
-'- t»;
i
[OOOOUlUDO 0
» 3 5J5 T 1 S 10
"« « t 11
00163
y
0 0 OlC 0 0 0 i!
11 tJ n 14 ISJiS 17 IB !9 "C
11 nit i n i
1
0,50
3
a o o o oi> o o o
21 22 23 24 25J2S 27 28 23 30
1 1 11 111 1 ' 1 1
1
>>"> 2 212 2 2 2 2
0,0136 3,5
4| 5
0 0 0 0 01 0 0 OiO 0 0 0 Old 0 0 0 0
:t 32 33 24 35J3S 37 33 39 40J41 «2 43 41 4f{45 4) 48 49 iC
11 1 1111 1 1 11 1 II 111 1 1 1 1
222,,,, .-
-13.0
6
0 0 0 0 DID 0 U 0
51 11 53 54 55|56 S7 58 59 £0
7
o o o i) oio o o o o
S! 63 S3 E4 6s[bS 67 62 E3 70
1 ' ' 1 111 1 1 1 1
8
ODD OOlOD 0 0 0
71 72 73 74 75JJ6 T7 '6 79 IS
1 1 1 1 111 1 1 ' 1
1
--1J22
Card #8 NFEET
NLAYER
NDEETH
FORiMAT (315)
number of air-solid interface increments
number of layers in the coal seam model
number of depth increments in the model
I 10
1
£5
2
" » o oio o o 11 p o a 0 CM o 0 o 0
* < iojn 12 c H IS|;E 17 is 13 2C
" ' 'U 1 1 1 1
I - -m,-^-n,;;;H
3
o o a o oio o o o o
.-in 21 14 !.(:!:>»» »
i n i Hi M n
1
. . , ,,
4| 5\ G| 7
00000100800
)! 37 33 34 3s[36 37 39 39 40
n 1 1 Hi H 11
t 1 2 2 212 2 1 ' "
0 0 0 0 OlC 0 0 0 0 a 0 3 0 CIO 0 0 0 00 0 0 fl OiO 0 0 0 0
11 1 1 ill 1 1! ill I ' 'M 1 11 1
8
0000 OIO 0000
71 72 73 34 7"3|?S n 73 79 jjj
11 1 1 1ll 1 1 1 1
1
** 1
91
-------
Card #9 DK - length of depth increments in feet.
ALKALI - conversion factor of acidity to alkalinity
of CaC03
FLOWMI - minimum minewater flow rate to cause
acid removal by leaching
PER - variable to determine the distance that
is inundated.
WSLOPE - hypothetical slope of water level.
COED - program constant, see ref. 22
FORMAT (2F6.2, F15-3, 3F10.3, F10.5)
I.00 £0,0 260,00 0,0001 1,1 0.05 0.80
itJt j ijll I? 13 14 Ij 16 1M3 -3 KJ.'I 2223 ' :S H 7! It:° ^o[]l 32 ; 34 35 36 3? 38 33 43|il 42 *j 45 46 47 43 4d ScJ^I 52 53 55 56 57 58 SS60J51 ' S3 64 65 65 E? 68 63 7QJ71 7? 73 74 75 76 71 76 79 EQ j
. , 1
10000 1 00 U
< 1
2
0 0 0 OiC 0 00 0
1 1 1t 111 1 1 1 1
1
3
0 0 '0 1 0000
11 I Mil 11 11
1
4
00 10000
1 11 1 ill 111
i
5l 6l 7
0 0 3 0 010 0 0 0 OlDO 1] 10 0 0 0 01 00 OlO 0 0 0 0
1 1 1 . "
8
a o o o clo a o o o
1 ' 1 1 111 1 1 t 1
Card #10 DI - length of air-solid interface increments
in feet.
TOP - datum plane for top of coal seam in feet
FORMAT (2F15.5)
100.0
13,50
1 1 J 3 4 t 6 ? 1 9 1
1
*" I) 0 0 OlO 0 0
* 1 1
U 1? 13 M i5 IS 11 13 .9 20
z
0 0 0 OiO 0 0 0 0
1 1 1 1 111 1 1 11
;t n 23 H i :s 11 is rs 'o
3
5 0 0 0 ClO 800
11 1 ill 1 1 1 1
1
31 32 n 34 35 36 3? 3B 33 40
4
2 a o o olo o o o o
1 1 11 lh 1 1 1 1
i
4! 42 4344 45 46 4) 484950
5
0 00 0 010 0 000
1 1 11 111 1 1 1 1
51 52 53 54 55 5S 57 S3 59 50
6
0 0 0 0 OlO 0 0 0 0
1 1 1 1 111 ' '
61 G: S3 b4 65 66 S? 68 63 70J71 n 73 74 75 76 77 73 79 BO
7\ 8
000 0010 0 0 0 OlO 000 OlO 0 300
!- "ll 11 1 1ll 1 1 1 1
Card #11 to Card #20 {Bs to Be, DO LOOP from 1 to NLAYER
times]
ROCK TYPE - literal strata descriptors
ALT - elevation of stratum relative to datum plane
in feet
REACT - oxygen consumption rate of pyrite
92
-------
PYCON - void fraction of the stratum
FORMAT (2AU, 2X, 3F10.3)
Here NIAYER = 10, therefore 10 cards
COAL
10,0
0,005
| 1 4 5 S ) I 3 10
COAL
f I TTs 7 e 9 to
SHALE
COAL
| , , s i , , , ,]
COAL
COAL
COAL
SHALE
COAL
SHALE
1 12 13 14 15 IS 13 19 >()
. ^
.
10,4 CUM 0,005
1 12 13 U 13 IS :s :9 20
?! r? 23 24 ? : :E ;* ;a in
3! 32 33 34 35 36 38 19 40J4i 42 43 44 4C 4G 4? 48 49 53
lu.y c,5 0,30
10,9
0,55
11.4 0.55
U, OU5
0 , 0 05
11,9 0,55 0,005
1£,4
15,9
1£,95
0,55 0,005
"d.*>
0.55
13,40 £,5
0,30
U, 11 UD
0,30
|3 12 33 34 li 15
'<""»->""«=»
5! 5? 53 54 55 56 5; SB 53 6G
SJ 02 63 64 65 56 5? 63 S9 JOl?! f2 13 7< 75 JS !7 'S 19 SO
Ul »H1 «J « » «Hi « t>
5i 525)5)55,8 SIM 59 so
SI5!HS4SS.,n=l JCT
*
!_ 0 0 G CIO 0 0 0 0 3 0 0 0 OiO 0 0 0
" i ill i M 11 n r it 11 1 1
"'> 7 2 2 212 2 2 2 2
" « It K
3
fi e o o uia o o n c
1 11 1 ill n n
I
2 2 2 2 21 ' 2 2 2 2
21 22 11 24 KJ2S 27 28 23 3C
- - 1H MIS
4
GOOflOl' 00 0
1 1 1 nil 1 1 n
2 2 2 2 212 2 2 2 2
31 32 3J 34 3'.J36 37 a 33 4£
3 3 3 3 313
5l 6| 7
0 0 0 0 OiO 0 0 0 CJ3 0 0 0 OiQ 0 0 0 n!3 0 0 0 0!0 9 0 0 0
1 1 1 1 till 11 111 11 1 IJ1 1 1 1 1)1 1 1 1 1ll 1 1 1 1
22222122'"'
4141 43 >*
8
000 0 OIO 000 0
1 ] 11 111 1 1 11
1
» 2 2 2 2
-"«*1
Card #21 TEMP
PIGMOL
DIF
CCPRPT
P
DIFF
GASC
DTHETA
SOX
FEACT
- mine temperature correction factor.
- volume occupied by gm moles gas
- base gravity diffusion constant
- constant to calculate pyrite reaction
rate constant
- mine pressure
- gas diffusivity in square feet per day
- gas concentration under mine conditions
- time increments length in days
- initial total acid storage in pounds
- fraction of stored product removal by
inundation
(3FG.3, F10.3, F6.0, F6.3,
93
-------
0.15 0,79 0.001 £9c'c:7.3<:, 454, 9,9650.OS'%1. 0 Q.Q 0.009
0 0 0 OlO 0 C C
III 1 1 1 1
2
000 Of 000
! 1 1 1 ill 1 11
1
00 OOCiOOO 0 D
11 1 1 111 1 I 11
1
i f>mTm
0 0 0 OCiOOOO 0
1 1 1 1 ih 1 1 1 1
i
1 ) 1 1 11-
5l 6I , '
0 0 010 0 0 Old 0 0 10 0 0 0 0 0 BIO U U U U
1 1 1 1 111
8
0 0 0 0 OlO 0 0 0 0
il U 73 X n|?5 "1 'i '3 £3
1 1 1 1 111 1 1 1 1
Card #22 to Card #6l {Cs to Ce, DO LOOP from 1 to NEEET,
1 to NIAYER, 1 to NDEPTH]
STORE - oxidation produce storage array. Here,
NFEET = 1, NIAYER = 10, NDEPTH = 2.5, with
8 values of depth increment per card, and
h cards for 25 depth increments. Therefore
total cards number 1 x 10 x k = ho cards.
FORMAT (8F10.2)
-------
1.34
1.35
1,15'
0.9
0.94
0,75
13 r0 i; t '" 'CJJI ?! 23 Jl
0 , 44
0,31
7-7 « (.1 £5 65 S7 SO TOb 72 73 7* 73 'S '
o.is
,16
roii
0.13
0.11
0,1 0
0, 03
0, 03
i ,66
1,24
0,33
0.71
0,54
0. 19
o. i;
0,15
0,11
0, 10
u, uy
u, u t
0,04
S.15
3,SO
3,31
2,64
h'.yy
1 . 69
1,14
1. 03
0.34
0. 67
0,64
U, D51
2, UU
1."
1,21
1.06
0.33
0,73
0 , 56
0,41
0, c'
0,25
0,t!c
0.19
0,16
0,14
0,12
7.7S
7,46
7.16
0,11
0. 03
£ . 25
0.36
0.29
0.10
2,13
0.35
0,29
0,11
1,34
0,72
0.26
0,10
4,71
2.03
0.63
0.45
1.64
0.70
0,30
0,14
1,
0,
0,
i.
0,
0
1,
0,
0,
4.
1,
0,
1.
0,
0,
yy
76
25
94
76
26
64
64
23
22
35
60
47
63
26
1,
0,
0,
1,
0,
o
1,
0.
0.
3,
1.
U.
1.
0,
0.
f' i'
bf
~c.'d
72
£7
23
46
57
20
30
70
""iT7
32
I'f'
24
1,57
u . sy
0.20
1 , 53
0,60
0,20
1,30
0,51
0,13
3,44
1 . 55
0.55
1.19
0,51
0,22
1,40
u , DC:
0,17
1 , 36
0 , 53
0.13
1,16
0.45
0,16
3.12
1.41
0,53
1 . 07
0.46
0.20
1.
u.
0,
1.
0,
0
1,
0,
0,
2,
1,
0.
u.
0,
0,
25
45
15
21
47
16
03
40
14
33
23
51
y*
42
13
1.
0,
ij .
1,
0,
0
0.
0,
0,
2.
1,
0,
0.
0,
0.
10
yy
13
07
40
14
91
:i-j
13
50
14
49
36
33
17
u , y ,'
0,33l
o.i ri
0,931
0, :-:o?
0.1:5)
1
0 , 3 i1
0 , 3 ij)
o.ir
*
2,23
0.33
0,47
1
0.77
0,3*1
0.15
*
6, 04
5,53
4,50
4.27
4.10
3,97
3,61
3.39
1
lOODOGliJ 0000
< 4 S|« 1 1 111
'Ml
2
0 0 0 0 ClO 0 0 0 0
ii tj a » rjj-t i? ig u TJ
1111111)111
1
3
so o o old a o o o
11 11 13 3* K\n ?U3 IS 30
11 1 till 1 1 11
1
*«-»»?l22222
4
0 00 0 0100 0 DC
Jl 3! 33 » X\X 31 a 1) II
11 1 1 ill 1 1 1 1
2 j 2 2 ?l" " *
5
Q 0 0 0 OiO 0 0 0 0
il« «3«4^«MJ 4JUHC
11 1 mi 1 1 1 1
6
a o a 0 010 o o o o
SI 52 53 It 5i(lS 57 53 59 60
1 11 1 111 1 11 1
7
300 ODlO 0000
»l 61 63 M 6^S "7 IS E9 7S
1 I 1 1 111 M 1 1
1
B
o o o o 010 o o o a
n n 73 Jt ^|:s "
-------
Card #62 IY
YEAR 1
YEAR 2
FORMAT (12, 2lk)
- number of water years being studied.
- beginning year of the water years
- ending year of the water years
119701971
6B 69 )0|/l 7? ?3 ?4 75 IS 7M8 ?9fiOj
1
00000! 0000
'Ml 11
21 31 4
3 o o o oli) o o a c
1 1 1 1 Hi 11 1 ]
1 __
D o o o alo o o o o
11 1 Mil I l 1 1
1
' " 1 212 2 2 2 2
0 0 00 010 0 0 0 C
1 11 nh 1 1 1 1
2 2 2 2 2J2 2 2 2 2
5
30 o colon oo o
1 11 Hill 1 11
2 2 2 2 21? ' "'
6j ^
0 0 0 0 010 0 0 0 B
1 1 1 I 111 1 I V
0 0 0 0 010 0 0 0 0
8
0 0 0 0 010 0 0 0 0
1 1 M III 1 1 1 1
Card #63 IYR
Am
FORMAT (Ik, 12A3)
the last two digits of YEAR 2
alphanumeric input to label the months of
the water year for the plotter.
[17345 7 I 3 1C
1
'no oo do oo
> i
14 IS 20
Z
0000 OiOOO 0 0
Ml 11 1 1 1 1
r
22 . 24 25 ?6 :c :; 'o
3
0 0 0 0 OlOO 0
1 1 111 1 1
1
" - * " "I** n i 1 o
31 33 J3 3* .36 33
-------
Card #65 DPY
FORMAT (13)
- number of days in the water year
365
1
"> 0 0 0 CIO 0 0 0 0
'« l 1 I 10
II 12 13 14 15 If 17 II 19 20
2122232425212)282930
2| 3
oo oo oia o o o o
11 12 B W I5JI6 17 13 19 T.
' « t 1 111 1 1 1 1
a o o oolo o oo o
21 22 23 24 2:|2G 27 23 23 3G
1 1 1 1 111 1 1 1 1
1
31 32 33 34 3a 36 37 3i 39 40 4; 42 43 44 45 46 47 48 49 50[5I 52 S3 54 55 55 57 58 59 60
4
00 DO 0100 00 0
3! 32 33 31 3i|:6 37 33 3? 4C
1 1 1 1 111 1 1 1 1
5l 6
31 52 S3 54656557(8 65 70
7
0 0 0 0 OIO 0 0 0 OjQ 0 0 0 OiO 0 0 0 0|0 0 0 0 OlO 0 0 0 0
41 42 43<4 45J1C47 4849SOJ5I 5'"" ' ' "1978
) 1 1 1 111 -
71 72 73 74 757" 77 ^ '3 ..7
6
00 0 OOlOOOOO
71 72 73 74 75J7S 77 "s 79 ec
III | 1 | 1
Card #66 N same as card #2
/ 20
i
00 OOIOOOOO
1 ) 4 SJS 1 1 1 10
11)1
2
00 00 OIO 00 00
11 1? 13 K KJI5 17 tS 19 ?C
1 1 1 1 111 11 11
1 ..,
21 21 23 2< 25 26 27 2S :9 30
3
00300100000
21 22 23 24 2s(:6 27 2S 29 3?
1 1 1 nil n 1 1
" 2 2 212 2 2 2 2
31 32 33 3< 35 36 37 33 33 '. (2 13 « 4f j« 47 « <9 sol11' " «' ", "^^ ** * " "'" « <3 64 65J66 Bi 53 63 7C
1111'" ' 1
n n 73 74 ?5 75 !7 78 73 S3
8
900 0 OlOOOO 0
n n 73 74 nJ7S n /a 79 eo
1 1 1 1 111! J 1 1
i
Card #6? ZZZ
FORMAT (20AU)
- alphanumeric input to label output heading
' DAILY INFILTRATION WATER REACHING GROUHPUATCR* BIG FOUR HOLLDM
1 Si)!
1
GOO 001 0000
1 ! ] 1 S|f I 1 I 10
T. 1111111 1
12 13 H . 16 IS 19 70^:. ' n 23 2o V - \ 33 35 JJ H J9 40
2| 3l «
30 001 0 0 00
n f? n M fifis n is 19 ic
Mil 11 1 1 1 1
" " 212 2 2 2 2
0 li CiO 0 0 0 0
21 !2 23 24 i j|:t 27 a 29 33
i i nil 1 1 i
1
22222122222
0 0 0 0 OiO 0 0 0
71 32 33 34 35J?.S 37 33 39 40
1 1 1 1 ill 1 1 1 1
22222122222
31 32 33 34 "*" '
Si 6
11 0 OIO 0 0 00 0 00 10 0 0 0 t
4! 42 43 41 1^46 47 48 49 *0pl 52 53 54 5:Ji6 57 58 59 fiC
11 1 111 1 1 1 "' ' " '
SO 0 CiO 00 0 0
M 62 13 64 6:Jii «7 68 S3 70
1 ' 1 1 111 1 1 1 1
6
a o o o cio o o o o
;i 72 73 74 i;|;6 71 18 73 ec
1 1 1 1 1111 1 I 1
1
-"17222
Card #68 to Card #98 SADD
FORMAT (12F6.4)
- infiltration reaching ground-
water from upper and lower
zones. These data are output
from the SWM
9?
-------
0,
ll
0,
u.
0.
0.
U.
0,
0.
u.
u.
0.
0,
0.
0.
0.
0,
u.
*0.
0,
0.
0.
0.
0,
0.
0.
0.
0.
0.
0.
0,
u.
L
0
3 4 i
U I.I /
i
1
0.
i
n.
0025
a '^_
il-, f
1 1 1 1 1 1 1 1 ' i , 1 1 ' i -;
u
u
u
u
u
0
UUb
UUc
0 0 0 1
n
U.
II
0
II
u.
I.I,
u.
0,
U I.I U O M .
170
007
I
M
0 f 1 5
IJIJ4
U 'J :
0 u-'
IIUI!
"!
f,
-i
Ij
f
t-
!
t-t
0 0 0 1
00 Ul
i.i U C
0
:3
II
M
II
''
U
II
II
U
u
U L
0 0 0 0 0
0 0 0
05 1
-?
u
II
90.0150L
00460.
001
UUU
0 0 1
036
045
001
u U 1
«
j
p*
u.
u.
0,
0,
004
uu-
Ul.lrJ
UUc
MXS
-1
"-
f'
I
I.I
I.I
, 00
* i;
. mi
u i
iiu
.U'.i
51
;i '.
-_ -.
- *"l
if
.0015
0,
>i
i
U,
i
U,
u
U i n -u.
, U U
ir-i
, U U U f
, i.iy
. (.I-:
, 04
'-':
:>L
^* -?
, U 0 4 i'
f 1 0
, Ul.
, 04
. iJi
:; 1.
15
~J -^
-f f
n
U.
0,
u.
0,
u.
u.
u.
I.I,
u.
0, !J l.l 4 -H.I,
1.
II
c'tJ, Ou44l
'-in.
i
0001
n
II
0 0 0 u u ,
00000,
0
0
039
(\7f
UlM
345
c
0,
u.
0,
3 0 ,
?
'
7 1
I'll :
IIII4
Illfr
UUc!
uul
f s n 1
0 0 1
0 1 b
005
9 mpi
4
-r
:
\
1
u u
~?
1
U
0
00
7
f
U
f
1.
i; n
, ML
.00
,U4
f|W
ir
Xf
56
xl
-!'-*
7-r
IIM7-
, 0 1
u::;
I.I,
n
u.
II
II
II
u.
, UIJbb'1.1,
III
^ "
0
, 00440,
, 0 033
,OC
35
. OuO,
)j 15
u.
0,
UL
00250,00340,0 0,0 O.G 0.0 0,0 0.0 0.0
::.!.>?: Ti-s:>-c|- jjj*jo;s3: 334o|^4?4) 4*4S4M;« :!5>iasiss '!ii"i'w.i i >j H " uti ' -^ :*[,-i ; n it n >i > > n
Illl- illl, Ilil. -;il(j , II 11,11 0 IIU'-|-'il,0 11,11 II, 'I 11,11
,in7iiii, un-7'i, H ii 0 0 OOiiiiO, 0 ii. 0 n, ii;-'74'i, ii-i-.-i
11-144:1,1111x411,11 ii 0 0 0 0,11 0,0 0. iixnxO. mm -'
IIII4XH, ii54:-;n, 0 11,11 ii,(i O.ii i), Ci.-i^»-'ii, mif-40. mum I
mi-1- ii, mi-, -MI, 11x1 xii, u u, us-'! n, n u, m in:-! u, u ill mi, n
Oir-'l n, ill O'-Ki. iin9 '-:n, n 0.1^7'2U,0 ii.O u, U. 0, 'J "*
;m;9ii. u-t -,ii, mi -:",( i, u n, nr-iir-iii, (i 0,0 n.u 0,0
uul- n. ill Hi ii. O'ilxn, 0 U. IIHXXH, 0 U. 0 0,iJ O.U
U U 1 \ 0 , U U -' U U . U 4 x. b IJ , U IJ , 0 U U 7 U , U U . 11 rj i U , U U , U
U U i U 0 , U IJ4 ; l.l , H IJ 4 U U , U U , U IJ iJ U V , U U , U5 ; 1 U , U U , U
0 0 0 9 0 , 0 0 5 4 0 , 0 0 3 0 0 , 0 0 , 0 b b 9 0 , 0 0 , 0 0 3 9 0 , 0 0 , U 'J 5 9
u:-;i xii, ni '-14 (i, O'il 7n, n n, MI, 114x1111, iiiinr-ni, u n, im-i7
n 4 2 5 0 , 0 0 3 3 J , 0 0 0 b 0 , 0 0 . 0 0 2 5 0 , 0 7 3 b 0 , 0 0 0 0 0 . 0 0 . 0 0 0 1 3
i U j x i.i , u 0 x x u , u 1 r t, LI , U 0 , 0 0 010. 0 0 4 6 0 . 0 2 4 9 0 , 0 0 , 0
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Card #99 to Card #136 FWRECD
FORMA.T (10F8.5)
- recorded minewater dis-
charge in cfs.
98
-------
0,00033
0.0 Od'54
0, 000jr
0,00036
0,00033
I 1 3 4 S I J 9 9 (0 tl 17 13 K
: S3 6* &5666I 6869 10 :i 77 73 7.
0,00040
0,00044
0,00043
n, 00 '"i 4'-)
0,00044
0,00046
|t 1 3 1 5 6 1 8 9 !Qp7
0, U i.i Hoy
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-------
Card #137 to Card #175 ACKECD - recorded acid load from
mine in Ib/day
FORMA.T (10F8.5)
0, 19^
0, 101
0.103
0.10 3
0.125
0.158
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0.1'54
0.407
0,179
0, ISO
0,132
0. 1*2
i VT < s <.J^L1.^]!1 -_ JjJl^-^^'T^L"?3 7<" :VT~'f.^ 1al3'i3'" _3S316J7 ^i"-40!
0,260
0.314
0,132
0.3U7
0,273
0,325
0,£b6
0.297
0.2b3
0,139
0.1S7
0,173
53 64 65 5^ 61 68 E1 70
0,211
0. 145
0,139
0,385
0,^406
0.445
1 l 3 4 5 t ? i a
M 5? M 54 55 55 5) 58 » 6o]Ei a; S3 6< 65 E6 8863 iQJ:l :l ?3 i* r3 T5 7f ?
0.236
0.158
0,143 'I
0, 141
0, 112
! 1 4 5 E J I S
0, 105
0,410
0.122
0.107
0, 147
0.127
0.247
0. 107
0.0945
0.109
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100
-------
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b. Run program
c. Obtain printed output plus punched card output to
plot on IBM 1627 the minewater flow and acid load.
3. Part Three - To plot Hydrograph (from Part l) and Minewater
Flow and Acid Load (from Part 2). See instructions on use of
IBM 1627 plotter or whatever model is being used.
101
-------
REFERENCES FOR APPENDIX A
1. Proceedings Fourth Symposium on Coal Mine Drainage Research. Mellon
Institute, Pittsburgh. 1972.
2. Clark, C. S. Oxidation of Coal Mine Pyrite. J. Sanitary Eng. Div.
ASCE. 92:127, 1966. Proc. Paper 4802.
3. Larez, A. L. Kinetics of Pyrite Oxidation. M. S. Thesis, The Ohio
State University. 1970.
k. Morth, A. H. Reaction Mechanism of the Oxidation of Iron Pyrite.
M. S. Thesis, The Ohio State University. 1965.
5. Smith, E. E., K. Svanks, and K. S. Shumate. Sulfide to Sulfate
Reaction Studies. Proc. Second Symposium on Coal Mine Drainage
Research. Pittsburgh. 1968.
6. Lau, C. H., K. S. Shumate, and E. E. Smith. The Role of Bacteria
in Pyrite Oxidation Kinetics. Proc. Third Symposium on Coal Mine
Drainage Research. Pittsburgh. 1970.
7. Smith, E. E. and K. S. Shumate. Pilot Scale Study of Acid Mine
Drainage. Program #l4oiOEXA, Contract 14-12-97.
8. Morth, A. H. Acid Mine Drainage: A Mathematical Model. Ph.D.
Dissertation, The Ohio State University. 1971.
9. Morth, A. H., E. E. Smith, and K. S. Shumate. Pyritic Systems: A
Mathematical Model. Project 1^010 EAH, Office of Research and
Monitoring, U. S. Environmental Protection Agency. November 1972.
10. Crawford, N. H. and R. K. Linsley. Digital Simulation in Hydrol-
ogy, Stanford Model IV. Department of Civil Engineering, Stanford
University. Technical Report No. 39. 1966.
11. L. D. James. Use of the Digital Computer to Analyze Hydrologic
Problems. Proc. 5th Annual Sanitary and Water Resources Engineer-
ing Conference. Department of Civil Engineering, Vanderbilt
University. 1966.
12. Clarke, R. D. Application of Stanford Watershed Model Concept to
Predict Flood Peaks for Small Drainage Areas. Civil Engineering,
Stanford University. Research Report. 1966.
102
-------
13. Drooker, P. B. Application of the Stanford Watershed Model to a
Small lew England Watershed. M. S. Thesis. Department of Soil
and Water Science, The University of New Hampshire. 1968.
lU. Balk, E. L. Application of the Stanford Watershed Model to the
Coshocton Hydrologic Station Data. M. S. Thesis. Department of
Civil Engineering, The Ohio State University. 1968.
15. Briggs, D. L. Application of the Stanford Streamflow Simulation
Model to Small Agricultural Watersheds at Coshocton, Ohio. M. S0
Thesis. Department of Civil Engineering, The Ohio State University.
1968.
l6. Owen, S. M. Modification of the Stanford Streamflow Watershed
Model IV to Improve Groundwater Simulation for Stratified Geo-
logic Regions. M. S. Thesis. Department of Civil Engineering,
The Ohio State University. 1970.
17. Mease, W. L. A Snowmelt Subroutine for Streamflow Simulation in
Ohio. M. S. Thesis. Department of Civil Engineering, The Ohio
State University. 1970.
18. Valentine, L. E. Modifications of the Stanford Streamflow Simu-
lation Model IV for Analysis of Small Watersheds. M. S. Thesis.
Department of Civil Engineering, The Ohio State University. 1970.
19. Warns, J. C. User's Manual for the Ohio State University Version
of the Stanford Streamflow Simulation Model IV. M. S. Thesis.
Department of Civil Engineering, The Ohio State University. 1971.
20. Ricca, V. T. The Ohio State University Version of the Stanford
Streamflow Simulation Model. Part I: Technical Aspects; Part II:
Computer Program; Part III: User's Manual. Water Resources Center,
The Ohio State University. 1972.
21. Shumate, K. S, E. E. Smith, and R. A. Brant. A Model for Pyritic
Systems. (Prepared for ACS Division of the Fuel Chemistry
Symposium, 157th National Meeting 13, No. 2.) 1969.
22. Chow, K. Y. Computer Simulation of Acid Mine Drainage. M. S.
Thesis. Department of Chemical Engineering, The Ohio State
University. 1972.
23. Eohler, M. A., T. J. Nordenson, and W. E. Fox. Evaporation from
Pans and Lakes. U. S. Weather Bureau Research Paper 38. 1955.
103
-------
APPENDIX B
THE REFUSE PILE AND STRIP MOTE POLLUTANT SOURCE MODELS
TECHNICAL DETAILS AND COMPUTER PROGRAMS
This appendix contains details on the pollutant source model as to its
history, modifications, and linking mechanisms.
An in-depth discussion of their application, showing input parameter
values and selection methodology, data assembly, and typical graphical
and tabular outputs is included.
The section concludes with a computer program listings for the source
model.
The material presented herein was taken as much as possible from publi-
cations (papers presented and Master of Science Theses) written as part
of this project during the research period.
INTRODUCTION
Today, with the shortage of some natural fuels, the coal industry may
again start to grow rapidly. In the early period of America's history
it was the coal industry that realized tremendous growth due to the
abundance and the relative ease of obtaining the coal. Since the turn
of the century through World War I the bituminous coal industry produc-
tion increased from 111 million tons to 579 million tons and the number
of mines increased from 2,500 to 95300. Presently, bituminous coal
production remains at about UOO-600 million tons per year. Similarly,
the anthracite coal industry saw a steady climb in production to a peak
output of 100 million tons in 1917; in 1971 the output has declined to
about 9 million tons,7*
^References listed at the end of this appendix.
-------
The coal mining industry uses two types of mining operations to extract
the coaldrift or deep mining, and strip mining. Each type of mining
and coal preparation operation produces a waste pile or refuse pile of
varying size, physical and mineral nature, and degree of homogeniety.
Refuse piles are composed largely of shales, clays and low grade coals
and often exhibit a high pyrite content. Strip mine spoil banks may be
highly variable in regard to both pyrite content and location with "hot"
strata and mass inclusions common. Since pyrite material near the sur-
face is exposed to both moisture and oxygen the pyrite is chemically
oxidized to produce the acid mine wastes of sulfates, ferrous iron and
sulfuric acid. Significant acid production at or near the surface re-
tards or prevents vegetative growth, and when precipitation falls on
the pile, the acid materials and sediment are washed down into receiving
streams where fresh pyrite material is exposed. This can lead to a
continuous cycle of acid from the pile entering the nearby receiving
streams. If pyrite is distributed throughout the pile, the acid load
will stop only when the pile is completely washed away or when the
pyrite is protected from exposure to oxygen by a natural or artificial
barrier.
Today, State and Federal agencies have recognized this pollution problem
and have established laws to control future mining operations. The
State of Ohio has put into effect, as of April 10, 1971, the Strip Mine
Act.3 One requirement for obtaining a strip mine license, as stated in
the Act, requires the operator to provide a plan that gives:
"a description of the methods and practices the applicant in-
tends to employ in strip mining and to prevent pollution of
waters of the state, erosion, deposition of sediment, land-
slides, accumulation or discharge of acid water, and flood-
ing."
The Federal government in 1969 passed the Environment Policy Act which
will stop all degradation of the environment.18 This act attacks the
problem from both directions in that it calls for both future pollution
prevention and for existing pollution sources to be corrected.
Acid mine drainage easily qualifies as a major pollution problem. It
has been estimated that approximately 500 billion gallons per year of
acid mine water containing from 5-10 million tons of sulfuric acid
pollute 10,000 miles of streams and receiving waters.12 A United
States Department of Interior report indicates that surface mining
operations alone seriously affect U,800 miles of streams.17
The task of correcting this adverse situation can be approached in two
ways: (l) by treatment of the waste or, (2) by an abatement program at
the source. As in any type of pollution control, the optimum treatment/
abatement alternatives for regional problems can seldom be identified
through a simplistic analysis. In general, the economic, physical, and
105
-------
chemical interactions across an affected basin must be accounted for in
greater or lesser degree. One approach would be to model a watershed
of coal mining operations and then work out an optimized program con-
sidering both treatment and abatement.
In order for this type of program to work, the acid loading from the
various sources must be known so that an effective program can be set
up to abate or treat the acid. The deep mine pollutant source model
was presented in the previous appendix. Efforts will be concentrated
in this section to modeling the refuse pile and strip mine pollutant
sources. The basic phenomenon for acid generation can be considered
the same for both sources; differences in the hydrology and reaction
kinetics do occur but these can be handled simply by modifications in
the model. The reader will be informed of these differences and shown
how they are modeled at the appropriate location in the narrative.
There has been limited prior work in strip mine and refuse pile models.
Morth8 has presented techniques that can be used in principle to esti-
mate the oxidation or the acid load for either system. Sternberg and
Agnew16 have undertaken the development of a model of drainage in a
surface mined area, where they were concerned with 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.
In looking specifically at developing a working model for a strip mine
or refuse pile there are two major areas that must be explored; how the
acid is produced, and how the acid is removed.
Good's work4 with acid production from a refuse pile at the New
Kathleen Mine, near Duquoin, Illinois, comes to three general conclu-
sions: (l) the zone of reaction extends only several inches into a
pile, (2) pyrite oxidation proceeds at a relatively constant rate be-
tween rains with the acid produced accumulating in the outer mantle
and, (3) only about 70fo of acid salt appears in runoff, the remaining
is carried into the interior of the pile later reappearing in seepage
around the pile.
Brown1 studied the transport of oxygen through layers of soil and
material from the New Kathleen refuse pile. In attempting to model the
transport, difficulty was encountered in estimating the diffusivity
through the soil. Brown's use of zero order reaction kinetics in a
refuse pile is also of questionable validity from a kinetics stand-
point, although the effect on calculated pyrite oxidation rates as com-
pared to a first order would not be great.8
Morth,8 in developing his drift mine model, suggests that the same
first order oxygen gradient developed for coal and shale binders could
be used for a refuse pile. Morth1s model did reasonably predict drift
mine acid load. The main problem Morth had in utilizing his model for
106
-------
the other mining operation was in the hydrology of the acid mine drain-
age. The previous appendix showed linkage of the deep mine model with
a more complicated and advanced hydrologic model than employed by Morth
by using The Ohio State University version of the Stanford Streamflow
Simulation Model.
The Ohio State University version of the Stanford Streamflow Simulation
Model,10 or simply the Stanford Model, is a mathematical model which
synthesizes a continuous hydrograph of streamflow from climatological
data and watershed parameters. The Stanford Model is designed to
describe mathematically the hydrologic cycle, and Figure B.I shows the
hydrologic cycle on a refuse pile. The model keeps a chronological
account of the quantities of moisture allocated to the various compo-
nents of the cycle. The model is good for large watersheds, and can be
applied to small watersheds down to one square mile. Thus, by knowing
the various hydrological parameter needed to run the Stanford Model the
streamflow hydrograph can be reasonably determined.
Therefore, if a description of the refuse pile is known, which includes
the hydrological parameters and the acid production and removal param-
eters, a computer model can be developed that could provide reasonable
predictions of acid loads in the receiving streams.
DESCRIPTION OF REFUSE PILE ACID
MINE DRAINAGE MODEL
Description of a Refuse Pile
In order to write a general computer program for acid mine drainage
from a refuse pile, a general sketch of a refuse pile must be given.
The following outline can be used to describe most piles. A refuse
pile of a coal mining operation is exactly what is says; it is a "refuse
pile," or a pile made out of the material that is mined with the coal
and rejected as being worthless. A pile normally consists of shale,
clay and low grade coal and often exhibits a high pyrite content.
Refuse piles are located near the mining operation and are associated
with both deep and drift mines. The pile shape will vary with the ter-
rain, with steep-sided piles often found in mountainous country, re-
sulting from the dumping of material over existing steep slopes. In
flat terrain, as in Illinois, the piles may be broad, and almost flat-
topped, as shown in Figure B.I. On large piles there may even be ponds
of water or the refuse may be used as a dam for slurry ponds if open
space is available.
The typical pile (see Figure B.l) can be divided into three zones. The
outer mantle, or first zone of the pile, may constitute a stratum where
much of the fines (clays, powdered shales, and coal dust) have been
washed out by precipitation. Thus, this zone is where the pyrite
10?
-------
Upper Zone Storage =
Interception Pius
Depression Storage PRECIPITATION
4r <& * v v
T
Ml III
Interception
i r
TTTT
Transpiration
Surface
Detention
Overland Flow
o
oo
Evaporation
Depression
Storage
THIRD ZONE
( Main Body )
Percolation
i_^ V
Water Table
Baseflow
Groundwater
^
To Deep
Storage
Figure B.I. Hydrologic cycle on a refuse pile
-------
oxidation occurs rapidly and where the acid products form and inhibit
any vegetative cover from forming. The second zone is a layer composed
of the clayey fines tightly packed by rain action into the pile and,
thus, having a low permeability. The layer does have discontinuities
so that water may enter the main pile but it is, on the whole, an effec-
tive water and gas barrier, preventing significant pyrite oxidation
from occurring any further into the pile. The third zone is the main
body of the pile and shows little evidence of weathering or pyrite
oxidation .
Acid Production of a Refuse Pile
In looking at the description of a refuse pile it can be seen that the
acid is produced in the outer mantle, wherein the two ingredients re-
quired for pyrite oxidation, oxygen and water, are available.
The oxidation of pyritic material can be represented by the following
equations :
FeS2 + 7/2 02 + H20 = Fe+2 + 2S04"2 + 2H+
Ie+2 + 1/U 02 + H+ = Fe+3 + 1/2 H20
Fe+3 + 3H20 = Fe(OH)3
These equations are stochiometrically balanced, but do not define reac-
tion mechanisms, intermediate products which may cancel out in the
overall equation, or factors affecting the rate of reactions. The first
equation describes the initial reactants and final products of the oxi-
dation of pyrite by oxygen in the presence of water. The products of
this initial step are the major pollutants; sulfates, ferrous iron and
sulfur ic acid.
Refuse Pile Model
Once the acid products have been produced in the outer mantle, water
flow dictated by the hydrologic cycle is the vehicle which flushes the
acid products into the stream. Now attention will be given to the
hydrologic parameters needed in the actual modeling of the pile.
Hydrologic Parameters -
In looking at Figure B.I, a schematic of the hydrologic cycle, each one
of the thirteen parameters will be analyzed as it applies to a refuse
pile. Linsley et al.6 provides a brief description of each parameter.
When rain falls, the first part of the storm is stored on the vegetal
cover as interception and in surface puddles as depression storage. As
rain continues, the soil surface becomes covered with a film of water,
known as surface detention, and flow begins downslope toward an
109
-------
established surface channel. Enroute to a channel, the water is desig-
nated as overland flow. At the same time, water is moving through the
soil surface into the soil as infiltration which is distinguished from
percolation, the movement of water through the soil. As the water is
absorbed by the root systems of plants, where only minute portions of
water remains in the plant tissues, virtually all of the water is dis-
charged to the atmosphere as vapor through the process known as transpi-
ration. The water known as soil moisture is near the surface where the
pore space contains both air and water.Some of the water which infil-
trates the soil surface may move laterally through the upper soil layer
until it reaches a stream channel. This water, called interflow, moves
more slowly than the surface runoff and therefore, reaches the streams
somewhat later. Some precipitation may percolate downward until it
reaches the water table, a theoretical line where the pore space con-
tains only water, and move into the ground water flow. During the rain
and afterwards, there is a continuous exchange of water molecules to
from the atmosphere; thus, the hydrologic definitions of evaporation is
the net rate of vapor transported to the atmosphere.
The objective here is to state if the parameter is needed in the refuse
pile model. Transpiration is the only parameter that might be totally
excluded, if the pile does not have any vegetal cover due to the acid
products being produced in the outer mantle. All of the other param-
eters must have quantities of moisture allocated to them. It will be
up to the model to see that the general water balance, inflow equals
outflow plus storage, is satisfied at all times. Referring to the
schematic, Figure B.I, precipitation is the inflow. The outflow con-
sists of evaporation, transpiration, overland flow, interflow, ground-
water flow, infiltration and percolation with interception, soil
moisture, depression storage and surface detention as the storage. For
a refuse pile the main concern is with the outflows of overland flow,
interflow, and groundwater flow, since these will have the opportunity
to transport the acid mine products.
Acid Production Parameters -
In keeping with developing a general model that will be applicable to
many refuse piles, the pile volume within which oxidation occurs, the
rate at which the oxidation occurs, and the rate of acid removal in
runoff must all be described. As a first approximation, the zone of
oxidation can be represented as a finite thickness outer layer of the
pile, in which acid is produced at a constant rate, and from which acid
is assumed to be removed at an assumed effective "saturation" concen-
tration in the surface or subsurface runoff. For piles meeting these
criteria, only the depth of outer mantle, the volumetric acid production
rate, and the acid solubility are needed to describe the pile. This
relatively simple model will be used for initial developments, and more
complex assumptions will be discussed later.
110
-------
Linking Process
In order to link the two processes it is important to know the specific
amounts of four quantities: l) acid products available, 2) precipita-
tion falling, 3) acid products being removed, and k) acid products re-
maining. Looking at Figure B.I, a schematic of the refuse pile, it can
be seen as the precipitation falls on the pile, the water will saturate
the area and will leave it by three main routes, overland flow, inter-
flow, and groundwater. Initially, it will be assumed that in each case
the water will become saturated with acid before it leaves. A small
explanation concerning the three routes is in order. Overland flow is
the water that does not enter the pile but simply runs down the outside
of the pile. Once the water enters the pile it will percolate either
into interflow or groundwater flow. Interflow will move through the
pile laterally until it reaches the side surfaces of the pile, where it
will seep out and flow overland to the stream. Because of the path
interflow water must make it will take longer than overland flow to
reach the stream. In order for the water to reach the groundwater flow
the water must pass completely through the pile. Upon reaching the
groundwater pool, the water will become baseflow to a stream or it will
move to a deep storage zone if one exists in the basin.
The refuse pile model will utilize The Ohio State University version of
the Stanford Streamflow Simulation Model to generate the hydrologic
cycle, and to keep account of the quantities of moisture assigned to
each parameter in the hydrologic cycle. The main quantities of water
needed are the amount of water that is assigned to overland flow, inter-
flow and groundwater flow. The acid in the outer mantle will be found
by calculating the acid produced since the last rain and adding it to
the existing acid in the mantle. Then when precipitation falls on the
pile the amount of acid products that become soluble in water and leave
the pile via overland flow, interflow and groundwater flow must be
calculated. The precipitation waters will continuously be saturated
with acid until there are no acid products left in the outer mantle to
be removed. If the precipitation stops before all the acid products
are removed, this remaining amount is added to the amount of acid being
produced between precipitation inputs. Once precipitation falls again
the cycle is restarted.
CALIBRATION OF PARAMETER COEFFICIENTS
Based on the general description previously stated, a refuse pile model
can be constructed. Figure B.2 shows a step diagram of the refuse pile
model. A detailed discussion of the operation of the program will
occur in a following section. Attention will now focus on how the main
hydrologic and acid production parameters will be formulated as needed
in Step 1, 3, and 5 of the sequel below. The identification variable
as used in the computer programs will be written in parentheses where
111
-------
Step1 Establish acid production characteristics of the refuse pile.
1. Depth of outer mantle. (DEPTH)
2. Acid production rate. (ACDPRO)
3. Solubility of acid products. (SOLACD)
Compute initial amount of acid available to be removed.
Find precipitation falling on the pile and apportion the rain
into h parts:
1. Precipitation entering the upper zone. (ENTRUZ)
2. Precipitation entering the lower zone. (ENTRLZ)
3- Precipitation as interflow storage. (RGX)
k. Precipitation as direct runoff. (VFLST)
Find amount of acid products removed by the precipitation.
Determine the amount of water entering the receiving stream by:
1. Overland flow. (DIRRNF)
2. Interflow. (iNTF)
3. Basefiow. (BASFLW)
Step 6 Calculate the amount of acid reaching the stream.
Ascertain the amount of acid left in the pile after the rain
has stopped and no flow is reaching the receiving stream.
Return to Step 2.
Figure B.2. Step diagram of the Refuse Pile Model
applicable. A complete listing of the variables along with their units
and definitions are given in Tables B.I, B.2, and B.3-
In the first step, finding the acid production* characteristics of a
refuse pile, the following parameters need to be calculated; the depth
of the outer mantle (DEPTH), the acid production rate (ACDPRO) and the
solubility of the acid products (SOLACD). These parameters are variable
and will have to be determined for each specific pile under study.
The depth of the outer mantle, the layer where the acid products are
produced, can be found only by field observation. As stated earlier,
the outer mantle is separated from the main pile by a second zone. The
second zone, about one inch thick, is composed of clayey fines tightly
packed by rain action and thus has a low permeability. In digging a
hole in the pile the second zone should be easily observed and the depth
of the outer mantle can be found. Where the outer mantle is of variable
thickness or composition, the decrease in oxygen concentration with
depth may require description in the modeling process, a refinement
which will be discussed in a later section.
*Acid Production is defined as the net result of dynamic acid formation
and product removal
112
-------
Table B.I. INPUT VARIABLES OBTAINED FROM
THE STANFORD WATERSHED MODEL
Variable
Units
Definition
BASFLW
DAY
DDYR1
DD23
DIRRNF
ENTRLZ
ENTRUZ
FA
INTF
J
OVFLST
PR
RGX
TOTFLW
in.
in.
in.
in.
in.
in.
in.
in.
in.
Current rate at which baseflow is
entering channel
Day of month
Last two digits of first year in
water year
Number of 15-minute periods
varies from 1 to h
Current rate at which direct
runoff is entering channel
Current rainfall entering the
lower zone
Current rainfall entering the
upper zone
Current month of the water year
Current rate at which interflow
is entering the channel
Hour of the day
Current rainfall entering direct
runoff
Current rainfall rate
Water entering interflow storage
Total flow
113
-------
Table B.2. INPUT VARIABLES INTO THE REFUSE PILE
Variable
Units
Definition
ACDPRO
AREA
DAY 1
DEPTH
FACDEP
FACDIR
FACFB
FACFD
FACFI
FACINT
FACLZ
FACRDS
FACREB
FACRED
FACREI
FACUZ
MONTH 1
NDAY
OPTI
SOLACD
YEAR 1
Ib acidity/acre-day/
unit depth
sq_. ft.
feet
mg/liter
Acid production rate
Area of refuse pile
Day to start specific output
Depth of outer mantle
Factor for depth of outer mantle
Factor for amount of acid going
into direct runoff
Factor for amount of water coming
from baseflow
Factor for amount of water coming
from direct runoff
Factor for amount of water coming
from interflow
Factor for amount of acid going
into interflow storage
Factor for amount of acid going
into lower zone
Factor for amount of acid going
into deep storage
Factor for amount of acid going
into channel by baseflow
Factor for amount of acid going
into channel by direct runoff
Factor for amount of acid going
into channel by interflow
Factor for amount of acid going
into upper zone
Month to start specific output
Number of consecutive days of
output requested
Variable to call temperature
change option
Solubility of acid products
Year to start specific output
-------
Table B.3. INTERNAL VARIABLES OF THE REFUSE PILE MODEL
Variable
ACDDIR
ACDINT
ACDLZ
ACDUZ
ARE
ARD
AREBFL
AREDIR
AREDSR
ARE INF
ARI
AMTACD
CF
CFBAS
CFDIR
CFINT
CFS
CFTOT
CK
COUNT
DAYEND
DDAY
EXADIR
EXAINT
EXALZ
EXAUZ
I
J
SAB
SAD
SAI
SBAS
SDRR
SINT
SLYEAR
SSBAS
SSDRR
SSINT
STACD
Units
Ib
Ib
Ib
Ib
Ib
Ib
Ib
Ib
Ib
Ib
Ib
Ib
-
cfs
cfs
cfs
-
cfs
-
-
-
-
Ib
Ib
Ib
Ib
-
-
Ib
Ib
Ib
cfs
cfs
cfs
-
cfs
cfs
cfs
Ib
Definition
Amount of acid going to direct runoff
Amount of acid going to interflow storage
Amount of acid going to lower zone
Amount of acid going to upper zone
Daily acid in baseflow
Daily acid in direct runoff
Amount of acid being removed by baseflow
Amount of acid being removed by direct runoff
Amount of acid being removed by deep storage
Amount of acid being removed by interflow
Daily acid in interflow
Amount of acid being produced
Conversion factor to convert inches to cubic
feet
Flow entering channel by baseflow
Flow entering channel by direct runoff
Flow entering channel by interflow
Conversion factor to convert inches to cubic
feet per second
Total flow in channel
Temperature correction factor
Counter
Number of periods specific day output is
requested
Day
Excess acid in direct runoff storage
Excess acid in interflow storage
Excess acid in lower zone
Excess acid in upper zone
Day
Month
Monthly acid in baseflow
Monthly acid in direct runoff
Monthly acid in interflow
Daily baseflow
Daily direct runoff
Daily interflow
Variable to see if current water year is a
leap year
Monthly baseflow
Monthly direct runoff
Monthly interflow
Monthly total acid
115
-------
Table B.3. CONTINUED
Variable
Units
Definition
STSTR cfs Monthly total flow
SUMA.B Ib Yearly acid in baseflow
SUMAD Ib Yearly acid in direct runoff
SUMAI Ib Yearly acid in interflow
SUMSB cfs Yearly baseflow
SUMSD cfs Yearly direct runoff
SUMSI cfs Yearly interflow
SUM3T cfs Yearly total flow
SUMEA Ib Yearly total acid load
T °F Current temperature
TACD Ib Daily total acid
TIME hr Time interval constant (Same as used in Stanford
Watershed Model)
TO °F Temperature at which acid production rate was
determined
TOTAL Ib Total amount of acid in outer mantle
TSTR cfs Daily total flow
YEARPR - Counter by years
YEARST - Beginning water year
YEARLP - Variable used to find what water year is a
leap year
The acid production rate (ACDPRO) could be empirically calculated. If
the bulk porosity of the refuse pile and the pyritic content were known,
the oxygen gradient could be calculated using a first order exponential
expression.8 Another way, which was undertaken by Good,4 presents the
rate information on the basis of pounds of acid formed per day per acre
of refuse pile area. Good's field data was checked by Brown's1 labora-
tory rates and agreed quite well. Brown determined laboratory scale
oxidation rates which can be used to estimate a rate constant for the
exponential gradient calculation. At this time it is believed that the
first approach would be to use Good's method in finding the pounds of
acid formed per day per acre of refuse pile area. Good4 set up a
small test plot (0.109 acre) and installed a sprinkler system. Then
by applying a known quantity of water and collecting all of the runoff,
the acid production rate can be estimated. The second approach would
be to run a laboratory study. Brown's work1 details the approach used
to obtain laboratory scale oxidation rates for refuse pile materials.
The third approach would be to determine the bulk porosity (and associ-
ated oxygen diffusivity) of the refuse and the pyrite content to find
the oxygen gradient as developed by Morth,8 that would lead to an acid
production rate.
116
-------
The third parameter needed for the pile is the solubility of the acid
products. This is an "effective" solubility, which reflects the varying
availability of acid to the runoff components on and within the pile,
and will reach, as a maximum value, the true solubility of the acid
products. In general, the effective solubility will be less than true
solubility, and must be determined by trial and error, with field water
quality data as a rough guide.
Step 3 deals with the initial precipitation, that must be assigned to
four zones in the pile. In the program this data will be input data
generated from a hydrologic model. In this study, The Ohio State
University version of the Stanford Streamflow Simulation Model will be
employed. The Stanford Watershed Model will also provide the amounts
of water reaching the streams, which will be needed in Step 5.
The Stanford Watershed Model is a complex program that keeps a chrono-
logical account of the quantities of moisture allocated to the various
components of the hydrologic cycle. The model simulates the actual
hydrologic condition of the watershed and works best with watersheds
of 100 acres or greater.
In order to understand how the Stanford Watershed Model computes the
parameters needed in Steps 3 and 5, a brief description will be given
of each parameter. The variable notation as used in the Stanford
Watershed Model will be retained. For a detailed explanation of the
parameters refer to the Stanford Watershed Model.10
The current rainfall rate (PR) is the current amount of precipitation
entering the pile. The Stanford Model includes a snowmelt subroutine.
In order to utilize this snowmelt option, the basic operation of the
subroutine will have to be recalibrated, as the snow on refuse piles
normally melts sooner than on the surrounding terrain.9 If the snow-
melt subroutine is used in the Stanford Model, then the precipitation
falling may be in the form of snow. The snow may not enter the pile
immediately, but will enter later when the snow melts by additional
rainfall, radiation, conduction, convection or condensation. Thus in
the winter months, November to March, the precipitation is checked to
see if it is rain or snow and then by considering the various snowmelt
mechanisms the current rainfall rate entering the pile is found. This
rate is based on hourly data, but can be subdivided into fractions of
an hour by linear approximation.
The current rain entering the upper zone (ENTRUZ) is equal to the cur-
rent rainfall rate (PR) minus the residual rainfall after soil surface
moisture depletion (Pk). Pk, the residual rainfall after soil surface
moisture depletion is found by finding the residual rainfall after
interception multiplied by the fraction of incoming moisture that is
not retained in the upper zone storage. The above calculation is based
11?
-------
on several factors; current interception rate, maximum interception
rate for a dry watershed, soil surface moisture index, lake evaporation,
daily pan evaporation and monthly pan evaporation coefficient.
The current precipitation entering the lower zone (ENTRLZ) is equal to
the residual rainfall after soil surface moisture depletion (P^) minus
the sum of the current moisture entering surface runoff plus interflow
(SHRD). This latter sum equals the square of residual rainfall after
soil surface moisture depletion (pU) divided by twice the current peak
infiltration rate (D^F). The two quantities, D^F and PU, depend on
evaporation, infiltration index, soil moisture index, interception and
moisture not retained in the upper zone.
The current direct runoff (OVFLST or RX) equals the sum of current
moisture entering surface runoff plus interflow (SHRD) divided by a
variable controlling entry of moisture into interflow (C3). SHRD has
already been defined. The variable controlling entry of moisture into
interflow (C3) is dependent on the interflow index and the current ratio
of soil moisture storage to the soil moisture storage index.
The current water entering interflow storage (RGX) equals the sum of
current moisture entering surface runoff plus interflow (SHRD) minus
the current direct runoff (RX). These quantities have been previously
described.
A check to see that the current rainfall rate equals the sum of its
four parts can be made as follows:
Current rainfall rate (PR) = current rain entering the upper zone
(ENTRUZ) + current rain entering the lower
zone (ENTRLZ) + current direct runoff (RX)
+ current water entering interflow storage
(RGX)
or
PR = (MTRUZ = PR - pU) + (MTRLZ = p^ - SHRO) + (RX = RX) + (RGX =
SHRO - RX).
Therefore, PR = PR.
After the initial precipitation is calculated, the Stanford Watershed
Model can then route the water through the pile or watershed; it simu-
lates the total stream flow and its component parts, overland flow,
interflow, and baseflow.
The current rate at which overland flow enters the stream is based on
turbulent range equations.10 The Chezy-Manning equation was used to
118
-------
derive a relationship between surface detention storage at equilibrium,
the supply rate to overland flow, Manning's n and the length and slope
of the flow plane. An empirical relationship developed by Crawford and
Linsley between outflow depth and detention storage for reproducing
experimental hydrographs was used. By combining the above equations a
rate of discharge from overland flow can be found.
Thus the Stanford Watershed Model simulates overland flow by continu-
ously solving the continuity equations, by setting the surface detention
at the end of the time interval equal to the surface detention at the
end of the previous time interval plus the increment added to surface
detention during the time interval, minus losses.
The current rate at which interflow is entering the channel or stream
(UTTF) is modeled by a logarithmic decay equation, S-j. = -q.t/^Kr, where
S^ is the storage at time t, q^ is the flow at time t,
natural logarithm of the interflow recession constant.
and #7zKr is the
The baseflow (BASFLW) is equal to the ground water baseflow (GWF). The
ground water baseflow (GWF) is computed by a logarithmic decay equation.
The equation is the same as for the stream's interflow, with a modifi-
cation which permits increased groundwater flow to reflect changes in
the recession constant due to wet antecedent conditions.
A basic description of the data needed for the Stanford Watershed Model
has been presented; a brief description of the input parameters needed
to run the Watershed Model now will be given. For detailed calculations
and formulas see reference (10).
DATA NEEDED
Topographic Map or
Aerial Photographs
Soil Borings or
Observation Wells
DERIVED INPUT PARAMETEBS
1. Time of concentration and time area
histograms
2. Watershed drainage area
3. Impervious fraction of watershed surface
^4. Estimate of stream and lake surface areas
5- Mean overland flow path length
6. Average ground slope of overland flow
surface perpendicular to the channel
1. Soil type
2. Soil porosity
3. Soil specific yield
IK Soils permeability
5. Groundwater fluctuation
119
-------
Climatologic Data 1. Daily dewpoint temperature
2. Daily wind movement
3. Daily solar radiation
U. Maximum and minimum daily temperature
5- Daily lake and pan evaporation
6. Hourly recorded rainfall
7. Storage-gage daily rainfall
Streamflow Data 1. Daily streamflow records
2. Daily diverted flows
Physical Inspection 1. Watershed cover
of the Area 2. Swamps and extensive soil cracks
3. Manning's roughness for overland flow on
soil surface
U. Manning's roughness on impervious surface
5. Manning's roughness value for stream
surface
6. Capacity of channel.
There are additional parameters that must be determined by a trial and
error approach. Therefore, for optimum calibration results, 3-5 years
of climatologic and streamflow data are required to permit the Watershed
Model to stabilize its soil moisture condition.
MODEL TESTING
Based upon the descriptions presented earlier, a computer program to
model a refuse pile was written. The program is very general in nature,
the intent being that it will be applicable to various refuse piles.
In developing the program three assumptions were made.
1. The Ohio State University version of the Stanford Stream-
flow Simulation Model, models a watershed in which the
refuse pile or piles are located. It is also possible to
have the total watershed as a refuse pile.
2. The acid is produced at a uniform rate and is stopped
when precipitation is falling because the outer mantle
will become saturated and insufficient amounts of oxygen
will be present for oxidation of the pyritic material.
3. The solubility concentration of the acid products is con-
stant, and the total volume of water will always be
saturated.
120
-------
Tables B.I, B.2, and B.3 list the nomenclature as used in the computer
program, i.e., the input variables obtained from the Stanford Watershed
Model, the input variables into the Refuse Pile Model, and the internal
variables in the Refuse Pile Model.
A step diagram was presented earlier (Figure B.2); at this time a
detailed explanation will be given to the computations in each step
using the actual computer language to explain all equations. The
computer variables are listed in Tables B.1-B.3 and the program state-
ment listing is included at the end of this presentation of the Refuse
Pile Model.
Since the acid production rate varies with a change in temperature, a
temperature option is available which will reflect the acid production
rate change as seen in equations (B.l) and (B.2).
CK = 2.**((T - T0)/l8.) (B.I)
Unit analysis:
None
ACDPRO = ACDPRO * CK (B.2)
Unit analysis:
Ib Ib
ACRE - DAY UNIT DEPTH (FT) ACRE - DAY UNIT DEPTH (FT)
The change will double the acid production rate for every 10°C temper-
ature change.12 Note: The above equation uses fahrenheit units.
Computing the initial amount of acid available to be removed was done
in Step 2. This amounts to keeping track of the amount of acid in the
outer mantle. When no precipitation is falling the acid in the outer
mantle is produced at a uniform rate, but if precipitation is falling
no acid products are being formed because the oxygen required for oxi-
dation is assumed to be absent and some of the products are being
washed out of the mantle. The program will check the input and if
there is no rain, the amount of acid formed is given by equation (B.3).
ACDPRO* TIME* AREA* DEPTH* FACDEP
^3500
121
-------
Unit analysis:
Ib
_ ACRE, DAY, UNIT DEFTH(FT)* HRS * FT2 * FT* Hone
HR * FTg
DAY ACRE
If it is raining, some of the acid products are washed out of the outer
mantle and the amount of acid remaining is found by equation B.U.
TOTAL = AMIACD - ACDDTT - ACDLZ - ACDUZ - ACDDIR
Unit analysis:
Ib Ib Ib Ib Ib Ib
Time Interval Time Time ~ Time ~ Time " Time
Interval Interval Interval Interval Interval
In Step 3, finding the amount of precipitation falling on the pile and
apportioning the rain into four parts, upper zone, lower zone, inter-
flow storage, and direct runoff, is done by the Stanford Watershed
Model. Refer to earlier dicussions for details.
Once the precipitation starts falling the water will become saturated
with the acid products. These products will move into the same four
areas along with the precipitation. Step k finds this amount by the
following equations:
ACDDIR = FACDIR* SOLACD* OVFLST* CF (B.5)
ACDOTT = FACINT* SOLACD* RGX* CF (B.6)
ACDLZ = FACLZ* SOLACD* SNTRLZ* CF (fi.?)
ALDUZ = FALUZ* SOLACD* ENTRUZ* CF (B.8)
Unit analysis:
Ib
= None
,.. _
Time FT3 Time in
Interval Interval
The above four equations ascertain the amount of acid removed by the
rain during one time interval. In order to keep track of the acid in
122
-------
each zone at all times, the products removed must be added together, as
accomplished by equations (B.9)-(B.12). These four equations show how
the computer updates the amount of acid in each zone after each time
interval; the variables are defined in Tables B.1-B.3-
EXADIR = ACDDIR + EXADIR (B.9)
EXAINT = ACDINT + EXAINT (B.10)
EXALZ = ACDLZ + EXA.LZ (B.ll)
EXAUZ = AIDUZ + EXAUZ (B.12)
Unit analysis:
Ib Ib , Ib
Time Time Time
Interval Interval Interval
In Step 5, the amount of water entering the receiving stream; by over-
land flow, interflow, and baseflow, was determined. This was explained
in detail earlier.
By knowing how much water reaches the receiving stream, it is possible
to calculate the amount of acid being carried to the stream by the
three routes of overland flow, interflow, and baseflow, as done in
Step 6. The equations used are:
AREDIR = DIRRNF* SOIAID* FACRED* CF (B.13)
AREINF = IBTF* SOLACO* FACREI* CF (B.lU)
AREBFL = BASFLW* SOLACO* FACREB* CF (B.15)
Unit analysis:
^ = i!b * 1* * None *
Time Time FTJ in.
Interval Interval
The computer variables are defined in Tables B.I, B.2, and B.5. The
above equations would determine the amount of acid products that would
reach the stream providing there were sufficient products available
throughout the runoff period; if not the quantities would become zero.
The acid products being conveyed in the overland flow would come from
storage on the surface and in the direct runoff until it is depleted.
123
-------
Next the acid products would be supplied by the acid stored in the
upper zone. Acid products being conveyed by interflow would be con-
trolled by the amount of acid retained in interflow storage and then
from the acid accumulated in the lower zone. Baseflow can only obtain
the acid products from the lower zone. There are also acid products
given to the groundwater which may not appear as baseflow but will go
to deep storage. This acid is obtained from the lower zone.
In ascertaining the amount of acid products left in the pile, done in
Step 7, the products leaving the pile to go to the receiving stream or
deep storage are subtracted from the acidic products brought to the
four areas in Step 4. The following equations show how this continual
updating was done
EXADIR = EXADIR - AREDIR (first this) (B.l6)
EXAUZ = EXAUZ - AREDIR (then this) (B.I?)
EXAINT = EXAfflT - AREINF (first this) (B.l8)
EXALZ = EXALZ - AREINF (then this) (B.19)
EXALZ = EXALZ - AREBFL (always) (B.20)
EXALZ = EXALZ - AKEDSR (always) (B.2l)
Unit analysis:
Ib Ib Ib
Time Time Time
Interval Interval Interval
Tables B.1-B.3 define the computer variables. The Refuse Pile computer
program (near the end of this Appendix) is listed for the operators
described in Steps 1 through 8 of Figure B.2. Prior to the program
listing are instructions detailing the necessary changes needed in the
Stanford Watershed Model to generate the information required, by the
Refuse Pile Model.
Presently, the program outputs various tables plus specific day(s)
information. The following Tables B.*JB.7 show the standard output
items for the daily acid load in direct runoff, interflow, baseflow and
the total acid load. Tables B.8-B.10 gives the daily flow reaching the
receiving stream by direct runoff, interflow and baseflow, and the total
flow reaching the stream is presented in Table B.ll. Monthly summaries
of acid load and flows are given in Table B.12; Table B.13 shows spe-
cific day output. The values listed in the tables have no specific
-------
Table E.h. DAILY ACID LOAD IN DIRECT RUNOFF
ro
Vix
DAY
1
2
?
4
5
6
7
8
10
11
12
13
14
15
16
17
18
19
20
21
22
23
2*
25
26
_2J
28
29
30
-31.-
OCT
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
o.o
0.0
0.0 .
0.0
o.o
0.0
0.0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
o.o
0.0
0.0
0.0
O.Q_
0.0
o.o
0.0
0.0 _
NOV
0.0
0.0
01,0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
O.CL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
Q.O
0.0
0.0 ..
0.0
0.0
0.0
********
DEC
o.o
0.0
0-.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
o.o
0.0
0-0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
o.o
0.0
.18.32
0.0
0.0
0.0
0.0 .
AN
SVNI1
JAN
35.0*
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Q.O . _
0.0
0.0
0.0
Q.O-....
2.84
9.03
0.0
0.0
0.0
0.0
142.48
-37035.92
0.0
o.o
0.0
O.Q .
0.0
0.0
0.0
0.0
5.72
_-_. 0.0
INUAL SUMMARY FOR WATER YEAR
XESIZED ACID LOAD IN DIRECT
FEB
0.0
0.0
6.97
0.0
0^£L-
0.0
0.0
0.0
--2234.01
12498.32
0.0
0.0
2.32
6.32
0.0
0.0
0.0
0.0
_. _.. 0.0
0.0
0.0
0.0
0.0
0.0
_ .- O.Q ..
0.0
o.o
0.0
********
I**:******
4*******
MAR
0.0
0.0
0.0
0.0
0 tQ
0.0
0.0 ..
0.0
0.0
0.0
0.0
0.0
0.0
0.0
36.22.
0.0
0.0
0.0
0.0
0.0
0.0
o.c
0.0
0.0
c.o
0.0
0.0
o.o
APR
0.0
576.86
0.30
0.0
0.0
0.0
0.0
0.0
- -0.0
0.0
0,0
0.0
0.0
0.0
0.0 -.
0.0
- . 0.0
0.0
_ 0.0
0.0
0.0
0.0
- O.Q
0.0
0.0
0.0
65.35
757.91
5.29
0.0 4.69
0.0 ********
HAY
0.0
0.0
0.0
0.0
Q.O
0.0
0.0
0.0
0.0
c.o
O.Q.
0.0
0.0
0.0
0.0
0.0
0,0_-
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0"
C.Q
0.0
..5..BOL.
0.0
0.0
JUN
0.0
0.0
0.0 -
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
68.83
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 -
7.61
O.Q
0.0
0.0
8.30
0.0
0.0
0.0 ..
0.0
********
JUL
0.0
0.0
0.0 .
0.0
o.o
0.0
0.0
0.0
0.0
0.0
Q_.Q
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 . ..
0.0
0.0
0.0
Q.O
0.0
0.0
0
0
0
0
Q
0
0
0
0
o
JDL
AUG
.0
.0
.0
.0
.n
.0
.0
.0
.0
.0
.0
0.0
0.0
0.0
- O.Q
0.0
Q.O
0
0
0
0
0
0
0
0
0
0
n
0
0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
SEP
0.0
0.0
0.0
0.0
0.0
O.Q
0.0
... 0.0 ....
0.0
0.0
0.0
0.0 .
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
O.Q
0.0
0.0
0.0
0.0-
0.0
********
-------
Table B.5. DAILY ACID LOAD IN INTERFLOW
ro
ON
ANNUAL SUMMARY FOR WATER YEAR 1958 - 1959
SYNTHESIZED ACID LOAD IN INTERFLOW IN POUNDS ... - .... - - -. - -
DAY
1
2
3
4
5
6
7
8
9
10
11
12
13
1*
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
OCT
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
JQ*0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
NOV
Q.O
0.0
_. 0.0.....
0.0
0.0
0.0
__. 0.0 _ .
0.0
.. . 0.0
0.0
0.0
0.0
0.0
0.0
0.47
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0 #O
0.0
0.0
0.0
0.0
0.0
0.0
0.0
********
DEC JAN
0.0 11526.72
139.04 1155.39
112.17 24.76
390.39 24.76
1005.21 24.76
102.97 24.76
24.76 . 24.76
24.76 24.76
24.76 .. 24.76
24.76 24.76
£4,_»76 13..4X.
24.76 0.0
24.76 0.0
24.76 1464.92
24.76 7051.47
30.61 733.61
..10.36. .24.76
8.60 24.76
82.42 9.29
25.84 5985.09
24.76 80054.87
223.10 5163.65
_5X)9,31 34,27
226.58 24.76
63.37 24.76
457.93 24.76
2552.98 24.76
125.50 24.76
_Z4.,7J» 652.27.
24.76 3996.66
24.76 265.92
FEB
24.76
24.76
1430.74
1655.42
J.2ji«ie
24.76
24.76
24.76
10560.96
41393.79
. 1174,91
24.76
1701.34
2022.99
666.06
24.76
24.76
24.76
24.76
24.76
156.20
276.07
,_1S85«2S
200.36
24.76
24.76
24.76
11.35
********
********
********
MAR
1079.42
628.75
42.99
0.0
189,95
205.51
16.51
16.51
676.43
92..S2
24.76
24.76
24. .76
2657.29
11634~«6
446.. 15
24.76
12.38
0.0
0.0
0.0
0.0
O.O..
0.0
0.0
1.20
3.22
b.25
8.25
8.25
8.23
APR
16.94
12779.44
1309.74
58.6^
24.76
24.76
24.76
24.76
20.64
0.0
. 0-0
0.0
0.0
0.0
0.0
0.0
. . . 0.0
0.0
0.0
3.57
<*.13
4.13
4.13...
4.13
4.13
15.44
11302.31
36864.66
... 2666.27
3236.04
********
MAY
651.53
24.76
24.76
24.76
24.76
24.76
24.76
24.76
24.76
17.28
16.51
856.62
19.6V
0.0
0.0
0.0
0.0
0.0
23B.49
24.76
27.56
24.76
... 4.13
0.0
0.0
4.73
60.67
22.83
1302.lt
773.68
24.76
JUN
83.80
26.87
0.0
0.0
.. O.O.. ..
0.0
0.0
0.0
0.0
0.0
0.0
4826.77
4136.71
31.13
24.76
24.76
24.76
24.76
24.76
24.76
20.64
2815.42
. 336.08
24.76
244.30
3146.36
636.27
24.76
20.64
0.0
********
JUL
0.0
0.0
0.0
0.0
..0.0.
0.0
0.0
0.0
0.0
0.0
_ 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
.... 0.0-
0.09
0.0
0.0
0.0
0.0
0.0
0.0
0.0
AUG
0.0
0.0
0.0
21.24
24.76
24.76
20.64
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
__. o.o
0.0
0.0
SEP
0.04
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
.0.0 ._
0.0
0.0
0.0
0.0
0.0
.. 0.0 .
0.0
0.0
0.0
0.0
0.0
o.c .
0.0
0.0
0.0
0.0
0.0
.0.0 ..
0.69
********
-------
Table B.6. DAILY ACID LOAD IN BASEFLOW
ANNUAL SUMMARY FOR WATER YEAR 1958 - 1959
^SYNTHESIZED ACID LOAD IN BASEFLOW IN POUNDS
DAY
JL
2
3
4
5
6
7
8
10
11
12
13
14
15
16
17
18
19
20
22
23
24
?5
26
_Z7
28
?9
30
-31
OCT
0.64
0.0
0.0
0.0
0.0
0.0
0.0
0.0
^tS.SA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
12.30
5.68
0.0
0.0
0.0.
0.0
0.0
0.0
15.48
2.58
7.48
0.0
0.0
NOV
6.84
33.02
33.0?
29.06
28.38
24.76
12.64.
6.28
25.28
32.50
28.89
27.69
24.76
24.08
28.89
35.43
33.02
31.64
34.57
33.02
28.89
28.20
24.76
24.59
20.64
25.11
28.36
24.76
24.76
22.01
DEC
67.07
143.43
324..18
576.81
770.29
866.60
827.39
782.67
737.44
692.04
647.67
603.64
561.51
521.78
463.43
452.99
423.73
420.31
434.41
JAN FEB
734.69 1444.79
1010.37 1338.16
943.47 -1248.22
876.40 1317.01
012.42 1383.05
MAR
975.11
1077.79
1043.73
905.14
906.1!)
752.06 1289.64 964.11
-695.65 1193.18 922.3.2
643.88 1103.24 852.13
_ 595.04 1106.16 851.46
549.98 1667.50 883.97
508.54 1708. 7B 316.8?
470.01 1590.45
434.42 1570.33
429.94 1537.31
682.23 1573.26
661.04 1461.81
818.44 1353.30 _
759.11 1250.62
704.25 1155.52
435.97 767.49 1067.98
_-407.42 1663.89 1011.23
416.02 1946.11 1002.63
559.10 1822.63 1081.05
670.02
695.65
686.54
705.45-
690. It
646.12
601.75
.-..558.93
1696.74 1182.18
.1573.60 1092.92 -
1456.14 1009.85
1346.93 ._. 933.15
1244.61 872.44
-J.234.JJL ********
1478.67 ********
1556.75 ********
754.93
697.71
855.24
1490.19
1570.51
1451.32-
1340.91
1240.31
1144.51
1057.49
977.35
_2Q3..23..
835.12
771.32
717.32
690.66
695.13
_ 6*2.17
593.49
548.78
APR
507.16
651.79
704.06
713.36
659^.68
609. B3
563.57
521.27
481.54
445.42
411.71
380.41
351.52
325.04
... 300.45
277.92
-.257.11.
237.50
219.44
222.37
212.57
196.40
.IB 1.95
168.02
. 155.30
144.46
725.06
1376.52
. .1650.4.8..
1721.33
********
MAY
1793.39
1657.01
1530.95
1414.69
1307.38
1207.97
1116.31
1031.87
953.62
699.27
-B42.52.
1162.06
1242.03
1148.99
1061.96
981.30
.. 907.16.
636.05
845.44
790.92
754.29
699.26
649.39
612.93
566.67
539.66
551.70
563.57
_ 564.43.
754. C4
699.09
JUN
679.83
693.24
640.62
592.63
505.96
467.95
432.70
399.85
369.75
454.19
1316.15
1224.14
1131.96
1045.97
. 966.69
893.42
825.84
763.24
705.62
1128.18
...1641.71.
1520.98
1480.91
1802.85
2320.33
2145.95
- 1962.22.
1632.94
********
JUL
1702.07
1596.30
1474.89
1362.76
1163.60
1075.21
993.17
917.84 .
848.02
784.22
729.70
674.49
623.25
575.95
532.27
492.20.
455.57
424.09
409.31
378.35
349.80
..-323.66 .
310.08
298.55 .
276.02
255.39
235.78
.... 21B.07.
206.72
193.30
AUG
178.86
165.27
152.72
198.64
203^2-
188.14
174.04
160.97
148.76
137.41
A Z I f °
123.48
114.37
105.59
97.51
90.12
-B3.75-.
76.87
71.54
65.87
60.88
56.41
^52.11
48.33
44.89
41.27
39.38
37.15
-33.71
31.99
28.89
SEP
28.72
45.40
. 44.20
41.27
37.15._
34.74
33.02
28.89
._ 28.20 .
26.83
28.72
24.76
24.76
20.98
20.64
19.26
16.51
16.51
15.99
12.38
12.38
12.38
8.94
8.25
8.25
8.25
8.25
8.25
32.85
********
-------
Table B.7. DAILY ACID LOAD
00
ANNUAL SUMMARY FDR WATER YEAR
SYNTHESIZED TOTAL ACID LOAD
DAY
1
2
..3...
4
_5__
6
.. T ...
8
...9 ...
10
JL1
12
13
14
15
16
OCT
0.64.
0.0
0.0
0.0
0.0
0.0
0.0 _
0.0
75.84
0.0
0.0
0.0
0.0
0.0
0.0
0.0
JL7 _L2.3Q_
16
19
20
21
22
23.
24
25
26
27
28
29
30
31
5.68
0.0
0.0
0.0
0.0
0.0
0.0
10.32
15.48
2.58
7.48
0.0
0.0
0.0
NOV
6.B4
33.02
33.02
29.06
28.38
24.76
12.64
6.28
25. 28
32.50
28.89
27.69
24.76
24.08
... 29.37
3S.43
33.02
31.64
34.57
33.02
28.89
28.20
DEC
JAN FEB
67.0JL_12295.44 1469.55
282.47
436.35
967.21
1775.51
969.56
._ 852.15
807.43
762.20
716.80
2165.77 1362.93
968.24 2685.92
901.16 2972.44
837.19 1506.82
776.82 1314.60
.720.41 1217.95
668.65 1128.00
619.81 13901.14
574.75 55559.64
672.43 521.95 2883.69
628.41
586.27
546.54
508.19
483.60
444j09_
428.91
516.84
461.80
f32.18
639.11
24.76 1068, 42_
24.59
20.64
25.11
2fa.38
24.76
24.76
22.01
********
896.61
759.02
1144.47
3276.76
815.65
670.. 88-.
626.51
563.69
470.01 1615.22
434.42 3274.00
1897.70 3566.63
7742.75 2239.33
1614.66 1486.58
.. 843.21..__1378.06 .
783.87 1275.39
713.53 11B0.29
6915.05 1092.75
******** 1167.43
7109.73 1278.70
1856.89 296.6.33.
1721.50 1382.53
1598.37 1117.69
1480.90 1034.62
1371.70 957.92
1269.37 883.79
_.1886. 39. .********
5481.01 ********
1822.67 ********
MAR
2054.54
1706.54
1066.73
965.14
.109.6.1.0
1169 .62
938,83
863 .66
1527.90
976.49
841,66 .
779.75
722.48
3512.54
13163.27
2016.66
1476.09
1353.30
1240.31
1144.51
1057.49
977.35
903.23
835.12
771.32
718.52
693.89
703.39
..650.42
601.75
557.03
APR
524.10
14008.09
2014.13
772.01
684.64
634.60
588.33
546.03
502.17
445.42
411.71
380.41
351.52
325.04
300.45
277.92
_ 257.11
237.50
219.44
225.94
216.69
200.53
186.08
172.15
159.42
159.90
12.092.70
38999. 0&
4322.04
4962.05
********
1958 - 1959
IN POUNDS ... - -
MAY
2444.93
1681.78
1555.71
1439.46
1332,14..
1232.74
1141.07
1056.63
978.38
916.56
. &59.03_
2018.68
1261.72
1148.99
lDol.96
981.30
907.18
838.05
1083.94
815.69
781.85
724.03
653.51
612.93
566.67
544.40
612.37
586.40
1872.38
1528.33
723.85
JUN
763.62
720.11
640.62
592.63
547.57
505.96
467.95
432.70
399.85
369.75
341.72
5349.79
5452.7V
1255.27
1156.72
1070.73
991.45
918.19
850.60
788.00
726.26
3951.22
1977.79
1545.74
1725.20
4957.49
2956.61
2170.71
2002.86
1832.94
********
JUL
1702.07
1596.30
1474.89
1362.76
1259.91
1163.60
1075.21
993.17
917. B4
848.02
784.22 ..
729.70
674.49
623.25
575.95
532.27
492.20
455.57
424.09
409.31
378.35
349.80
323.66
310.16
298.55
276.02
255.39
235.78
218.07
i.06.72
193.30
AUG
178.86
165.27
152.72
219.87
_^28.39_
212.91
194.68
160.97
148.76
137.41
_127.78
123.48
114.37
105.59
97.51
90.12
83.75
76.87
71.54
65.87
60.88
56.41
52.11
48.33
44.89
41.27
39.38
37.15
. 33.71
31.99
28.89
SEP
28.76 -
45.40
44.20
41.27
37.15
34.74
33.02
26.89
28.20
26.83
._ 28.72...
24.76
24.76
20.98
20.64
19.26
16.51
16.51
15.99
12.38
12.38
12.38
.._ 12.38
8.94
8.25
8.25
8.25
8.25
... 8.25 _
33.54
********
-------
Table B.8. DAILY DIRECT RUNOFF REACHING RECEIVING STREAM
MD
DAY OCT
1 O-O
2 0.0
4 0.0
5 O.O
6 0.0
7 0*0
8 0.0
9 0.0
10 0.0
11 0.0
12 0.0
J.3- Q..Q
14 0.0
JL5 Q.Q
16 0.0
17 0.0
18 0.0
19 O.n
20 0.0
2. 1 Q . Q
22 0.0
23 0.0
24 0.0
26 0.0
28 0.0
?9 O-O
30 0.0
11 O.O **
NOV
0.0
0.0
0.0
0.0
0.0
O.O
0.0
O.O
0.0
0.0
0.0
O.O
0.0
O.O
0.0
0.0
0.0
0.0
0.0
..Q.O
0.0
0.0
0.0
0*0
0.0
O.O
0.0
0.0
0.0
*******
DEC
Oj-Q
0.0
0.0
O.O
0.0
O.O
0.0
0-0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
O.Q
0.0
Q.Q65.2
0.0
0.0
0.0
O.Q.-. ....
AN
SY HIKES
JAN
Q.1247
0.0
0.0
0.0
O.O
0.0
0.0
0.0
O.Q
0.0
0.0
0.0
0.0
0.0101
0.0321
0.0
0.0
0.0
O.Q
0.5070
131.7953
0.0
0.0
0.0 '
0.0
0.0
0.0
0.0
o.o
0.0203
-0.0
NUAL SUMMARY FOR WATER YEAR 1958 - 1959
1Z£D.J21RE£T RUNOFF IN CUBIC FEET PER SECOND ... ..
FEB
O.Q
0.0
-. 0.0248
0.0
O.O
0.0
0.0
0.0
7.9499
44.4763
0.0
0.0
0.0083
0.0225
Q.O
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
********
********
********
MAR
o.a
0.0
0.0
0.0
O.o
0.0
Q.O
0.0
Q.O
0.0
0.0
Q.O
0.0
0.1360-
0.0
O.O
0.0
-0.0
0.0
Q.O
O.O
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
0.0
APR
0.0
2.0528
0.0011
0.0
Q.Q. -
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
.. 0.0 .....
0.0
0.0
0.0
0.0
0.0
... 0.0
0.0
0.0
0.0
0.0
0.0
0.2326
2.6971
0.0188
0.0167
********
MAY
0.0
0.0
0.0
0.0
Q.D
0.0
0.0
0.0
0.0 ..
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
O.JI.Q
c.o
0.0
0.0
0.0
0.0
D. 02,07
0.0
0.0
JUN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-JQ.O .
0.2450
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0271
0.0
0.0
0.0
0.0295
0.0
0.0
0.0 -
c.o
********
JUL
0.0
0.0
0.0
0.0
JL.Q
0.0
0.0
0.0
0.0
0.0
-Q..Q- .
0.0
0.0
0.0
0.0
0.0
Q.Q
0.0
0.0
0.0
0.0
0.0
JQ.Q..
0.0
0.0
0.0
0.0
0.0
0.0 .
0.0
0.0
AUG
0.0
0.0
0.0
0.0
Q...Q
0.0
0.0
0.0
0.0
0.0
...0.0 ...
0.0
0.0
0.0
0.0
0.0
O.Q
0.0
0.0
0.0
0.0
0.0
Q.a.0
0.0
0.0
0.0
. 0.0
0.0
Q.O.
0.0
0.0
SEP
0.0 ...
0.0
0.0
0.0
0.0
.-0.0 -
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 ....
0.0
0.0
0.0
0.0
0.0
********
-------
Table B.9. DAILY INTERFLOW REACHING RECEIVING STREAM
o
DAY
1
2
4
5
6
7
8
10
.11
12
13
14
15 .
16
.17.
18
19
20
21
22
_23
25
26
27
28
^2LSL-_
30
31
OCT
0.0
0.0
0.0
0.0
0.0
0.0
0.0 . _
0.0
0.0
0.0
0.0
0.0
0.0 ^
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Q tQ
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 *<
NOV
0.0
0.0
0.0
0.0
0.0
0.0
0.0 _
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0017 . _
0.0
0.0
0.0
0.0 _ .
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
I******
DEC
0.0
0.4948
0.3992
1.3892
3.5771
0.3664
0.0881
0.0881
0.0881
O.CB81
0.088L
0.0881
0.0881
0.0881
0.0881
0.1089
ANNUAL SUM*
SYNTHESIZED I*
JAN FEB
-41.0152 0.0881
4.1115 0.0881
0.0881 5.0914
0.0881 5.B909
0.0881 0.4405
0.0881 0.0881
0.0681 0.0881
0.0881 0.0881
0.0881 37.5821
0.0881 147.3032
0.0477 4.1810
0.0 0.0881
_... 0.0 6.0544
5.2130 7.1990
..25.0932 2.3702
2.6106 0.0081
0.0881 0.0881
0.0306 0.0881 0.0881
0.2933 0.0330 0.0881
0.0920 21.2984 0.0881
0.0881 284.8818 0.5559
0.7939 18.3752 0.9824
_L..8124_ 0.1219 6.7089
0.6063 0.0881 0.7130
0.2255 0.0881 0.0681
1.0296 0.0881 0.0881
9.0850 0.0881 0.0881
0.4466 0.0881 0.0404
Q.O&81 2.3212 ********
0.0681 14.2225 ********
0.0881 0.9463 ********
IARY FOR WATER YEAR 1958 - 1
ITERFLOW .. IN CUBIC FEET PER S
MAR
. 3.6412
2.2375
0.1530
0.0
0.6760
0.7313
. 0.0588
0.0568
2.4071
0.3293
O.OU81
0.0881
9.4562
41.4035
1.5677
0.06S1
0.0441
0.0
0.0
0.0
0.0
.-..0.0
0.0
0.0
0.0043
0.0115
0.0294
. .0.0294
0.02V4
0.0294
APR
0.0603
45.4767
4.6608
0.2087
0..0881
0.0881
0.0881
0.0881
0.0734
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0127
0.0147
0.0147
0.0147.
0.0147
0.0147
0.0549
40.2201
131.1858
9.4881 .
11.5157
********
MAY
2.3185
0.0861
0.0881
0.0881
.0.0861
0.0881
0.0881
0.0881
0.0881
0.0615
0.0588 .
3.0484
C.0701
0.0
0.0
C.O
0.0
0.0
0.8467
0.0881
0.0981
0.0&81
0.0147
0.0
0.0
0.0166
0.2159
C.0812
4.6338
2.7532
0.0861
959
ECOND
JUN
0.2982
0.0956
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
17.1765
14.7209
0.1108
0.0881
O.OB81
0.0881
0.0881
0.0881
0.0881
0.0734
10.0189
1.1960
0.0881
0.8693
11.1966
2.2642
0.0681
0.0734
0.0
********
JUL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
...0.0 . _
0.0003
0.0
0.0
0.0
0.0
0.0
0.0
0.0
AUG
0.0
0.0
0.0
0.0756
a.oeei
0.0881
0.0734
0.0
0.0
0.0
0.0.
0.0
0.0
0.0
0.0
0.0
.0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 ...
0.0
0.0
SEP
0.0002
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 ..
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
. ..0.0
0.0
0.0
0.0
0.0
0.0
. 0.0
0.0024
********
-------
Table B.10. DAILY BASEFLOW REACHING RECEIVING STREAM
DAY OCT
2 1.0667
3 0.9865
4 0.9119
5 0.8439
6 0.7803
__7 0.7215
8 0.6677
_._9 0.6218
10 0.5826
11 0.5392
12 0.4988
_13_ 0.460B __.
14 0.4266
_15 0.3941_.
16 0.3648
17 0.3372
18 0.3152
J.5 Q.29QL
20 0.2699
_21 0.2485.._..
22 0.2295
_Z3 CL^iiaO
24 0.1971
..25 0.1618
26 0.1726
J27 0.1603 ...
28 0.1475
29 0.1365
NOV
-CL.JL095
0.1175
0.1175
0.1034
0.1010
0.0881
0.0881
0.0759
0.0900
0.1157
0.1028
0.0985
0.0881
0.0857
.0.1028
0.1261
0,1175
0.1126
Q.123Q__.
0.1175
0.1028 __
0.1004
ji.jmai
0.0875
0.0734.....
0.0894
0.1010 _
0.0881
0.0881
30 0.1285 0.0783
.31 -0.1175 ********
DEC
0^2387
0.5104
1.1536 __.
2.0526
2.7411
3.0839
2.9443 __
2.7852
2.6242
2.4627
2.1481
1.9982 _.
1.6568
1.7203 _
1.6120
1.4957
1.5459 ._
1.5514
1.4498 ,.
1.4804
1.9896
2.3643
2.4755
2.4431
2.5104
2.4559
2.2993
2.1414
1.9890 ...
ANNl
5YNTHES
JAN
2.6144
3.5955
.3.3574 ..
3.1187
_JL»fiill
2.6763
2.4755 ...
2.2913
..2.1175 . _
1.9572
1.8097
1.6726
. 1.5459
1.5300
_ 2. 42 78 .
3.1353
_Z.2125
IAL SUMMARY FCR WATER YEAR 1958 - 1959
IIZED..BASEFLOW IN CUBIC FEET PER SECOND
FEB
5.1414
4.7620
4.4419
4.6867
4.9?17
4.5900
4.2460
3.9260
3.9364 ..
5.9339
6.0808
5.6596
5.5bb2
5.4706
5.5986
5.2020
4.8158
2.7014 4.4504
2.5061 . 4.1120
2.8023 3.fa005
. 5.9211 .3.5985
6.9254 3.5679
-JJ...4860 3 .647.0....
6.038U 4.2069
5.5998 3.8892
5.1818 3.5936
4.7932 . 3.3207
4.4290 3.1047
_4..»3-9JL7_ ********
5.2620 ********
5.5398 ********
KAR
3.4700
3.8354
3.7142
3.4345
-.3.. 22.46
3.4309
3.2821
3.0324
. 3.0300
3.1457
-2.9070.
2.6867
2.4629
3.0^35
5.3030
5.5£i88
5.1647
4.7717
4.4137
4.0728
3.7632
3.4780
...3.2142.
2.9718
2.7*48
2.5526
2.4578
2.4737
...2.2 (>52
2.1120
1.9529
APR
.. 1.8048
2.3195
2.5055
2.5386
2.3482.
2.1701
2.0055
1.8550
1.7136
1.5851
.1.4651
1.3537
1.2509
1.1567
1.0692
0.9149
0.8452
0.7809
0.7913
0.7564
0.69B9
_._5»6475.._..
0.5979
0.5526
0.5141
2.5602
4.8984
5.8733
6.1255
********
MAY
6.3819
5.8966
5.4480
5.0343
4,. 65 24
4.2987
3.9725
3.6720
3.3935
3.2001
2.9982
4.1353
4.4198
4.0888
3.7791
3.4921
3.2283
2.9823
3.0086
2.8146
2.6842
2.4884
.2.3109
2.1812
2.0165
1.9204
1.9633
2.U055
2.0086
2.6654
2.4878
JUN
2.4192
2.4670
2.2797
2.1089
J..9486 ,
1.8005
1.6652
1.5398
1.4229
1.3158
. 1.2160 . .
1.6163
4.6B36
4.3562
4.0282
3.7222
.. . 3.4400 -
3.1793
2.9388
2.7160
2.5110
4.0147
.5.8421 ..
5.4125
5.2699
6.4156
b.2571
7.6365
7.0539
6.5227
********
JUL
6.0570
5.6806
5.2485
4.8495
.4.4835
4.1408
3.8262
3.5343
3.2662
3.0178
.2.7907
2.5967
2.4002
2.2179
2.0496
1.8941
1.7515-..
1.6212
1.5092
1.4565
1.3464
1.2448
1.1518 _
1.1034
1.0624
0.9823
0.9088
0.8391
0.7760 ..
0.7356
0.6879
AU6
0.6365
0.5881
0.5435
0.7069
0^7-246.
0.6695
0.6193
0.5728
0.5294
0.4690
J.4547
0.4394
0.4070
0.375P
0.3470
0.3207
0.2980.
0.2736
0.2546
0.2344
0.2166
0.2007
...0.1854
0.1720
0.1597
0.1469
0.14C1
0.1322
. 0.1200.
0.1138
0.1028
SEP
0.1022
0.1616
0.1573
0.1469
0.1236
0.1175
O.1028
0.1004
0.0955
CU1022_
0.0881
0.0881
0.0747
C.0734
0.0685
0.0588
0.0569
0.0441
0.0441
0.0441
.0.0441 ...
0.0318
0.0294
0.0294
0.0294
0.0294
0.0294
0.1169
********
-------
Table B.ll. DAILY FLOW REACHING RECEIVING STREAM
to
ANNUAL SUMMARY FOR WATER YEAR 1958 - 1959
SYNTHES1IE0..STREAMFLOW IN CUBIC FEET PER SECOND _ . ... - .
DAY
1
2
3
4
5
6
7
8
9
10
JLL_
12
13
14
15
16
_11_
18
19
20
21
22
_2i_
24
25
26
27
28
^29_
30
31
OCT
2.4307
1.0667
0.9865
0.9119
0.8439
0.7803
0.7215
0.6677
0.6218
0.5626
__0,5392_
0.4988
0.4608
0.4266
0.3941
0.3648
_.0.3372_
C.3152
0.2901
0.2699
0.2485
0.2295
_JU213fl-
0.1971
0.1818
0.1726
0.1603
0.1475
0.1365
0.1285
0.1175
NOV
0.1095
0.1175
0.1175
0.1034
0.1010
0.0881
0.0881
0.0759
0.0900
0.1157
_O.IP26._
0.0985
0.0881 _
0.0857
0.1045
0.1261
0.1175
0.1126
0.1230
0.1175
0.1028
0.1004
DEC
0. 236:7
1.0052
.-1.5528
3.4419
6.3183
3.4503
3.0324
2.8733
2.7124
2.5508
JAN
43.7543
7.7071
3.4455
3.2069
2.9792
2.7644
2.5637
2.3794
2.2056
2.0453
FE8
5.2295
4.8501
9.5581
10.5777
5.3622
4.6781
4.3342
4.0141
4V. 4683
197.7135
__2.»i9Z? 1 . 8.5J4___10 .2619
2.2362
2.0863
1.9449
1.8084
1.7209
I,i80.3-
1.5263
1.8392
1.6434
1.5379
2.2743
1.6726
. 1.5459
6.7531
27.5531
5.7459
3.0006.
2.78V5
2.5392
24.6076
422.5950
25.3006
Q.QB.81 3_,802.0_.__.6,6079,
0.0875
0.0734
0.0894
0.1010
0.0881
0,Q8.81_
0.0783
********
3.1907
2.7010
4.0727
11.6606
2.9025
6.1261
5.6879
5.2699
4.8813
4.5172
2.3874 6...7129
2.2295
2.0771
19.5047
6.4&61
6.747V
11.6508
12.6921
7.9688
5.2901
.... 4.9039
4.5336
4.2001
3. £886
4.1544
4.5504
.10.5559
4.9198
3.9774
3.6818
3.4088
3.1451
********
********
********
MAR,
7.3113
6.0729
3.8072
3.4345
3.9006
4.162.'!
3.3409
3.091;!
5.437.2
3.4749
_.2.9951
2.774S
2.5710
12.4997
46.8426
7.1765
. 5.2528
4.8158
4.4137
4.0728
3.7632
3.4780
3.,il42
2.9718
2.7448
2.5569
2.46S2
2.5021
... .2.311-6
2.141.4
I.V623
APR
1.8651
49.8490
7.1e>74
2.7472
2,4364
2.2583
2.0936
1.9431
1.7870
1.5851
1.4651
1.3537
1.2509
1.1567
1.0692
0.9690
0.91V?
O.S452
0.7809
0.3040
0.7711
0.7136
0.6622
0.6126
0.5673
0.5690
43.0328
138.7814
15.3603
17.6579
********
MAY JUN
8.7005 2.7174
5.9847 2.5626
5.5361 2.2797
5.1224 2.1089
..4.7405 1.9486
4.3868 1.8005
4.0606 1.6652
3.7601 1.5398
3.4816 1.4229
3.2616 1.3158
3.0569 1.2160
7.1836 19.0377
4.4899 19.4042
4.0688 4.4670
3.77V1 4.1163
3.4921 3.8103
3.2283 3.5282
2.9823 3.2674
3.8573 3.0269
2.9027 2. 8042
2.7023 2.5845
2.5765 14.0607
2.3256 7.0381
2.1812 5.5006
2.C165 6.1393
1.V373 17.6416
2.1792 10. 52.13
2.0868 7.7247
6.6630 7.1273
5.4387 b.5227
2.5759 ********
JUL
6.0570
5.6806
5.2485
4.8495
4.4835
4.1408
3.8262
3.5343
3.2662
3.0178
2.7907
2.5967
2.4002
2.2179
2.0496
1.8941
1.7515
1.6212
1.5092
1.4565
1.3464
1.2448
1.1518
1.1037
1.0624
0.9823
0.9088
0.8391
0.7760
0.7356
0.6879
AUG
0.6365
0.5881
0.5435
0.7824
. 0.8127
0.7577
0.6928
0.5728
0.5294
0.4890
0.4547
0.4394
0.4070
0.3758
0.3470
0.3207
0.2980
0.2736
0.2546
0.2344
0.2166
0.2007
..,0.1854
0.1720
0.1597
0.1469
0.1401
0.1322
.._ 0.1200
0.1138
0.1028
SEP
0.1024
0.1616
0.1573
0.1469
0.1322
0.1236
0.1175
0.1028
0.1004
0.0955
0.1022_.
0.0881
0.0881
0.0747
0.0734
0.0685
0.0568
0.0588
0.056V
0.0441
0.0441
0.0441
0.0441
0.0318
0.0294
0.0294
0.0294
0.0294
0.0294
0.1193
********
-------
Table B.12. MONTHLY SUMMARY" OF ACID LOADS ATO FLOWS
ANNUAL SUMMARY FC
OCT NDV DEC JAN FEB MAR
SYNTHESIZED AC. in ( DAD IN DIRECT RUNOFF IN POUNDS
0. 0. 18. 37231. 14748. 38.
SYNTHESIZED ACID LOAD IN INTERFLOW IN POUNDS
SYNTHESIZED ACID LOAD IN BASEFIQW IN POUND-!
130. 786. 17420. 31110. 35546. 29237.
H-'THESIZED TOTAL ACID LOAD IN POUNDS
13O. 786. 23827. 18&817. 113899. 47111.
SYNTHESIZED OIRFCT RUNDFF IN r.ijftic FEET PER SECOND
0. 0. 0. 132. 52. 0.
SYNTHESIZED INTERFLOW IN CUBIC FEET PER SECOND
O. Q. 23. 422. 226. 63.
SYNTHESIZED BASEFLQW IN CUBIC FEET PER SECOND
15. 3. 62. 111. 126. 104.
SYNTHESIZED TOTAL AMOUNT OF WATER ENTERING THE STREAM IN
15. 3- RS. AfeS. 405. 168.
IR WATEI
APR
1410.
6839 3..
15373.
85177.
5.
243.
55.
CUBIC
... 303.
R YEAR 1958 - 1959
MAY JUN
6. 85.
4268. 16523.
29688. 30855.
33963. 47463.
0. 0.
15. 59.
10e>. 110.
FEET PER SECOND
.. . 121. 169.
JUt AUG SEP YEAR TOTAL
0. 0. 0. 53536.
0. 91.' -I* 295585
21140. 3140. 669. 215095.
21141. 3232. 670^. 564216.
0. 0. 0. 191.
0. 0. 0.- 1052.
75. 11. 2. 781.
75. 12. _ -.2*.. ..2023.
-------
Table B.13. SPECIFIC DAY OUTPUT
YR HO DY MR PO
tREINF
58
58
58
58
58
58
58
58
4
*
4
4
4
4
4
4
4
58 4
58 ..4
58 4
58_4
58 4
58 4
58
__58
58
58
58
58
58
_ 58
58
58
58
58
58
__58_
59
58
58
58
_ 58
58
58
58
58
58
58
58
58
58
58__
58
.58
58
.58
58
58
58
58
58
58
58
58
4
.4
4
4
4
_4_
4
4
4
4
4
-4.
4
4
4
4
_4_
4
4
4
4
4
_4_
4
4
4
4
4
_4_
4
4
4
4
4
4
4
4
4
4
4
4
58 4
5B_ 4
58 4
58 4_
58 4
58 *
20
20
?0
20
20
20
20
20
?o
20
20
20
20
20
JJ>
1
1
1
1
2
2
2
2
3
3
3
...4
4
4
20 4
20 5
20 5
20 5
20 5
JO 6.
20 6
20 6
20 6
20 7
20 7
20 7
20
20
20
20
20
_2£L
20
20
20
20
20
JLQ.
20
20
20
20
20
.20
20
20
20
20
20
?n
20
20
20
20
20
20
2D
20
20
20
20
7
8
8
8
_i.
9
9
9
10
10
.1.0.
10
11
11
11
11
J.2_
12
12
12
13
13
_13_
13
14
14
14
14
15
15.
15
16
16
16
1
2
3
4
1
2
3
4
_L_
2
3
4
I -
2
4
1
2
.3.
4
_1
2
3
4
1
2
3
4
1
2
3
4
_1
2
3
4
1
2
3
4
1
2
3
4
_1
2
3
4
1
2
3
4
1
2
3
4
1
2
4
1
2
3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
fi^CL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.c
0.0
-Oj.0_
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Q.JL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0_
0.0
0.0
_0
0
0
0
.. _ 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
3
4
4
5
6
6
7
8
9
10
11
12
13
14
15
16
17
18
.._ . 19
19
.20
20
21
_
-
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,
0
0
0
0
0
.0
0
0
0
0
0
0
0
0
0
0
0
3670
7309
0319
5478
0638
493 t
9236
6116
2135
6154
3744
1213
9652
6961
3840
3729
3618
2646
0816
3264
4893
5641
5960
2728
0037
7346
2936
8525
3254
7.0512
7.0512
7.0512
7.0512
7.0512
7.0512
7.0512
7.0512
7,0082
7.0082
7.0062
7 . 00 62
7.0062
7.0082
7.0082
7.0082
6.9652
6.9652
6.9652
6.9652
.6,9652
6.9652
6.9652
6.9652
6.9222
6.9222
6.9222
6.9222
6.9222
6.9222
6.9222
6.9222
6.V222
6.9222
6.9222
6.9222
7.0512
7.0512
7.0512
7,0512
7.2231
7.2231
7.2231
7.2231
7.43B1
7.4381
7.4381
7.4381
7.6961
7.6961
J.6961
7.6961
7.9970
7.9970
7.9970
7.9970
8.2980
6.2960
8.2980
8.5990
8.5990
8.5990
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
6
6
6
6
.. .6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
6
9
9
9
10
11
12
12
n
14
15
15
17
18
^as.
19
21
22
23
24
_25
26
27
28
28
29
29
.0512
.0512
.0512.
.0512
.0512
.0512
.0512
.0512
,0082.
.0082
.0062
.0082
.0082
.0082
.0062
.0082
.9652
.9652
.9652
.9652
,9652
.9652
.9652
.9652
.9222
.9222
,9222.
.9222
.9222
.9222
.9222
.9222
.0512
.3091
.6531
.9540
.5990
.1149
.5449
.9748
.8347
.4366
.0366
.5975
.6294
.4033
.1342
.6221
.0689
.0576
,960.7..
.7776
.3254
.4663
.5612
.5930
.7539
.5706
.3017
.0326
.8925
.4515
.9244
CFOIR
0.0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
..0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0.
0.0
0.0
0.0
0.0
0.0
. 0.0
0.0
0.0
0.0
0.0
0.0
..0,0
0.0
0.0
0.0
0.0
0.0
. 0..0
0.0
0.0
0.0
0.0
0.0
0.0 .. .
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.c
0.0
0.0
CFINT
0.0
c.o
0..0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0005
0.0014
0.0026
0.0037
0.0055
0.0073
0.0089
0.0104
0.0129
0.0150
0.0171
0.0191
0.0220
0.0248
0.0274
0.0298
0.0234
0.0369
0.0401
0.0430
0.0474
0.0516
0.0554
0.0591
0.0621
0.0650
0.0676
0.0702
0.0722
0.0742
O.0759
CFBAS
0.0251
O.0251
0.0251
0.0251
0.0251
0.0251
0.0251
0.0251
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
0.0251
0.0251
0.0251
0.0251
0.0257
0.0257
0.0257
0.0257
0.0265
0.0265
0.0265
0.0265
0.0274
0.0274
0,0274
0.0274
0.0285
0.0285
0.0265
0.0285
0.0295 .
0.0295
0.0295
0.0295
0.0306
0.0306
0.0306
CFTOT
0.0251
0.0251
0.0251
0.0251
0.0251
0.0251
0.0251
0.0251
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0249
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0248
0.0246
0.0246
0.0246
0.0246
0.0246
0.0246
v . 0246
0.0246
0.0251
0.0260
0.0272
0.0283
0.030o
0.0324
0.0340
0.0355
0.0386
0.0407
0.0428
0.0448
0.0485
0.0513
0.0539
0.0563
0.0607
0.0643
0.0675
0.0704
0.0759
0.0800
O.OB38
0.0875
0.0916
0.0946
0.0972
0.0998
0.1028
0.1048
0.1065
-------
c
c
0.0
0.04
0.08
0.12
- 0.16
o
IE 0.20
o
^ 0.24
0.28
2400 -
o
JC
CO
XI
- 1200
o
o
3456
Time (hours)
8
Figure B«3» Acid load for continuous rain
135
-------
meaning; they are meant only to show the data format if the model were
being applied to a specific refuse pile.
At the present time there is not sufficient data available to test the
model. The data lacks in length of record and in determination of acid
production parameters. A discussion will follow shortly giving what
data is available and what data is yet needed. Therefore, for now,
hypothetical data had to be applied (see topic on "Synthesized Data"
later in this appendix). This synthesized data has no valid meaning,
the purpose being to test and see that the computer program functions
and that reasonable results can be obtained.
Three types of rain period, long drought followed by a long continuous
rain, short drought followed by a long continuous rain, and a nonuniform
rain, which would show that the model was working correctly, were
applied. In each case, the acid load and stream flow hydrographs were
plotted. The refuse model will print in tabular form the associated
points (see Table B.13, Specific Day Output) for the hydrographs.
Later, if desired, a subprogram could be incorporated to plot the curves
using the IBM 1620 plotter. The first case was to find the acid load
by 15-minute intervals if a long continuous rain was applied to the
refuse pile preceded by a long drought. The selected storm was plotted
along with the acid load curve in Figure B.3. The result appears to
follow the expected trend. The load would increase to a maximum value
and remain constant, provided the mantle were not depleted of acid.
The second case was to find the acid load if a long continuous rain
were applied to the pile, with only a short interval since the last
rain. Figure E.h shows the results of a short interval continuous rain.
Again the acid curve responded as might be predicted, in that it peaks
and then falls off rapidly, a result of the preceding rain washing out
most of the acid products.
The third test was to find the acid load produced by a nonuniform rain
of short duration, as shown in Figure B.5. The acid load curve appears
to give the results as would be anticipated. Thus, it is felt that the
refuse pile model should be capable of reliably determining the acid
load from a refuse pile. The lack of field data with which to test the
model makes validation of the model structure impossible at this time.
Although the assumption of constant values of ACDPRO, DEPTH, and SOLACD
(see Table B.2) may appear to be oversimplifications, it is recommended
that initial calibrations, when more complete field data become avail-
able, be attempted using the Refuse Pile Model variable definitions as
defined in the preceding pages. If sufficiently accurate calibration
is not possible, then the modified version of the Refuse Pile Model,
referred to as the Combined Refuse Pile-Strip Mine Model (CKPSMM), is
recommended. The CRPSMM modification of the basic Refuse Pile Model is
described in a later portion of this appendix.
136
-------
^ 0.00
> 0.02
0.04
0.06
0.08
0.10
_c
.£
"o
M-
o
cr
8 10 12 14 16 18
Figure B.4. Acid load for short interval continuous rain
137
-------
^ 0.02
- 0.04
c
_ 0.06
0.08
oc
12 16 20 24 28 32 36
Time (hours)
Figure B.5. Acid load for nonuniform short duration rain
138
-------
The factors in the Refuse Pile Model should be set equal to unity and
when sufficient field data is available the factors can be adjusted
accordingly. With each experimental pile, the factors can then be set
into general classes so that, eventually, the model will be able to
predict the acid load based only on physical observations. Until that
time, general guidelines will be given for each factor. The factors
are listed below.
A detailed discussion of each of the factors will follow:
FACDEP - Factor for depth of outer mantle
FACDIR - Factor for amount of acid going into direct runoff
FACFB - Factor for amount of water coming from baseflow
FACFD - Factor for amount of water coming from direct runoff
FACFI - Factor for amount of water coming from interflow
FACINT - Factor for amount of acid going into interflow storage
FACLZ - Factor for amount of acid going into lower zone
FACRDS - Factor for amount of acid going into deep storage
FACREB - Factor for amount of acid going into channel by
baseflow
FACRED - Factor for amount of acid going into channel by direct
runoff
FACREI - Factor for amount of acid going into channel by
interflow
FACUZ - Factor for amount of acid going into upper zone
The factor FACDEP is used to vary the amount of acid being produced in
the outer mantle. The acid production rate was from a surface experi-
ment and thus expresses a rate based on the unit depth. It is known
that the production rate changes with depth, but in this model the rate
was assumed constant through the outer mantle. Therefore, depending on
the depth of the outer mantle, FACDEP should be increased to reflect
the fact that more or less acid is being produced. If enough field
data is available, this factor could be determined by looking at a long
continuous rain that would wash all the products out of the pile. If
the synthesized model runs out of acid products before the field data
then the factor FACDEP should be increased.
The four factors FACDIR, FACINT, FACLZ, FACUZ all affect the amount of
acid being taken by the precipitation into the four areas of direct run-
off, interflow storage, upper zone and lower zone. If the pile is the
average condition of the watershed, then the four factors might be
equal to unity, but if this is not the case, the factors must be
greater or less than unity. These factors involved the amount of acid
transported to the four areas of the refuse pile. If, by field inspec-
tion, it is felt more water is going into one of the zones than the
average condition of the watershed, then that factor should be in-
creased. If the opposite is true, then the factor should be decreased.
139
-------
Until ample true field data is available it would be best to set the
factors equal to unity. Once actual detailed data is available the
factors can be adjusted to reflect the true case.
To adjust the amount of acid leaving the pile by the four routes of
direct runoff, interflow, baseflow and deep storage flow, four adjust-
ment factors have been included FACKED, FACKEL, FACREB and FACROS.
These factors are dependent on the location of the refuse pile with
respect to the receiving stream. Once adequate field data is available
these factors can be adjusted to reflect the variable situation. If,
by looking at the simulated acid hydrograph and the actual acid hydro-
graph obtained from a field refuse pile, it is noted that the simulated
acid hydrograph's peak is not high enough, this would indicate more
acid needs to be coming off in direct runoff, so FACRED would have to
increase. FACREB would have to be increased if the simulated curve
has less baseflow than the actual refuse pile. If as time increases it
is noted that the simulated curve lags the true curve, FACREI should be
increased. As an alternate, if the curve still is lagging, the factor
for deep storage flow would have to decrease. If the reverse case is
found for any of the preceding conditions, the factors should be
adjusted accordingly.
The actual flow from the pile has three factors for adjustment. The
factors FACFD, FACFI, and FALFB affect the flow coming from direct
runoff, interflow, and baseflow. Again the actual and simulated hydro-
graphs can be constructed and compared. The adjustments are the same
as was outlined for the factors affecting the acid leaving the refuse
pile.
Once these factors are set for a pile, the pile can simulate any condi-
tion desired.
A brief summary of the information required to use the model follows:
1. The streamflow simulation of the watershed from the
Stanford Watershed Model.
2. The acid production rate.
3. Depth of the outer mantle.
4. The area extent of refuse pile.
5- The solubility of acid products.
With this data the Refuse Pile Model can simulate the acid load from a
refuse pile. There are 12 adjustment factors in the model so that when
sufficient field data is available the simulation can be adjusted until
acceptable synthesis is obtained.
140
-------
DATA FROM THE STANFORD WATERSHED MODEL
At the present time the Stanford Watershed Model has been tested using
data obtained from the North Appalachian Experimental Watershed located
near Coshocton, Ohio. This data is commonly known as the Watershed 9U
data. Since this data was available it was chosen to be used as the
input hydrologic data into the Refuse Pile Data. Because of the length
of data (5 years) the input data will be kept on a 9 track magnetic
tape. The tape label is APRPM1 and the slot number is Mill.
The following will tell exactly what program statements in the Stanford
Watershed Model must be added or deleted. Three new JCL card must be
added after JCL statement number SM0010. (Reference 10 Part II)
JCL cards are:
//Go.F To 3F001 DD DSN = STANDATA, UNIT = T360, LABEL = (l,SL),
DISP = (NEW, KEEP),
// VOL = (PRIVATE, RETAIN, SER = APRPMI),
// DCB = (RECFM = FC, LRECL = $4, BLKSIZE = 3360)
In subroutine DYLOOP the following changes must be made:
Statement Change To
0983 If(j.EQ.I. and .0023.EQ. l) go to 55555
0984 Delete
0985 Delete
0986 Delete
098? Delete
0988 55555 DAY = MDD(I, DDLM)
1000 Write (3,129) DDYR1, FA, DAY, J, DD23, PR, ENTRUZ, ENTRLZ,
RGX, OVFLST, DIRRNF, INTF, BASFLW, TOTFLW
1001 Delete
LV0120 129 FORMAT (ik, kl2, 9F8.6)
Later two additions should be made:
1. Baseflow should be made equal to GWF.
2. ZTEMP should be added to statement 1000, for temperature
option.
Synthesized Data
The following data was inputed into the refuse pile model in order to
recreate the synthesized data for the three test cases of long drought
141
-------
followed by a long continuous rain, short drought followed by a long
continuous rain, and a nonuniform rain.
In all three cases the hydrologic data was obtained from the Standard
Watershed Model, applied to Watershed 9^, near Coshocton, Ohio. The
following data was constant in each case:
ACDPRO = 210. FACDEP = 1.
SOIACO = 5000. FACLZ = 1.
DEPTH = 11. FACRED = 1.
AREA = 6609666. FACREE = 1.
OPTI = 0. FACREB = 1.
FACFI = 1. FACFD = 1.
FACFB = 1.
Case 1: Acid Load Continuous Rain used the following input data
FACDIR = 1. YEAR 1 = 58
FACINT = 1. DAY 1 = 10
FACUZ = 1. MONTH 1 = k
FACRDS = 0. NDAY = 30
The data plotted was from the twentieth day and twentieth hour to the
twenty-first day and sixth hour.
Case 2: Acid Load Short Interval Continuous Rain used the following
input data.
FACDIR =0.01 YEAR 1 = 58
FACINT = 0.1 DAY 1 = 10
FACUZ =0.01 MONTH 1 = h
FACRDS = 1. NDAY = 30
The data plotted was from the fifteenth day and sixth hour to the
sixteenth day and first hour.
Case 3: Acid Load Nonuniform Short Duration Rain used the following
data.
FACDIR = 1. YEAR 1 = 59
FACINT =1. DAY 1 = 11
FACUZ = 1. MONTH 1=3
FACROS = 0. NDAY = 30
The data plotted was from the twelfth day and seventh hour to the
thirteenth day and nineteenth hour.
-------
REFUSE PILE COMPUTER PROGRAM
C THIS IS THF C^PHTFP pRpr,p*M FOP THF M'-'ULATTriM PF Ann ;tj*'F
_C _ PBO:l_
_ _ _.._ _____- _
C FRPi>> THE PHIP ST/iTF I'l" JVFPS VTY VFHSjni- "nc ~JHF CTAwFuVn S~fiS r.nM^Tonr.TFp AS PART OF
C A WttSTFR THESIS. TH'S IS THP " CF PRII'AP Y" "i<>7? WPP'S IPM'."
C * * » * * * * * w * * * * & * » * a * * if * * * a y * * t * * * * a *
RFAL INTF
».l'''l'>|F_nt Vf_/iRPR_lYf i_P_STtCTl|i^Tt n/1AYtnA_₯TlnTji f,A YFMn
L. 3_LLj-S_L /ICIUiZJ. ilSI«il ~±> 3.U ., S_T SliUXil 5 .SHP .?. LL 2 , 3 L ) _,
2t SIMTI !?,?!) iSSIHTf 12) ,Sa6SI 1.2,^1 ) , SS'^ASI 1. ? ) tr
C lNIT!ALli"fi THF ftMQUMT fiF ACin IM THF FOliP 7PMFS PI.HS THP Tnjjil
C AMPl'lNT PF Affin IM"fhF PILF" """ " " ' "
» _*_*_*_:*_ *.
EXADIR=0.
EXAINT=0.
EXALZ=(U
C
C *************»:;*****#*** ^****v*X:t
i-:. RATF _=
__ _.. . _ _
C ACPPRO ""fw" P('i)>hs riF *cfniT"Y~p>"f< ACKP-HA'Y ""?)" sr>u'aiLiTY HF "*ci"n
_C __ PROniiCTS = SHLACn IM >-'G PFR L ITCR ___ H) nFPTM_ng n.HJFjJ "A'.'TI,F =_
C DEPTH iV>PFT ^) fiPPs HF PPFIISF"""PIL'F = 7.BFA iro"so!i4Q
2001
C
_C S_PFC IFir, RFFMSP P.ILE
BEAD! 5 , ?00? 1 F/SCPFP ,FAC»tR >Ffic T^:T ,FAC17
l,FACRnS»FArFn,F6CFI,FfiCF«
2002 FORMAT!
C
C *********** ***************a*\: ******
C IF YDU "A^T Tn RUM PRPGRs'1 Tn anjHST THF trjn PRonnr.TIPn RiT= ni|c TH
_C _ TEMPERATIIRF CHAMGgS TMPM CALL FPB npTl = ]_. _ LE_vnJ L£* kkTltlS ___
C OPTIPN MAKF SURF THAT YPII PFAP IM THF TF^PFR ATHR = T/ALl'lRS ~V fJH
_C __ THF PTHFB IiMPIIT SflTA FROM THF STAMFPRn i-'ATCPSHFO JlnJlFL_. _ LP._YPL! _
C 00 MPT WISH TP IISF THIS PpflPW THFM LFT nPTl'-=n. ~
C ***********************************
OPT1
2200 FPRMATIF1.0.0)
C
c ***********************************
C CHANGING SPLACH TP PPIINOS PCR CI'RIC FFFT
1 C FACTOR TO CHAMGF I.«CHPS PF RIIMPFF PF aPFHSF PRF TP CimiC FFCT PFR
C SECONO PF RIIMPFF
« C FACTPR T[l CHfl'-T-P INCHES OF RIIMPFF FRPM RFFMSF PTLF TP THRIC FFFT PF
C RUNOFF (RASFO PM 15 ^INHTF INTFBVAL)
i c ***************** ******************
snLACO_
-------
£ **«se*s***«***ae#*«*****»*a********
C THF K'EXT LFAP YC/SP '-'ILL nrr.HR |M '-'HAT MATFH YFAR - t'ST TV"
C nivinFn HY t
C THE START 1ST- i-ATPR YFAR OF TMP IMPIIT HATA FJRO_M_TMF_j;TA_^FriKO__ |j*JF_aSHFO_
C TTrir^fil ~
C »»*«r#»««e«««****6* * <'
c
C *s*e »*«**«»****=fi-
C READING H OeTA FHR SPFf IP If. risY YOU "UAMT OMTpTrr - ' SFT Ff'« fl'''F TI''>F
PFP l-'ATFP YFA^. YPiPt= MATFR YFAR, I'OK TM1 = t'f.MTH, HA Yl = r>_AY_.
c TO S>TAPT'ni'Tpi'T, ^fi/w = ^fiMHFR"oF"r.n^sFr.TivF HAY"; nn OUTPUT
C RFOIIFSTf-n
C THC TI;'E IS H6Sl-n 1^' A '-'ATf^ "YF'AR UHFPC'TMC FIRST i-iiMTH IS
C
C ****** K: *»*';=£*-# *)*£*** V !;:$*##*** :;;fr**A**
9100 RFADI j>t2000) YEAH1 ..^D'-'THl ,
*****
C
; *****«**»*«««*««***
IFIYFaRl .FI.I. n) an Tn o?no
2000 FORMATI^IS)~~
^ ^EA********^**^^****^*******^****^^*
C FOR EACH WATER YE/'H INITII. IZF TMF DAILY, ''HMTHLV, A'-'O YFiRLY V-ALI'FS.
C SET EVERY THTiMf. FOUAI. TO 7F^n
*****:**££ $$$$£S**t:S#*s*##**#*#**:C:<"- **
nAYHMT=l
8900 Dr»AY(
nn. jot
on ?o
ARDI I
ARK I
TACDI
TSTRf
SORRI
SINTI
SBASI
) 1=1,12
t J = 1»M
J)=f).
,J)=0.
t J)=0.
, J ) = n .
, J)=o.
t J)=0.
? j ) =n.
201 ARB( I ,JJ =_0_.
SAD( !')=().
SAH I)=0.
STACPU > = 0.
STSTRII)=0.
SSORR(I 1=0.
SSINK I )=0.
SSRAS(I)=0.
200 SABII)=0.
StlMAn=0.
SUMAJM).
SUKAP=0.
SIIMTA = 0.
SUMST=0.
SHMSR=0.
SUMS 1=0.
si»Msn=o.
***»»»««******«****#«***«*«*«««*«««
-------
C PROCEDURE SO THAT THE EXTRA DAYS IN THE MONTH w T L L CRFATE AM OVFR-
_C FLOW IN THF OUTPUT DATA. HILL ADJUST FOR TMF LFAP YEAR.
C **********************************
I YFARST1/4.
COUNT--0.
7000 1=31
7001 ARD(J, I 1 = 100000000.
ARRIJ,I1=100000000.
...ARI ( Ji 1 1 = 100000000.
TACDIJ,I)=100000000.
TSTRtJ,l1=100000000.
SDRRIJ,I 1 = 100000000.
SINTtJ,I 1 = 100000000.
SBASt J,11=100000000.
COUMT=COUNT+1.
IFICOUNT .P.O. 1.) J = 7
IFICOUNT .FO. 3. } J = 12
IFICOUNT .FO. ?.} J=9
.FO. 4.)
IFICOUNT .FO. 5.) GO TO 700^
IFICOUNT .FO. 6. .AMD. SLYEAR ,EO. YEARLP) GH TO 700?
IF (COUNT .EO. 6. 1 GO TO 7003
IF (COUNT .FO. 7.) GO TCI 7005
GO TO 7000
7004 1=30
GO TO 7001
7002 YFARLP=YFARLP+1.
GO TO 7005
7003 1=29
GO TO 7001
7005 CONTINUE
C
£ ******* * ************************* X:
C READING IN HYOROLOGIC DATA FRO" THF STANFORD i-iaTFRSHFO MODFL.THTs~
_C INCLUDES THE RAINFALL DEPOSITION A^n THF STR FAHFLOV. THF Tli'lE
C IS BASE ON A WATER YFAR IF OCTOBER FIRST TO SEPTEMBER 30TH.
_C THE VARAIBLES ARE THF YEAR = DDYR1, NO^TH = FA, DAY = DAY,
c HOUR = J, HOUR INTERVAL = no?3, THE RAIN = PR IN INCHES, THE
C WATER GOING TO UPPER ZONE = FNTRUZ IN INCHES, THF HATER GOING
C TO LOWER ZONE = EMTRLZ IN INCHES, THF STRF6MFLOH COMING FROM
_C DIRECT RUNOFF = D1RRMF IM INCHES, THF STRFfl MFLQI-' COMING FROM
~C INTERFLO'-' = INTF IM INCHES, THE STRFA^FLO'-! COMING FROM BASFFLOH
_C = BASFLW IN INCHES, AND THF TOTAL STRFAMFLni.i = TOTFLH IN INCHES.
8800 READI3.129I DOYR 1, FA , DAY , J , PD23 , PR , FNTRUZ , ENTRLZ , RGX , OVFI.ST,
1 DIRRNF, INTF,BASFLI<',TOTFLW
129 FORMAT!14,412,9F8.6)
C
r ^c^:^:^5!!;^:^:^;^!iJ;^i^iiJ;^;i;;^;^:^r^;^^'iS'i'":I''!!'v'S^TS^^T'^5{:^=
__ ^^ojyj-fj^Q ACir, PRODUCTION RATE OUF TO TF f/ipFR ATIIR F CHANGF
C TEMPERATURE SHOULD BF IN DEGREES FAHRPNHFIT
~CTHE ADJUSTMENTIS THE RULE OF THU^B THF RATF DOUBLES FOR A 10
tTOIS THE TEMPERATURE AT WHICH THE ACID PRODUCTION RATE WAS
C DETERMINED.
C T IS THE INPUT TEMPERTURE FROM THE STANFORD MODFL
C ***********************************
T0=77_'''-
IFIOPTl -EO. 0.) GO TO 5555
GO TO 5556
-------
c
c
c
c
c
c
c
c
c
c
***********.*************
IF CK=1. THEN THE ACID PRODUCTION IS MOT BFING
TEMPERATURE CHANGES
5555 CK=1.
5556 ACDPRO=ACDPRO*C.K
* * *
********
ADJUSTED FOR
* * *
***************************
TIME IS 15 MIMUTFS OR 0.?5 HOUR. MUST CORRESPOND WITH
INTERVAL FROM THF STAMFORD WATFRSHFD MODEL
******************** * * * *
* * *
********
********
THE TIME
********
TIME=0.25
IFtPR'.NF. 0.0) TIMF=0.
C
C
c
c
c
c
c
c
**************** X= * * * * * * *
CALCULATING THE AMOUNT OF ACID BEING PRODUCED
AMTACD=ACOPRO*T]|v!E*ARFA*DEPTH*FAf,nEP/( 74.
****************** * * * * * *
CALCULATING THE AMOUNT OF ACID BEING RFN'OVF DIIR
********* X; * * * * * * * * * * * * * *
ACDDIR=FACDIR*SOLACn*OVFLST*CF
* * *
*435
* * *
IMG THF
* * *
,3,,,*****
********
on. ) +AMTACD
PRECIPITATION
********
ACDINT=FACINT*SOLACn*RGX*CF
ACDLZ=FACLZ*SOLACn*FNTRLZ*CF
ACOUZ=FACUZ*SOLACD*FNTPI'Z*CF
_ = AMTACD-ACniNT-ACDLZ-AC.nuZ-Ar,DDTR
IFITOTAL .LE. 0.01GO TO 60
* * * * * * * * * * * * * x
STORING ACID IN FOUR ZONFS
***********
EXADIR=ACnDIR+FXAnlR
EXAINT=ACDirvT + FXAI
EXAUZ=ACOUZ+EXAUZ
C **********
C REMOVING THF ACID
C CHECKING TO MAKF SURE THFRF IS ACID TO RF RFMOVFD
C ************* * * * * * * * ********
*******
60 IFIDIRRNF .EO. 0.0) C
AREOIR=DIRRNF*SOLACD*
in 22
IFIEXADIR
IFIEXADIR
.LF.
.LF.
0.)GO TO ?l
AREDiR) ARFDIR=FXADIR
' EXADIR=EXADIR-ARFDIR
GO TO 23
21 IF(FXAUZ
IFIEXAUZ
.LE.
.LE.
0.) GO TO 22
ARFDIR) ARFDIR=FXAU7
EXAUZ=EXAUZ-ARFDIR
GO TO 23
22 AREDIR=0.0
23 IF1IMTF .EO.
0.0) GO TO
AREINF=INTF*SOLACD*FACPFI*CF
IF(EXAINT .LF. 0.) GO TO 31
IFIEXAINT .LE- AREIMF)
EXA I MT = EXA INT-ARE INF
ARE I
INT
GO TO 30
31 IFfEXALZ .LE.
0.) GO TO 32
1FIEXALZ .LE. ARF.INF)
EXALZ=EXALZ-ARF IMF
ARFIMF=EXALZ
-------
GO TO 30
32 AREINF=0.
30 IFfBASFL!' . EO. O.u) GO Tf)
..
IFCEXALZ .16. n. ) (:.'! TO ^3
IF( EXALZ .LE. ARFfrFL 1 ARESFL=EXALZ
EXALZ=EXALZ-AREHFL
GO TO 40
A3 AREBFL=0.
40 IFUNTF .P.O. 0.0) On Tn 51
IF(EXALZ .L5. 0.) PO T^ 52
IF(EXALZ .15. ARFfVSR)
EXALZ=EXALK-ARFDS"
GO TO 51
52 AREDSR=0.
FINDING THE DAILY
51 CFDIR=OIRR''F*CFS*FACFn
CFINT = Ii-ITF*CFS*FACFI
CFRAS=K.ftSFLM*Cf:S*F/ir.F:-;
ARETOT=AREO IR + AkE II (- + /),
ARD( FA>nAYigAP.FOIP-!-ARI;
ARI ( FA , DAY ) =AUE II !--I-AK ! ( F A , n/\y )
ARB( FA,QfiY) = ,tRr--PAY)=r.FIf T-i-SIl ~( F'-.,n/-Y ) _
SnRR(FA,nAY)=Ci-DiI!-!-S '(: (FA, "AY)
TSTR( Fft,OAY)=C-Tf.T-i-TST!) (F.SD'''.Y ) _ ___
T AC D ( F A ,nl>. F. :) I f- +*> i-. p I :'- H + .-> I-' - 1-; h L + T/>. r. r, ( F / , r. A Y i
65 IF1YFAR1 .FO. PI1YK1) Gr Tn 1?0
GO TO 100
C
{^ & :|; ;|: =;= ;;; ^s ;;; i|; ;|: =;; % ;,; >','- ;]; ;]: ;;: ',: & :|: >;; :J; X* -!- :l:
C CHECKIIvG IF THIS IS SPECIFIC OAY TO BE "HTPUTEn
120 IF(Kini\:THl .EO. FA .OK. PAYOUT .GT. 1) Gn TO i. ?. n
GO TO 100
130 IFfnAYl .EO. OAY .PP.. iVYPUT .^T. 1) <~-r Tn
GO Tn 100
131 IFIDAYOUT .En. 1]
C CHECKING IF THIS IS THE EW OF T]-|E SP-CI-!
£ % :£ ^: ^: ;;: X: £ & * # :r= # :l- :!: -!: :i- # :l; -! =o =i:
IF( DAYOUT . GT. HAYENf)) Gn TO 100 "~
3030 FORMAT! '1 ",94H YR .'H DY SR PO AnE'Ur A
1TOT CFOIR _ CFH-'T _ C F F. A S _ CFTfTl
_ _ _
WRITE! 6,3031) nr>YR 1 , FA ,n.f Y, .1, fin 2? , ARFD I P , A^cT N'F , AH Fn-FL , ARETOT , CFD
lIR,CFIilT,CFP.AS,CFTPT
3031 FDRMATC ' , 5 ( IX , I 2 ) , C ! 1 ;' , F9 .4 ) )
100 YFA.RPR = YEARST+1
IFfYEARPR .Efi. nfmu .Al:n. FA .50. i) r,n Tn
cn Tn fiaoo
c
(; #*
-------
8000 DO 700 1-1,17
on 701 j=i,3i
IF(ARDd.J) .EC. lOOOOnOOO.l GO TO 70?
SAOI i > = ARm i ,j i+SAni i i
SA1I 1 i-ARl I 1. J)+SAI( 1 )
SABI I ) = ARRI I , J 1+SARI I )
SSRASI ! >=SRAS( I , J) +-SSB4M I )
SSINTI 1 ) = SIM( ! Jl+SSIMTI I )
SSORRI I ) = Sr>RR( I ,J)+SSr>PP( I )
STSTR(I)=TSTR(I,J >+STSTP(!I
STACO(I)=TACO(I,J)+STACD(I)
702
701
CONTINUE
CONTINUE
SUMA1=SAI(I)+SU"AI
SUMAR=SAR(
SUMTA= STACD( I
SIIMSR=SSBAS( I
suMsn=ssnRR ( i
+SUMTA
lll^ll
+ SI K-: SI
700 CONTINUE
£ * * ***********##** ** * --- .;«******* ** ** *
C OUTPUT ING THF * HA ILY T^RLPS PL"S THP v>> ft^LY SM^MARY
********** ******#***«-£*************
HRlTf=( 6.B012I YFARST,YPARPR __
_
WRITF!6i3003)
3003 FnRfJATI' , 3fiX.
THFS I ZFH
LOAn Jf-i
RIIMflFF IM pnilNOS
1)
WRITFt 6,30131
on 300 1=1,31
WRITEI6.3011) nnAY(I),(ARn(J,I),J=l,l?)
300 CONTINUE
WR1TFI6,3012) YFARST,YF4RPR
WRITF(6,3002 )
300? FORMAT!' ' , 39X , 4AHS YMTHFS 1 ZFO ACTO LOAD
TMTFRFLOl'i IM PntlMQS)
WRITF.I6, 30131
nn 301 1 = 1,31
_ ____
WRITF(6,3011 ) DDAYf I),URI(J,I>,J = 1,
301 CONTINUE
WRITF.16, 3012 ) YEARST , YF ARPR
3001 FORMAT!' ', 39X , 43HS YKTHFS I ZFD AGIO LOAD IK' RASFFLOW IN POUNDS)
WRITF(6,3013)
00 302 1=1,31
WRITF< 6,3011 I
I1,(ARR(J,I),J = 1
302 CONTINUE
HR1TF(6,3012) YFARST , YF ARPR
_ _ _______
WR1TE16, 3004)
300A FORMAT1' ' , 42 X. 37HS YNTHFS IZFD TOTAL ACin LOAQ IN POUNDS) _
KRITf{6, 3013)
_ DO 303 1 = 1 ,31 _ _________ _
WRITE (6, 3011 ) DRAYI I ) , ( T ACH ( J, I 1 , J= 1 , 1 ? )
303 CONTINUE _ _ _ ___ _
WRITE (6,3012) YFARST , YFARPR ~~~~ ~
_ WRITFJ6.3006) _ _____ _
3006 FORMAT!' ' , 35X , 50HS YNT HES I ZED DIRECT RUNOFF IN CUBIC FEET PER SECO
1ND)
00 305 1 = 1,31
148
-------
WRITF(6,3020) DDAY! I ) , ISDRfU J, I ),J = l,1?)
305 CONTINUE
WRITF(6,3012> YEARST,YFARPR
WRITF(6,3007)
3007 FORMAT!' ' , 37X, 46HSYNTHFSI ZFD INTFRFLni-' IN CUP 1C FFF.T PER SECOND)
WRITE(6,3013)
DO 306 1=1,31
WRITF! 6,3020) ODAY! 11, ISINT!J,I ), J=l, lj>J
306 CONTINUE
WRITF! 6, 301?) YFARST.YFARPR
WRITF(6,3008)
3008 FORMAT!' ' , 37X, 45HS YNTHFS IZFD PASFFLO" IN CUBIC FFFT PER SECOND)
WRITF(6,3013)
nn 307 1 = ),31
WRITF(6,3020) nDAYII).I SBAS(J,I),J=1,1?)
307 CONTINUE
WRITF(6,3012) YFARST.YFARPR
WRITFI 6,3005)
3005 FORMAT! ' ' , 37X ,47HS YMTHFSI ZFD STRFAMFLOl-i IN r.URIC FFFT PFR SECOND)
WRITF(6,3013)
00 304 1=1,31
WRITF(6, 30?0) DDAY I I ) , ( TSTR IJ , I ), .) = ! , 1 ? )
304 CONTINUE
WRITE! 6,3012) YF ARST , YPARPR
WRITF(6,4005)
WRITF(6,4005)
4005 FORMAT!'-',3X,3HOCT,6X,3HNOV,6X,3HDFC,ftX,3HJAM,6X,3HFFR,6X,3HMAR,6
1X,3HAPR,6"X,3HMAY,6X,3HJUN,AX,3HJUL,6X, 3HAUG , 6X , 3HSFP, 3X, 10HYFAR TO
2TAIJ
WRITFI6.4000)
WRITF! 6,4000)
4001
4004
4006
4007
4008
4010
4011
4012
7
t 3011
3012
s
3013
4
3020
, 4000
4002
4009
9000
9200
WRITF(6,4001)
FORMAT 1 in'. 4RHSYNTHFC;T7Fn
WRITF(6,4002 ) (SAD! I ) , 1 = 1,
WRITF(6,4004)
FORMAT! '0' ,44HSYNTHF.S I?FD
WRITF(6,4002)
-------
DESCRIPTION OF THE COMBINED REFUSE
PILE - STRIP MINE MODEL (CRPSMM)
The Refuse Pile Model described in the preceding sections is intended
for use in cases where there is a high rate of acid production at the
surface of a refuse pile, or strip mine spoil bank,, In cases where
acid production rates are relatively low, or where acid producing
strata may lie buried beneath a layer of relatively inert material,
then the simplifying assumptions of the Refuse Pile Model relating to
acid production and acid removal rates may not be sufficient to allow
calibration of the model within the limits of accuracy required. For
such cases, the Combined Refuse Pile - Strip Mine Model has been
developed. The CRPSMM differs from the Refuse Pile Model primarily in
the handling of acid production and acid removal simulation, with these
refinements superimposed on the basic Refuse Pile Model. For a more
detailed disucssion of the CRPSMM, the reader is referred to Maupin.19
ACDPRO Program Description
So that the Refuse Pile Model may be extended to include the simulation
of strip mined areas and refuse piles, and to provide for pyrite
oxidation rate-determining factors other than temperature, the sub-
routine ACDPRO has been developed to replace the constant acid produc-
tion rate used in the Refuse Pile Model. A second major modification
in the acid removal simulation will be described later.
From the standpoint of precise simulation, an ideal approach would be
to use a three-dimensional finite difference unsteady state model of
oxygen diffusion and reaction in the spoil or refuse. However, the
computer program for such a model would require inordinately long com-
puter run times even if adequate soil profile information were available
to build and adjust such a model.
The alternative chosen for this study is a steady-state model of oxygen
diffusion and reaction in a column of soil of unit surface area, with
diffusion constrained to the vertical direction only. By measuring the
surface areas of a representative acid producing region in a watershed,
and multiplying the areas by the appropriate specific acid production
rate (corresponding to similar soil columns), an adequate estimate for
the entire composite area can be calculated. The assumption of steady-
state is considered to provide a sufficiently accurate estimate of the
average acid production rate since, in the simulation, acid production
is stopped during periods of rainfall, and the error of stopping the
reaction too soon (before rainfall infiltration lowers oxygen diffu-
sivity and stops the reaction) is somewhat balanced by the error of
restarting the reaction too soon (before the soil moisture has drained
sufficiently to allow oxygen diffusion again). The assumption of oxygen
diffusion in the vertical direction only is justified since the areas
150
-------
to be modeled are large (usually several acres in size) and can be con-
sidered as infinite plates on which the edge effects may be neglected.
ACDPRO is the computer subroutine developed to model the acid production
of a generalized column of soil as shown in Figure B.6. The generalized
column is divided into two sections, a pyrite layer overlain by an
inert soil layer, which may or may not be present. The basic strategy
of the solution is to find by iteration of steady state oxygen concen-
tration at the interfacial boundary between the two layers (XA ) which,
in turn, allows calculation of the rate of reaction in the reactive
layer. This is possible since at steady-state the rate of oxygen dif-
fusion through the inert layer is equal to the rate of pyrite oxidation
in the pyrite layer. In the special case of no inert layer, the known
atmospheric oxygen concentration at the air -pyrite interface again
allows computation of the overall oxidation rate.
For the pyrite layer, the equation of continuity (Bird et al.^0) in
cylindrical coordinates is
RA
where C/\ = the concentration of oxygen (m/^3)
r = the radial dimension (z}t
9 = the angular dimension (it,},
z = the vertical dimension (j),
v = the bulk gas velocity ($/t),
DA-D = the diffusivity of 02 in the other
gases present (^2/t), and
R = the volumetric generation term
for oxygen
By applying the assumptions of steady-state diffusion in the vertical
direction only, all derivatives with respect to time (t) and the angular
and radial direction ($,} are set equal to zero. Since diffusion is
through a porous solid, an effective diffusivity (Deff ) is substituted
for DAB and the first order specific reaction rate equation (Ae~^E/-R-C'cA)
is substituted for RA. Equation (B.22) then becomes
151
-------
Ground Surface
Z = 0
for equation (B.28)
Z
neg.
INERT
LAYER
PYRITE
LAYER
Figure B.6. Soil column
152
-------
dC d?C -^
A A TRT
Yz "17" = Deff ~fl7~ + Ae CA (B.23)
which is a second order differential equation with a variable coeffi-
dCA
cient vz. The term vz accounts for the bulk flow of oxygen through
Q.Z
the reaction layer (this is also known as enhanced diffusion). A
finite difference solution of equation (B.23) has shown that the
enhanced diffusion term accounts for approximately 20% of the total
reaction rate for the Column. This error is decreased if the upper
surface of the pyrite layer is not exposed to the full atmospheric
oxygen concentration. If the enhanced diffusion term is dropped, an
analytical solution of equation (B.23) is made possible. From a prac-
tical standpoint, this is fully justifiable since the error thus intro-
duced can be compensated by using a higher diffusivity or higher
reaction rate constant and in any case the program variables must be
further adjusted to simulate any available recorded data when the model
is applied to a watershed. The simplified equation becomes
(B.2U)
The analytical solution to this equation is given below along with an
approximate solution (equation (B.25)) which will be used in this work.
Equation (B.2U) can be rewritten as
CA = 0
since the reaction term for oxygen consumption is negative and where
f> ~RT ,
or is Ae /Deff
The general solution to equation (B.2U) is
CA = Cxe02 -i
153
-------
If the constants of integration GI and C2 are evaluated using the
boundary conditions
CA = CA2 at
dz
= 0 at z =
the solution is
If instead the boundary conditions are approximated as
dx
= 0 at z = -c
the solution is
CA = CA2 e02 (B.25)
This approximation is much more readily handled by hand calculation or
in an iterative computer solution, and has a maximum error of 17^>.19
This approximation is justified since the model must be adjusted to the
acid production area based on field data.
The description of diffusion through the inert layer is based on the
equation for diffusion through a stagnant gas film given by Bird
et al.20
c DAB(XAI - xA2)
where NAg = ^e rate of mass transfer through the gas film,
c = the total concentration (ib. moles/ft3),
-------
mo^-e fraction oxygen in the atmosphere,
XA2 = "the mole fraction oxygen at the interface,
(Za-Z],) = gas film thickness (ft)
B2 "" "^"Bl
(Xg) = - -j r = log mean mole fraction of all gaseous
Hm i B^ i components other than oxygen
\XB1/
Xg2 - 'the mole fraction of other gases at the
interface , and
Xg-j_ = the mole fraction of other gases at the surface.
It should be noted that this equation accounts for the enhanced dif-
fusion of oxygen in the inert layer.
Again an effective diffusivity Deff is substituted for D^g and Z]_ is
substituted for (Z2 - Zx) in equation (B.26), giving
c Deff(XA1 - XA2)
At steady-state NA2 is equal to the rate of oxygen consumed in the
pyrite layer for a soil column of unit area. The consumption rate in
the pyrite layer can be calculated independently by integrating equa-
tion (B.25) over the thickness of the pyrite layer,
f2
= kj c XA2 e
= k c XA2
Jeff
(B.28)
thereby allowing for the solution of XA2 by iteration. An initial
estimated value of XA2 is assumed and RAZ is calculated using equation
(B.28). RAAZ is set equal to the flux NA£ and a new value XA2 is cal-
culated by equation (B.27). If the estimated and calculated values of
155
-------
X^2 are not equal, an improved estimate is calculated based on the
Wegstein convergence method as given by
X(n-l)*Y(n) - Y(n-l)*X(n)
x(n-l) - X(n) + Y(n) - l(n-l)
where X(n+l) - the improved estimate of
X(n) = the current estimate of
X(n-l) = the previous estimate of
Y(n) = the calculated value of X^2 using
estimate X(n), and
Y(n-l) = the calculated value of X^2 using
estimate X(n-l).
The computer listing of ACDPRO is given in Figure B.7, and a flow chart
of the program is given in Figure B.8. It should be noted that if there
is no inert cover the program solves directly for the oxidation rate
using equation (B.28). After the interfacial mole fraction (Xjy?) is
calculated the amount of acidity produced is computed, together with
the mole fraction of oxygen at the lower surface of the pyrite layer .
DO, an input variable having the dimension of length, is then introduced
to separate the acid produced into two layers, a top layer which can be
leached by direct runoff, and a lower layer which is leached by water
going to interflow or baseflow only. The calculation of the rate of
acid production above DO is calculated by setting Z2 equal to the depth
of pyrite above depth DO and solving equation (B.28) using the calcu-
lated interfacial mole fraction (X^g)- Tne acid production rate below
DO is then obtained by difference .
By using this simulation program, acid production can be made responsive
to changes in the following variables :
(l) Depth of inert cover
(2) Thickness of pyrite layer
(3) Diffusivity of both pyrite layer and inert layer
(h) Soil temperature
(5) Total pressure
(6) Reactivity of pyrite
ACDPRO inputs and outputs are listed in Table B.l^. The inputs R and
DBOR are known. Z1} Z2, P, T, and X^-j_ can be measured in the field and
adjusted if necessary. The variables DOZ, DOZA, A, and DO will probably
156
-------
c
c
:
910
ACID PRODUCT IftM SUPROUTJME
SUBROUTINE ACPPRO
= ,NR, APO
DIMENSION! XA(25), YAI25)
ZI=-Z2
C=P/(R*T)
Y1=A/EXP(DEOR/T)
XB1=1.0-XA1
MC = 0
Z=SORT( Yl/nOZA)
DIFF=0.
!F( Zl. LF..OOODGO TO 10
920 XB2=1.0-XA2
925 XRN-(XB2-XBll/ALnGIXB2/XRl
RA=Y1*XA2*C/Z
RAZ=RA*RA3
XA2N=(C*DOZ*XAl-( Z 1 )*XRN*R4Z )/(C*Dn7! )
X = XA2
Y=XA2M
JFIABSI(X-Y1/IX+Y)1.LT..1E-9)GO TO 6
IFCK'R.GT.^OIGO TO 6
IF(NC.LE.l) CO TO 5
' )l.LT..1E-91GO TO 6
XT = ( XAl KR )*Y-YA ( N'R ) *X ) / ( X A ( MR ) -X+Y-YA (f-'R ) )
NR=W+1
XA(NR)=X
YAINRI^Y
XA2=XT
GO TO 920
10 XA2N=XA1
XA2=XA1
RA=Y1*XA2*C/Z
RA3=1. 0-EXP(Z~:ZI
RAZ=RA*RA3
GO TO 6
5 XA(NR)=X
YA(N'R)=Y
XA2=Y
NC=2
GO TO 920
6 XAg=XA2M
AP=RAZ*55.7
lF(nn-zii?on>2no,2in
zoo APO=O.
GO TO 220
210 ZO=PO-Z1
IFtZn.GT.Z? )7.0=72
zn=-zn
220 API=AP-APO
JFfZl.LF. .0001 )T,0 TO 20
20 XA 3 =_XA 2<-f;XPIZ-ZI )
"
looi REURN
END
Figure B.7. ACDPRO Program listing
15?
-------
CRPSMM COMMON
,Z2>P,R,T,IX)Z,DOZA
INITIAL CALC.
C = P/(R*T)
Z = (Y1/DOZA)1/J
Zo. = -Z2
DIFF = 0.
NR = 1
NC = 0
XA2 = .10
X = i.o - X
B2
XBN =
" X
A2
RA = Y1*XA2*C/Z
RAZ = RA * R
Ao
C*DOZ*X
AI -
C*DOZ
X =
Y =
IF
XA(NR) = x
YA(NR) = Y
*A2 = Y
NC = 2
FIRST
ITERATION
ONLY
IF
CONVERGENCE
XR =
XA(NR)*Y - YA(NR)*X
XA(NR) - X + Y - YA(NR)
NR = NR + 1,XA(NR) = X,YA(NR) = YjX^a = XT
Figure B.8. ACDPRO flow chart
158
-------
Figure B.8. Continued
159
-------
Table B.lA. ACDPRO PROGRAM INPUT AND OUTPUT
ACDPRO INPUTS
Zi Inert layer thickness (ft)
Z2 Pyrite layer thickness
P Pressure (atm)
R Gas Law constant
T Temperature (°R)
DOZ Diffusivity of inert layer (ft2/hr)
DOZA Diffusivity of pyrite layer (ft2/hr)
A Frequency factor of Arrhenius form (hr-l)
DO Depth washed by direct runoff (ft)
XA1 Mole fraction of oxygen in atmosphere
DEOR r of Arrhenius form
K
ACDPRO OUTPUTS
XA2 Mole fraction of oxygen at inert-pyrite interface
X^o Mole fraction at lower boundary of pyrite layer
AP Total acid production rate per hour (as Ib CaC03)
API Acid production rate per hour below DO (as Ib CaC03)
DIFF Final difference between flux through inert layer and oxygen
consumed in the pyrite layer
NR Number of iterations
APO Acid production rate per hour above DO (as Ib CaC03)
160
-------
have to be adjusted until the model simulates known data but laboratory
tests on soil from the site may provide initial trial values. The
errors introduced by the approximate iterative solution can be compen-
sated for and the method is considered adequate and more practical than
a more exact (but computer time consuming) method since the model must
be calibrated against field data in any case. The use of ACDPRO by
CRPSMM will be described in the following section.
CRPSMM PROGRAM DESCRIPTION
The Combined Refuse Pile - Strip Mine Model (CRPSMM) is a modification
of the Refuse Pile Model previously presented and can best be described
by comparing the CRPSMM with the original program (attached as Refuse
Pile Computer Program). CRPSMM consists of four parts: an ACDPRO sub-
routine described earlier, two other subroutines termed ACDSEC and
ACSTR, and the main program of the Refuse Pile Model as modified to
accept the three above named subroutines.
ACDSEC, along with ACDPRO, replaces the constant acid production rate
used by the Refuse Pile Model. For each acid producing area in the
watershed the ACDSEC subroutine inputs the parameters which describe
each area to ACDPRO, which calculates the acid production rate for that
area only. These individual acid production rates along with the soil
volume above the DO line are available to the main program through a
common storage. Figure B.9 is a listing of the ACDSEC subroutine.
ACDSTR is a subroutine which, when called, prints for each acid pro-
ducing area the amount of acid stored in the watershed and the amount
of acid removed during the simulation period. There are six storages
for acid in the watershed and four flows for acid removal. The sub-
routine subdivides each of these into substorages and subflows corre-
sponding to the individual acid producing areas. The ten variables
output by ACDSTR are described below and have a subscript identification
which corresponds to the numbering of the acid producing areas.
AMTACU - acid stored in soil above DO line (ib)
AMTACL - acid stored in soil below DO line (ib)
EXADIR - acid dissolved in direct runoff storage water (ib)
EXAUZ - acid dissolved in upper zone storage water (ib)
EXAINT - acid dissolved in interflow storage water (ib)
EXALZ - acid dissolved in lower zone storage water (ib)
ARDIRT - total acid removed in direct runoff (ib)
ARINFT - total acid removed in interflow (ib)
ARBFLT - total acid removed in baseflow (ib)
ARDSRT - total acid removed to deep storage (ib)
The above variables are all cumulative amounts, updated for each time
increment (15 minutes, normally) in the SWM. A listing of the ACDSTR
161
-------
C ACID PRODUCTION SECTION
C
SUBROUTINE ACOSEC
PI T^
COMMON/ANM2/Z1 ,12 ,P,R , 1 ,D02 , A ,00, X Al , DEOR , D02 A, XA 2, XA?, AP, API,DIFF
, NR , APQ ____ __ ________ _ _ , ___
1 FORMAT! 5F12. 6)
4 FQRMATi ' n APQT _ APIT __ APT! )
6 FORMAT! '0 THE HOURLY ACID PRODUCTION CALCULATED IS1)
APT T=nTn
APOT=0.0
A1D=0.
Z1=APD(1,1)
-Z2=APD4-U-2-4-
DOZ=APDF1 n.4,Fin. 1 ,F1 g^A)
D0420I=1,N
HR1TE(6t_5)I , ( APD ( T f .1) T.I = R , 1 4 1
RATE=APOT/A1D
WRlTE(6.b_L&PT.APnT.APIT.A1D.RATF
FORMAT{'OTOTAL WATERSHED ' ,F7.3,2F10.3,F10.0,F12.7)
RETURN
END
Figure B.9. The ACDSEC Subroutine Program
162
-------
subroutine is given in Figure B.10, and the main (CRPSMM) program list-
ing is given at the rear of this appendix. All lines which have been
modified or added to the Refuse Pile Model are identified with the
initials ANM and a card number on the right hand side in columns 73 to
80. Internal variables are defined in Table B.15. Lines 1 through 57
provide common storage for variables (shared with ACDPRO, ACDSEC, and
ACDSTR), initialize default values, and read in and print out the input
parameters to the model. These input parameters are defined in Table
B.l6. Many of the input parameters are subscripted so that each indi-
vidual acid producing area of the watershed is treated separately. The
use of individual calculation of acid production and acid removal for
each area of the watershed that differs in inert cover thickness, pyrite
thickness, diffusivity in pyrite or inert cover layer, reactivity of
pyrite, and the depth leached by direct runoff allows much flexibility
of the model. Each area of the watershed that differs significantly
from any other area in any of the above six parameters is handled
separately. Areas that are not adjacent but are not significantly dif-
ferent should be combined as a single effective area since the model
can not differentiate on basis of location within the watershed. The
choice of size and numbers of effective acid producing areas must be
based on a site inspection and laboratory analysis of parameters such
as soil diffusivity, pyrite reactivity, and pyrite location in the soil
column. The final choice of areas should be based on the accuracy of
simulation required. For some uses one or two areas would be adequate,
but in other situations further subdivisions might be made.
Line 58 calls subroutine ACDSEC, which operates as described above.
Lines 59 to 63, 7^ to 8U, and l8l to 19U control the output options and
the length of time simulated by the model. Output options are con-
trolled by input parameter NOPI. If NOPI is 0, the program will simu-
late several years of data from the SWM but will give storm details for
any one continuous period of time during each water year, which may be
an entire year or any fraction thereof. If NOPT is 1, the program
simulates a short time interval; in this case initial conditions of
acid stored in the soil and dissolved in the water must be input. The
storm details are output but the yearly summaries are not. If NOPT is
2, the program operates the same as when NOPT is 1 but the yearly
summaries are also output. They will, of course, be incomplete as the
simulation would not normally extend over a full year, but the data are
useful for some types of work.
Lines 6U and 65 reads the initial value of acid stored in the watershed
at the start of the simulation. The variables are subscripted so that
the program reads values for each acid producing area in the watershed.
Line 66 calls subroutine ACDSTR which prints out these initial values.
Lines 67 to 73 read the input from the SWM and change the temperature
of the air over the watershed ZTMP from °F to °R as variable T.
163
-------
SUBROUTINE ACDSTR
_COMNON/ANH1/AP.J.T.,APQ.T,A1.T,A1D,APD(.10,H1,M .
COMMON/ANM5/EXADIR(10),EXAINmO),EXALZ( 10),EXAUZ(10J,AMTACU<10) ,
_*AHI A C LL1Q J ;
COMMON/ANM6/DDYR1 ,FA,DAY, J
CQMMON/ANM7/ARD1R.T-HO 1 .ARJ.Nf.T-t 1 Q) ,~AR-8F-L.TIL01 , ARDSRJ-tJLO-i
WRITE (6, DDOYR1 , FA, DAY, J
WRITE(6,3)
FORMATf ' O _ I A Ml Af. 1 1 _ AMTAfll _ gX APIR _ gXAUZ _ FXA 1 MT
* EXALZ1)
100 WRITE(6,8)I,AMTACU(I),AMTACLU),EXADIR(I )|EXAUZ{I).EXAINTII),EXALZ
^! | I )
8 FORMAT!I6.6F10.3)
WR1TF(6,4 1
4 FORMAT!'OTOTAL ACID REMOVED')
W-B I TE I 6 .5J
5 FORMAT!'0 I ARDIRT ARINFT ARBFLT ARDSRT')
110 HRITE(6,2)I,ARDIRT(I),ARINFT(I),ARBFLT(I)fARDSRT(I)
? FHRMATt T
RETURN
END
Figure B.10. The ACDSTR Subroutine Program
-------
Table B.15- CRPSMM INTERNAL VARIABLES
EXADIR(l) Weight of acid dissolved in direct runoff storage
EXAINT(l) Weight of acid dissolved in interflow storage
EXAUZ(l) Weight of acid dissolved in upper zone storage
EXALZ(l) Weight of acid dissolved in lower zone storage
AMIACU(l) Weight of acid adsorbed in upper zone
AMTACL(l) Weight of acid adsorbed in lower zone
FACDIR(l) Acid concentration in water entering direct runoff
FACUZ(l) Acid concentration in water entering the upper zone
FACINT(l) Acid concentration in water entering interflow
FACLZ(l) Acid concentration in water entering lower zone
ACDDIR(l) Acid removed from soil by direct runoff
ACDUZ(l) Acid removed from soil by water entering upper zone
ACDINT(l) Acid removed from soil by interflow
ACDLZ(l) Acid removed from soil by water entering the lower zone
AREDIR(l) Acid load from direct runoff - Ib acidity as CaC03
AREINF(l) Acid load from interflow - Ib acidity as CaC03
AREBFL(l) Acid load from baseflow - Ib acidity as CaC03
AREDSR(l) Acid routed to deep storage - Ib acidity as CaC03
API)(l,ll) Hourly acid production in upper soil
APD(l,12) Hourly acid production in lower soil
AH)(l,13) Volume of acid producing soil washed by direct runoff
M Ratio of acid producing area to area of watershed
I Number of acid producing area
AKDIRT(I) Acid removed by direct runoff during simulation
AROTFT(l) Acid removed by interflow during simulation
ARBFLT(l) Acid removed by baseflow during simulation
ARDSRT(l) Acid removed to deep storage during simulation
ARRDIR Total acid removed by direct runoff during time interval
ARRINF Total acid removed by interflow during time interval
ARRBFL Total acid removed by baseflow during time interval
165
-------
Table B.l6. CKPSMM INPUT VARIABLES
C0(l) Exponent affecting leaching of acid
CEU(l) Exponent affecting leaching of acid
upper zone
OFF(l) Constant affecting leaching of acid
UZF(l) Constant affecting leaching of acid
upper zone
IFF(l) Constant affecting leaching of acid
LZF(l) Constant affecting leaching of acid
lower zone
SOLACD Acid solubility in mg/,0
AREA Total watershed area (ft2)
FACRED Adjustment factor for acid entering
direct runoff
FACRUZ Adjustment factor for acid entering
direct runoff from the upper zone
FACREI Adjustment factor for acid entering
interflow
FACRLZ Adjustment factor for acid entering
interflow from the lower zone
FACREB Adjustment factor for acid entering
baseflow
FACRDS Adjustment factor for acid entering
FACED Factor to adjust direct runoff
FACFI Factor to adjust interflow
FACFB Factor to adjust baseflow
by direct runoff
by water entering the
by direct runoff
by water entering
by interflow
by water entering
receiving water by
receiving water by
receiving water by
receiving water by
receiving water by
deep storage
166
-------
Lines 85 to 88 set ARRDIR, ARRINF, ARRBFL, and ARRDSR equal to 0 before
the calculations in the fractional hour loop are made. These variables
sum the acid removed by direct runoff, interflow, baseflow and that
routed to deep storage, respectively, for later use in calculating the
yearly summaries. All acid removed from the watershed is included in
these totals.
Lines 89 to 17^ is the DO loop, which is run once for each acid pro-
ducing area of the watershed. The operations will be described com-
pletely for acid removed by direct runoff and other flows will be
described only when handled differently from direct runoff. The loop
itself is included in a larger loop which is used once for each set of
input data from the SWM. The SWL outputs data on a time interval that
corresponds to the approximate time of water flow between isochrones of
the basin studied. The CRPSMM time interval must correspond to the SWM.
Line 90 computes AA which is the ratio of the acid producing area to
the watershed area. Lines 91 "to 92 add the acid produced to the soil
storages. The variable TIME is zero if it is raining, so that the model
simulates acid production only when the watershed is not receiving pre-
cipitation. The single soil storage used in the Refuse Pile Model
(AMTACD) is divided into that part leached by direct runoff (AMTACU)
and that part not leached by direct runoff (AMIACL). Definition of
these storages conform to the ACDPRO subroutine; i.e., AMTACU is above
depth DO and AMTACL below DO.
In the Refuse Pile Model the acid removed by water entering direct run-
off storage is simulated by
ACDDIR = FACDIR*SOLACD*OVFLST*CF
where ACDDIR = the acid removed in 15 minutes in Ib acidity
as CaC03
FACDIR - an adjustment factor,
SOLACD = the assumed value of acid solubility in lb/ft3,
OVFLST = the water entering direct runoff storage in
inches of precipitation, and
CF = a conversion factor to convert inches of
precipitation to ft3
Essentially this definition .of ACDDIR calls for the removal of acid at
a constant concentration determined by SOLACD and FACDIR.
In CRPSMM the definition of FACDIR is altered in accordance with the
equation in line 9^-
FACDIR(l) = OFF(l)*(AMTACU(l)/APD(l,13))/(OWLST*APD(l,7)/AREA)**CO(l)
16?
-------
where FACDIR(l) = the concentration of acid going to direct
runoff storage from area I in lb/ft3,
OFF(l) = an input parameter for area I,
AMTACU(l) = the acid stored in the upper soil in
area I (ib),
APD(l,13) = the volume of upper soil in area I (ft3),
OVFLST = as defined above,
APD(l,7) = the area of area I (ft2),
AREA. = the total watershed area (ft2), and
C0(l) = an input parameter for area I.
This equation was developed for two reasons: First, the New Kathleen
Refuse Pile4 data indicated that the log acidity and log flow rate
followed an approximately linear relationship. This is an equation of
the form
Y = K/Xn
where Y is acidity and X the flow rate. Secondly, both fundamental
mass transfer considerations and the limited field data observed re-
quire that the acid in direct runoff decrease as the amount of acid in
the soil leached by direct runoff decrease. To reflect this the con-
stant of proportionality k is replaced by OFF(l)*(AMTACU(l)/APD(l,13)).
The ratio AMTACU(l)/AH)(l,13) is an approximation of the "effective
concentration" of acid adsorbed on the soil in the upper layer. Both
OFF(l) and C0(l) are input adjustment factors used to fit the model to
actual data. Line 95 tests FACDIR(l) to see if it is greater than
SOLACD- If so, it is replaced by SOLACD, the limiting solubility input
to the model. The defining equation for ACDDIR(l) line 103 then be-
comes
ACDDIR(I) = FACDIR(I)*OVFLST*AA*DF
where ACDDIR(l) is the acid going to direct runoff storage
from area I,
FACDIR(I) replaces both FACDIR and SOLACD from the
Refuse Pile Model, and the variables are as
described above, and
AA adjusts the amount of acid removed so that
it includes the precipitation on the
specific acid producing area only.
In lines 99 and 10^ FACUZ(l), the concentration of acid entering the
upper zone, and ACDUZ(l), the amount of acid entering the upper zone,
are determined in an analogous way. However, different input param-
eters are used. FACIHT(l), the concentration of acid entering inter-
flow storage, and FACLZ(l), the concentration of acid entering the
lower zone, are defined as a fraction of the maximum solubility (SOLACD)
by input parameters IFF(l) and LZF(l), respectively, in lines 105 and
168
-------
107- The determination of the amount of acid removed by these two
flows ACDHTT(l) and ACDLZ(l) are also analogous to ACDDIR(l).
The acid to be removed from the soil is subtracted from the layer above
DO (that washed by direct runoff) AMTACU(l) in line 111 is there is
sufficient acid there. If not, the acid removed by water going to
interflow storage and lower zone storage are removed from the lower
soil layer. AMACL(l), in line 113? a*id the acid removed by direct
runoff and water going to the upper zone are set at zero, since these
flows can not contact the lower soil layer by definition. If there is
no acid in the lower soil storage, then all acid removal flows are set
equal to zero. The assumption is made in the model that acid will be
removed preferentially from the upper soil since this is the layer
leached first by incoming precipitation.
The acid removed from the soil is stored as a water solution in four
places; the direct runoff storage (EXADIR(l)), the upper zone
(EXAUZ(l)), interflow storage (EXAOTT(l)), and the lower zone
(EXALZ(I)).
It is assumed that the ratio of weight of acid in direct runoff reaching
the measuring point (AREDIR(l)), to the acid stored in direct runoff
storage EXADIR(l) is proportional to the ratio of direct runoff to
direct runoff storage. This is accomplished by line 128,
AKEDIR(I) = (DIRRNF/OVLDST)*EXADIR(I)*FACRED*AA
where DIRKNF - the direct runoff entering the stream in
inches of precipitation,
OVIDST = the direct runoff storage in inches of
precipitation, and
FACRED = an input adjustment factor and the other
variables are as defined above.
Again the concentration is tested in line 130 to ensure it does not
exceed SOLA.CD.
The acid removed from the other three storages EXAUZ(l), EXAZNT(l), and
EXALZ(l) is calculated in an analogous manner. This method of calcu-
lation assumes that the water and acid in each storage are completely
mixed. The paths of acid flow from the four water storages are the
same as in the Refuse Pile Model. A block diagram of water and acid
flow is given in Figure B.ll. Acid removed by direct runoff comes first
from EXADIR(l), then from EXAUZ(l) if EXADIR(l) is depleted. If direct
runoff stops before EXAUZ(l) is exhausted the remainder is added to
AMTACU(l) in line 139- This acid is mostly in depression storage from
which the water will evaporate, thus precipitating the acid back to the
upper soil storage AMTACU(l). EXAINT(l) can only be depleted by inter-
flow. If this storage is exhausted the acid in interflow will be drawn
169
-------
PRECIPITATION
PR
Acidity
Flow
Figure B.ll. CRPSMM (Combined Refuse Pile - Strip
Mine Model) block diagram
-------
from the acid stored in the lower zone, EXALZ(l). The acid components
removed by baseflow and routed to deep storage are also drawn from the
lower zone.
Three variables, UZSN, LZSN, and ZTMP(l,j), which are obtained from the
SWM, are not used in the present form of CRPSSM. These have been re-
tained, however, to provide for future modifications of the model.
There is a possibility that the diffusivity of the soil can be corre-
lated with UZSN or LZSN and that ZTMP(l,J) can be used to define the
soil temperature if it is found that the acid production rate should be
calculated on a monthly or daily basis due to temperature changes. The
latter modification can be made simply by calling ACDSEC when the
variable DAY = 1 if a monthly calculation is desired or when J = 1 if
a daily calculation is desired. Another possibility to account for
temperature variable acid production rate is to input and use measured
average monthly soil temperatures and call ACDSEC each month.
171
-------
COMBINED REFUSE PILE - STRIP MINE MODEL (CRPSMM) COMPUTER PROGRAM
c
_C _ COMBINED-REFUSE P-IJ.E----SIRI P-M] J^-MOOEL
AN-M - J-
COMMON/ANH2/Z1,Z2 ,P,R,1,DOZ,A,DO,XAl,OEOR,DOZA,XA2,XA3,AP,API,D IFF
-*,NR,APQ__- ! ANM 2-
COMMON/ANM3/FACOIRI10),FACUZI 10),FAC INT!10),FACLZ(10) ANM 3
COMMON/A NM4/CO( 10 ) , CEU I 10 ) ,OFF MO-)-, IFF ! 10 ) »UZF ( 10),LZF(10-) AMI"
COMMON/ANM5/EXA01RI10),EXAINT(10) , EXAL2 ( 10) , EXAUZ(10)fAMTACUI10) ,
gAMTAf.l I 101 , AHM-
COMMON/ANM6/OOYRl,FA,DAY,J
COiliinN/AJvIH3/ARDIRTtlO).^RlKElU.OJ-,Ji.RBF-LT-( 10)-, ARDSRTI-10*
REAL LZS,LZSM,INTF,IFF,LZF
lD023,MCNED,YEARPR,YEARST,COUNT,DOAYtDAYOUT,OAYEND
l-2 ) ,SAI( 1 2 )
1,TACD112.31),S7ACD!12),TSTR(12,31),STSTR112),SDRRI12,31),SSDRR! 12)
;>t,
C FORMAT SECTION
r
1 FORMAT(6F12.6) ANM 11
9 pngMATI'l THE INPUT DATA 1 <: ' 1 ANM ] ?
403 FORMATI '0 I Zl Z2 OOZ DOZA
401 FORMATI2110)
4 FORMAT(3F12.6,£12
4OA FORMfiTI IS,4F)n.S.
240 FORMAT! 6F12.1)
3 FORMAT! '0 P
, p,n - - ]? 0,
.4.F12.6)
F12.5, Fl 0.5.F12.0)
R XA1
ANM 14
ANM 1 S
ANM 16
ANM 1 8
ANM IS
DEOR » ANM 1<9
5 FORMATI '0 CO CEU OFF UZF IFF
» LZF ') ANM ?O
*»****«*t*S*i »<»«.»»». _*_*_ f * » ...
-------
K=0 ANM 32
D0101I=1,N
ARDIRTI I 1=0.
ARINFTI I)=0.
ARRFI Tl I )=<1.
ARDSRTI I)=0.
FXAOIRI 1 )=O.
EXAINTI 1!=0.
FX4I 71 1 1 =n.
EXAUZ(1)=0.
AHTACIK1 )=QT
101 AMTACLI 1 1=0.
00 4001=1, N
ANM 34
ANM 1«i
ANM 36
ANM 37
ANM 38
ANM 39
ANM 40
ANM 42
ANM 43
ANM 44
ANM 4K
ANM 46
*PDU,7)
400 UR1TFI6,4Q411 ,CAPDI t ,.11 ,.1 = 1 ,71
WRITE (6, 5)
READ! 5tl 1COII ) ,CEU( 1 ) ,OFF ( I ) ,UZF 1 1 ), IFF! 1 ) , LZFtI )
410 HRtTFIfe, 1 ICDI I 1 ,CFLJf T 1 , HFFf T 1,II7F I I 1, 1PF( 1 1 , I 7 F( I )
REAO(5,2001)SOL4CD,AREA
HRITE(6,2001)SOLACO,AReA
AH
WRITE (6,2002) PACKED, FACRUE ,FACRE! ,FACRLZt FACR£B,FACRDS, FACFD.FACF I
C CHANGING SOLACD TO POUNDS PER CUBIC FEET
EACJCR TO-CHANCe I-NCHE-S-O6-RUNOFF OF Rf^^SE-C-tUE TO CUBJC-^SE
C SECOND OF RUNOFF
C FAr,Trm Tn THflMr.p T|Ljrn':'= "P miMfiFP PPHM PFFH<:P PT^F TQ rijR|C-
C RUNOFF (BASED ON 15 MINUTE INTERVAL)
SOLACO= SOUCD*2. 205/135310)
CF=CFS*60.*15.
C
c
C
c
C
c
c
c
c
£
c
THE NEXT LEAP Y~AP WILL CCCU
DIVIDED BY 4
THE STARTING WATEP YEAP OF T
MODEL
VEARLP=14.75
YEAPST-^8
READING IN DATA FOR SPECIFIC
TO START OUTPUT, NDAY =
THE TIME IS BASED ON A
.flCTOBER
HE »INPUT DATA FPOM THE STANFORD WATERSHED
DAY YOU WANT OUTPUT - SET FOR ONE TIME
WAT" YEAP, MrWTHl - MONT", PAY1 - PAY
NUMBER OF CONSECTIVE DAYS OF OUTPUT
WATER YEAR WHERE THE FIRST MONTH IS
173
-------
***********************************
c
C »»»»««»<<#*-*--
FOR EACH WATER YEAR 1NITILIZE THE DAILY, MONTHLY, AND YEARLY VALUES.
S£T EV-6RY TH1W^-E-OUA4- TO ZERO
C *»*»*»e:*7*tt$:**e»«*««««*«**«*4S8#*«*
*n*ri pAvmiTsrn AMMfr-0
8900 DDAY(11=1.
DO-2JO 1=1,12
DO 201 J=l,31
-ARD1I,J)=0.
ARI(I,JI=0.
TACD«I,J)=0.
SDRR(I,J)=0.
C ,MTI \ , 1 1-A
SBAS(I,J)=0.
APR t T ^ i>_n
SADC1)=0.
SAI 11 i=n.
STACO(1I=0.
SSDRR!I)=0.
SSBASU)=0.
t T i=n_
SUHAD-0.
SUHAB=0.
SUMST=0.
SUMS 1=0.
,siiHsn-o..
C PROCEDURE SO THAT THE EXTRA DAYS IN THE MONTH WILL CREATE AN OVER-
_C F-LDW IN THF nUXEUJL-CAJA. HlLL_AD.JULS-t-.^OR-..THE_LEAP_XEAiU
SLYFAR=FI
COUNT=0.
J-2
7000 1=31
ARl(.UUUJLOQaOOOClJl^.
TACDIJ,! 1=100000000.
7OQ1 ARnf.i, l l^i
ARBCJ, 11=100000000.
TSTRI.1. 1 ) = innnnnnnn,
SORRU, I 1 = 100000000.
SBAS( J,I )= 100000000.
CDllN.I?COUN.I±i. _
-------
IFCCOUNT .EQ. 1.) J=7
.1 E.lCOUNI_..E.a*_3 ..1 .1 = 1Z -
IF(COUNT .EQ. 2.) J=9
IF(COUNT .EQ. 4.1 J=S
IFtCOUNT .EQ, 5.1 GO TO 7004
_l£U:nu.NJ_£a»_&.^AND._SI_Y£AR
IF (COUNT .EO. 6. ) GO TO 7003
iFir.oiiNT .FO. 7.1 r,n TH ?nns
XEA&L.P 1 r.D-IO-I002-
GO TO 7000
GO TO 7001
GO TO 7005
GO TO 7001
K=l
ANM 61
r IKIPIIJ FBQH STANFOPP HATEPSHEO MODEL
C *********«:4:********s:#
*s^n TFiNfiPT-i F.nir.n TO SROO
8810 KCOUNT=0
r INPUT STARTING VALUES OF AC TO STORAGE
63
004201=1,N ANM 64
4?n PFan(«iT74n)flM-iAriin ) T*MTACL(1 >TE*AOTgn )i£*AU? !T)»EXA1NT1 I> ,g*"LZ(
*I) ANM 65
fAi i Ar.rKTR &MM A A
8800 READ (5 , 129 JOOVR1 ,FA ,DAY, J,0023,PR,ENTRUZ ,ENTRLZ,RGX,OVFLST
READ (5,135)OIRRNF,INTF,BASFLW,TOTFLW,OUTFLW,SFX
134 FORMAT! 7F10. 6)
ANM 67
iN(\| A«
ANM 69
_AUH 70
ANM 71
T=ZTMP+460.
JF(MHPT.LF,n)Gn Tn
IF{KCOUNT.GT.l)GO TO 71
_»U DDYR-1-,F,OV£EAR14-C
GO TO 8800
GO TO 8800
, Fn .
TO 230
GO TO 8800
230 CON-TJ NUE
KCOUNT=KCOUNT+1
ANM 79
C * <
_d
C INTERVAL FROM THE STANFORD WATERSHED MODEL
f
-------
C
C
ARRRFL=0.
004301 = 1 ,N
AMTACUI I )=4PO(1 ,11 )
AHTAGL(I)~APDII,f23
CALCULATING THE AMOUNT
JTIHE + AHTACUU1
* T1ME+AMTACL ( I )
OF ACID REMOVED
ANM 87
ANM Be
ANM 89
ANM 90
ANM 91
ANM °>-
;_3 <««»» * if i
1F(OVFLST.LE.O.O)GO TO 80 ANM 93
'ACPI". 11 1^0FC(I )- UMTACU(-I4-/-AP-O H-rl3>->-/-< OVF-LST-*APO(-I-r-7> /AREA-)-**COI
>!) ANM 94
C
C
f.
C
t-
c
, r.
C
rr
C
GO TO 82
RO FArntR ( r i -n.
82 IF(ENTRUZ.LE.O.O) GO TO 81
*"fe»r,,7.,,, TT f> AHTATt ( I )=O,
ACDINTI 11=0.
Arm 71 n=n.
A**************:-***,:^***
REMOVING THE ACID
r.HFrKjNia fn MAKF <;IIRF THFRF jc ACIP TO BE REMOVE
lft*i*(niRRNF* *o* * ni*r,n tn*?5 ********
1FIEXADIRII l.LE.O. (GO TO 21
iFmvi n<;TtLF.n.)nri Tn 71
AREOIRi Il = ID!RRf!F/CVLDST)*EXAO!Rtl 1=FACREO*AA
IF|FXtniR(l).|P.^!'PniRU))/'-RFDIRlI)-exA.01R-tn
1FIAREOIRI I ) .GT.SOLACO*OIRRNF*CF«AA) AREOIRI I )
..EXADIR1I 1=EXA01R( Il-AREDIRtI )
ANM 96
ANM °7
ANM 98
'*APO( I i7)-/ARE-A4**CEU(
ANM 99
ANMlnn-
ANM101
ANM103
AMM104
ANM105
ANM 10 5
ANM107
ANM109
ANM110
( I )-A*"PLZ( I ) ANH111
ANM112
ANM1 1 ^
AMI 14
fl*Wl\c>
A Mil 16
ANHll 7
AW118
ANMH9
ANM120
AT^122
A ly U 1 ? ^
A Nf H 12*^
ft N M 1 ? *»
**s*te***at
***********
ANM126
ANM12S
= SOLACD*OIRRNF*CF*AA ANM130
176
-------
GO TO 23
-ANM132
IFtUZS.LE.O.lGO TO 22
ARED1RI1 »=.1D1RRHF/U7S1CEXAU? t t 1 *FAdRUZSftA
IF(EXAUZ( D.LE.AkEDIRII ) 1AREOIRCI >=EXAUZ( I)
ANM135
f
c
c
EXAUZ(I)=EXAUZ(I 1-AREOIRII)
nn Tn ?^
22 AREOIRI I)=0.
A) AMTArill J )=AMTAril( I )+FXAIIJ( 1 >
EXAUZ(I)=0.
2* jF^CRf;* FOT n n) cp TO ^\
AREINFI I)=(1NTF/SRGX)*EXAINT(I )*FACREI*AA
IPIFXA1NT | I J T! F 0 )Gn Tfl H
IFlEXAINTI H.LE.AREINFtl ) ) ARE INF (I I = EXAINT ( I )
tFf ARFINFm.GT.Sm Am» IIMTPsf F*AA 1 ARF INF 1 t l=^ni Am*T MTP*r F* AA
EXAINTI I)=EXAINTIII-AREINFU)
en TO in
31 IFILZS.tE.O.lGO TO 32
IFCEXAtZI I1.LE.ARE1NFU) ) ARE INF (I )=EXALZII)
IFIARFINFfll-fiT-SniirDsINTFsrF^AAlARFlNFII l=<;ni Af-n=I NTP*rp* A A
EXAU(I) = EXAU(I I-AREINFII 1
ixn Tn 7n
32 AREINFI I)=0
^ft IF(PA^FL« -FOT n,n) r,n rn f»
JFILZS.LE.0.1GO TO 43
IF(EXALZ(I).LE.O.) GO TO 43
|P(P5f»LZ(T).LF.snf:ReL'I))ABEBf:L(I )~EXALZ ( I )
IFUREBELd ) .GT.SOLACD*BASFLH*CF*AA) AREBFL ( I )=SOLACD*BASFLW*CF*AA
GO TO 40
A* ARFRF( ( | 1 =f1.
AO IFCINTF .EO. 0.0) GO TO 51
AREDSRI 1)=(INTF/LZS)*EXALZ1I )*FACRDS*AA
1F(FXALZ (I ) .LF.n. K-QTQ 52
IFIEXALZ(I).LE.AREOSRII) ) AREDSRI I )=EXALZII)
EXALZ(I)=£XALZ( I 1-AREOSRI1 )
Rn Tn «;}
52 AREOSR(I)=0.
51 CONTINUE
ARRINF=ARRINF+AREINF(I I
AR1NFTC I1=AR1NFT( I 1+AREINFI I)
A^PCLTII)-A00FLT(I)+AREBFL(I1
AROSRTI II=AROSRT(I)+AREDSR(I I
faft ADR g FL=APPP PL*A Q FB PL C I )
FINDING THE DAILY VALUES
CFOIR=DIRRNF*CFS*FACFO
ANH137
ANMI 3 8
ANMI 40
ANM141
ANH142
ANM143
ANMI 44
ANMli
-------
ARB(FA,DAY!=ARRaFL+ARB(FA,DAY)
_SBAS(FA,DAY)=.CFBAStSBAS.(FA,DAY)_
SINT(FA,OAY)=CF!N7+S1NT( FA, DAY)
TSTR(FA,DAY)=CFT07+TS TRIP A, DAY)
65 IFIYEAR1 .EO. OOYR1) GO TO 120
GO,,, TO100
ANM178
ANM179-
C CHECKING IF THIS IS SPECIFIC DAY TO BE OUTPUTEO
120 IFIMONTH1 .EO. FA .OR. PAYOUT .GT. 1) GO TO 130
OO Id-100 - . . -
130 IFIDAY1 .EO. DAY .OR. DAYOUT .GT. 1) GO TO 131
,,.,fin,. TO ion _
l|P(navniiT,go.O)i;n TQ 132
GO TO 133
WRITE [ft
c f.H=rjAYQU.t..FQ.DAYFMD>Gn Tn fin Q
AHH134 .....
100 YEARPR=YEARST+1
.po, nnvRi
-AN"-
.PP. ii fin fn .annn
GO TO 8800
THE MrwTHiv
FINDING YEARLY VALUES
8000 DO 700 1=1,12
nn 7ni .1=1 ,71
1F1ARDII.J) .EO. 100000000.) GO TO 702
SAI(I)=ARI(I,J)+SAI(I )
( 1 I=ARRII,.IH-«;6R( j I
SSBAS(1)=SBAS(I,J)+SSBAS(1)
_SSTNTll)=SlNTfl..l)4.SSlNTIII.
SSDRR(I)=SDRR(I,J)+SSDRRII)
S TS TR ( 1 ) = TS TR M , .1.1 +.S TS TALLL
STACDI I) = TACO(I,J)-*STACO(I)
70?_r.nMTI NU E
701 CONTINUE
I+SUMAD_
SUMAI=SAI( D+SUMAI
SUHTA = STACD! I I+SUMTA
SUHSB=SS3AS!II+SUMSB
SUMSO=SSDRRIIJ+SUMSO
700 CONTINUE
178
-------
C OUTPUTING THE "8" DAILY TABLES PLUS THE YEARLY SUMMARY
CALL ACDSTR ANM185
MR1TEI6.301?) YFARST.YEARPR _
NR1TE(6,3003>
3003 FORMAT! ' ' ,3RX,4flH^YNTHF';i7Fn flf.Tn jnAp IN DIRECT RUNDEF_lM_ROUNaS _
1)
HRlTEt6,3Q13| _
00 300 1=1,31
WHITFC ft , ^ni i I nnaYiTi,iARnfj,Ti,i=i,i?i
300 CONTINUE
HRITE(6,3002)
FHRMA T( ' ' r ^9 X i 4AH5 Y^THES I ZED AC If) LOAD IN INTE R FL OW _ I J4 P-QUWO-S-)
HR1TEI6.3013)
rtn ^ni T =1 , "*,]
WRITE (6, 3011) OOAYII) , (ARK J,I ),J=1, 12)
WRITE(6',3012) YEARST, YEARPR
HR1 TE { 6« ?001 )
3001 FORMATI ' ,39X,43HSYNTHESUED ACID LOAD IN BASEFLOW IN POUNDS)
WRITFtft,
DO 302 1=1,31
, ?01M PPAV 1 1 ) 1 1 ABP( J, I ) 1 J=l ,1?)
302 CONTINUE
UPl TF( h.^m? I VFABCT.VFAPPB
WRITE (6, 3004)
WRITE(6,3013)
nn ?m T=i , ^1
WRITE IfrrSOll) DDAY!i;,(TACO(J,I),J=l,12)
WR1TE(6,3012) YEARST,YEARPR
3006 FORMAT!' ' .35X.50HSYNTHESIZED DIRECT RUNOFF IN CUBIC FEET PER SECO
HRITE(6,3013)
WRITE 1 6 , 3020 ) DDA Y ( I ) , (SDRR ( J , I ) , J= 1 , 1 2 )
f nM T ; MI i f
WRITE(6,3012) YEARST, YEARPR
TE ( fr ?007 )
3007 FORMAT!' ' ,31X,46HSYKTHESI ZED INTERFLOW IN CUBIC FEET PER SECOND)
DO 306 1=1,31
nnAVMi.i<:iMTfi. 11. i= 1.171
306 CONTINUE
n?) YgARST,Y£ARPR
WR1TE(6,3008)
aoa&_F-OR.MAxt-i'-^aj-x-^ASHS-YjaHe^-i-zEO BASEFLOW IN cus-tcFEET PERSCCONDI
HRITE(6,3013)
pp ?n7 1=1,?]
WRITE 16, 3020) DDAYU ), ISBAS ( J , I ) , J=l, 12)
?Q7 CONTINUE
WRITE(6,3012) YEARST, YEARPR
3005 FORMAT!' « ,37X .47HSYNTHESI ZED STREAMFLOW IN CUBIC FEET PER SECOND)
DO 30*. 1 = 1,31
304 CONTINUE
WRUEt 6.^304 24-*EARSJ-,-Y£ARPR~
179
-------
WRITEI6.4005)
-A005-FHRMATLJ-! f3X,3HQC.T ,AX,3HNOV ,6X , 3HOEC,6X,3HJAN,6X, 3HFEB, 6X.3HMAR ,6
1X,3HAPR,6X,3HMAY,6X,3HJUN,6X,3HJUL,6X,3HAUG,6X,3HSEP,3X,10HYEAR TO
2TALJ ___
WRIT6<6,4000>
_WR.lJtI6,400CU_
WR1TE(6,4001)
^OOi_EORMA-TiJ-0!-,48HSyNTHESIZED-AC10-LOA0-IN-01REC*-RUNOFF
HR1TE 16,4002! (SADtl),l=l,12) ,SUNAO
-MB.il E I 6, 4O0
4004 FORMAT! 'O1 ,44HSYf)1HES I ZED ACID LOAD IN INTERFLOW IN POUNDS)
KRHE(&,4002)(SA.U-Ur-l-l-.i-.lr-S
WRITE(6,4006)
FOR^AJ-l-'-a!-^43
HRITE(6,4002) 1SA81I),1=1,12!,SUMAB
4007 FORMAT! «0' .37HSYNTHESI ZED TOTAL ACID LOAD IN POUNDS)
40021 (STACDI I)
WRITE(6,4008)
&OOS. FORMAT! '0' ,£OHS-'NTH£.S-IZEO-01RECJL-RUNOE-EIN-CU8-ICFEE-JPE«&ECONB-)-
HRITE(6,4009) ISSDRR(I),1=1,12),SUMSD
4010 FORMATl '0' .46HSYNTHESI ZED INTERFLOW IN CUBIC FEET PER SECOND)
-WHITE I ft, 4.0091 ISS4-NT1 Ii ,1=1, 12) , SUM SI
WRITE(6,40H>
4011 FORMAT! '0' ,4
WRITE (6, 4009). (SSBAS ( I ) , I =1 ,12),SUMSB
WRITE! ft. 40 121
4012 FORMATl '0' .76HSYNTHES I ZED TOTAL AMOUNT OF WATER ENTERING THE STREA
_ In IN-CU&JC FFFT PFft SfcCOJ^LU __ _____ - .
WRITE(6,4009) (SISTRfI),I=1,12),SUMST
FflRMATM ,^X,l?f1?MX,FOt1 1 1
3012 FORMATl '!' ,40X, 32HANNUAL SUMMARY FOR WATER YEAR 19 , 1 2, IX, 1H-, IX,
1?Hiq.l?l _ __
3013 FORMATl '-' ,3X,3HDAY,5X,3HOCT,6X,3HNOV, 6X, 3HDEC, 6X ,3H JAN, 6X,3HFEB,6
_ 1X.3HMAR.6X, 3HA PR , feX , ^|j:'ia Y , ftX , ^H.IIIM , fey , ^H.lll L_,_6iX ,3H&IIQ , »X , ?H
VEARST=YEARST+1
GO TO 9100 ANM187
inn
CALL ACOSTR ANM189
GO TO inn tKyjoo
510 1F(NOPT.G£,2)GO TO 8000 ANW191
. CALL ACDSIB ------------- tN M192
GO TO 9100 ANM193
.S?0fl, f.AI I. »FXIT ANH194-
END
180
-------
REFERENCES FOR APPENDIX B
1. Brown, W. E., "The Control of Acid Mine Drainage Using an Oxygen
Diffusion Barrier," M.S. Thesis, The Ohio State University, (1970).
2. Chow, K. Y., "Computer Simulation of Acid Mine Drainage," M.S.
Thesis, The Ohio State University, (1970).
3. General Assembly of the State of Ohio, Amended Substitute House
Bill No. 928, "An Act," File No. 239, April 10, 1972.
U. Good, D. M., "The Relation of Refuse Pile Hydrology to Acid Pro-
duction," M.S. Thesis, The Ohio State University, (1972).
5. Hill, R. D., Chief of Mine Drainage Pollution Control Activity,
Federal Envinronmental Protection Agency, Personal Communication
(1973).
6. Linsley, Jr., R. K., Kohler, M. A., Paulhus, J. L. H., Hydrology
for Engineers, McGraw-Hill Book Company, Inc., New York (1958).
t
7. Mihok, E. A., Moebs, N. N., "U.S. Bureau of Mines Progress in Mine
Water Research," Fourth Symposium on Coal Mine Drainage Research,
Pittsburgh, (1972).
8. Morth, A. H., "Acid Mine Drainage: A Mathematical Model," Ph.D.
Dissertation, The Ohio State University, (1971).
9. Ricca, V. T., Associate Professor, The Ohio State University,
Personal Communication (1973).
10. Ricca, V. T., "The Ohio State University Version of the Stanford
Streamflow Simulation Model," The Ohio State University, Water
Resources Center (1972).
11. Ricca, V. T., Chow, K. Y., "Acid Mine Drainage Quantity and Quality
Generation Model," The Ohio State University, (1973).
12. Rice, P. A., Rabolini, F., "Biological Treatment of Acid Mine
Water," Fourth Symposium on Coal Mine Drainage Research,
Pittsburgh, (1972).
13. Smith, E. E., Professor, The Ohio State University, Personal
Communication (1973)
181
-------
lU. Smith, E. E., Shumate, K. W., "Development of a Natural Laboratory
for the Study of Acid Mine Drainage Production," Second Symposium
on Coal Mine Drainage Research, Pittsburgh, (1968).
15. Smith, E. E., Shumate, K. S., "Pilot Scale Study of Acid Mine
Drainage," Program #1^010 EPA Contract 1J+-12-97 (1971).
16. Sternberg, Y. M., Agnew, A. F., "Hydrology or Surface Mining -- A
Case Study," Water Resources Research, (1968).
17. "Surface Mining and Our Environment," U.S. Department of Interior,
(1967).
18. 91st Congress, S. 1075, Public Law 91-190, "National Environmental
Policy Act of 1969," January 1, 1970.
19. Maupin, A. N., "Computer Simulation of Acid Mine Drainage from a
Watershed Containing Refuse Piles and/or Surface Mines," M.S.
Thesis, The Ohio State University, (1973).
20. Bird, R. S. et al. Transport Phenomena, New York (i960).
i
182
-------
APPENDIX C
OPTIMIZATION MODEL FOR RESOURCE ALLOCATION
TO ABATE MINE DRAINAGE POLLUTION
In preceding sections, models and procedures have been described for
predicting mine drainage pollution levels, stream flow quantities, and
costs to implement actions for reducing the effects of mine drainage
pollution. Several distinct methods for reducing or eliminating the
effects of mine drainage pollution have been outlined, and these methods
are as diverse as sealing and flooding to slow pyrite oxidation and
treatment to neutralize the acid in mine drainage effluent. For each
method, both the effects on stream quality and the implementation costs
will vary from site to site. Moreover, stream quality is a dynamic
phenomenon in that weather will cause large variations in stream quality.
Based upon inputs from the physical models of pollutant sources and the
cost model, the optimization model has two principal objectives in ana-
lyzing the allocation of resources to control mine drainage pollution
in a watershed:
1. Determine a least cost allocation to achieve a specified
quality level, and
2. Determine the most effective allocation for a specified
cost.
The initial research task in designing an optimization model to achieve
the above objectives was directed toward the construction of a dynamic
model of a single-stream basin having multiple sources of mine drainage
pollution. The model is dynamic in that pollutant and stream flows are
functions of time; however, these functions are regarded as determinis-
tic. The effects and costs of resource allocation to reduce pollutant
effects are represented in this dynamic single-stream model which will
be identified by the mnemonics DSS. An analysis of DSS indicates the
types of optimization models which will be required to represent the
resource allocation options available with varying levels of realism.
Two optimization models are developed and they are defined below along
with their identifying mnemonics:
183
-------
1. Deterministic "worst-case" minim-urn cost (D₯MC) model,
2. Deterministic "worst-case" maximum effectiveness (DWME)
model,
A detailed description of the DWMC and DWME models is contained in this
appendix along with computer program flow charts and input data instruc-
tions. Because the DSS model served as a basis for the two optimization
models mentioned above, the DSS model is described first.
DYNAMIC SINGLE-STREAM MODEL (DSS MODEL)
Consider a watershed having N mine drainage pollution sources > and-
resource allocation strategies for this watershed are to be determined
to satisfy two different objectives, viz., l) minimum cost to maintain
a desired stream quality level and 2) maximum quality for a fixed cost
budget. Initially a model to satisfy objective 1 above is outlined and
then later this model is extended to satisfy objective 2. To illustrate
the proposed optimization methods, a simplified stream is considered
having no tributaries since the extension to include tributaries is
straightforward. The watershed is illustrated in Figure C.I.
Figure C.I. Single-stream watershed
-------
The first step in the model formulation process will be to define basic
flows and decision variables. Then, these variables will be used to
formulate criteria and constraint equations for the two objectives
(minimum cost and maximum effectiveness).
BasicFlow and Decision Variables
Each mine, noted as a small square in the figure, is represented as
draining into the stream at a node point, defining N node points. With-
out action tp control pollutant effluent, the ith mine produces pollu-
tants at a rate of Pj[(t) kilograms per hour at time t (hours) where
i = 1, 2, ..., N. For example, the pollutant might be acid and P
would specify the total acidity of the effluent from mine i. Negative
values of Pj_(t) would specify an alkaline condition. Also the stream
carries a fluid flow, exclusive of pollutant, of Q,j(t) (kg per hour) at
node point i at time t. The value of Qj_(t) is assumed to be unaffected
by actions to control stream pollution levels.
In addition to pollutant inputs from mine sources, the stream has
natural pollutant inputs occurring throughout its length. These natural
inputs are assumed to be distributed continuously between nodes, but the
stream reach between each pair of nodes may have its own unique input
rate. Let P^n(t) be the natural pollutant input rate in kg per hour
occurring between nodes i-1 and i. For example, a natural acid
input rate of -.05 kg per hour between two nodes would indicate an
alkaline condition alleviating part of any potential acid mine drainage.
A survey of possible methods for controlling mine drainage pollution
indicated that these methods can be classified into three categories as
far as the optimization model is concerned. These categories are:
1. abatement at the mine site,
2. treatment at the mine site, and
3. treatment in the stream channel.
Abatement is assumed to reduce the pollutant flow but not necessarily
eliminate it. That is, site i produces a flow of Pj_a(t) if abatement
is performed at site i, where Pj_a(t) < Pj_(t) for all t. Examples of
abatement are flooding or sealing of deep mines; covering, leveling,
compacting, burying, or grading of gob piles; and grading, covering, or
replanting of strip mines. All of these methods have the potential for
reducing pollutant flows, but their effectiveness will vary from site
to site.
Treatment, whether in the stream channel or at a site, is assigned to
reduce pollutant flow to zero (without affecting the stream flow exclu-
sive of pollutant; i.e., values of Q^(t)), but treatment will not affect
185
-------
a condition where the stream pollutant measure is already negative.
Using our acid mine drainage example again, the treatment facility will
neutralize an acid stream until it has zero total acidity, but it will
not affect an alkaline stream. The assumption is being made here that
once the decision is made to install a treatment facility the most eco-
nomical solution is to remove all acid conditions but do not change
alkaline conditions. The effect of a treatment facility is shown
graphically in Figure C.2. The performance of a treatment facility can
be represented mathematically by a clip function, L(X),
where L(x) =
if x ^, 0
1 x if x < 0.
Thus, LlPj! (tn would represent the output of a mine source having
treatment facility.
a
LU
§
-I
o
Q_
>- Treatment -v
/ Facilities t
A B
DISTANCE FROM STREAM HEAD
Figure C.20 Effect of instream treatment facilities
Three decision variables are used at each node to specify the pollution
control measures to be used, if any. They are:
d,a =
1 if abatement is done at site i
0 if otherwise
186
-------
( 1 if site treatment is done at site i
di =
\ 0 if otherwise
II if instream treatment is done at site i
0 if otherwise
Site treatment, if implemented, is regarded as being capable of treating
all pollutant effluent before it reaches the stream. Also, the assump-
tion is made that instream treatment facilities treating all of the
fluid passing through a node adjacent to a mine site could be located
at any node; moreover, a mine site having an instream treatment facility
would treat the effluent from its local mine source before its effluent
enters the stream channel.
CONSTRAINT EQUATIONS AND CRITERION
FUNCTION FOR MINIMUM COST MODEL
The minimum cost model selects values for the three decision variables,
defined above, at each node in order to maintain stream quality through-
out the watershed while minimizing total cost. The constraint equations
guarantee that quality is maintained, and the criterion function speci-
fies the minimum cost objective. The constraint equations are presented
first.
The quality standard specifies that the pollutant concentration must be
less than Qg in parts per million (ppm) throughout the watershed. We
will regard this to mean that the standard can be satisfied by having a
quality of Q or better at each node. This assumption implies that
satisfactory quality just downstream of node i together with a natural
pollutant input between nodes i and i+1 will not violate the standard
so long as quality is maintained just down stream of node i+1. If
Pj^(t) is the total pollutant flow rate at node i (after considering
all upstream sources, natural pollutant inputs, and abatement and treat-
ment procedures), then
10s
< Q0 or
- s
<
18?
-------
for i = 1, 2, ..., N and for all values of t. Note that this quality
standard must be met continuously throughout time.
The principal task in constructing the constraint equations is to specify
P^Ct). Consider the node i. Decisions with respect to the source are
specified by the variables dj_a and d^. The mine pollution output rate
after considering the abatement decision is given by
- dia)Pi(t).
Including the site treatment decision, the pollution output rate from
a mine source is defined as Pj_s(t), and is given by
P^Ct) = ditL[diaPia(t) -f (l - dia)Pi(t)]
+ [i - a1t][a1apia(t) + (i - a^Pift)]
i = 1, 2, ..., N (C.2)
In addition to the site decisions, dj_a and dj_ , the pollutant flow from
node i is a result of the interaction among the pollution flow rates,
P^Ct^ - TJ[_I) just downstream of node i-1, the natural pollutant input
rate Pj_n(t), and the instream processor decision dj_s. TI_I is the time
delay for a particle of water to flow from node i-1 to node i and is
assumed to be constant for all values of t. The value of P-j_*(t) is
given by
Pi*(t) = diSL[pin(t) + Pi!x(t - T^) + Pis(t)]
+ [l - dis][pin(t) + P^t - Ti.O + PiS(t)] ;
i = 1, 2, ..., N (C.3)
where PQt('fc) = 0 .
Substitution of C.3 into C.I gives the complete set of constraint
equations. Notice that these constraint equations are nonlinear func-
tions of the decision variables dj_a, d-p, dj_s.
In order to specify the minimum cost criterion function, several cost
variables need to be defined. All costs incurred by these pollution
188
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control measures are assumed to be equivalent annual costs which include
recovery of capital, operating and maintenance costs. If abatement is
performed at site i, a cost of Cj_a is incurred. Annual treatment costs
involve two cost components; i.e., a variable cost that is directly
proportional to the annual amount of pollutant processed and the equiva-
lent annual cost exclusive of the variable cost component. An example
of the variable cost component would be the cost of chemicals for
neutralization of acid. For treatment processors the following cost
variables are used:
C^ = annual cost for a treatment processor at mine site i
exclusive of the variable cost (dollars),
Cis = annual cost for an instream treatment processor at node
i exclusive of the variable cost (dollars), and
Cy = variable cost to treat one unit of pollution (dollars
per kg).
To determine the variable annual costs for treatment, the following addi-
tional annual pollutant loads are required as input:
Aj_ = annual pollutant load emitted from source i without
site abatement (kg),
Aj_a = annual pollutant load emitted from source i with site
abatement (kg)
Aj_n = annual natural pollutant input between nodes i-1 and i
(kg).
Note that values for Aj_n and A^a may be negative indicating a flow of a
substance that can "neutralize" the pollutant. The assumption is made
that the effluent A-|_a from a mine site after abatement is either con-
tinuously positive or negative and does not alternate between positive
and negative values. Similarly, the assumption is made that any nega-
tive pollutant inputs to the stream for all values of d-j_a, dj_% dj_s
will not cause the stream at a particular location to alternate between
positive and negative states. This assumption is made so that the above
annual pollutant inputs can be added at instream treatment processors to
calculate annual variable treatment costs. Recall that only positive
values of pollutant flow are treated at a treatment processor.
Using the costs and annual pollutant flows defined above, the total
resource allocation cost, C^., can be calculated by
189
-------
N
= £
1 ~ 1
where A^ is the annual pollutant load passing stream node i considering
^a, d-? , dj
the upstream decision variables da, d-? , dS; for j = 1, 2, ..., i.
Values for A^ are calculated in a manner similar to P-jt). First, the
annual inputs from individual mine sources are given by Aj_s and calcu-
lated by
i = 1, 2, ..., N (C.5)
These values of A±s are inserted in the following expression for Ai*.
in
Ai* = disL(Ain + ^ + Ais) + (l - dis)(A
i = 1, 2, ..., N (C.6)
where A * = 0 .
0
Equations C.k and C.I with their inputs C.2, C.3, C.5, and C.6 complete
the formulation of the minimum cost version of the DSS model. Equation
C.h is the criterion function, and the value of C^ given by that equa-
tion is to be minimized by choice of values for dj_a, dj_*, dj_s, for
i = 1, 2, ..., N. Of course, the constraint equations given by C.I
must be satisfied for all values of C considered.
CONSTRAINT EQUATIONS AND CRITERION FUNCTION
FOR THE MAXIMUM EFFECTIVENESS MODEL
The purpose of the maximum effectiveness model is to allocate a fixed
budget in the most effective manner. The effectiveness measure has been
designed to indicate the relationships between pollution levels, envi-
ronmental impact, and land use in the vicinity of the watershed. These
relationships are reflected in the effectiveness measure using two con-
cepts which are:
190
-------
1. The basic value of a stream based upon maximum pollution
concentration level.
2. The relative importance of the stream between two nodes
based upon its land use.
The above concepts are applied to individual stream reaches between
adjacent stream nodes to compute a reach effectiveness measure which is
the product of its relative importance and its basic value. Total water-
shed effectiveness is assumed to be the sum of the individual reach
effectiveness measures. These concepts are described in more detail
below and illustrated by examples. Following the examples the mathe-
matical notation is developed for the criterion function and constraint
equations.
The basic value of a stream reach is a number between zero and ten that
indicates the reach's value based on observable effects from pollution
concentrations. These effects include phenomena such as aquatic life,
aesthetics, and water supply processing which are assumed to be related
to the maximum pollution concentration experienced. To portray the
variation in basic value, maximum pollution concentrations are classi-
fied into intervals within which the observable effects are assumed to
be constant. Table C.I illustrates the variation of basic value with
pollution concentration.
For each stream reach between two nodes, the basic value is determined
and is weighted by the relative importance of the stream reach to give
the effectiveness measure for this same stream reach. Relative impor-
tance is a quantity varying between zero and ten that specifies the
importance of controlling pollution levels in each stream reach between
adjacent nodes, land use in the vicinity of the stream reach^ and the
impact of pollution on this land use. Also, the length of the reach
can be considered in assigning relative importance values. The distri-
bution of relative importance values throughout the watershed is deter-
mined in several steps. The first step is to select the most important
stream reach (as defined by the stream between two adjacent nodes). The
most important stream reach is given a relative importance value of ten.
Then all other stream reaches are assigned values consistent with the
difference "between their importance and the importance of the most
important stream reach.
The application of the above concepts is illustrated by the stream por-
trayed in Figure C.3. The predominate land uses are noted in the
figure. The most important reach with respect to the impact of pollu-
tion is the reach between nodes 1 and 2; thus, this reach is assigned
a relative importance of 10.0. The other reaches are evaluated to have
relative importances of 7.0 downstream of node k, 5.0 between nodes 2
and 3} and 2.0 between nodes 3 and U. Using these relative importances,
the effectiveness measures for each stream reach can be obtained by
191
-------
Table C.I. ILLUSTRATIVE VARIATION OF BASIC VALUE WITH
MAXIMUM POLLUTION CONCENTRATION
(ppm)
Maximum pollution
concentration
Observable effects
Basic value
> 10
8-10
6-8
k-6
< k
Fish cannot survive, noticeable
odor, strong discoloration, water
treatment costs increased by 100$.
Game fish cannot survive, high
scavenger fish mortality, notice-
able odor, water treatment costs
increased by
High game fish mortality, scavenger
fish will not reproduce, water
treatment costs increased by 25$.
Game fish will not reproduce.
Aquatic life unaffected.
0
7.5
10
Recreation \ Agriculture
i
D
Figure C.3. Single stream with adjoining land uses
192
-------
determining basic values for each reach and multiplying these basic
values by their respective relative importances. For specified values
of dia, dj/k, and dis, let the maximum pollution concentrations be 6.8,
5-9, 5-5, 6.1 ppm starting at the head of the stream (node l) and pro-
ceding downstream. Then using Table C.I, the basic values for each
reach are k, 7.5, 7-5, and k, respectively. Multiplying by the reach
relative importances, the individual reach effectiveness measures are
1+0.0, 37^5, 15.0, and 28.0, respectively. Summing these reach effec-
tiveness measures, the stream effectiveness measure is 120.5.
Having presented an example, the mathematical notation necessary to use
the effectiveness measure will now be defined.
Let E«5 = the basic value for the.jth maximum pollutant concen-
tration interval, 0 < E3 < 10; j = 1, 2, ..., N*;
N* = total number of pollutant concentration intervals;
Q,J = the upper limit on the maximum pollutant concentra-
tion for the jth interval; j = 1, 2, ..., N*;
Q°= 0;
RJ_ = relative importance of the stream reach between nodes
i and i+1, i = 1, 2, ..., n; 0 < Ri < 10;
Ei = effectiveness of pollution control actions on the
stream reach between nodes i and i+1,
i = 1, 2, ..., I.
To compute the basic value of reach i, the maximum pollutant concentra-
tion over all time values is determined, and this value is used to
determine the pollutant concentration interval. That is, the value of
j is determined for reach i such that
< Q^ (C.7)
using this value of j then
E, = E, . EJ . (C.8)
193
-------
After determining values of Ej_ for i = 1, 2, ..., N; then, the total
watershed effectiveness, E, is computed by
N . .
£ % (C.9)
1 = 1
The above equation is the criterion function for the maximum effective
ness model.
Since the constraint for the maximum effectiveness model is the total
annual cost budget, B, then the total resource allocation cost, C^,
given by equation C.U can be used in the constraint equation. It
follows that
Ct < B (C.10)
ANALYSIS OF THE DYNAMIC SINGLE-STREAM MODEL
Analysis of the minimum cost and maximum effectiveness models formulated
in this section shows that both optimization problems have the following
characteristics:
1. set of admissable decisions is discrete,
2. number of possible decisions is 8 ,
3. constraint equations and criteria functions are nonlinear
functions of the decision variables.
Note that the number of possible decisions will be overwhelming with
values of N as large as 20 or 30. Even with only 10 mine sources the
the number of possible decisions is in excess of one billon.
In addition to the characteristics mentioned above, another factor com-
plicating any solution procedure is the dynamic stochastic nature of
pollutant and stream flows. That is, the functions Pj_(t), Pj_n(t),
Pj_a(t), and Qi(t) for i = 1, 2, ..., N are time varying and stochastic.
These functions will be difficult to handle in equations such as C.I
and C.2 even if they are regarded as deterministic. Since these func-
tions are strongly influenced by precipitation patterns, they are in
fact stochastic. One way of handling their stochastic nature is to
adopt a conservative approach by selecting very long time traces from
194
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the Pollutant Source and Hydrologic Models; or, even better, analyses
of the pollutant source models can be conducted to indicate which pre-
cipitation patterns give the maximum pollution concentrations. In this
way, confidence can be gained in the fact that quality constraints will
be maintained in the minimum cost model (equation C.l) and that effec-
tiveness measures will be properly calculated (equation C.7). The
basic assumption being made is that optimizing in this manner will
yield a solution that provides quality and/or effectiveness measures
at least as good as the worst case analyzed so frequently that any
violations can be ignored.
Going one step further, a much less cumbersome and more useful optimi-
zation algorithm can be obtained by completely suppressing the dynamic
stochastic nature of the functions Pj_(t), Pin(t), Pia(t), and Q,-j_(t).
This approach will be called the "deterministic worst-case analysis."
The basic idea inherent in this approach is to select a set of single
values from the functions Pi(t), Pin(t), Pia(t), Qj_(t), i = 1, 2, ..., N;
that represents the most adverse situation from a quality viewpoint.
Then, an optimal solution using these values should almost always give
better quality or more effectiveness in actual practise than considered
in the solution procedure.
Two models have been developed to evaluate the deterministic worst-case
approach. These models are the DWMC and DWME models defined in the
introduction to this appendix. Both models can analyze a basin having
multiple streams with tributaries, and the method for representing mine
sources and streams in this basin is described in the following section.
The deterministic models are described in detail in subsequent sections.
BASIN MINE SOURCE AMD STREAM DESIGNATION SYSTEM
In this section, notation used to define the basin stream network, mine
sources, pollutant flows, and pollution control costs is defined. This
notation is used in both of the deterministic worst case optimization
programs, and standard FORTRAN symbols are used to designate variables
to avoid use of an additional set of mathematical notations.
The basin is assumed to have mine sources draining into a stream net-
work having a hierarchy of at most level three. That is, the basin
outlet is a third-level stream being fed by second-level streams, and
the second-level streams are fed by first-level streams. Note that only
second-level streams can feed the third-level stream and that only one
third-level stream is permitted. Of course, basins with only a single
stream or with only a hierarchy of level two can be represented by the
optimization models. In these cases the basin outlet stream would still
be a level three stream and there would be no level one streams. In
the single stream case there would only be a single level three stream.
195
-------
A set of nodes are denoted along each stream and there exists three
different functions that can be performed at each node; i.e., a pollu-
tion source, an instream treatment site, or a stream confluence. All
nodes are source nodes or possible points at which pollutants may enter
the stream from mines. Any pollutant flow from mines is assumed to
enter the stream at the node location. In addition natural pollutant
inputs may occur between stream nodes. These natural pollutant inputs
may be positive, increasing pollutant concentrations, or negative,
neutralizing pollutant concentrations. Quality checks are made at each
node to determine whether pollutant concentrations are less than the
standard or to determine the effectiveness of a given resource alloca-
tion. These quality checks are always made gust downstream of each
node.
Treatment nodes are possible locations for instream treatment facilities
removing pollutants from the entire stream flow. The DSS model per-
mitted all nodes to have the potential for an instream treatment
facility; however, economies with respect to the number of alternatives
to evaluate are achieved by evaluating only the most likely locations.
It should be noted that the models can be operated with all nodes being
treatment nodes if the additional computer time is considered worth-
while. A mine source at a treatment node is assumed to feed the in-
stream treatment facility directly, if the decision is made to implement
the facility; thus, the source at an instream treatment site would not
degrade stream quality.
In addition, some nodes, called confluence nodes, are fed by another
lower level stream. An example is shown in Figure C,k where nodes h
on second level stream number 1, 2 on the third level stream, and k on
the third level stream are confluence nodes. Note that the confluence
is located between the node and the next upstream node. Also, nodes 5
on second level stream number 1 and 3 on the third level stream are
treatment nodes.
Each stream is designated by its level and streams having the same level
are numbered. Thus, for level 1 streams, the streams are numbered one
through NS(l) where NS(l) is the total number of level one streams.
Similarly, level two streams are numbered one through NS(2). There is
only one level 3 stream; i.e., NS(3) = 1. Also, the variable KL is used
to designate the lowest level stream represented in the basin. If the
basin has only two levels in its stream network, then NS(l) = 0 and
KL = 2. Moreover, a single stream network would have NS(l) = NS(2) = 0
and KL = 3=
As depicted in Figure CA, the nodes on each stream are numbered start-
ing with the most upstream node. Thus, node I on stream J is upstream
of 1+1 on stream J. Using the three coordinates; i.e., node number I,
stream number J, and stream level K; an individual node is uniquely
specified within the basin by the ordered triple (l,J,K). The array
196
-------
Second level
stream No. I
Second level
stream No.2
First level
stream No.
Third level
stream No.I
Source or confluence node
Possible instream
treatment site
Figure C.k. Illustration of stream and node designation
ND specifies the number of nodes on each stream. Values for ND are
specified as input data and are defined by
ND(j,K) = number of nodes on stream J of level K.
Several arrays are employed to permit tracing from a level one stream
to the basin outlet, or backwards from the basin outlet to the stream
heads. The array JU permits tracing upstream and is prepared as input
data to the optimization models. 'Values for
-------
JN(I,J,K-1) =
NF if node I on level K stream J is a con-
fluence node where NF is the level K-l
stream feeding J, and
0 if (l,J,K) is not a confluence node
for K = 2,3.
Also J₯(I,J,0) will be defined to be zero.
Note that the last node or node ND(NF,K-l) on stream NF would be the
next upstream node feeding node (l,J,K). Also note that the first
node on any stream is not permitted to be a confluence node since there
is no need for two streams in this case.
To permit tracing downstream through the stream network, the optimization
programs create two arrays from the array JN. The array NFN gives the
nodes receiving flow from level 1 and 2 streams, and values for NFN are
defined by
NFN(J,K) = confluence node on the level K+l stream receiving
flow from level K stream J.
Since there is only one level 3 stream, all level two streams feed level
three stream number one. The array NFS gives the level 2 streams re-
ceiving flow from level 1 streams, where
NFS(j) = level 2 stream receiving flow from level 1 stream J.
Potential instream treatment sites are designated in a manner similar
to that used to denote confluence nodes. Treatment nodes are specified
by the array INT, where
INT(I,J,K) =
NT if node (l,J,K) is a potential instream
treatment site where NT is the instream
treatment site number, and
0 if otherwise
NT can take on the values between one and NINST where NINST is the total
number of instream treatment sites considered.
At each node a set of variables is used to depict the stream flow,
pollutant flows, and costs associated with each pollution control
measure. Recall that the deterministic worst case optimization models
are based on the assumption that pollutant and stream flows are selected
to represent the most adverse situation from a pollution viewpoint. It
is assumed that the worst case has been identified for the variables
defined below. The stream flow at each node is given by
Q(l,J,K) = stream flow at node (l,J,K) exclusive of pollutant.
198
-------
Input values for Q,(l,J,K) are in cubic meters per second, and the pro-
gram converts these amounts to kilograms per hour for the computational
procedure. The pollutant flow rates for each mine source are given as
input by
P(l,J,K) = pollutant flow emitted from the source at node
(l,J,K) without implementation of any pollution
control measures (kilograms per hour ) , and
PA(l,J3K) = pollutant flow emitted from the source at node
(l,J,K) if abatement is implemented (kilograms
per hour) .
Also, the natural pollutant inputs are specified as input data by
PN(l,J,K) = pollutant input to the stream between nodes
(l-l,J,K) and (l,J,K) due to natural sources
(kilograms per hour).
If 1=1, PN(l,J,K) represents all of the natural pollutant input above
the first node. If (l,J,K) is a confluence node, PN(l,J,K) is the
natural pollutant input betwe'en (l-l,J,K) and (l,J,K) plus the natural
pollutant input between stream (J,K) and the last node on stream
Corresponding to these "instantaneous" pollutant flow rates given above,
a set of mean annual pollutant flows are required to calculate treatment
variable costs. These annual pollutant flows are specified as input
data by
AP(l,J,K) = mean annual pollutant load emitted by the source
at node (l,J,K) if no pollution controls are
implemented (kilograms)
APA(l,J,K) = mean annual pollutant load emitted by the source
at node (l,J,K) if abatement is implemented
(kilograms )
APN"(l,J,K) = mean annual pollutant input due to natural
sources between node (l,J,K) and the next up-
stream node (or nodes when (l,J,K) is a con-
fluence node) in kilograms.
In addition to pollution and stream flows, a set of costs for each
alternative control measure at each node is specified as input. The
array C gives the equivalent annual costs for abatement and treatment
(exclusive of variable chemical costs), and values for the array C are
defined by
199
-------
annual costs to abate the mine source at
(I,J,K) for ID = 1 ($)
C(ID,I,J,K) =
" annual cost to implement a treatment processor
for the mine source at (l,J,K) for ID = 2($)
The equivalent annual costs to implement instream treatment processors
are specified by the array CI, where
Cl(NT) = equivalent annual fixed cost to implement instream
treatment at instream treatment site number NT ($)
for
NT = 1, 2, ..., NINST; and
CI(0) = 0.
The variable chemical cost for treatment processors is given by VC, in
dollars per kilogram, specified as input data.
DETERMINISTIC "WORST-CASE" MAXIMUM
EFFECTIVENESS (DWME) MODEL
In this section, the DWME model is described, and the algorithm for
determining the maximum effectiveness solution is presented. This
algorithm is performed by program MAXEF to determine a maximum effec-
tiveness solution. To simplify the understanding of MAXEF, the same
notation is used to describe the algorithm as is used in the program.
Thus, FORTRAN variable names are employed in this section. Computer
program flow charts and input data instructions are contained in a later
section of this appendix.
Criterion Function and Constraint Equation
The DWME model is specified by its criterion function and constraint
equation. These equations are obtained simply by converting the cor-
responding equations for the DSS model to represent a network of streams
and to incorporate the "worst-case" pollutant and stream flows defined
in the previous section.
The DWME analogue of the criterion function given by C.9 is
3 NS(K) ND(J,K)
EFF = E E E E(I,J,K) , (C.ll)
K = KL J = l 1 = 1
200
-------
where E(l,J,K) = effectiveness of pollution control actions on
the stream reach between node (l,J,K) and the
next downstream node on stream J.
EFF = total basin effectiveness of a set of pollution
control actions.
If (l,J,K) is the last node on stream J; i.e., I = ND(J,K), then the
next downstream'node is interpreted to be the outlet of stream J.
Individual reach effectiveness values are determined by
E(I,J,K) = R(I,J,K) EJ(I,J,K) (C.12)
K = 1,2,3; J = 1,...,NS(K); I = l,...,ND(j,K)
\
where R(l,J,K) = relative importance of the stream reach between
node (l,J,K) and the next downstream node on
stream J, 0 < R(l,J,K) < 10;
EJ(l,J,K) = basic value of the stream reach between node
(l,J,K) and the next downstream node on stream J.
0 < EJ(I,J,K) < 10.
To compute the basic value of a stream reach, the pollution concentra-
tion "as a result of a set of control actions is determined and compared
with a set of pollution concentration intervals and their correspond-
ing basic values, specified as input data. That is, M is determined
so that it satisfies
where QJ(M) = upper limit on the pollution concentration for the
Mth interval (input values are in parts per million
(ppm) but Qj(M) values are converted later to
decimal fractions),
QJ(0) = 0
NI = total number of pollution concentration intervals
M = 1, 2, .., NI, and
201
-------
PLl(l,J,K) = pollutant flow rate in kilograms per hour just downstream
at node (l,J,K) resulting from a specified set of control
actions.
This value of M is used to specify the individual reach basic values by
EJ(I,J,K) = BV(M), (
where BV(M) = basic value for pollution concentration interval M.
In order to determine the pollution flow from a set of control actions,
values of PLT(l,J,K) must be determined. PLT(l,J,K) is the deterministic
"worst-case" multi-stream analogue of Pj_^(t) given by equation C.3j or
the total pollutant flow just downstream of node (l,J,K). Pollutant
may reach each node from one or more of the following sources:
1. flow past next upstream node,
2. natural flow originating downstream of next upstream node,
3. tributary if (l,J,K) is a confluence node, and
4. mine source at (l,J,K).
The flow past the next upstream node is given by PLT(l-l,J,K), and the
case where I,J,K is at the head of a stream is handled by defining
PLT(O,J,K) = o
for J = 1,2,...,NS(K);
K = 1,2,3.
The natural flow is given by PN(l,J,K). Pollutant flow from a tributary
is represented by
PT(J,K) = pollutant output rate of stream J of level K
(kilograms per hour);
where PT(J,K) = PLT(ND(J,K),J,K) if J > 0 and K > 0,
PT(0,K) = 0;
PT(J,0) = 0;
PT(0,0) = 0;
J = 1,2,...,NS(K); and
K = 1,2,3.
202
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Also, pollutant output from a source is defined by
PS(l,J,K) = pollutant output rate from source (l,J,K) given
the site abatement and treatment decisions
(kilograms per hour).
In addition, pollutant may be removed from the stream by implementing
an instream processor. Decisions to do so are specified by
0 if instream processor site NT is implemented
DINT(NT) =
1 if otherwise.
NT = 1,2,...,NINST.
If the node (l,J,K) cannot have an instream processor, then
NT = INT(l,J,K) = 0 and DINT(O) = 1. Then necessity for defining
DINT(NT) = 0 if the instream processor is implemented will be apparent
when the optimization procedure is presented. Using the above relation-
ships, the pollutant flow just downstream of node (l,J,K) is given by
PLT(I,J,K) = DINT[INT(I,J,K)]-[PN(I,J,K) + PLT(I-I,J,K) + PS(I,J,K)
+ FT(JN(I,J,K-I),K-I)] + (i - DINT[INT(I,J,K)])
L[PN(I,J,K) + PLT(I-I,J,K) + PS(I,J,K)
+ PT(JW(I,J,K-I),K-I)] (
for I = 1,2,...,ND(J,K);
J = 1,2,...,NS(K); and
K = 1,2,3.
Recall that L(X) is the clip function defined earlier.
The four equations above require values for the pollution output rate
from a mine source after allowing for the site abatement or treatment
decisions. Let these decisions be represented by
1 if abatement is performed at mine source
M(I,J,K) = (I'J'K)' ^
0 if otherwise
203
-------
DT(I,J,K) =
1 if site treatment is to be performed at site
d»J.K), and
0 if otherwise.
The deterministic "worst-case" multi-stream analogue of equation C.2
is used to compute values for PS(l,J,K). Thus,
PS(I,J,K) = DT(I,J,K) -L(DA(I,J,K) PA(l,J,K) + [l-DA(l, J,K) J
(DA(I,J,K) PA(I,J,K) + [
Equations C.ll through C.16 can be used to compute values for the
criterion function of the DWME model. The cost constraint is
TTC < BUD , (C.I?)
where BUD = maximum allowable annual pollution control cost ($),
and
TTC = annual pollution control cost expected as a result of
decisions represented by DINT, DA, and DT arrays.
The total pollution control cost is calculated using the multi- stream
"worst-case" analogue of equation C.4. That is,
3 NS(K) ND(J,K)
TTC = E £ £ (CS(I,J,K) + [1-DINT(INT(I,J,K))]
K = KL J = l 1 = 1
- VC L[-APLT(I,J,K)]]) ;
where CS(l,J,K) = annual cost of pollution control decisions at
mine source (l,J,K) in dollars;
APLT(l,J,K) - annual pollutant load in kilograms passing
stream node (l,J,K) considering the upstream
decision variables given by the DINT, DA, and
DT arrays; and
APLT(O,J,K) = o .
-------
Values of CS(l,J,K) are given by
CS(I,J,K) = M(I,J,K) -C(1,I,J,K) + DT(I,J,K) [c(2,I,J,K)
+ VC ([1-DA(I,J,K)] -AP(I,J,K)
- DA(I5J,K) L[-APA(I,J,K)])] (
Values of APLT(l,J,K) are determined in a manner quite similar to
PLT(l,J,K). That is,
AFLT(I,J,K) = DDJT[INT(I,J,K)] (APN(I,J,K) + APLT(I-I,J,K) + APS(I,J,K)
+ APT[JN(I,J,K-I),K-I]) + [I-DINT(INT(I,K,K))]
L(APN(I,J,K) + APLT(I-I,J,K) + APS(I,J,K)
+ APT[JN(l,J,K-l),K-l]) ; (C.20)
where APT(j,K) = annual pollutant output of stream J of level K
in kilograms, [APT(J,K) = APLT(ND(j,K),J,K) if
J > 0 and K > 0];
APT(0,K) = 0;
APT(J,0) = 0;
APS(l,J,K) = annual pollutant output rate from source (l,J,K)
given the site abatement and treatment decisions
(kilograms ) ;
I = 1,2,...,KD(J,K);
J = 1,2,...,NS(K); and
K = 1,2,3.
The values for the annual source outputs are given by
APS(I,J,K) = DT(I,J,K) . L(DA(I,J,K) APA(I,J,K) + (
AP(I,J,K)) + (1-DT(I,J,K)) (DA(I,J,K) -APA(l,J,K)
AP(I,J,K)) (
for I = 1,2,...,ND(J,K);
J = 1,2,...,NS(K); and K = 1,2,3.
205
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Equations C.l8, C .19, C.20, and C.21 can be used to evaluate the DWME
cost constraint.
Optimization Algorithm
As pointed out by the DSS model, the criterion function and constraint
equations for the DWME model are nonlinear functions of discrete vari-
ables, viz., the DINT, DA, and DT arrays. Thus, available optimization
algorithms such as linear programming, nonlinear programming, game
theory, decision theory, geometric programming, and stochastic program-
ming are inappropriate. Dynamic programming is a possible solution
method, but preliminary investigations indicated that computer require-
ments for a dynamic programming would be more extensive than the method
selected. This conclusion results from the requirement to determine
the optimal resource allocation function at each node for all admis-
sible cost values. The algorithms developed as a result of this
research (for the DWME and DWMC models) are modifications and exten-
sions to the partial enumeration method for discrete optimization prob-
lems formulated by Lawler and Bell.1
The Lawler-Bell algorithm is designed to solve discrete optimization
problems of the following form:
Minimize gQ(X),
Subject to gi;L(x) - g12(x) > 0,
§21(x) - S2200 > 0,
> o,
where X = (xl5 x2, ..., xn), and
Xj = 0 or 1; j = 1,2,...,n; and
where the restriction is applied that each of the functions gn(x),
g-Q^X), ..., g^OO is monotone nondecreasing in each of the variables
xl 5 X2' ' } xn
The basic concept behind the Lawler-Bell algorithm involves ordering
each possible vector X and then proceeding through the list of vectors
XE. L. Lawler and M. D. Bell, "A Method for Solving Discrete Optimiza-
tion Problems," Operations Research, Vol. lU, No. 6, Nov.-Dec 1966
pp. 1098-1112. ' '
206
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to evaluate each vector which could be optimal. Naturally, those
vectors which could not be optimal are skipped. A lexicographic or
numerical ordering is obtained by giving each vector the integer value
/ % n-1 n-2 0
n(x) = Xl2n 1 + x02 + ... -t -
In addition to the numerical ordering, a vector partial ordering is
obtained by regarding
X < Y if and only if x-j < y-j for j = l,2,...,n
where Y = (y±, yl5 ..., yn).
Note that X < Y and Y ^ X are not equivalent expressions. Let X* denote
the first vector following X in the numerical ordering where
X X* .
Lawler and Bell show that X* can be obtained from X readily on a digital
computer by
1. regarding X as a binary number,
2. subtracting 1 from X,
3. logically "or" X and X-l to obtain X*-l, and
h. adding 1 to obtain X*.
The procedure described by Lawler and Bell to identify the optimal solu-
tion involves proceeding through the list of possible solutions and ^
keeping a record of the least costly solution currently identified. X
denotes this solution, and g0(X) is the minimum criterion function value.
Procedure starts with X = (0,0',. ..,0) and ends when X = (1,1,1,.. ,,l).
Letting X denote the vector that is currently being examined, the fol-
lowing rules indicate which vector is evaluated after X:
1. If g0(X) > g0(x), skip to X*. Since X* is the first
vector in numerical order following X where X ^ X*,
then X+l,X+2,...,X*-1 are all greater than or equal to
X in the vector partial ordering. Also, because g0(x)
is monotone nondecreasing, none of the vectors
X+1,X+2,...,X*-1 can have values of g0(X) less than
g0(x).
20?
-------
2. If X is a feasible solution satisfying all constraints
and gQ(x) < g0(x), then X is substituted for X.
3- If X is a feasible solution satisfying all constraints,
skip to X*. Because g0(x) is monotone nondecreasing,
none of the vectors X+l, X+2, ..., X*-l can have values
of the criterion function less than g0(x).
h. If gil(x*-l) - gi2(x) £ 0 for any 1=1,2,...,m, skip to
X*. Note that Y = X*-l maximizes gi:L(Y) and Y = X
maximizes -g,p(Y) f°r a*17 vector between X and X*-l.
Thus, if gi;L(X*-l) - gi200 ^ 0, then no vector Y between
X and X*-l can satisfy constraint i.
5. Skip to X+l if conditions 1, 3, and k do not apply.
Lawler and Bell give representative compute times to solve typical prob-
lems to illustrate the potential efficiency of their method. Using the
procedure listed above, they solved problems involving as many as 30
binary variables with compute times ranging from 10 to 20 minutes on an
IBM 7090. However, third generation computers are considerably faster
than an IBM 7090. Although the increase in compute time for increasing
numbers of variables appears to be less than an exponential function,
it increases at a faster rate than a linear function. Thus, there
appears to be an upper limit on the number of nodes than can be analyzed
in a single problem, and it is important to select an algorithm that is
rapid.
With emphasis upon this efficiency objective, the following extensions
were accomplished in constructing the DWME optimization algorithm:
1. The number of possible alternatives at each mine source
to be evaluated in the optimization algorithm was reduced
from four to three. This modification saves considerable
computer time because Un is much larger than 3n where n
is the number of possible mine sources.
2. The criterion function and constraint equations were
modified so that the criterion function is equivalent to
a nondecreasing function of each of the decision variables
that is to be minimized.
3. The decision variables for a stream network were trans-
formed so that they could be expressed as a vector X.
U. A procedure was developed for determining the next feasi-
ble solution subsequent to any point in the numerical
ordering of the decision vector X. Note that condition k
208
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in the Lawler-Bell procedure defined above only allows
for a test to be made to determine if decision vector
values can be skipped and does not identify exactly the
next feasible solution.
5. The last decision vector, noted as XL, that needs to be
evaluated in the numerical ordering to find the optimal
solution was identified to reduce the number of iterations
required. That is, decision vectors beyond XT in the
numerical ordering will not be optimal.
These extensions listed above are described next in the following dis-
cussion of the optimization algorithm.
Reduction of the Number of Alternatives at Each Mine Source -
The objective of reducing the total number of possible alternatives is
to decrease the number of iterations by the optimization program to
identify an optimal pollution. To illustrate the potential for improve-
ment, consider a basin having three sources and no potential instream
processing sites. Four alternatives exist at each source when one con-
siders all possible combinations of site treatment and site abatement.
Letting the variable MS denote these alternatives
MS =
0 if no pollution control actions are to be performed
1 if abatement but no source treatment is to be performed
2 if treatment but no abatement is to be performed
3 if both treatment and abatement are to be performed
Thus, direct enumeration of all possible combinations of control actions
gives M or 6k alternatives to be considered. However, the pollutant
output of a mine source, say (l,J,K), can have, at most, three possible
values which are P(l,J,K), PA(l,J,K), and zero kilograms per hour if
site treatment is performed. Thus, from a source output viewpoint there
are only y or 27 alternatives to be considered as opposed to 6k origi-
nally.
Zero pollutant output can be obtained in two ways; i.e., site treatment
alone and site treatment combined with abatement; and there are no
interactions to be considered in evaluating these two ways with regard
to stream quality. Obviously, the preferred alternative would be site
treatment or site treatment combined with abatement depending on which
is cheapest. Thus, the zero pollutant output alternative would be both
site treatment and abatement if the annual cost of this alternative is
less than site treatment alone. That is, if
C(2,I,J,K) - VC.L(-APA(I,J,K)) < C(2,I,J,K) + VC . AP(l,J,K)
209
-------
select site treatment and abatement for the zero pollutant output
alternative. Otherwise, select site treatment alone.
From a mine output viewpoint, there are further potential reductions in
alternatives to be considered. Some mines may cost more to abate than
to treat. This may occur when sealing or other abatement procedures
are potentially very expensive. Thus ignore the alternative of abate-
ment alone if
C(2,I,J,K) + VC -AP(l,J,K) .
The result of the tradeoffs described above to reduce the number of
basin alternatives is recorded in several arrays for ready reference
during the optimization procedure. In addition to no pollution control,
two control actions are considered and they are identified by the de-
cision variable ID, where
0 if no pollution control is to be implemented at a
source
ID =
1 to identify the lowest cost pollution control alter-
native (usually involving abatement alone), and
2 to identify the pollution control alternative involv-
ing treatment
Three arrays are employed to completely specify pollution control alter-
natives, their costs, and their pollutant output rates. These arrays
are RALT, CALT, PI and API; where
RALT(lD,I,J,K) = value of MS for pollution control alternative
ID at source (l,J,K);
CALT(lD,I,J,K) = annual cost in dollars for pollution control
alternative ID at source (l,J,K);
Pl(l,J,K) = instantaneous pollutant output rate in kilo-
grams per hour for pollution control alterna-
tive 1; i.e., ID = 1; and
APl(l,J,K) = annual pollutant output in kilograms for
pollution control alternative 1.
Note that the pollutant output rate for pollution control alternative 2;
i.e., ID - 2, is zero kilograms per hour and that the pollution output
rate in the absence of pollution control action is P(l,J,K) kilograms
210
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per hour. Values for the above arrays can be obtained by the relations
shown below:
If C(1,I,J,K) < VC (AP(I,J,K)+ L(APA(I,J,K))),
then RALT(2,I,J,K) = 3
CALT(2,I,J,K) = C(1,I,J,K) + C(2,I,J,K)- VC L(-APA(l,J,K))
, RALT(1,I,J,K) = 1
CALT(I,I,J,K) = C(I,I,J,K)
P1(I,J,K) = PA(I,J,K)
AP1(I,J,K) = APA(I,J,K) .
If C(l,I,J,K) > C (2,I,J,K) + VC AP(l,J,K) ,
then RALT(1,I,J,K) = RALT(2,I,J,K) = 2
CALT(1,I,J,K) = CALT(2,I,J,K) = C(2,I,J,K) + VC -AP(l,J3K)
Pl(l,J,K) = 0.0
AP1(I,J,K) = 0.0 .
Otherwise,
MLT(2,I,J,K) = 2
CALT(2,I,J,K) = C(2,I,J,K) + VC -AP(l,J,K)
RALT(1,I,J,K) - 1
CALT(l,I,J,K) = C(1,I,J,K)
Pl(l,J,K) = PA(l,J,K)
AP1(I,J,K) = APA(I,J,K) . (C.22)
In addition to reducing the alternatives to be considered at a mine
source, another case exists where the alternatives upstream of an active
instream processor should be limited. Recall that abatement costs might
be so inexpensive that treatment at a mine source should always be
coupled with abatement. For the same reason, sources with inexpensive
abatement costs providing influent to an active instream processor
should involve abatement (or treatment and abatement) to achieve minimum
system cost. In this case, no pollution control would be more expensive
than abatement, but treatment and abatement may be implemented to achieve
211
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better stream quality. This situation is identified by the array BS,
where
BS(I,J,K) =
-1 when KALT(2,I,J,K) = 3 and the source at
(l,J,K) provides influent to an active instream
processor, and
0 if otherwise.
Modification of the Criterion Function and Constraint Equations -
Recall that the decisions at each instream treatment site are specified
by the DINT array as defined on page 203; however, the decision alterna-
tives at each mine source have been redefined in the previous section.
The decision variable ID specifies the decision at each node, but the
significance of this variable must be checked to insure that it con-
forms to the Lawler-Bell algorithm.
A requirement of the Lawler-Bell algorithm is that the criterion function
is to be minimized, and it must be nondecreasing in each of the decision
variables X]_,X2,... ,xn. Before the source and instream treatment de-
cisions are reordered to correspond to elements of the vector X, the
maximum effectiveness optimization problem must be transformed to
satisfy the above requirement. If the criterion function; i.e.,
equation C.ll, is multiplied by -1, then the maximization problem is
transformed to a minimization problem. Eecognition of this "trick"
implies that the Lawler-Bell algorithm will work for a maximization
problem where the criterion function is a nonincreasing function of
each decision variable.
However, the criterion function as defined in equation C.ll is an in-
creasing function of the decision variable at each mine source noted by
ID as defined above. Consequently, the decision at each mine source is
specified by
2 if no pollution control is to be imple-
mented at source (l,J,K)
D(I,J,K) = 2-ID =
1 if the lowest cost pollution control
alternative (usually abatement) is imple-
mented at (l,J,K), and
0 if the pollution control alternative
involving treatment is implemented at (l,J,K)
Note that the criterion function will be a nonincreasing function of
each element in the D array and that it already is a nonincreasing
function of the DINT array elements, defined on page 203, specifying
decisions at each instream treatment site.
212
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To incorporate the newly defined decision variables in the criterion
function, equation C.16 giving the pollutant output rate from source
(l,J,K) must be rewritten. Using the definitions given in equation
C.22,
PS(I,J,K) -
P(I,J,K) if D(I,J,K) = 2
P1(I,J,K) if D(I,J,K) = 1
0.0 if D(I,J,K) = 0
(C.23)
Thus, the criterion function is evaluated using equations C.22, C.23,
C.15, C.13, C.l^, C.12, and C.ll. The optimization program uses
Function EFFECT to evaluate the criterion function, and the procedure
for EFFECT is described in Figure C.8 starting on page 303.
The cost constraint is modified in a similar manner. That is, the cost
to control pollution at a mine source given by equation C.19 is replaced
CS(I,J,K) =
CALT(2,I,J,K) if D(I,J,K) = 0
CALT(1,I,J,K) if D(I,J,K) = 1
0 if D(I,J,K) = 2
(C.2U)
In addition, the annual pollution output from a mine source given by
equation C.21 becomes
APS(I,J,K) =
AP(I,J,K) if D(I,J,K) = 2,
AP1(I,J,K) if D(l,J,K) = 1, and
0.0 if D(l,J,K) = 0
(C.25)
Hence, the cost constraint is evaluated using equations C.22, C.2U,
C.25, C.18, C.19, and C.20.
Construction of the Solution Vector X and Identification of the Ne^b
Vector to be Evaluated -
Having defined the decisions variables, the next step in developing the
DWME optimization algorithm is to define a solution vector X consisting
213
-------
of these decision variables. Note that the decision variable at each
mine source can assume three possible values; thus, the solution vector
X consists of both binary and tertiary elements necessitating a new pro-
cedure for specifying the next vector, i.e., X*, to be evaluated. Both
the solution vector X and the procedure for identifying the next vector
to be evaluated are defined in this section.
As specified before, the vector X has n elements or
X = x-j_,X2, . . . jXmjXm+l' >xn '
where n = number of instream processors plus the number of mine sources,
That is,
3 NS (K)
n = NINST + £ £ ND(J,K) .
K = KL J = l
Xju represents the decision at an instream processor or the decision at
a mine source. Hence,
xm = D(I,J,K)
or
= DINT(NT)
These decision variables are assigned as elements of the vector using
the following rules:
1. If % = DINT (NT), then x^ = D(l,J,K); where NT = INT(l,J,K).
That is, the instream processor decision variables are
placed to the left of their corresponding mine source
nodes.
2. The decision variables for each stream always appear
together and ordered so that x^^ is upstream of x^
assuming XJQ represents the decision at a mine source.
214
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3. If ^ represents the most -upstream node of stream J of
level K and J > 1, then xm+]_ represents the most down-
stream node of stream J-l of level K.
h. If xm represents the most upstream node of stream 1 of
level K and K > KL, then x^i represents the most down-
stream node of stream NS(K-l) of level K-l.
The above rules are designed to order these decision variables so that
the downstream decisions are recorded to the left of upstream decisions .
To illustrate the application of the above rules, consider a basin con-
sisting of one level -three stream, two level- two streams, and two level
one streams. Each stream has two nodes, and the downstream nodes of
each level- two stream have potential instream processor sites. Then
X = [D(2,l,3), D(l,l,3), DINT(l), D(2,2,2), D(l,2,2,), DINT(2),
The Lawler-Bell algorithm examines vectors in sequence by ordering each
possible solution vector and working from the first to the last solution
vector. This order is achieved by assigning a number to each solution
vector and placing the vectors in numerical order. This numerical value
for a solution vector is given by
n(X) so
X is evaluted before Y if n(x) < n(Y).
As specified by Lawler-Bell, the elements of the solution vector must
be binary, thus n(x) is just a binary number. For the DWME optimization
model, n(x) must give a numerical value to X where some elements are
binary and some elements are tertiary. Thus,
n
m=l
b n-m-b,.,
where nm = 2 m 3 , and
bm = number of binary elements to the right of xm, i.e.,
sm+2'*"'Xn
215
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Note that the function n(x) assigns integral values to the possible
vectors X ranging from 0 to riQ. To illustrate the numerical ordering
provided by n(X), consider a system composed of a single stream having
two nodes, and the upstream node has a potential instream treatment
site. Thus,
x;j_ = 0, 1, or 2
Xp = 0 or 1
Xo = 0, 1, or 2
A listing of each possible vector in numerical order is shown below:
X n(X) X n(X)
(0,0,0) 0 (1,1,1) 10
(0,0,1) 1 (1,1,2) 11
(0,0,2) 2 (2,0,0) 12
(0,1,0) 3 (2,0,1) 13
(0,1,1) 1+ (2,0,2) llj-
(0,1,2) 5 (2,1,0) 15
(1,0,0) 6 (2,1,1) 16
(1,0,1) 7 (2,1,2) 1?
(1,0,2) 8
(1,1,0) 9
In the optimizing algorithm, we must be able to take an arbitrary
vector X and find the next vector in the numerical ordering. That is,
we must be able to regard X as a number, i.e., the function n(x), and
add one to X giving Y so that n(Y) = n(x) + 1. The following procedure
is used to add one to X:
1. Starting from the rightmost element of X, i.e., xn, find
the first element noted as xa where xa is less than its
maximum possible value. That is, xa < 2 if xa is tertiary
and xa = 0 if xa is binary.
2. Add one to xa, or ya - xa + 1.
3. Set Ya+lsYa+l,,yn &11 equal to zero.
The proof that the above procedure always gives n(l) = n(x)+l is done
by induction on a. If xa is the rightmost element, then it is obvious
that n(Y) = n(X)+l. If a = n-1, then yn_]_ = xn_-L + 1, yn = 0, and xn
216
-------
equals its maximum possible value. Since
n-2
n(x) + 1 = £ xm ' nm ^ xn-l ' nn-l + xn
m=l
and nn_i = xn + 1, then
n-2
n(X) + 1 = £ xm nm +(xn_i + l) nn_i and
m=l
n(Y) = n(x)
To show n(Y) = n(X) + 1 for all values of a, assume that n(Y) = n(X) + 1
for a and then show that this assumption implies n(Y) = n(x) + 1 for
a-1. Thus we assume that
a-1 n
n(x) + 1 = £ xm nm + xa . na + £ x^ . nm
m = 1 m = a+1
a-1
Z xm ' nm + (xa
m=l
= n(Y)
when xa is less than its maximum value and xa+]_,xa+2j . 3xn are all
equal to their maximum values. Note that the above expression must also
be valid for the case where xa is equal to its maximum value if it is
true when xa is less than its maximum value. For the a-1 case assume
that xa,xa+i,... ,xn are all equal to their maximum values and xa_]_ is
not. Expanding the expression for n(x),
a-2 n
n(x) + 1 = £ xm . nm- + xa_i na_]_ + ^ xm . nm
m = 1 m= a
21?
-------
Based on our assumed relationship for the a case,
a-2
n(x) + 1 = £ xm ' nm + xa-l na-l
m=l
Note that (xa+l) na = na_i because xa is equal to its maximum value.
Thus,
a-2
n(x) + 1 = £ xjn nm + (xa_i + l)na_l ,
m= 1
which proves that the procedure for adding one to X is valid.
This procedure for adding one to X to find the succeeding vector in the
numerical ordering must be extended to handle two additional cases.
These cases occur when x^ represents a mine source at (l,J,K), and they
are:
1. If RALT(l,I,J,K) = 2, then the decisions % = 0 and
:% = 1 are identical since abatement is more expensive
than treatment. Thus, the decision xm = 1 may be skipped.
2. If BS(l,J,K) = -1, then the decision represented by y^ = 2
is not permitted since an instream treatment processor
downstream of (l,J,K) is active and no pollution control
at (l,J,K) is more expensive than abatement.
The extended procedure incorporating the above cases for proceeding
from X to Y, the next vector in the numerical ordering, is shown below:
1. Set m = n.
2. Set (l,J,K) = node coordinates for xm.
If x^ = 2, go to step 5-
If Xjn = 1, xm represents a mine source, and BS(l,J,K) = -1,
go to step 5.
If xm = 1 and Xjjj represents an instream processor, go to
step 5-
218
-------
3. *m is less than its maximum value.
Set ym = xm + 1.
If ym = 1, xm represents a mine source, and RALT(l,I,J,K) = 2,
set ym = 2.
U. Go to step 6.
5. xm is eq.ua! to its maximum value.
Set ym = 0.
m - 1 -» m. (The operation a + b -» a means add b to a and
record the sum as the new value of a.)
Go to step 2.
6. Set y-j_ = Xi>y2 = X2' J^m-l = -^m-l- T^e nex* vector in
the numerical ordering has been determined.
Regard XQ, if encountered in the above procedure, as equal to zero.
In addition to the numerical ordering, the vector partial ordering is
important since X < Y implies that Y cannot have greater effectiveness
than X. The vector partial ordering is defined by
X < Y if and only if x^ < ym for m = 1,2, ... ,n .
For example, if X = (l,l,2) and Y = (2,0,0), then X ^ Y and Y ^ X, but
n(x) < n(Y).
As before, let X* denote the first vector following X in the numerical
ordering where
X X* .
The basic procedure for determining X* is outlined below:
1. Starting from the rightmost element of X, i.e., xn, find
the first nonzero element. Designate this element as xa.
2. Set xa* equal to the maximum value of xa. Also, set all
elements to the right of xa* equal to the maximum values
of their respective elements. Set x^ = xm for
m = 1,2, ... ,a-l.
3. Add one to X*.
219
-------
Note that the vector X* obtained at the completion of step 2 above
satisfies
X < X* .
This is true since there is no element of X* (as determined by step 2)
which proceeded past its maximum value in the numerical ordering between
X and X*. By adding one to X* in step three, xa* becomes zero and
smaller than xa. Thus X ^ X*.
More explicitly, the procedure for determining X* is outlined below:
1. Set m = n.
2. Set (l,J,K) = node coordinates for the decision variable
Xjjj. If xm> 0, go to step 5.
3. Set Xjn* = 2 if xm represents a mine source and BS(l,J,K) / -1.
Otherwise, set xm* = 1.
k. m - 1 -» m.
Go to step 2.
5. If x^ represents a mine source and BS(l,J,K) / -1, set
*m* = 2.
Set x-j-j* = X]., for b = l,2,...,m-l.
6. Replace X* with the next vector in the numerical ordering
subsequent to X*.
7. The procedure is complete, i.e., X ^ X*.
Several examples are shown below to illustrate the procedure.
Example 1:
X = (0,1,1,0,2,1,0),
where x^ represents an instream treatment facility.
Then X* = (0,1,1,1,0,0,0).
Example 2:
X = (0,1,1,1,0,0,0),
220
-------
where x? represents an instream treatment facility.
Then X* = (0,2,0,0,0,0,0).
Example 3
X = (0,1,1,1,2,1,0),
where x^ represents the mine source at node (2,1,3), RALT(2,2,1,3) = 35
BS(2,1,3) = -1,
Xo represents the mine source at node (3,1,3), and BS(3,1,3) = -1.
Then X* = (0,2,0,0,0,0,0).
Example k:
X = (0,1,1,2,0,0,0),
where xo represents the mine source at node (3,1,3) and BS(3,1,3) = -1.
Then X* = (0,2,0,0,0,0,0).
Determination of the Next Feasible Solution -
The value of X* obtained in the procedure described above may be more
effective than X, but X* may not be a feasible solution since it could
violate the cost constraint. At this point in the Lawler-Bell algorithm,
a check is made to determine whether X* is feasible. If so, the pro-
cedure outlined in extension 3 above is repeated. Otherwise, checks are
made to determine if more vectors could be skipped to find a feasible
solution. This search for a feasible solution would involve many
iterations.
A much more efficient method is used by the DWME algorithm where a
procedure has been developed which identifies precisely the next feasi-
ble solution in the numerical ordering beyond an arbitrarily selected
point. Since this procedure does not require much more computational
effort than to evaluate the cost constraint, the overall efficiency of
the optimization algorithm has been clearly enhanced. Subroutine
NEFESE is used to specify the next feasible solution. The method
employed by NEFESE is outlined in this section, and a flowchart of the
subroutine is presented in Figure C.10 on page 309.
The basic idea inherent in the procedure to identify the next feasible
solution makes use of the lexicographic nature of the numerical order-
ing of possible values for X. The numerical ordering given by n(x) is
lexicographic because addition of one to an element, e.g., xa, increases
221
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the numerical value of X by more than the possible contribution of all
elements to the right of xa. This is true because
n
(xa + l)na = 1 + £ Xm nm ,
m= a
where xa+;j_,xa+2j... ,xn all have their maximum possible values.
Because of this lexicographic property, the next feasible solution pro-
cedure can start with the leftmost element, i.e., x-[_, determine its
value for the next feasible solution and then do likewise for elements
on the right. To specify this basic procedure, let
X = (xl3X2,...,xn) = the current solution (not necessarily
feasible)
X* = (x3_*,X2*,.. .,xn*) = the next feasible solution vector
equal to or after X in the numerical
ordering.
Note that X* = X if X is feasible. Consider the determination of x^_*
to illustrate the procedure. Compute the cost of the decision X]_ under
the assumption of no pollution control costs to the right of X]_, and
note this cost as TTC. If TTC is less than BUD, the maximum allowable
pollution control expenditure, then allocate TTC out of BUD and
set XT* = XT . If TTC is greater than BUD, then XT_* must be greater than
X-, to achieve a feasible solution. If x-,* is forced to be greater than
X]_, no intervening feasible solutions between X and X* are skipped if
X2,xo,...,xn are all set to zero. Setting x^_* to be greater than x^_ if
required is permitted because of the lexicographic nature of the numeri-
cal ordering and the assumption that no pollution costs are incurred as
a result of decisions to the right of x^_. After X]_* is determined, xg*
is determined, but now the allowable budget is BUD - TTC. Again, the
lexicographic nature of the numerical ordering permits a serial alloca-
tion of available budget in this manner.
The calculation of TTC when xj_ is a decision variable that represents a
mine source is straightforward; however, instream treatment processor
decisions are complicated by the fact that upstream pollution control
decisions change treatment variable costs. Increasing pollution con-
trol upstream will always decrease treatment variable costs; however,
most upstream pollution actions will increase total system cost. An
exception is made when upstream abatement will decrease total cost, and
this situation is identified when BS(l,J,K) = -1. The principle that
222
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TTC will represent the minimal increase in total system cost will be
invoked to calculate TTC for an instream processor decision. Conse-
quently, the cost TTC when Xn represents a treatment processor consists
of the sum of the following components:
1. Cl(NT), the instream treatment processor fixed cost.
2. VC -APINS(NT), where APINS(NT) is the annual pollutant
flow past instream processor NT under the assumption the
only upstream pollution control actions taken will be
when abatement reduces total system cost, i.e.,
BS(I,J,K) = -1.
3. The total cost to perform abatement at each upstream node
where BS(l,J,K) = -1. This cost is computed by Function
CABAT (see Figure C.6 on page 296 for flow chart of
CABAT).
At upstream nodes, the calculation of costs to determine values of xm*
must consider interactions with active downstream treatment processors.
Two arrays are used to determine if a decision variable is upstream of
an active downstream treatment processor. These arrays are:
1 if mine source at (l,J, K) is upstream of
KNINT(I,J,K) =
0 if otherwise
an active treatment processor
KB INT (NT) =
1 if the instream processor site NT is up-
stream of another active instream processor,
and
0 if otherwise
These arrays are maintained by subroutine TONE whenever an instream
processor is initiated and subroutine TOFE when an instream processor
is deactivated. Moreover, these subroutines maintain the array BS to
specify when abatement or treatment and abatement is required at up-
stream nodes. See Figures C.ll and C.12 for flowcharts of these
routines. If a decision variable is upstream of an active instream
processor, then function CSAVE can be used to determine the reduction
in treatable annual pollutant flow at the downstream treatment site that
can be realized by a particular decision at the upstream site. The
value returned by CSAVE can be used in determining the savings in treat-
ment costs by virtue of a pollution control decision at the upstream
site. CSAVE uses an array APST to maintain a running balance of the
annual pollution flow past each instream treatment site, where
223
-------
APST(NT) = annual pollution flow in kilograms past treatment
site NT based on the current values of X*.
The values for APST(NT) are initially set equal to APINS(NT), and then
they are altered as values for X* are determined at upstream nodes. Of
course, CSAVE only recognizes a reduction in treatable or positive
values of APST(NT).
With the above mechanisms for handling interactions with instream pro-
cessors, the computations for determining a value for xm* can be
specified. Let TTC now represent the total allocated pollution control
cost for decisions XjL*,x2*,...,x|_x; thus, the cost calculations for xm*
determine the increase in TTC such that TTC < BUD and xm* > :%. Also,
let TC represent the trial total allocated pollution control cost for
the decision represented by x^, and TTC will become equal to TC if
TC < BUD.
If xm represents the decision at instream processor NT, the following
procedure is used to specify xm*:
i. if xm = i (or DINT(NT) = i), go to step 8.
2. Set (l,J,K) equal to the node coordinates for NT.
3. Compute the trial allocated cost, i.e.,
TC = TTC + CI(NT) + APINS(NT) vc + CABAT(I,J,K,IS) if
APINS(NT) > 0; otherwise
TC = TTC + CI(NT) + CABAT(I,J,K,IS).
(The variable IS is only used to improve the efficiency
of the computer program and is not necessary to understand
the basic computational procedure.)
h. if KSINT(NT) = o, go to step 6.
5. Set SAVE equal to the savings in treatable annual
pollution flow; i.e., SAVE = CSAVE(-1,I,J,K,IS,NX);
where NX is determined by function CSAVE and is the
active downstream site treating flow from NT.
TC - VC SAVE -» TC.
6. If TC < BUD, go to step 9.
7. The budget will not permit NT to remain active; thus,
xm* = i or DINT(NT) = i
CALL TOFE(NT,I,J,K)
CALL ZOE(I,J,K)
22k
-------
Subroutine ZOE sets the decision variables
xm+l'xm+2''^n ^° zero to avoid skipping any feasible
solutions. The computations are complete.
8. xm* = i or DINT(NT) = i
The computations are complete.
9. The budget will permit NT to remain active.
TTC = TC
APST(NT) = APINS(NT)
if KSINT(NT) = i, set APST(NX) - SAVE-* APST(NX).
%* = o
The computations are complete.
If Xjn represents the decision at the mine source located at (l,J,K).
the following procedure is used to specify xm*:
1. If Xjjj = 2, go to step 10.
2. If x^ = 1, go to step 6.
3. TC = TTC + CAI/T(2,I,J,K)
If KNINT(J,J,K) = 0, go to step 5.
U. (l,J,K) is upstream of an active instream treatment
facility. Set SAVE equal to the savings in annual pollu-
tion flow if treatment is implemented at this site.
SAVE = CSAV(0,I,J,K,IS,NX)
TC - VC SAVE -» TC
if BS(I,J,K) = -i, TC - CALT(I,I,J,K) -» TC.
5. If TC < BUD, go to step 8.
xm* will be at least one, so set xm = 1.
Call subroutine ZOE to set %ri-l»:xnri-2s »xn equal to
zero so that no feasible solutions are skipped.
6. If B3(I,J,K) = -1, go to step 10.
TC = TTC + CALT(I,I,J,K)
If KNIHT(I,J,K) = 0, go to step 7.
Compute the annual savings in pollution flow at the down-
stream processor; i.e., SAVE = CSAV(l,I,J,K,IS,NX)
TC SAVE VC -> TC .
7. If TC < BUD, go to step 10.
The budget will not permit pollution control action at
this site.
%= 2.
Call subroutine ZOE to set Xjn+i,xlttf25 >xn ^
225
-------
Go to step 10.
8. Increase the resource allocation by
TTC = TC
If KNINT(I,J,K) = 0, go to step 10.
9. Update the annual pollution flow at the downstream treat-
ment site
APST(NX) - SAVE-^ APST(NX).
10. xm* - xm.
Specification of the Last Decision Vector to be Evaluated -
In addition to providing for a more rapid method of searching the list
of decision vectors, savings in computational effort can be gained by
recognizing when further searching will not uncover a more effective
solution. The Lawler-Bell algorithm requires that the entire list of
decision vectors be examined; thus, the search can certainly terminate
when X.Q becomes greater than zero or n(x) = ng. Actually the search
can terminate prior to this point, and the stop criterion is described
below.
The last decision vector in the numerical sequence would be made up of
maximum values for each decision variable. The physical significance
of this vector is that no pollution control action would be taken, and
the cost of this vector would be zero. Another decision vector exists
in the numerical sequence, called XL, where all vectors beyond XL merely
reduce control action specified by XL without adding any new control
action. If XL is feasible, there is no need to evaluate decision
vectors beyond XL since the criterion function or system effectiveness
will be nonincreasing at that point.
The stopping decision vector, XL, can be determined by allocating the
pollution control budget to the rightmost elements of the decision
vector. All other elements would be set to their maximum values. It
follows that decision vectors past XL in the numerical sequence will
only reduce the allocation specified by XL. Let XL = (x1L,x2L,...,xnL);
and let XL be made up of decision elements at mine sources, where
DL(l,J,K) = value of the stopping decision vector element at
the mine source (l,J,K)
and decision elements at instream treatment processors, where
= value of the stopping decision vector at the
instream treatment site NT.
226
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The procedure for determining values of these elements is summarized
below:
1. Set TTC = 0.0.
TTC will be used to accumulate the allocated budget.
1 = 1
J = 1
K = KL
PUL = 0.0
PUL will be used to accumulate annual natural pollutant
flow.
2. If K = KL, go to step 3.
NF = JN(I,J,K-1)
If NF < 0, go to step 3.
This is a confluence node. Add in flow from the tributary.
PUL + PTL(NF,K-1) -> PUL, where
PTL(j,K) = pollutant output from stream (J,K)
3. Set TTC1 = TTC + CALT(2,I5J,K)
If TTC1 > BUD, go to step 10.
k. DL(I,J,K) = o
TTC = TTC1
PUL + APN(I,J,K) -» PUL
NT = INT(I,J,K)
If NT < 0, go to step 6.
5. This node has a potential instream treatment site.
TTC1 = TTC + CI(NT) + VC PUL if PUL > 0; otherwise
TTC1 = TTC + Cl(NT)
If TTC1 > BUD, go to step 10.
DINTL(NT) = o
TTC = TTCl.
6. If I > ND(J,K), go to step 7.
I + l-» I
Go to step 2.
7 PTL(J,K) = PUL
PUL = 0.0
If J > NS(K), go to step 8.
J + 1-* J
T _ "1
Go to step 2.
8. If K > 3, go to step 9
J = 1
22?
-------
K + l-> K
Go to step 2.
9. There is sufficient budget to implement each possible con-
trol action in the entire basin. Computations are complete.
10. The budget has been allocated. Set the remaining decision
vector elements to their maximum values. Computations
are complete.
Note that large pollution control budgets will give lower values of XL
in the numerical ordering. However, a large budget will also give
lower values of X for the first feasible pollution. Thus, an interest-
ing interplay exists between budget size and the set of solutions to be
evaluated.
Overall Computational Procedure for DWME Model -
Program MAXEF determines the maximum effectiveness solution for the
basin. MAXEF incorporates the extensions described above to the Lawler-
Bell algorithm in determining the optimal solution. This optimal set
of decisions is recorded in the two arrays whose elements are defined
below:
0(l,J,K) = optimal value of D(l,J,K)
0INT(NT) = optimal value of DINT(NT).
To determine the optimal solution, the most effective or maximum value
of the effectiveness function is recorded in the variable EF. As new
feasible decision vectors are found with greater effectiveness than EF,
EF is increased, and the decision vector is stored in the 0 and OINT
arrays. Note that there is likely to be more than one solution that
can give the same value for EF. As new feasible solutions are uncovered
with effectiveness measures equal to EF, the lowest cost solution is
retained in the 0 and OINT arrays. The cost for the solution currently
recorded as optimal is recorded in the variable TC.
The procedure followed by MAXEF in determining an optimal solution is
outlined below:
1. Initialize variables
TC = 1031
EF = -1031
Set the D and DINT arrays to zero values.
Compute the elements of the stopping vector, i.e., the
values of the DL and DINTL arrays.
228
-------
2. Call subroutine NEFESE to determine thei-nextufeasible
solution which is recorded in the D and DINT arrays.
NEFESE also sets TTC = cost of feasible solution given
by D and DINT arrays.
3. Compute the effectiveness of this solution using function
EFFECT, and record the effectiveness in EFF.
U. If EFF < EF, go to step 5.
If EFF = EF and TTC > TC, go to step 5.
Record a new optimal solution in the 0 and OINT arrays.
EF = EFF
TC = TTC.
5- Using the procedure outlined in extension 35 skip to the
next decision vector in the numerical ordering which
could have greater effectiveness than EF. Record this
decision vector in the D and DINT arrays.
6. Check to determine whether the decision vector in the D
and DINT arrays is past the decision vector made up of
elements from the DL and DINTL arrays in the numerical
ordering. If so, go to step 8.
7. Go to step 2.
8. The optimal solution is recorded in the 0 and OINT arrays.
Its effectiveness is EF and cost is TC.
A description of program MAXEF appears in Figure C.5 starting on page
258.
Deterministic "Worst-Case" Minimum Cost (DWMC) Model -
In this section, the DWMC model is presented, and the optimization
method for finding the minimum cost solution to achieve a fixed quality
standard is described. A considerable amount of the notation and method
for this optimization model is. based on the notation and equations
explained earlier for the DWME model. As much as possible, the same
variable names are used for both optimization models to facilitate the
understanding of both programs. Thus, references will be made to equa-
tions developed earlier.
A complete description of the model is obtained in three steps. First,
the criterion function and constraint equations are specified to present
the model. Next extensions to the Lawler-Bell algorithm are presented
and outlined. The overall procedure used by program ALCOT is then
described. Finally, computer program descriptions, input data instruc-
tions, and flow charts are contained in a later section of this appendix.
229
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Criterion Function and Constraint Equations
The minimum cost model uses an expression for the total pollution con-
trol cost as its criterion function and expression for the allowable
pollution concentration at each node as the constraint equations. The
corresponding expressions developed for the maximum effectiveness model
can be used with one significant modification. Recall that the partial
enumeration algorithm requires a nondecreasing criterion function of
each decision variable for a minimization problem. Since the decision
variables, as defined for the DWME model, would decrease cost as they
are increased, their meaning must be inverted for the minimum cost
model. Hence, the following definitions are used for DWMC model:
DINT(NT) =
1 if instream processor NT is implemented where NT > 0
0 if otherwise
2 if the pollution control alternative
involving treatment is implemented at
D(I,J,K) = ID =
1 if the lowest cost pollution control
alternative (usually abatement) is performed
at mine source (l,J,K), and
0 if no pollution control actions are taken
at mine source (l,J,K)
Incorporating the above definitions into the expression for total
system cost; i.e., equation C.18, the criterion function for the DWMC
model becomes
3 NS(K) ND(J,K)
E Z E [CS(I,J,K) + DOTT(INT(I,J,K))-(CI(INT(I,J,K))
= KL J = 1 1 = 1
- VC L(-APLT(I,J,K)))] (C.26)
The annual cost of pollution control decisions at mine source (l,J,K),
CS(l,J,K), is now specified by
CS(l,J,K) =
CALT(2,I,J,K) if D(I,J,K) = 2
CALT(I,I,J,K) if D(I,J,K) = i
o if D(I,J,K) = o
(C.27)
230
-------
Also, the annual pollutant load passing stream node (l,J,K) becomes
APLT(I,J,K) = (1-DINT(INT(I,J,K)))'(AHT(I,J,K) + APLT(l-l,J,K)
+ APS(I,J,K) + APT(JW(I,J,K-1),K-1))+DINT(IIIT(I,J,K))
L(APN(I,J,K) + APLT(I-I,J,K) + APS(I,J,K)
(C.28)
The annual pollution output from a mine source is an input to the above
equation and is specified
APS(l,J,K) =
0 if D(I,J,K) = 2,
AP1(I,J,K) if D(I,J,K) = 1, and
AP(I,J,K) if D(I,J,K) = 0. (C.29)
Equations C.26 through C.29 constitute the DWMC model criterion function
which is to be minimized. Function TCOST is used by the DWMC model to
compute values of system cost given the decision arrays D and DINT, and
a flowchart at TCOST is shown in Figure C.22 on page k3/S.
The constraint equations for this DWMC model are derived from the
objective of maintaining the maximum pollutant concentration below a
specified level. Let
QS = maximum allowable pollution concentration in ppm.
Thus,
PLT(I,J,K)
PLT(I,J,K)
10
-6
for I = 1,2,...,ND(J,K);
J = 1,2,..., US (K); and
K = KL, KL + 1,3 (C.30)
231
-------
Using the decision variable definitions specified above, in equation
C.30, the pollution flow just downstream of node (l,J,K) is
PLT(I,J,K) = (1-DINT(INT(I,J,K)))-(PN(I,J,K) + Hff(l-l,J,K) + PS(l,J,K)
+ PT(JN(I,J,K-I),K-I)) + DINT(INT(I,J,K))-L(PN(I,J,K)
+ PLT(I-1,J,K) + PS(I,J,K) + PT(JN(I,J,K-1),K-1))
(c
for I = 1,2,...,ND(J,K);
J = 1,2,...,NS(K); and
K = KL, KL + 1,3-
The pollution output rate from source (l,J,K), required for the above
equation, is given by
PS(I,J,K) =
0 if D(l,J,K) = 2
P1(I,J,K) if D(I,J,K) = 1
P(I,J,K) if D(I,J,K) = 0.
The constraints for the DWMC model are given by equations C.30, C.Slj
and C.32.
Optimization Algorithm
The criterion function and constraint equations defined above are
already in a suitable form for application of a partial enumeration
optimization algorithm. The requirement for a nondecreasing criterion
function of each decision variable in a minimization problem has been
satisfied. Also, the rules for expressing the set of decision vari-
ables, i.e., the D and DINT arrays, as elements of a vector X can be
applied directly from the DWME algorithm.
In a manner similar to the DWME algorithm, several extensions to the
Lawler-Bell algorithm have been developed to substantially reduce com-
putation effort. These extensions include a method for specifying the
next feasible vector in the numerical ordering and a method for desig-
nating the stopping vector in the numerical sequence. Moreover, a
method for decomposing the basin system into subsystems has been
developed for the minimum cost algorithm. This decomposition permits
substantial additional reductions in the number of iterations. The
instream treatment facilities, when implemented, are natural points at
which this decomposition is made.
232
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Decomposition at Instream Processors
The interaction between decisions upstream of an active instream
processor and the remainder of the basin is nil. In that case the pol-
lutant output of the instream processor node is fixed at zero, and the
decisions which minimize the criterion function are those which give a
minimum cost solution upstream of the instream processor regardless of
the decisions in the remainder of the basin. Consequently, once a
minimum cost solution upstream of an instream processor has been found,
this solution will be optimal whenever the instream processor is imple-
mented.
Implementation of this decomposition at active instream processors is
facilitated by the basic numerical order, or lexicographic order, in
which the possible solutions are enumerated. That is, once an instream
processor is implemented, its decision variable ^ in the decision
vector X is changed from zero to one; and all decisions to the right of
Xjjj, i.e., Xjn-t-ijXm+2' '%' mVLS^ cycle completely through their numeri-
cal sequence from each element having a value of zero to each element
being equal to its maximum value. More explicitly, once the instream
processor is activated, then
1. Its decision variable y^ in the decision vector X is
changed from zero to one ;
2 . All decision variables to the right of x^ must cycle
through all alternatives from
= 0)
to
where x m = maximum value of decision vector element a
y m - 1 ?
Xa - J-,^,
3. The remainder of the decision vector to the left of x^
is held constant until
-'Tftt-l' xm+2 = xm+23 '% /
is reached.
The least cost feasible solution occurring while the numerical sequence
from (xm = 0, x^i = 0, xn = o) to (xm+1,xj£+2j . . . ,xnm)'is being searched
is an optimal upstream solution to the instream processor. This is true
because the vector (xm+]_,xm+2j 5xn) contains all the nodes upstream
of xm. Although this vector may have nodes in addition to those
233
-------
upstream of xm, all possible combinations of those nodes upstream of xm
and those not upstream of xm but to the right of xm are searched.
To capitalize on this decomposition, the first time that an instream
processor is activated, the optimal upstream solution is determined as
each upstream decision vector is searched. Then the next time the in-
stream processor is activated, its optimal upstream solution is immedi-
ately implemented and used until the processor is deactivated.
The mechanism for implementing this decomposition by program ALCOT is
described below. Four variables are used in the process of determining
the optimal upstream solution, and they are:
(1 if instream processor L has had an optimal
upstream solution calculated
WJ.V.AJ/ - I
lo if otherwise,
IO(l,J,K,L) = optimal value of D array for source (l,J,K)
and upstream solution to the instream processor
L,
IOl(NT,L) = optimal value of DINT array for instream pro-
cessor NT and upstream solution to instream
processor L,
CIST(L) = total cost of solution recorded in 10 and 101
arrays for upstream solution to instream pro-
cessor L;
where L = 1,2,...,NINST;
I = 1,2,...,ND(J,K);
J = 1,2,...,NS(K);
K = KL, KL+1, 3; and
NT = 1,2,...,NINST.
When instream processor L is activated, subroutine TON is called to
prepare upstream variables. TON can determine whether L has an optimal
upstream solution calculated by the value of Ol(L). The first time the
processor is activated, TON sets BS(l,J,K) = -1 for each upstream node
where abatement is cheaper than no pollution control due to savings in
treatment variable costs. Also, TON initializes CIST(L) to a large
number. As program ALCOT determines feasible basin solutions having
lower cost than CIST(L), then these solutions are stored in the 10 and
101 arrays; and the value of CIST(L) is adjusted. Later, when ALCOT
progresses sufficiently through the numerical sequence of the solution
vector to deactivate instream processor L, then ALCOT calls subroutine
234
-------
TOFF to record the fact that the upstream solution for L in the 10 and
101 arrays is optimal by setting 01(L) = 1. Also, TOFF resets
BS(l,J,K) = 0
D(I,J,K) = 0
for any upstream node where
BS(l,J,
K) = -1.
Once the above procedure has been completed, subsequent activations of
the instream processor will be accompanied by immediate jumps to the
optimal upstream solution. Two additional arrays are employed by pro-
gram ALCOT to freeze the upstream solution at its optimal value.
These variables are:
1 if the decision variable for source (l,J,K)
is not being varied because it is frozen as part
of an optimal upstream solution,
BS(I,J,K) =
BT(NT) =
0 if no restrictions are being placed on the
decision variable for source (l,J,K), and
-1 if abatement or treatment and abatement must
be performed at source (l,J,K) because it is
upstream of an active instream processor and no
control is more expensive than abatement.
1 if the decision variable for instream proces-
sor NT is frozen as part of an optimal upstream
solution, and
0 if no restrictions are being placed on the
decision variable for instream processor NT.
If subroutine TON is called after instream processor NT is activated
and an optimal upstream solution has been calculated, i.e., 01(NT) = 1,
then TON sets the values in the D and DINT arrays upstream of NT to the
optimal values recorded in the 10 and 101 arrays. In addition, each
node upstream of NT has its values in the BS and BT arrays set to one.
The BS and BT arrays prevent any changes to elements of the D and DINT
arrays upstream of NT. Later, when NT is deactivated, the entries in
the D, DINT, BS, and BT arrays upstream of NT are set to zero.
235
-------
The procedures noted above to take advantage of possible decompositions
at active instream processor sites necessitate changes in the procedure
to skip solutions that are obviously nonoptimal. Recall that a proce-
dure is specified on page 219 for skipping from an arbitrary vector X
to a vector X* which is the first vector subsequent to X in the numeri-
cal ordering which could be optimal. That is, X* is the first vector
subsequent to X in the numerical ordering where
X X*.
This procedure requires another procedure to determine the next vector
in the numerical ordering in which blocked and redundant solutions are
skipped. The amended procedure for finding Y the next vector in the
numerical ordering subsequent to X is outlined below:
1. Set m = n.
2. If % represents an instream treatment facility, go to
step 7.
3. Set (l,J,K) = node coordinates for xm.
If BS(l,J,K) = 1, go to step 6.
If xm = 2, go to step 5.
U, Xjjj is less than its maximum value.
Set ym = ** + 1-
If ym = 1 and BALT(l,I,J,K) = 2, set ym = 2.
Go to step 10.
5. Xjn is equal to its maximum value.
If BS(l,J,K) = -1, set ym = 1; otherwise set ym = 0.
m - 1 -* m.
Go to step 2.
6. % is frozen at its current value.
Set ym = xm.
m - 1 > m
Go to step 2.
7. Set NT = the instream treatment number for x^.
if BT(NT) = i, go to step 6.
If Xjn = 1, go to step 9-
8. Xjjj is less than its maximum value.
Set Xjn = 1.
Go to step 10.
236
-------
9. xm is equal to its maximum value.
Set xm = 0.
m - 1 -> m
Go to step 2.
10. Set y-L = xl5y2 = x2,...,ym_i = %_i-
The next vector in the numerical ordering has been deter-
mined.
The procedure for determining X*, which is the first vector subsequent
to X in the numerical ordering that could be optimal, is listed below.
1. Set m = n.
2. If % represents an instream treatment site, go to step 7-
3. Set (l,J,K) = node coordinates for the decision variable
^HL*
If BS(l,J,K) = 1, go to step 6.
If BS(I,J,K) = -1 and xm = 1, go to step 5.
If xm = 0, go to step 5.
k. xm is greater than its minimum value.
Set xj = 2.
Go to step 10.
5. xm equals its minimum value.
Set x* = 2.
m - 1 -> m
Go to step 2.
6. x-m is frozen at its current value.
*
bet xm - xm.
m - 1 -> m
Go to step 2.
7. Set NT = the instream treatment site number for decision
variable xm.
if BT(NT) = i, go to step 6.
If xm = 1, go to step 9.
8. Xjn is equal to its minimum value.
Set xj = 1.
m - 1 -> m
Go to step 2.
23?
-------
9. xm is greater than its minimum value.
.-x-
Set xj = 1.
10. Set xb = xb for b = l,2,...,m-l.
Replace X* with the next vector in the numerical ordering
subsequent to X*.
Determination of the Next Feasible Solution -
For the same reasons as implemented in the DWME algorithm, a procedure
has been developed for the DWMC algorithm to determine the next feasible
solution in the numerical ordering given an arbitrary decision vector
X. A considerable number of iterations can be saved by proceeding
directly to the next feasible solution in one step. Let,
X = X]_jX2,... ,xn = the current solution (not necessarily
feasible); and
X* = X2_*,X2*5... jXn* = the next feasible solution vector
equal to or after X in the numerical
ordering
The vector X* is determined in the algorithm by subroutine NEXFES (see
Figure C.I? for a flowchart of NEXFES).
The procedure for determining the next feasible solution relies heavily
upon the lexicographic nature of the numerical ordering and is illus-
trated by considering the problem of determining x^_*. Let QMAX be the
maximum pollutant that can be emitted from the node represented by x-,
without violating the quality constraint. In calculating QMAX, assume
that treatment is being performed at all upstream nodes. If the
decision implied by X]_ emits pollutant at a rate less than or equal to
QMAX, then xj_* must equal x^_ because intervening feasible solutions in
the numerical ordering would be skipped otherwise. For example, the
solution with treatment being applied at each upstream node would be
skipped if X]_* > X]_. The other cases occur when the decision implied
by XQ_ emits more pollutant than QMAX. When this occurs, x^_* must be
greater than xj_, but X]_* is set to the smallest value such that the
pollutant output is less than or equal to QMAX. Also, if XT* is forced
to be greater than xj_, then X2,X3,...,xn are all set to zero for subse-
quent computation in the procedure. Setting these variables to the
right of x-j_ to zero when x-j_* is greater than x-j_ is required because of
the lexicographic nature of the numerical ordering and to avoid skipping
intervening feasible solutions. Subroutine ZD, flowcharted in Figure
C.25, is used to set decision variables to zero.
238
-------
After X]j* is determined, then X2* is determined in the same manner but
based upon the value of x^_*. Thus, QMAX must be calculated considering
the quality standards at the nodes for X2 and X]_ and the node for X]_
receives pollutant at the rate specified by X]_*. The lexicographic
nature of the numerical ordering permits this sequential solution pro-
cess.
A minor change in the previously defined variable PN(l,J,K) simplifies
calculations performed by subroutine NEXFES considerably. Eecall that
the calculation of QMAX for a specified node is based upon all upstream
decision variables having treatment specified. Then the only pollutant
input to the specified node would be natural pollutant that was not
removed by instream treatment processes. Let this natural pollutant
input be
PN(l,J,K) = natural pollutant input to node (l,J,K) in kilo-
grams per hour from all upstream sources assuming
all instream treatment processes are activated.
Note that this definition implies that PN(l,J,K) is the natural pollutant
flow just upstream of (l,J,K). The definition of PN(l,J,K) has been
changed solely for the convenience of the program and all subsequent
references to PN(l,J,K) will conform to the revised definition unless
input data formats are being discussed. Natural pollutant input data
values will be the incremental inputs between nodes as defined previously.
Using the above definition, the value of QMAX can be readily calculated.
QMAX represents the maximum input from a specified node that can be
tolerated at the node and at all downstream nodes.. Thus, a relationship
for determining the maximum additional pollutant flow that can be
accepted at a node without violating the quality standard is used. Let
PLT(l,J,K) be the total pollutant flow including natural pollutant that
exists just downstream of node (l,J,K) and let PM(l,J,K) be the maximum
additional pollutant flow that can be accepted at the node. Using these
variables and Q(l,J,K), one obtains the equation,
PLT(I.J,K) + PM(I,J,K) _ . 10-6 _
PLT(I,J,K) + PM(I,J,K) + Q(I,J,K) ~ ^
«
PM(I,J,K) = j_ _ Qg.io-a -ft(l,J,K) - PLT(I,J,K),
(c.33)
if the node does not have an active instream treatment facility. With
an instream treatment facility, PM(l,J,K) can be as large as desired.
239
-------
As outlined earlier, the procedure for determining the next feasible
solution involves a recursive procedure starting with x-[_* and working
toward xn*. The method for performing one step in the recursive pro-
cedure; given the results of computations defining X]_*,X2*5... >Xjn_i*j
is outlined below. The procedure operates more efficiently when x^
represents an instream processor if both xm* and x^i* are determined
in the same recursive,step. In this case, note that :%+!* will always
represent the mine source decision for the same node as x^*.
1. Set (l,J,K) equal to the node coordinate for x^
NT = INT(I,J,K)
PC = PN(I,J,K)
PE = additional pollutant that could be released if an
instream treatment facility were not used.
PE = 0.0
If NT = 0, go to step 3.
2, xm represents an instream treatment facility.
If PC < 0, go to step 3.
If x^ = 1, PC = 0.0
If Xjn = 0, PE = PC.
3. PLT(I,J,K) = PC
If this decision variable is frozen, i.e., if BS(l,J,K) = 1
or BT(NT) = 1, go to step 11. If this mine source already
has treatment specified and pollutant would not be released
by an inactive instream treatment facility, i.e., if
D(I,J,K) = 2 and PE = 0.0, go to step 11.
U. Initialize QMAX to a large number. Examine each node be-
tween (l,J,K) and the basin outlet to determine QMAX
using equation C.33«
5. If natural pollutant would not be released by an inactive
instream treatment facility; i.e., PE = 0, go to step 6.
If QMAX > PE, go to step 6.
Activate NT by
a. calling subroutine TON,
b. setting x^* = 1.
c. setting xm+1* = 0 if BS(l,J,K) = 0
d. calling subroutine ZO.
Stop, the procedure is complete.
6. QMAX - PE-s. QMAX
If XJQ* represents an instream treatment facility,
set Z = xm+]_; otherwise, set Z = xm.
If Z > 0, go to step 8.
240
-------
PL = P(I,J,K)
If QMAX > PL, go to step 10.
PL = P1(I,J,K)
Call subroutine ZO
If QMAX > PL, go to step ?.
Z = 2
PL = 0.0
Go to step 10.
7. Z = 1.
if RA.LT(I,I,J,K) > i, z = 2
Go to step 10.
8. If Z = 2, go to step 9.
PL = Pl(l,J,K)
If QMK > PL, go to step 10.
Call subroutine ZO
Z = 2
9. PL = 0.0
10. If Xjjj* represents an instream treatment decision,
xm* = xjn and x^i* = Z; otherwise, xm* = Z.
Set PLE = pollutant released from this node based upon
xm* (and x^.3_ if NT > 0). Adjust downstream values of
PLT(l,J,K) for this value of PLE.
This procedure is complete.
11. Set xm* = Xm.
If xm* represents an instream treatment decision,
xm+l = xm+l-
This procedure is complete.
Determination of the Stopping Vector -
The stopping vector, X^, is the last vector in the numerical ordering
of X that needs to be evaluated in searching for the optimum decision
vector. In the cases evaluated by the DWMC model, extending the
Lawler-Bell algorithm by efficient selection of a stopping vector per-
mitted reductions in computer effort by several orders of magnitude.
The basic concept behind the calculation of elements of the stopping
vector is based upon calculating the maximum admissible pollutant flow
at a node; i.e., the maximum possible pollutant flow from all feasible
decision vectors. Let POUT be this maximum possible pollutant flow at
the next upstream node from the basin outlet, and let PLTMAX be the
maximum allowable flow based on the quality standard QS. Consider the
following relationship to illustrate the potential economies of a
-------
stopping vector. If (l,J,K) are the coordinates of the basin outlet
node, then x^ = 0 if POUT + P(l,J,K) < PLTMAX, where xj1 is the first
element of X^. The above relationship is based upon the observation
that the optimal solution would certainly not include expenditures for
pollution control if they were not required to meet the quality standard.
In addition the above relationship states that no feasible decision
vector would merit pollution control expenditures at this node. The
potential for making substantial cuts in computer effort is also illus-
trated by the above relationship since setting X]_L to zero cuts the
number of possible decision vectors into one third of its previous
value.
To extend the above illustration, several additional relationships are
employed. First, inequalities are needed to specify the situations
where x-j_L = 1 and x-j_L = 2. Also, procedures are used to specify the
stopping vector elements at upstream nodes and at instream treatment
facilities. In going to upstream nodes, the definition of the upper
limit on the allowable pollution flow must change to account for the
value of downstream stopping vector elements. For example, setting
x " = 0 implies that the outlet node will emit pollutant at the rate of
P(l,J,K); thus, the maximum allowable pollutant at the next upstream
node must be sufficiently low so that an effluent of P(l,J,K) from the
last node will be feasible.
The maximum allowable pollutant is, of course, affected by natural
pollutant flows. In this procedure for determining the stopping vector,
the natural pollutant flows are more readily used in the following form:
PNT(l,J,K) = total natural pollutant flow past node (l,J,K)
assuming no instream processors are activated
upstream.
In fact all pollution flows used in this procedure are computed relative
to the natural pollution flow of PNT(l,J,K) as an origin. That is, the
absolute flows are POUT + PNT(l,J,K) and PLTMAX + PNT(l,J,K).
The stopping vector XL is actually recorded by program ALCOT using the
following array elements:
DL(l,J,K) = value of the stopping decision vector at mine
source (l,J,K)
DHJTL(NT) = value of the stopping decision vector at instream
treatment site NT.
The relationships presented below are employed by program ALCOT in
determining elements of the arrays DL and DINTL. These relationships
are used to determine the stopping vector element at the node (l,J,K);
-------
thus, (l+l,J,K) is the next downstream node and its stopping vector
element or elements have already been determined. Let PLTMAX be the
maximum allowable pollutant flow that was used in determining the
stopping vector elements at node (l+l,J,K). Then, PLTMAX at node
(l,J,K) is determined by
MinfpLTMAX - PP, ^ ' 10-,n-e Q(l,J,K) - PNT(l,J,K)~| -» PLTMAX,
|_ 1 - tyb « J-U j
(c.3^0
where PP = pollutant produced at node (l+l,J,K) based upon stopping
vector decisions at that node.
Note that the pollutant flows are regarded as being relative to the
natural pollutant flow which would occur if no upstream instream pro-
cessors were employed. Subroutine PTMK takes an allowable pollutant
flow at a node, such as PLTMAX, and computes the maximum flow less than
or equal to the allowable flow which would occur. In the procedure,
PTMX computes POUT, the maximum admissible flow at node (l-l,J,K) that
is less than or equal to PLTMAX. If (l,J,K) is the head of a stream,
POUT is regarded as zero. Assuming that (l,J,K) is not a potential
instream processor site, then
DL(I,J,K) = o if POUT + P(I,J,K) < PLTMAX;
DL(l,J,K) = 1 if POUT + Pl(l,J,K) < PLTMAX < POUT + P(l,J,K) and
EALT(I,I,J,K) < 2, and
DL(I,J,K) = 2 if otherwise. (C.35)
If (l,J,K) is a possible instream processor site, then a check must be
made to determine whether the maximum pollutant flow will merit the con-
sideration of an instream processor. To perform this check, compute
POUT without restrictions from upstream decisions; i.e., without con-
sidering PLTMAX as computed by equation C.3^5 then the only restriction
on POUT is that it is an admissible flow at node (l-l,J,K). Assuming
that mine source treatment is always cheaper than instream treatment,
the only case in which the maximum flow will merit activating the in-
stream processor is when POUT > PLTMAX, where PLTMAX is determined by
C.3^. This is true because in any other case a feasible solution can
be obtained by mine source treatment.
In order to initiate the above procedure at the outlet of a stream,
some special rules need to be invoked to obtain an initial value of
PLTMAX, and they are discussed below. If the stream is the basin out-
let stream; i.e., the level 3 stream, then PLTMAX can be based purely
on the quality standard. That is,
243
-------
PLTMAX = Q 1" ' Qd,J»K) - PNT(I,J,K), (C .36}
where (l,J,K) is the basin outlet node. PLTMAX is not based purely on
the quality standard if the stream is a level 2 or a level 1 stream.
Designate this stream as stream (J,K) where K equals 1 or 2. Then,
PLTMAX is determined from calculations made by subroutine PTMX to deter-
mine the maximum allowable flow POUT at the confluence node receiving
flow from stream (j,K). As requried, PTMX records the flow to a con-
fluence node in the variables POD, the input from the tributary, and
PJD, the input to the confluence node from upstream; thus,
POUT = POD + PJD.
Then, program ALCOT sets PLTMAX equal to PJD for calculations upstream
to a confluence node, and ALCOT stores POD for later use by setting
PLT(J,K) = POD.
The reader can refer to the flow chart of program ALCOT, Figure C.lU,
for a detailed presentation of the computational procedure for deter-
mining values of the DL and DIWTL arrays given maximum admissible flows.
The method for determining the maximum admissible flows is presented in
the following discussion.
Subroutine PTMX is given an upper limit, PLTMAX, on pollutant flow past
a particular node, (lM,JM,KM), and the subroutine is to calculate the
maximum pollutant flow, POUT, which meets quality standards and is less
than PLTMAX. PTMX uses a recursive procedure to determine POUT starting
from the head of level one streams and working downstream to (l,J,K).
The procedure employed treats confluence nodes in a completely different
manner than it treats nodes void of stream confluences. The procedure
for nodes not having stream confluences is described first, and then
the method is extended to account for stream confluences.
The basic method for determining POUT at nodes without stream confluences
involves calculating a maximum pollutant flow, called PMAX, and using
the value of PMAX to determine the corresponding value of PMAX at the
next downstream node. The following relationships are used to specify
PMAX at node (l,J,K) given the value of PMAX at node (l-l,J,K). Let
QST = MinpU,
n[
-------
where PU is initially set equal to PLTMM. QST represents the upper
limit on pollution flow at node (l,J,K). Also, let
QSN - QST + PNT(I,J,K) - PN(I,J,K),
where QSN is the upper limit on pollution flow which can be emitted
from node (l,J,K) when maximum control actions are exerted upstream.
.Recall that PN(l,J,K) is the natural pollution flow under the assump-
tion that all upstream instream processors are activated.
If P(l,J,K) > QSN, then PMAXO = PMAX
If P(l,J,K) + PMAX < QST, then PMAXO = P(l,J,K) + PMAX (C.37)
If P1(I,J,K) > QSN, then PMAXO-* PMAXO
If P1(I,J,K) + PMAX < QST, then MaxfpMAXO, Pl(l,J,K) + PMAX~| -» PMAXO
L J (C.38)
after evaluating the above expressions,
Max (PMAX, PMAXO) -> PMAX . (C.39)
The above relationships, if satisfied, clearly lead to a new value of
PMAX and they must be evaluated in the order shown. However, the
result is unclear if one or more of the three conditions listed below
exist:
1. P(l,J,K) < QSN
and P(l,J,K) + PMAX > QST, (
or 2. P1(I,J,K) < QSN
and Pl(l,J,K) + PMAX > QST, (
or 3. PMAX > QST (C.U2)
In other words, there may exist a pollution flow less than PMAX at the
next upstream node which could result in a larger maximum flow rate at
(l,J,K). The three cases depicted by C.hO, C.hl, and C.k2 are called
uncertain maxima until the existence of pollution flows less than PMAX
is known.
245
-------
Once an uncertain maximum is encountered, the procedure is halted tem-
porarily until the uncertain maximum can be clarified. Clarification
of the uncertain maximum is performed by setting PU in the equation for
QST to a new value and restarting the procedure at the stream head.
The new value of PU is
PU = QST - P(I,J,K) (C.U3)
if equation C.^0 generated the uncertain maximum or
PU = QST - P1(I,J,K) (C.M+)
if equation C.Ul generated the uncertain maximum or
PU = QST (C.U5)
if otherwise. When the uncertain maximum is first encountered, sub-
routine PTMX calls subroutine PTMAX in an attempt to resolve the uncer-
tain maximum. Assuming that PTMAX can determine the maximum flow less
than PU without creating a new uncertain maximum, then PTMAX sets PTM1
equal to this maximum flow. The uncertain maximum is resolved by one
of the three relationships below.
1. If equation C.^4-0 generated the uncertain maximum, then
PMAXO = Max[PTMl + P(l,J,K), PMM] (C.U6)
and the procedure is restarted at equation C.38.
2. If equation C.41 generated the uncertain maximum, then
Max[PMAXO, PTML + P(l,J,K) 1-> PMAXO (0.4?)
and the procedure is restarted at equation C.39.
3. If equation C.U2 generated the uncertain maximum, then
Max(PMAXO, PTML) -> PMAX (C.48)
246
-------
The procedure described above may generate a number of uncertain maxima,
and information concerning these uncertain maxima is recorded on an
uncertain maximum list. That is, in the event PTMAX encounters a new
uncertain maximum, an entry on the uncertain maximum list is created.
This entry records the situation as it existed when the original uncer-
tain maximum waa created. The values stored are:
[MUl(L), MUJ(L), MUK(L)] = objective coordinates for entry L
on the uncertain maximum list.
PUL(L) = upper limit on pollution flow rate to be used in
formula for QST for entry L on the uncertain
maximum list.
PMA.L(li) = maximum pollution flow rate for entry L on the
uncertain maximum list.
PMALO(L) = maximum pollution flow rate corresponding to
PMAXO for entry L on the uncertain maximum list.
MU = number of entries on the uncertain maximum list.
The objective node for each entry is the node to which the procedure
was directed when the Lth uncertain maximum occurred; thus,
[MUl(l), MUJ(l), MUK(l) ] is. always the node for which PTMX is computing
the maximum pollution flow less than or equal to PLTMAX. That is,
MUI(1) = IM, MUJ(1) = JM, and MUK(l) = KM. Note that [MUl(lH-l),
MUJ(lH-l), MUK(lH-l)] is the node at which the Lth uncertain maximum
occurred. After storing an entry on the uncertain maximum list, PTMX
then calls PTMAX again in an attempt to resolve the newest uncertain
maximum. Once PTMAX is successful in resolving an uncertain maximum
by equation C.U6, C.i+7, or C.kQ, PTMX then restarts its basic procedure
in an attempt to resolve the last entry on the -uncertain maximum list
using equations C.37, C.38, and C-39.
In the event (l,J,K) is also a potential instream processor, then checks
are made to determine whether activating the instream processor will
increase the value of PMAX. In any event, PMAX must be less than or
equal to PU, the upper limit on pollution flow rate. Recall that PMAX
and PU are relative to an origin at PNT(l,J,K). Thus, the output of an
instream processor would be -PNT(l,J,K) regardless of the input so long
as the input is positive. The assumption is made that proper selection
of upstream decision variables can always be made to yield a positive
input. The following relationship is used at an instream processor to
determine a new value for PMAX.
If PMAX < -PNT(I,J,K) and QST > -PNT(l,J,K), then -PNT(l,J,K) -» PMAX
24?
-------
Calculation of PMAX values downstream of a confluence node is a more
complex process. The confluence node is characterized by the fact that
there may be a large number of possible pollution flowrates from both
the tributary and the main stream. Accordingly, subroutine FTMX builds
a list of the possible flow rates that are input to a confluence node.
Each confluence node is designated in the list by the tributary stream
feeding the confluence node, and each tributary stream is either a
level 1 or a level 2 stream. The variables used to tabulate the list
of possible inputs to confluence nodes are defined below.
P01DIS(l,j) = Ith admissible output pollutant flow from
level 1 stream J.
P02DIS(l,j) = Ith admissible output pollutant flow from
level 2 stream J.
PJ1DIS(I,J) = Ith admissible pollutant flow from the main
stream and input to the confluence node
receiving flow from level 1 stream J.
PJ2DIS(l,J) = Ith admissible pollutant flow from the main
stream and input to the confluence node
receiving flow from level 2 stream J.
Each of the above arrays is ordered so that the Ith admissible pollut-
ant flow is greater than the I+lst admissible flow. In understanding
the procedure, it is important to note that the first value computed
as output from a stream and as input from the main stream to a con-
fluence node will always be the most unconstrained value or largest
value. The computational procedure already provides for calculating
values of P01DIS(l,j) P02DIS(l,j), PJ1DIS(l,j), and PJ2DIS(l,j).
Smaller flow values, or values for values of the subscript I greater
than 1, have to be computed by special request as needed.
Subroutine CONO is used by PTMX to determine the output value of PMAX
from a confluence node. If insufficient values for the node input dis-
tribution values are available, then CONO generates an entry to the
uncertain maximum list and restarts the computational procedure for
PTMX with a value of PU slightly lower than the last tabulated value
of an input distribution array; i.e., P01DIS, P02DIS, PJ1DIS, or PJ2DIS.
Thus, PTMX will compute the next lower input distribution value.
Assuming that the confluence node (l,J,2) in question receives flow
from level 1 stream NF, then the procedure used by CONO to determine
if sufficient node input distribution values have been calculated is
summarized below:
1. Set Q£5T = upper limit on pollution flow from confluence
node (I,J,2)
QSN = QST - PN(l,J,2) + PNT(l,J,2)
248
-------
CHK = lowest possible input from stream J to the
confluence node
CHK = QST - QS1
CHO = lowest possible output from stream NF
CHO = PN[ND(NF,1), NF, 1] - PNT[ND(NF,1), NF, 1]
PP = P(I,J,2)
If PP < QSN, go to step 2
PP = P1(I,J,2)
If PP < QSN, to to step 2
PP = 0.0.
2. Set NO = number of values tabulated in the array P01DIS
for stream NF
NU = number of values tabulated in the array PJ1DIS
for stream NF
PCK = QST - PP
If P01DIS(NO,NF) < CHO, go to step k
if PO:LDIS(NO,NF) + PJIDIS(I,NF) < PCK, go to step k.
3. Set P01DIS(NO,NF) - EPSN-* PU, where EPSN is a small number
Go to step 6.
k. if PJIDIS(NU,NF) < CHK, go to step 7
if PJIDIS(NU,NF) + POIDIS(I,NF) < PCK, go to step 7.
5. Set PJUHS(NU,NF) - EPSN-> PU, where EPSN is a small number.
6. Return to subroutine PTMX.
Record current situation in uncertain maximum list.
Restart procedure to calculate another value for the
P01DIS or PJ1DIS array.
Procedure is complete.
7. Sufficient values have been computed for the P01DIS and
PJ1DIS arrays.
Compute maximum output from this confluence node.
The basic elements of the procedure to compute the stopping vector X^
include the above method for determining the maximum output from a con-
fluence node and the maximum output from nodes not having stream con-
fluences . When the procedure finally reaches the node (IM,JM,KM), then
PTMX has completed the calculation of the maximum flow at this node;
thus, POUT is set equal to PMftX, and the computations are complete.
Then, program ALCOT uses this value of POUT in determining the elements
of the stopping vector or the DL and DINTL arrays. See the flowcharts
of program ALCOT and subroutines PTMX, PTMAX, and CONO in Figures C.lU,
C.20, C.19, and C.15 for more details concerning this procedure.
249
-------
Overall Procedure of the DWMC Algorithm -
The basic computational procedure followed by program ALCOT in deter-
mining the least cost solution for satisfying the quality constraint of
Q5ppm is described in this section. The optimal set of decisions is
recorded in the two arrays whose elements are defined below:
0(l,J,K) = optimal value of D(l,J,K)
OINT(NT) = optimal value of DINT(NT)
To identify when a better solution is found, the least cost value of
the currently recorded optimal solution is recorded in the variable TC.
As new feasible decision vectors are found with less cost than TC, the
value of TC is updated, and the decision vector is stored in the 0 and
OINT arrays.
The procedure followed by ALCOT in determining an optimal solution is
summarized below.
1. Initialize variables
TC = 1031
Set CIST(NT) = 1031 and 01(NT) = 0 for NT = 1,2,... ,NINST.
Set D and DINT arrays to zero values.
Compute the elements of the stopping vector; i.e., the
elements of the DL and DINTL arrays.
2. Call subroutine NEXFES to determine the next feasible
solution which is recorded in the D and DINT arrays.
3. Call function TCOST to compute the total cost for the
decision vector given by the D and DINT arrays. Record
the result in the variable TTC.
k. If TC < TTC, go to step 5.
Record a new optimal solution in the 0 and OINT arrays.
Set TC = TTC.
5. Set NT = 1.
6. if oi(NT) / o or DINT(NT) / i, go to step 7.
If CIST(NT) < TTC, go to step ?.
Record a new optimal upstream solution for instream pro-
cessor NT in the 10 and 101 arrays.
Set CIST(NT) = TTC.
7. If NT > NINST, go to step 8;
otherwise, NT + 1-* NT, and go to step 6.
250
-------
8. Using the procedure outlined in extension 2, skip to the
next decision vector in the numerical ordering which
could have less cost than TC. Eecord the decision
vector in the D and DINT arrays.
9. Check to determine whether the decision vector given
by the D and DINT arrays is past the vector given by
the DL and DIMTL arrays in the numerical ordering.
If so, go to step 11.
10. Go to step 2.
11. The optimal solution is recorded in the 0 and OIWT arrays,
and its cost is TC.
PROGRAM MAXEF
Purpose
Program MAXEF determines the maximum effectiveness resource allocation
to control mine drainage pollution within a watershed for a specified
budget constraint.
Method
A stream network is defined and decision nodes indicated. At each mine
source decisions can be made to treat or not to treat, to abate or not
to abate; and all possible combinations of these decisions are considered.
At each potential instream processor site, the site may be implemented or
not used. The cost and effectiveness of each decision at each node is
determined. For a given maximum budget allocation, the most effective
feasible pollution control scheme for the network is then determined
using a modification of the Lawler-Bell alogrithm. Effectiveness is
calculated as a function of the maximum pollutant concentration along
each reach between decision nodes.
251
-------
Definition of Variables
AP(I,J,K) =
AP1(I,J,K) =
APA(I,J,K) =
AFN(I,J,K) =
APINS(NT) =
APST(NT) =
BS \IjJjKj ^
BUD =
BV(J) =
C(1,I,J,K) =
C(2,I,J,K) =
CI(NT) =
CALT(ID,I,J,K)
D(I,J,K) =
D(I,J,K) =
DINT(NT) =
DINTL(NT) =
DL(I,J,K) =
DOUT =
EF =
EFF =
INT(I,J,K) =
Annual pollutant load emitted from source I on stream
J of level K (kg).
Annual pollutant load emitted from source I on stream
J of level K when source allocation alternative 1 is
selected (kg).
Annual pollutant loading emitted from source I on
stream J of level K after abatement (kg).
Annual pollutant load at node I on stream J of level
K due to natural sources (kg).
Annual pollutant flow at potential instream treatment
site NT under the assumption all upstream sources have
no pollution control measures (kg). Exception is made
at those sources where cost to abate is less than
variable cost of treatment.
Annual pollutant flow just upstream of potential
treatment site NT (kg).
1-1 if abatement or treatment must be performed at
site (I,J,K),
0 otherwise.
Maximum allowable resource cost.
Basic value for the Jth maximum pollution concentra-
tion interval.
Cost to abate source I on stream J of level K.
Fixed cost to treat at source I on stream J of level
K.
Fixed cost to perform instream treatment at instream
treatment site NT.
Cost of resource allocation alternative ID for source
Allocation alternative selected for source (l,J,K).
2 if no mine drainage control measures are to be
performed at source (l,J,K).
1 if cheapest control measure is to be performed at
source (l,J,K).
0 if treatment is to be performed at source (l,J,K).
0 if instream treatment is to be performed at instream
treatment site number NT,
(l if otherwise.
Value of DINT(NT) in stopping vector.
Value of D(l,J,K) in stopping vector.
(True if next solution vector is to be written out.
(False if otherwise.
Optimal value of pollution control effectiveness.
Trial value of pollution control effectiveness.
INT if node (l,J,K) is a treatment node where NT is
the treatment site number.
0 if otherwise.
252
-------
JN(I,J,K) =
KBW =
KL =
KIA =
KNINT(I,J,K)
KNT =
KNTLIM =
KOPT =
KOUT =
KSINT(NT) =
KU =
MNINST =
MO =
MIOS =
MNS =
IB =
ND(J,K) =
NFN(J,K)
NFS(J) =
HI =
NINST =
NS(K) =
NSO =
0(I,J,K)
OINT(NT)
P(I,J,K)
0 if node I on level K+l stream J is not a confluence
node.
NF otherwise where NF is the stream of level K feeding
node I on level K+l stream J.
KU - KL + 1.
Level of the lowest level stream represented.
KL + 1.
II if node (l,J,K) feeds an active instream treatment
site.
0, if otherwise.
Number of times the criterion function has been
evaluated.
Upper limit on the value of KNT for this run.
Value of KNT when the optimal solution was evaluated.
The interval between output of solution vectors.
[l if instream treatment site NT feeds an active
Iinstream site, and
(O if otherwise.
Level of the highest level stream represented.
Dimensioned value of all arrays subscripted by instream
treatment site number.
Dimensioned value of the node number subscript in all
arrays subscripted by node number.
MHO'MNS.
Dimensioned value of the stream number subscript in
all arrays subscripted by node number.
0 if neither abatement nor treatment is to be performed.
1 if abatement but no source treatment is to be per-
formed.
2 if source treatment but no abatement is to be per-
formed.
3 if both abatement and source treatment is to be
performed.
Total number of nodes on stream J of level K.
Confluence node on level K+l stream receiving flow
from level K stream J.
Level 2 stream receiving flow from level 1 stream J.
Total number of pollution concentration intervals.
Total number of possible instream treatment site
locations.
Total number of streams of level K.
3-MNOS.
Optimal allocation alternative selected for source
Optimal value of DINT(NT).
Pollutant loading emitted from source I on stream J
of level K (kg/hr).
253
-------
Pl(l,J,K) = Pollutant output for resource allocation alternative
1 for source (l,J,K) (kg/hr).
PA(l,J,K) = Pollutant loading emitted, from source I on stream J
of level K after abatement (kg/hr).
PL(l) = Level of Ith stream to process.
PH(l,J,K) = Natural pollutant incremental flow occurring at node
(I,J,K) (kg/hr).
PS(l) = Ith stream to process.
PT(j,K) = Pollutant input from stream J of level K, K = 1,2.
Q(l,J,K) = Stream flow at node (l,J,K) excluding the pollutant.
(input as cubic meters per second converted to
(kg/hr)).
Qj(j) = Upper limit on the maximum pollution concentration for
the Jth interval (ppm as input-converted to decimal
fraction).
R(l,J,K) = Relative importance of the stream reach between nodes
(I+1,J,K) and (l,J,K).
RALT(ID,I,J,K) = Value of MS for source (l,J,K) for resource allocation
alternative ID (ID = 1 for lowest cost alternative,
ID = 2 for alternative involving source treatment).
TC = Cost of maximum effectiveness solution.
TTC = Trial total cost value.
VC = Annual variable cost to treat one unit of pollution
($/kg).
254
-------
Input Data:
Card Number
1
1
1
1
1
1
1
1
1
1
2
2
3
3
NI+2
NI+2
NI+3
(see note l)
NI+5-KL
Variable Name
NS(l)
NS(2)
NS(3)
VC
MNO
MNS
Note: Columns 36-^5
NINST
MNIST
KOUT
HI
BUD
BV(1)
QJ(1)
*
BV(NI)
QJ(NI)
ND(1,1)
ND(2,l)
ND(3,1)
*
ND(NS(1),1)
ND(1,2)
Columns Used
1-5
6-10
11-15
16-25
26-30
31-35
are blank
U6-50
51-55
56-60
1-5
6-15
1-10
11-20
1-10
11-20
1-5
6-10
11-15
(5NS(l)-if)-5NS(l)
1-5
Format
Integer
Integer
Integer
Real
Integer
Integer
Integer
Integer
Integer
Integer
Real
Real
Real
Real
Real
Integer
Integer
Integer
Integer
Integer
Integer
NI+6-KL
(see note 2)
NI+7-KL
ND(1,3)
*
ND(NS(3),3)
1-5 Integer
(5NS(3)-^)-5NS(3) Integer
1-5 Integer
6-10 Integer
11-15 Integer
NI+8-EL
JN(ND(1,2),1A)
)-^)5ND(1,2) Integer
1-5 Integer
6-10 Integer
255
-------
(see note 3)
WI+8+NS(2)-KL
NI+9+NS(2)-KL
NI+10+NS(2)-KL
NI+11+NS(2)-KL
(see note k)
NI+7+NS(2)-KL
+2W
NI+7+NS(2)-KL
+2W+NIN
(see note 5)
NI+8+NS(2)-KL
+2W+NIN
(see note 6)
NI+9+NS(2)-KL
+2W+NIH
(see note 7)
JW(ND(I 3),.
PAuYl)
AP(l'l'l)
APA(I 11)
Q(I i'i)
PN(l,l,l)
APN(l,l,l)
INT(l,l,l)
0(1,1,1,1)
0(2,1,1,1)
P(2^l'l)
PA(2 1 l)
AP(2'l'l)
APA(2,1,1)
PN(2 1 l)
APN(2,1,1)
IET(2 1,1)
0(1,2,1,1)
0(2,2,1,1)
ci(i)'
01(2)
01(3)
ci(8)
ci(9)
CI(NINST)
KOPT
KNT
KNTLIM
EF
TO
D
BS
0
KNINT
DINT
KSINT
OINT
1 2) (5ND(l, 3 )-)+) 5ND(l,3)
' 1-10
11-20
21-30
3l-Uo
ill -50
51-60
61-70
71-75
1-10
11-20
21-30
1-10
11-20
21-30
31-^0
1+1-50
51-60
61-70
71-75
1-10
11-20
21-30
1-10
11-20
21-30
71-80
1-10
(10 NINST-80 BIN) -(10 NINST-80
1-10
11-20
21-30
Integer
Real
Real
Real
Real
Real
Real
Real
Integer
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
Integer
Real
Real
Real
Real
Real
Real
Real
Real
Nil) Real
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
256
-------
Notes:
1. The number of the first KD array card depends upon the value
of HI
2. The number of ED array cards is variable, depending on the number
of stream levels. For a 3-level network there are three ED
array cards; for a 2-level network there are two ED array cards;
for a 1-level network there is one ED array card. These input
data instructions assume a 3-level network.
3. The number of JN array cards depends upon the total number of
streams of all levels. J₯ array cards are sequenced numerically
according to the lowest level streams, next lowest level, etc.
Hote that if there is only a level-three stream in the network,
this sequence of cards is skipped. If there are only level-two
streams and a level-three stream, there is only one JE array
card. If there are level-one streams, a JE array card is provided
for each level-two and level-three stream. The above input data
instructions assume three stream levels exist.
k. There are two cards entered for each node using the format speci-
fied for the following inputs: P(l,J,K), PA(l,J,K), AP(l,J,K),
APA(I,J,K), Q(I,J,K), PE(I,J,K), APE(l,J,K), IFT(l,J,K), C(l,I,J,K),
C(2,I,J,K), and R(l,J,K). The nodes are entered in sequence start-
ing with the first node on the first stream of level KL. Eodes for
this stream are entered, the next stream of level KL is entered,
one node at a time. After recording the data for all level KL
streams, then level KL + 1 streams are entered. The last node
entered is the last node on the level 3 stream. A total of
3 ES(K)
W = ]|T] ]]P ED(J,K) nodes are entered on 2W cards.
K=KL J=l
[ 1 if ETEST > 8
5. EIH = {
{ 0 if otherwise
6. For the initial run of a basin to be analyzed, set KOPT and KM?
to zero.
7. This sequence of cards is not used on an initial run and is only
used when a run restarts after KFT solution vectors have been
evaluated. If an optimal solution is not realized within KETLIM
iterations, a sequence of cards will be punched. The first card
punched contains current values of KOPT and KET, to which a value
of KETLIM must be added for subsequent runs. The remaining cards
are placed behind the one containing the new values of KOPT, KHT,
KETL1M to restart the run. The previous KOPT, KET, KFTL1M card
257
-------
is removed and the program may be restarted using the new data.
The new data give values for the D, BS, 0, MINT, DINT, KSINT,
OINT arrays as shown.
Common Areas and Contents
COMMON/KST/KNINT, KSINT, APINS, BUD, APST
COMMON/ZER/MNS
COMMON/EFF/BV, QJ, NI
COMMON/NEX/MNOS, MND, NS, ND, D, INT, DINT, BS, R, NFN, NFS, PN, PI,
Q, P, KL, KU, KBW, KLA
CCMMON/TCO/Jlf, PT, AP, API, CALT, CI, VC, APN
COMMON/TONN/NSO, RALT
Subroutines Required
Function CABAT - calculates cost to perform abatement at all nodes up-
stream of (l,J,K) where abatement is cheaper than treatment variable
cost.
Function CSAV - determines the savings in annual pollutant load at a
downstream instream processor if decision ID is implemented at source
(I,J,K). If ID < 0, then the decision is to implement a new instream
processor is activated at (l,J,K).
Function EFFECT - determines the effectiveness of the solution vector
given by the D and DINT arrays.
Subroutine ERROR - used to abort the run, operate a traceback in the
sequence of routines called, and force a core dump when an error is
detected in the program.
Subroutine NEFESE - used to determine the next feasible solution. The
current solution provided by the DINT and D arrays is obtained if it
is feasible.
Subroutine TOFE - processes upstream decision and status variables
when an instream treatment processor is deleted.
Subroutine TONE - processes upstream decision and status variables
when an instream treatment processor is implemented.
Subroutine ZOE - zeroes out all decision variables that are lower
order than (l,J,K).
258
-------
Read IS(l), KB(2), 1S(3), VC, MNO, MIS, WINST, MNIST, KDUT
Read HI, BUD
Read BV(l), QJ(l) for I = 1, KI
Is HS(2) = 0?
Are there level 2 streams?
Yes
Is MS(1) = 0?
Are there level 1 streams?
Yes
KBW
KLA
KLT - KL + 1
KL + 1
Figure C.5 Program MAXEF
259
-------
Set K = KL
Set KK = NS(K),
1
Read ND(«J,K),
Number of nodes on stream J of level K,
for J = 1,KK
No
D
Is K = KU?
Yes
Is KL = 3? \
Is level 3 the lowest level? T
Yes
No
Set K = KL
M = NS(K+1)
1
Set J = 1
L = ND(J,K+1)
Figure C.5 Erogram MAXEF
260
-------
Read Jl(l,J,K), I = 1,L
JH(l,J,K) = 0 unless (I,J,K) is a confluence node
Is J = M
Yes
Is K = 2
Yes
Initialize variables ,.
TO = 1030 EF = -103° CFAC = 3.6 x 1CT
Set DOUT = .TRUE., LOUT = 0
Convert QJ array from parts per million to
a decimal fraction
QJ(I) = 10~6 .
Figure C.5 Program MAXEF
261
-------
Set K = KL
ESI = ES(K)
I
Set J -
EDI = ED(J,K)
Set 1=1
Read
P(l,J,K), PA(I,J,K), AP(l,J,K), APA(l,J5K)5
), PN(I,J,K), APW(I,J,K), IKT(I,J,K),
,K), C(2,I,J,K), K(I,J,K)
1=1+1
No
Is I = EDI?
Yes
Figure C.5 Program MAXEF
262
-------
J m J -f 1
No
K = K+ 1
No
Is J = WS1
,Yes
Is K = KU
,Yes
Read input data for instream
treatment sites
Read Cl(NT), for NT = 1, NINST
Figure C.5 Program MAXEF
263
-------
Determine values for arrays
EPS and MFN
Yes
Is KL = 3?
No
Set K = KIA
NS1 = HS(K)
Set J = 1
HD1 = ED(J,K)
Set 1=1
Figure C.5 Program MAXEF
264
-------
K
70 -*-
Yes
70 H-
Yes
NF = J1T(I,J,K - 1)
Is m < 0?
Is node I on level K stream J
not a confluence node
No
Node (I,J,K) is a
confluence node
NFN(NF, K - 1) = I
f Is K 1 21
( Are we looking at a confluence
X^node on a level 3 stream?
No
NFS(EF) = J
Figure C.5 Program MAXEF
265
-------
Initialize decision arrays at each node
D(I,J,K) = 0, BS(I,J,K) = 0,
KNIHT(I,J,K) = 0, 0(1,J,K) = 0
I = 1,...HD(J,K)
J = 1,«»»NS(K)
K = KL,...KIJ
Initialize decision variables for instream treatment
sites.
DINT(WT) = o, OINT(HT) = o, KSIWT(WT) = o, KT = IJ-'-
Figure C.5 Program MMEF
266
-------
STOP = .FALSE.
STOP is .TRUE, when stopping vector
elements will specify no pollution
control
TTC = 0.0
TTC is the total cost expended in
calculating stopping vector elements
HEF =0.0
HEF is the highest possible effec-
tiveness
Determine values for APINS(NT) at each potential
treatment site, determine last feasible solution
to be evaluated, and determine the decision
alternatives for each source.
Set K = KL
Set J = 1
PU = 0.0
PUL = 0.0
PUL is annual natural pollutant flow with all in-
stream processors active. PUL is only used in
calculating the value of TTC. PU is total annual
pollutant flow with no pollution control measures
(with exception of abatement when it is cheaper
than variable treatment cost).
Figure C.5 Program MAXEF
26?
-------
W
**.
72
Yes
Set
Does K = KL?
NF =
-------
Yes
MPA = Max(0.0,APA(l,J,K))
I
Is
,J,K) > VC«[AP(I,J,K) - MPA s
i.e., is cost of abatement and site treatment
at (l,J,K) greater than cost of site treat-
ment alone?
No
Site alternative 2 will involve both treat-
ment and abatement
<
RALT(2,I,J,K) = 3
CALT(2,I,J,K) = C(1,I,J,K) + C(2,I,J,K)
+ VC AAPA
IRALT = 3
Site alternative 2 will involve treatment only
Figure C.5 Program MAXEF
269
-------
Yes
RALT(2,I,J,K) = 2
CALT(2,I,J,K) = C(2,I,J,K)
+ VC AP(I,J,K)
IRALT = 2
Is
C(l,I,JJK)
-------
R H-
No
HJ = RJ + APW(I,J5K)
Accumulate annual natural pollutant
load
Is IRALT = 3, i.e., is abatement
cheaper than treatment variable cost?
D
Yes
HJ = HJ + APA(I,J,K)
Accumulate annual pollutant load after
abatement
Figure C.5 Program MAXEF
-------
HI = PU + AP(I,J,K)
Accumulate annual pollutant load from
source (l,J,K)
HEF is the highest possible effective-
ness.
HEF = HEF +BV(1) * R(l,J,K)
NT = IHT(I,J,K)
No
Is NT > 0?
.Yes
AEOrS(HT) = PU
DL(l,J,K) is the element of the stopping vector
at source (l,J,K). DINTL(NT) is the element of
the stopping vector at instream treatment site
NT. The procedure below computes values for
these elements.
Yes
Is STOP = .TRUE.?
No
Figure C.5 Program MAXEF
2?2
-------
TTC1 = TTC + CALT(2,I
1
,J,K)
Yes
Is TTC1>BUD, i.e., is
budget exceeded in calculating
stopping vector elements?
No
TTC = TTC1
DL(I,J,K) = 0
Stopping vector element at this
source will specify maximum
pollution control.
HJL = HJL + APN(I,J,K)
Accumulate annual natural
pollutant load.
STOP = .TRUE.
Recalculate TTC1 for a lower cost alter-
native at source (l,J,K)
TTC1 = TTC + CALT(l,I,J,K)
Is TTC1 > BUD, i.e.,
is budget exceeded in calculating
stopping vector elements?
Figure C.5 Program MAXEF
273
-------
DL(I,J,K) = i
DL(I,J5K) = 2
No
Yes
NT > 0? V*
Yes
DINTL(NT) = i
< o?
No
TTC1 = TTC + CI(NT)
Figure C.5 Program MAXEP
-------
Yes
/PUL < 0? J
No
TTC1 = TTC1 + VC . PUL
RJL = 0
Yes
TTC1 > BUD, i.e., is
budget exceeded in calculating stopping
vector elements?
No
TTC = TTC1
= 0
DINTL(NT) = i
STOP = .TRUE.
= ND(J,K)?)
lYes
©
Figure C.5 Program MAXEF
275
-------
Yes
Is K = 3?
No
PT(J,K) = HJ
PTL(J,K) = PUL
Is J - NS(K)?
Yes
Is K = KU?
Yes
Write stopping solution vector
Write HEF, maximum possible
effectiveness
Figure C.5 Program MAXEF
276
-------
Read
KOPTjKIT,, KRTLIM
i
,
Yes
Is MT ^ 0, i.e., is
this a restart case?
No
Initialize KHINT and KSIHT arrays
by the following procedure
Set K = KL
Set J = 1
Set 1=1
NT = INT(I5J,K)
Figure C.5 Program MAXEF
27?
-------
Yes
ET
< 0-M
No
Call subroutine TOHE(lT,I,J,K). KBIKT
and KNI1T arrays are adjusted by
subroutine TONE to specify that all nodes
upstream of NT are upstream of an active
instream processor
Is I = HD(J,K) ?
Yes
Is J = IS
(K) ? )
Yes
Is K = KLT ?
Yes
Figure C.5 Program MAXEF
2?8
-------
Read EP, TC
Read D(l,J,K), BS(l,J,K),
C(I,J,K), KNIKT(I,J,K)
I = 1,»«»ND(J,K)
J = 1,"»NS(K)
K = KL,»»«KU
Read DIWT(MT), KBIWT(MT),
OINT(NT) NT = I,»..MEEST
Determine -whether the stopping vector
has been reached by the following
procedure
Set K = 3
Set J = NS(K)
Figure C.5 Program MAXEF
279
-------
Yes
Set I = ND(J,K)
ID = D(I,J,K)
IL = DL(I,J,K)
Is IL < ID, i.e., is the allocation
alternative selected for source (l,J,
K) greater than the allocation alter-
native for (l,J,K) in the stopping
vector?
Yes
Is ID < IL, i.e., is the stopping
still beyond the current solution
vector?
1 = 1-1
J = J - 1
No
No
Is 1=1?
Yes
Is J = 1 ?
Yes
Figure C.5 Program MAXEF
280
-------
K - TC - 1
I 20i
\*_- -
it N° (
IJ
^
To IT
^^
i
KNT = P
TTT 9 1
Yes
[RT + 1
Yes
I
/Is KNT > K1TLIM ? J
No
Call NEFESE(TTC)
Determine next feasible solution
and store this solution in the D
and DINT arrays. The cost of
this solution is recorded in TTC
Compute effectiveness
Call function EFFECT(X)
EFF = EFFECT(X)
Is the effectiveness of this solution greater
than that of the best solution previously
computed ?
Figure C.5 Program MAXEF
281
-------
Yes
Is the effectiveness of this solution
vector less than all previously computed
solution vectors; i.e., is
EFF < EF ?
Is
EFF = EF and TTC > TC, i.e., is the
effectiveness of this solution vector
equal to the maximum effectiveness
value computed and is the total cost
of this solution vector at least as
great as the cost of the previously
determined maximum effectiveness
solution?
No
Record new maximum effectiveness solution
EF = EFF
TC = TTC
EOPT = KMT
DOUT = .TBUE.
Figure C.5 Program MMEF
282
-------
Yes
Write out maximum effectiveness
solution vector number KIT
Set 0(1, J,K) =
for I = l,«»»j
J= I,--,
K = KL,«»«,
I
Set OINT(NT) =
NT = 1, ...
D(I,J,K)
ND(J,K)
NS(K)
HJ
DIKT(NT)
, KINST
j f
f Is EF < HEF ?
j Is optimal value of pollution control
~l effectiveness less than highest possible
\ effectiveness?
Write out optimal solution vector number
KDPT
Figure C.5 Program MAXEF
283
-------
LOUT = LOUT + 1
Accumulate count of solution vectors
computed since previous "writing of a
solution vector
Yes
Is LOUT < KOUT and
is DOUT = .FALSE.?
Write out the solution vector. DIMT values are
noted by the symbols TO, Tl; D values by the
symbols MO, Ml, M2. // separates streams of
different levels. / separates streams of the
same level. DOUT is a flag which forces the
next vector to be written. Thereafter every
KOUTth vector is written.
DOUT = .FALSE.
Figure C.5 Program MAXEF
284
-------
No
Is LOUT > KQUT ?
Yes
LOUT = 0
Skip solutions which have
less effectiveness than EF
by the following procedure.
ZERO = .TRUE.
Set K = KL
Set J = 1
Set
I =
1
Figure C.5 Program MAXEF
285
-------
Yes
51 H-
Is ZERO = .FALSE.?
Yes
I
No
Is D(I,J,K)
1
No
NT = INT(I,J,K)
No
Is (l,J,K) a potential treatment site,
i.e., is NT > 0?
Instream treatment
is being performed
at site NT
Yes
Yes
Is DINT(NT) = 0?
No
ZERO = .FALSE.
DINT(NT) = 0
Call TONE(NT,I,J,K) to perform necessary
bookkeeping at nodes upstream of NT as a
result of activating IT
Figure C.5 Program MAXEF
286
-------
Yes
ds BS(I,J,K) 1 -1, i.e., is the
ource at (l,J,K) permitted to
xist without abatement after con
idering downstream treatment
acilities?
\^
No
Call
ERROR
Yes
Is D(l,J,K) = 2, i.e., is no mine
drainage control to be performed at
No
First nonzero decision variable
encountered
D(I,J,K) = 0
ZERO = .FALSE.
Figure C.5 Program MAXEF
28?
-------
Yes
Is BS(l,J,K) / -1, i.e., is the source
at (l,J,K) permitted to exist without
abatement after considering downstream
treatment facilities?
No
Is D(l,J,K) = 1, i.e., is the lowest
cost alternative to be implemented at
Yes
No
D(I,J,K) = 0
Set D(I,J,K) = 1
Yes
Is D(I,J,K) > 2?
Is no pollution control to
be implemented at (l,J,K)?
Figure C.5 Program MAXEF
288
-------
D(I,J,K) = D(I,J,K)
1
200 H-
Yes
/Is D(I,J,K) >X2-M
,No
No
Is MLT (1,I,J,K)= 2, i.e., is the
lowest cost pollution control alter-
native to include treatment?
^
D(I,J,K) =
2
Figure C.5 Program MMEF
289
-------
D(I,J,K) = 0
NT =
INT (I
,J,K)
No
Is node (l,J,K) a potential
treatment site, i.e., is
NT > 0?
JYes
is DINT(NT) =f o, i.e., is
instream processor site NT
not implemented?
No
DINT(NT) =
Call TOFE(NT,I,J,K) to deactivate the
instream processor and perform necessary
bookkeeping for upstream nodes
Figure C.5 Program MAXEF
290
-------
DINT(NT) = o
Call TOHE(NT,I,J,K) to initiate
the instream processor and per-
form necessary bookkeeping.
T
_ _
- 1
No
Is I = ND(J,K)?
Yes
,T
r + i
No
Is J = NS(K)?
Yes
K =
K +
1
No
Is K - KU?
d
All feasible solutions have
been evaluated, vector KOPT
is optimal
Yes
Punch EF, TC, and the following arrays
to permit restarting at this point: D,
BS, 0, MINT, DINT, KBINT, OINT. Write
out effectiveness of best solution to
this point by the following procedure.
PU will be used to accumulate the pol-
lutant flow under the optimal solution.
Figure C.5 Program MAXEF
291
-------
Set K = KL
Set J = 1
Set 1=1
No
Is
Yes
HJ = 0
Yesf , ; \ /~VY Is
Is 0(I,J,K) y 2?JW320Hp(l,J,K) ^ 1 ?
No
HJ = HJ + P(I,J,K)
No
HJ = PU -l- P1(I,J,K)
Figure C.5 Program MAXEF
292
-------
Yes
No
Yes
Is K = KL ?
No
NF = J₯(I,J,K-1)
Is (l,J,K) a confluence node, i.e.,
is m > 0 ?
1
Yes
HI = HJ + PT(NF,K-1)
Add in the flow from the tributary NF
Add in the natural pollutant
HJ = HJ + PN(I,J,K)
NT = INT(I,J,K)
Is there an instream treatment site
at this node, i.e., is NT >0 ?
No
Figure C.5 Program MAXEF
293
-------
Does the optimal solution specify
that NT should be activated, i.e.,
is OINT(NT) = o?
I Yes
No positive pollution
is possible
Is HJ < 0?
No
HJ = 0
Yes
Yes
No
Is 1D(J,K)
or K 4 3 ?
No
Store the accumulated pollution
at the end of the stream, i.e.,
PT(J,K) = HJ
CONC = PU/(PU + Q(I,J,K)
QUAL = CONG . 10°
Calculate concentration
and stream quality for
this node
Figure C.5 Program MAXEF
-------
JS = JS + 1
Calculate effectiveness by
the following procedure
Set JS = 1
Is QJ(JS) > CONG ?
No
JS =
Yes
EFFF = BV(JS)-R(I,J,K)
Optimal value of effectiveness at
each node
JS is smallest integer such that
QJ(JS) > CONG
JS = MI if QJ(L) < CONG for
L = 1, , NI
Find optimal decision for the mine
source at (l,J,K) using 0(l,J,K) and
RALT(ID,I,J,K)
Figure C.5 Program MAXEF
295
-------
J = J + 1
K = K + 1
Write out quality and effec-
tiveness for optimal decision
at node (l,J,K).
No
No
No
is i = HD(J,K) ?
Is J = MS(K) ?
D
Yes
Is K = KU ?
Figure C.5 Program MAXEF
296
-------
Function CABAT(lI,JJ,KK)
CABAT calculates cost to perform abatement at all
nodes upstream of (II,JJ,KK) where abatement is
cheaper than treatment variable cost. This
cost is accumulated in TC. OT is the number of
entries on the tributary list.
TC = 0.0,
J JJ,
o.
K = KK
I = II,
No
/
/Is BS(l,J,K) = -1, i.e., is
/ abatement cheaper than treat
1 ment variable cost at this
\node?
I Yes
TC = TC + CALT(l,I,J,K)
Add in cost of abatement
Yes
Is K
< KL J
,No
m =
Figure C.6 Function CABAT
297
-------
No
If "i
.L "- -L
]
fls this a confluence node, A
^i.e., is KF > 0 ? J
Yes
1 r
m = m + i
increment the length of the
tributary list
NO r
1
V >30 ^
JYes
Call ERROR
The program permits only
30 storage locations for
the tributary list
J
1
PS(OT) = KF
PL(HN) = K - i
HF is the tributary stream
number
K - 1 is the stream level
>
NO r ^
A
1 'J
lYes
rtS
Figure C.6 Function CABAT
298
-------
CABAT =
TC
Return
/^ Is OT < 0?
( Have all tributaries been
\ examined?
No
Remove a stream from the
tributary list.
J = PS(M)
K = PL (EN)
I = ND(J,K)
ror = M - i
Figure C.6 Function CABAT
299
-------
Function CSAV(ID,II,JJ,KK,IS1,KX)
IA = ID, I = II, J = JJ, K = KK
CSAV = 0.0, MX = 1
CSAV = savings in annual pollutant load
at downstream processor KK if decision
ID is implemented at (II,JJ,KK). If
ID < 0, then a new instream processor
is implemented at (II,JJ,KK)
Is IA < 0, i.e., is an instream
processor activated at (l,J,K) ?
NT = INT(I,J,K)
PS = APINS(NT)
No,
Is PS > 0?
Yes
Return
No
^"
Is BS(l,J,K) = -1, i.e., is
the source at (l,J,K) feeding
an active instream processor
V and is some form of pollution
\control required at (l,J,K)
Yes
PS = AP1(I,J,K)
1
PO =
AP(I,J,K)
Figure C.7 Function CSAV
300
-------
No
Is IA = 1 ?
,rYes
PO = AP1(I,J,K)
PS = PO - PS
PS is actual saving in
pollutant
EDI = ED(J,K)
IT = INT(I,J,K)
/ Is (l,J,K) a potential instream
I treatment site, i.e., is NT > 0 ?
No
Yes
Is NT active, i.e., is DINT(NT) = 0?
Yes
Figure C.7 Function CSAV
301
-------
f Return V*-
NX = NT. NX is the downstream processor
number.
PCK = APST(NT); APST(NT) is annual pollu-
tant flow just upstream of potential
treatment site NT.
Yes
/ Is PCK < 0 ? J
,,No
CSAV = min (pCK,PS,
CSAV is annual savings in pollutant load
at a processor downstream of (l,J,K)
( Return J
Figure C.7 Function CSAV
302
-------
No
Is I = ND ?
Yes
Is K = KU ?
Yes
Call ERROR
Not possible to move to
level K + 1 stream
I = KFN(J,K)
NFN(J,K) is confluence node on level
K + 1 stream receiving flow from
level K stream J.
No
/Is K = 1 ? J
Yes
J = KFS(J). NFS(J) is level 2 stream
receiving flow from level 1 stream J
Figure C.7 Function CSAV
303
-------
Function EFFECT(X)
EFFECT computes the effectiveness of
the decision vectors D and DINT. The
variable EFF will be used to accumu-
late the effectiveness
EFF =0.0
Set K = KL
Set J = 1
PTC will be used to accumulate the
pollution flow in stream J
PTC =0.0
Set 1=1
Yes
lo
/Is K < KL ? J
NF = JN(I,J,K-1)
Is(l,J,K) a confluence node,
i.e., is HF > 0 ?
Yes
Figure C.8 Function EFFECT
304
-------
No
PTC = PTC + PT(KF,K-1)
Add in pollutant input from the tribu-
tary stream HF of level K-l
PTC = PTC + PN(I,J,K)
Add in natural pollutant load occurring
at node (l,J,K)
Is D(I,J,K) > 2, i.e.,
is no control measure to be performed
at (I,J,K) ?
Yes
PTC = PTC + P(I,J,K)
Add in pollutant load emitted from
source (l,J,K).
r
Is D(I,J,K) = 1 ?
Is cheapest control alternative to be
\^_^/ \ performed at I,J,K)?
Yes
Figure C.8 Function EFFECT
305
-------
PTC = PTC + P1(I,J,K)
Add in pollutant output for resource
allocation alternative 1 at source
NT = INT(I,J,K)
No I Is HT > 0, i.e., is (l,J,K) a
potential treatment node?
No
Yes
Is DINT(NT) = 0, i.e., is instream
treatment to be performed at (f,J,K)?
Yes
Figure C.8 Function EFFECT
306
-------
No
[is PTC > 0 ?
Yes
PTC = 0
JS = JS + 1
So J Is
JS = El?
No
Determine the pollution concentra-
tion at node (l,J,K)
CONS = PTC/(PTC + Q(I,J,K))
Set JS = 1
Is QJ(JS) > CONS, i.e., is interval
JS the maximum pollution concentra-
tion interval containing CONS?
Yes
EFF = EEF + BV(JS)-R(l,J,K)
Increment effectiveness for
this reach
Figure C.8 Function EFFECT
30?
-------
1 = 1 + 1
No
Is I = ND(J,K)?
Yes
EFFECT = EFF
£
Yes
Is K >KLJ ?
( Return J
No
Store the output of this stream
PT(J,K) = PTC
J = J + 1
No
Is J = ETS(K) ?
,, Yes
K = K + 1
Figure C.8 Function EFFECT
308
-------
Subroutine ERROR
Write
ERROR DETECTED IN EXECUTION
Call ERRTRA
Write
BUFFERS ARE CLEARED
ten times
Force an ABEND with a traceback
J = 60 000
L = K(J)
STOP
Figure C.9 Subroutine ERROR
309
-------
Subroutine NEFESE(TCOST)
NEFESE determines the next feasible
solution. If the current solution
provided by the DINT and D arrays is
feasible, that solution is obtained.
TCOST is the total cost of the next
feasible solution.
ZERO = .FALSE.
TTC = 0
Set K = 3
Set J = NS(K)
Set
I . HD(J,K)
Figure C.10 Subroutine NEFESE
310
-------
No
Is ZERO = .TRUE. ?
I
Yes
call ZOE(I,J,K).
Zero out all decision
variables of lower order
than node (l,J,K). Zero
out node (l,J,K)
ZERO = .FALSE.
IT = INT(I,J,K)
No
Yes
Is (l,J,K) a potential instream
treatment site, i.e., is NT > 0?
Yes
Is DINT(NT) = 1, i.e., is instream
processor NT not implemented?
Figure C.10 Subroutine NEFESE
311
-------
No
Determine whether we can afford
to keep NT active by the follow-
ing procedure.
TC = TTC + CI(NT)
Cl(NT) is fixed cost to perform
instream treatment at site NF.
Is APINS(NT) > 0 ?
Is annual pollutant flow past NT
without treatment by NT positive?
Add
TC = TC +
in variable
VC-APINS
cost to
(NT)
treat
by NT
Figure C.10 Subroutine HEFESE
312
-------
No
Is KSrNT(lW) = 1, i.e., is there
an active instream processor down-
stream of site NT?
Yes
ID = -1
SAVE = CSAV(ID,I,J,K,ISI,MS)
Determine annual savings in pollutant
load at downstream instream processor
if decision ID is implemented at node
TC = TC - SAVE * VC
TC = TC + CABAT(I,J,K)
Add in cost to perform abatement at all nodes
upstream of (l,J,K) where abatement is cheaper
than treatment variable cost.
Figure C.10 Subroutine HEFESE
313
-------
Yes
Is TC < BUD, i.e., is
budget constraint satis.-
fied?
No
Cannot afford to keep NT active
DINT(NT) = i
Call TOFE(NI5I,J,K)
Delete instream treatment
processor at NT and perform
necessary bookkeeping on up-
stream variables
ZERO = .TRUE.
D(I,J,K) = 0
Set D(l,J,K) to zero to avoid skipping
feasible solutions. Setting ZERO to
.TRUE, will set all decision variables
to the right of (l,J,K) to zero.
Figure C.10 Subroutine NEFESE
-------
TTC = TC
APST(NT) = APINS(NT)
Annual pollutant flow just upstream
of potential treatment site NT
equals annual pollutant flow past
NT without any upstream pollution
control other than abatement where
it is cheaper than treatment vari-
able cost.
Is KBINT(NT) = 1, i.e.,
is there an active instream processor
downstream of NT?
Yes
APST(NX) = APST(NS) - SAVE
NX is instream processor downstream
of node (l,J,K)
KNI = KNINT(I,J,K)
Figure C.10 Subroutine HEFESE
315
-------
equal 0.
, .
D(I,J,K)-1?
GT.O.
LT.O.
Pollution control alternative involving
treatment is implemented at (l,J,K)
No
ID = 0
ID = 0 denotes that treatment is to be
performed
TC = TTC + CALT(2,I,J,K)
Add in cost of control alternative in-
volving treatment.
,Is KMT = 1, i.e.,
is there an active processor downstream
of (I,J,J)?
SAVE =
TC =
Yes
CSAV(ID,ISJ,
TC - SAVE
K,IS,NX)
VC
Figure C.10 Subroutine HEFESE
316
-------
No
Is BS(I,J,K) = -1, i.e.,
is pollution control in-
volving at least abatement
required at (l,J,K)?
Yes
TC = TC - CALT(l,I,J,K)
Subtract cost of lowest cost
alternative
Yes
Is TC < BUD, i.e.,
is budget constraint met?
Cannot afford treatment. Zero out
decision variables to the right of
(l,J,K) to avoid skipping feasible
solutions. Examine possibility of
performing lowest cost pollution
control.
ZERO = .TRUE.
D(I,J,K) = 1
Figure C.10 Subroutine WEFESE
31?
-------
No
|Yes
D(l,J,K) = 2 means that no
being implemented. BS(l,J
implies that abatement of
should be performed at (I,
Logical contradiction
call ERROR
J
control is
,K) = -1
treatment
J,K).
Yes
Is BS(I,J,K) = -1 ?
Wo
ID = 1
TC = TTC + CALT(1,I,J,K)
Figure C.10 Subroutine IEFESE
318
-------
No
Yes
Is KNIKT(I,J,K) = 0, i.e.,
is (l,J,K) upstream of an
active instream processor?
SAVE =
TO =
Yes
CSAV(ID,I,J,K,JS,NS)
TC - SAVE-VC
Is budget constraint met,
i.e., TC < BUD ?
Cannot afford lowest cost pollution
control alternative. Zero out
decision variables to the right of
(l,J,K) to avoid skipping feasible
solutions.
ZERO = .TRUE., D(I,J,K) = 2
Figure C.10 Subroutine EEPESE
319
-------
Expend the cost TC
TTC = TC
^ / Is (l,J,K) upstream of an active
instream processor, i.e., is
KNIHT(I,J,K) = 1
Yes
APST(NX) = APST(WS) - SAVE
1=1-1
= J - 1
No
K = K - 1
No
Is 1=1?
.Yes
Is J = 1 ?
rYes
Is K = k - KBW ?
Yes
TCOST = TTC
f Return J
Figure C.10 Subroutine 1EFESE
320
-------
Subroutine TOFE(NT,II,JJ,KK)
Subroutine TOFE performs bookkeeping on all
states and decision variables as a result
of deactivating instream processor NT at
(II,JJ,KK).
m = o, i = n, j = jj, K = KK
DINT(NT) = 1
Is K = 1 ?
No
KL = K - 1
No
HR = IHT(I,J,K)
Is node (l,J,K) a potential instream
treatment site, i.e., is HR > 0?
Yes
Figure C.ll Subroutine TOFE
321
-------
Record that KR is no longer upstream
of an active instream processor, i.e.,
KSINT(NR) = o
Is DIHT(WR) = 0, i.e., is instream
treatment to be performed at site
MR?
No
Set BS(I,J,K) = 0
KNIMT(I,J,K) = 0
Record that (l,J,K) is no longer
upstream of an active instream
processor
Yes
Is K < KL ?
.No
HF = JU(I,J,K1)
Is this node a confluence node,
i.e., is HF > 0?
Yes
Create an additional entry on
the tributary list
m = HN + i
Figure C.ll Subroutine TOFE
322
-------
No
is m > 30 ?
Yes
No more than 30 tributaries can be
stored by the program
Call ERROR
PS(NN) = NF = tributary stream number
PL(NN) = Kl = stream level
1=1-1
No
Is 1=1?
Yes
( Return \
Yes
Is NN<0 ?
Have all tributaries
been examined?
,,No
Remove an entry from the tributary list
J = PS(NN)
K = PL(NN)
i = ND(J,K)
NN = FN - 1
Figure C.ll Subroutine TOFE
323
-------
Subroutine TONE(WT,II,JJ,KK)
Subroutine TOME performs bookkeeping
on all upstream status and decision
variables as a result of implement-
ing instream processor MT at (II,JJ,
KK)
BN = 0, I = II, J = JJ, K = KK
FIRST = .TRUE.
Yes
Is K < 1 ?
No
KL = K - 1
Record that (l,J,K) is upstream of an
active instream processor
KMINT(I,J,K) = 1
Yes
Is FIRST = .FALSE. ?
tNo
FIRST = .FALSE.
NR = IWT(I,J,K)
o
Figure C.12 Subroutine TONE
-------
No
Is (l,J,K) a potential in-
stream treatment site, i.e.,
is HR > 0?
Yes
Record that HR is upstream
of an active instream pro-
cessor
KSINT(NR) = 1
Is DINT(HE) = 1, i.e., is instream
processor MR site not implemented?
Yes
Is MLT(2,I,J,K) ^ 3 ?
Is control alternative involving
treatment not to include abatement?
Figure C.12 Subroutine TONE
325
-------
No
Is D(l,J,K) = 2, i.e., is
no pollution control to be
implemented at (l,J,K)
Yes
D(I,J,K) = 1
Revise decision. Choose
abatement at (l,J,K) to
reduce cost
BS(I,J,K) = -1
to note that pollution
control involving abate-
ment must be performed
at (I,J,K)
Yes
Is K < KL ?
NF =
KO
JN(I
,J,KL)
Figure C.12 Subroutine TONE
326
-------
No
Is (l,J,K) a confluence node?
i.e., is NF > 0?
Yes
m = EN + i
Increment the count of the
number of tributaries remain-
ing to be evaluated.
No
is m > 30 ?
The program permits only
30 storage locations for
tributary streams
Yes
Call ERROR
PS(OT) = IF
EL(NN) = Kl
HF is the tributary stream number
Kl is the stream level
Figure C. 12 Subroutine TONE
32?
-------
E V
J
T T - 1
/" ^.v^^ _
^N°/ri- I
'< I -Lu J-
if) 1 fc
-S \
-lA
J
Yes
Is m < 0 ?
Have all tributary streams
been examined?
No
J = PS(UN)
K = PL(NN)
I = KD(J,K)
m = m - i
Remove an entry from
the tributary stream
list
Figure C.12 Subroutine TONE
328
-------
Subroutine ZOE(I5J,K)
ZOE zeroes out all decision variables
in the solution vector to the right
of (I,J,K)
Set KB = K
JH = NS(KB)
No
Is KB = K ?
,,Yes
JH = J, i.e.,
skip all streams to the
left of (J,K)
Set JB = JH
EDI = ED(JB,KB)
Figure C.13 Subroutine ZOE
-------
No [ Is KB > K
and JB = JH?
Yes
RD1 = I, i.e.,
skip all nodes to the left
of (I,J,K)
Set IB = HD1
NT = IWT(IB,JB,KB)
Figure C.13 Subroutine ZOE
330
-------
/ Is this node a potential
treatment site, i.e., is
NT > 0?
Yes
Yes
Is DIHT(IT) =01
LNo
Zero out the decision
at this processor
DINT(NT) = o
Call TOME (NT, IB, JB, KB)
to process upstream vari-
ables since HT is acti-
vated
Zero out the decision at
this node
D(IB,JB,KB) = 0
Is IB = 1 ?
No
I Yes
C Is JB = 1 ? >
fles
Is KB = KL ?
1 Yes
Return
No
No
IB = IB - 1
JB = JB - 1
KB = KB - 1
D
Figure C.13 Subroutine ZOE
331
-------
PROGRAM ALCOT
Purpose
Program ALCOT determines the least cost resource allocation to control
mine drainage pollution for a fixed quality standard within a water-
shed.
Method
A stream network is defined and decision nodes indicated. At each mine
source decisions can be made to treat or not to treat, to abate or not
to abate, and all possible combinations of these decisions are con-
sidered. At each potential instream processor site, the site may be
implemented or not used. The cost and effect on stream quality of each
decision at each node is determined. For a given level of maximum
allowable pollution concentration at each node, the least cost feasible
pollution control scheme for the network is then determined using a
modification of the Lawler-Bell algorithm.
332
-------
Definition of Variables
AP(I,J,K) =
AP1(I,J,K) =
APA(I,J,K) =
AHJ(I,J,K) =
BS(I,J,K) =
BT(NT) =
C(2,I,J,K) =
CI(NT) =
GALT(ID,I,J,K)
CIST (NT) =
D(I,J,K) =
D(I,J,K) -
DINT(NT) =
ID =
INT(I,J,K) =
IO(I,J,K,]ST) =
JN(I,J,K) =
KBW =
KL =
Annual pollutant load emitted from source I on stream
J of level K(kg).
Annual pollutant load emitted from souce I on stream
I of level K when source allocation alternative 1 is
selected (kg).
Annual pollutant loading emitted from source I on
stream J of level K after abatement (kg).
Annual pollutant load at node I on stream J of level
K due to natural sources (kg).
1 if source (l,J,K) is not being examined.
-1 if some form of pollution control must be performed
at this source
0 otherwise.
11 if treatment site NT is not being examined.
0 if otherwise.
Cost to abate source I on stream J of level K.
Fixed cost to treat at source I on stream J of level K.
Fixed cost to perform instream treatment at instream
treatment site NT.
Cost of resource allocation alternative ID for source
Minimum total cost for solution upstream to treatment
processor NT.
^Allocation alternative selected for source (l,J,K).
2 if treatment is to be performed at source (l,J,K).
1 if lowest cost pollution control alternative is to
be performed at source (l,J,K).
0 if no pollution control measures are to be performed
at source (I,J,K).
'l if instream treatment is to be performed at instream
treatment site number NT.
0 if otherwise.
1 for lowest cost alternative.
2 for alternative involving source treatment.
NT if node (l,J,K) is a treatment node where NT is
the treatment site number.
0 if otherwise.
Optimal values of D array for source (l,J,K) and
upstream solution to instream processor NT.
Optimal values of DINT array for treatment site NT
and upstream solution to instream treatment processor
I.
0 if node I on level K+l stream J is not a confluence
node.
NF otherwise where NF is the stream of level K feeding
node I on level K+l stream J.
KU-KErU
Lowest level stream represented, (KI>1 if 3 stream
levels are used, KL=2 if 2 stream levels are used,
333
-------
KLA. =
KNT =
KOPT =
KOUT =
KSINT(NT) =
KU =
MDIS(I,K) =
MNIST =
MNO =
MNS =
MS =
ND(J,K) =
NDIS(I,J,K)
NFN(J,K) =
NFS(J) =
KENST =
NS(K) =
0(I,J,K) =
OINT(NT) =
OI(KT) =
P(I,J,K) =
PL(I) =
KL=3 if 1 stream level is used).
KM..
Number of times the criterion function has been
evaluated.
Value of KNT^when the optimal solution was evaluated.
the interval between output of solution vectors
II if instream processor site NT is upstream of an
active instream processor.
0 if otherwise.
Highest level stream (must be 3)
Maximum number of pollutant flows that can be stored
for confluence nodes receiving flow from level K
streams. 1=1 for output from the level K stream,
1-2 for upstream flow on the level K+l stream.
Dimensioned value of the first subscript of the 101
array.
Dimensioned value of the node number subscript of all
arrays subscripted by node number.
Dimensioned value of the stream number subscript of
all arrays subscripted by node number.
0 if neither abatement nor treatment is to be per-
formed.
1 if abatement but no source treatment is to be per-
formed.
2 if source treatment but no abatement is to be per-
formed.
3 if both abatement and source treatment are to be
performed.
Total number of nodes on stream J of level K
Number of admissible pollutant flows calculated for
the confluence node receiving flow from level K
stream J. I = 1 for level K stream J output flow,
1=2 for upstream flow on level K+l stream receiving
flow from level K stream J.
Confluence node on level K+l stream receiving flow
from level K stream J.
Level 2 stream receiving flow from level I stream J.
Total number of possible instream treatment site loca-
tions .
Total number of streams of level K.
Optimal allocation alternative selected for source
Optimal value of DINT(NT).
II if this instream treatment has had an optimal up-
stream solution calculated.
0 if otherwise.
Pollutant loading emitted from source I on stream J
of level K (kg/hr ).
Pollutant output for resource allocation alternative
1 for source (l,J,K) (kg/hr ).
Level of Ith stream to process.
-------
ELT(I,J,K) = Total pollutant load just downsteam of node I on
stream J of level K given resource allocation speci-
fied by D and DINT arrays (kg/hr).
EN(l,J,K) = Cumulative natural pollutant load occurring at node
(l,J,K) without mine drainage assuming all instream
processors are used (kg/hr). lote that input values
are incremental flows between (l,J,K) and the next
upstream node.
ENT(l,J,K) = Natural pollutant flow at node (l,J,K) assuming no
instream processors are used.
PS(l) = Ith stream to process.
PT(J,K) = Pollutant input from stream J of level K,K=1,2
Q(l,J,K) = Stream flow at node (l,J,K) excluding the pollutant
(input as cubic meters per second converted to kg/hr).
QS = Quality standard expressed as maximum pollutant con-
centration (ppm).
RALT(ID,I,J,K) = Value of MS for source (l,J,K) for resource allocation
alternative ID.
TC = Optimal value of total cost.
TTC = Trial total cost value
VC = Annual variable cost to treat one unit of pollution
($/kg).
335
-------
Input Data:
Card Number
1
1
1
1
1
1
1
1
1
1
2
2
2
2
U-KL
II-KL
5-KL
(see note l)
5-KL
6-KL
Variable Name
US(1)
NS(2)
US (3)
vc
MNO
MWS
03
HOST
MWIST
KOUT
ND(l,l)
ND(2*1)
BD(3,1)
ro:(NS(i),i)
ND(1,2)
*
*
ND(HS(2),2)
KD(1,3)
;
ND(HS(3),3)
JN(l,l,l)
JN(2,l,l)
Jisr(3,i,i)
Columns Used
1-5
6-10
11-15
16-25
26-30
31-35
36-^5
1+6-50
51-55
56-60
1-5
6-10
11-15
(5NS(1)-1|)-5NS(1)
1-5
(5NS(2)-10-5MS(2)
1-5
*
(5NS(3)-i)-5NS(3)
1-5
6-10
11-15
Format
Integer
Integer
Integer
Real
Integer
Integer
Real
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
Integer
6-KL
(see note 2)
6+NS(2)-KL
7+NS(2)-KL
7+NS(2)-KL
84-NS(2)-KL
8+NS(2)-KL
JTST(HD(1,2),1,1)
JW(MD(1,3),1,2)
(5HD(1,2)-U)-5ND(1,2) Integer
1-5 Integer
6-10 Integer
(5MD(l,3)-^)-5KD(l,3) Integer
0(2,1,1,1)
1-10
11-20
21-30
31-^0
Ul-50
51-60
61-70
71-80
1-10
11-20
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
336
-------
9+NS(2)-KL
10H1S(2)-KL
10+E3(2)-KL
(see note 3)
6+2w+ES(2)-KL
APA(2,1,1)
APN(2,1,1)
0(1,2,1,1)
0(2,2,1,1)
ci(D
01(2)
1-10
11-20
21-30
31-^0
41-50
51-60
61-70
71-80
1-10
11-20
1-10
11-20
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
(see note
7+2w+lS(2)-KMIIN
(see note 5)
8+2w+NS(2)-KL+NIN
(see note ,6)
Notes:
CI(NINST) (10EIEST-9-80NIE-10NINST-80EIN) Real
KOPT
KNT
KNTLIM
DL,DINTL,TC,
D,BS,0,10,101,
DINT,BT,01,
KSIET,OIET,CIST
arrays
1-10
11-20
21-30
Integer
Integer
Integer
3.
The number of ED array cards is variable, depending on the number
of stream levels. For a 3-level network there are three ED array
cards; for a 2-level network there are two TO array cards; for a
1-level network there is one ED array card. These input instruc-
tions assume a 3-level network.
The number of JE array cards depends upon the total number of
streams of all levels. JN array cards are sequenced numerically
according to the lowest level streams, next lowest level, etc.
Note that if there is only a level-three stream in the network, this
sequence of cards is skipped. If there are only level-two streams
and a level-three stream, there is only one JN array card. If there
are level-one streams, a JN array card is provided for each level-two
and level-three stream. The above input data instructions assume
three stream levels exist.
There are two cards entered for each node using the formal speci-
fied for the following inputs: P(l,J,K), PA(l,J,K), AP(l,J,K), A
APA(I,J,K), Q(I,J,K), PN(I,J,K), AHJ(l,J,K), INT(l,J,K), C(l,I,J,K),
and C(2,I,J,K). The nodes are entered in sequence starting with
the first node on the first stream of level KL. After the nodes
for this stream are entered, the next stream of level KL is entered
337
-------
one node at a time. After recording the data for all level KL
streams, then level KL+1 streams are entered. The last node
entered is the last node on the level 3 stream. A total of
3 NS(K)
w = £ £ ND(j,K) nodes are entered on 2w cards.
K=KL J=l
fl if NINST > 8
k. NIN = <
(o if otherwise
5- For the initial run, KOPT and KNT should be set to zero.
6. This sequence of cards is not used on an initial run and is only
used when a run restarts after KNT solution vectors have been
evaluated. If an optimal solution is not reached within KNTLIM
iterations, a sequence of cards will be punched. The first card
punched contains current values of KOPT and KNT, to which a value
of KNTLIM must be added for subsequent runs. The remaining cards
are placed behind the one containing the new values of KOPT, KNT,
KNTLIM to restart the run. The previous KOPT, KNT, KNTLIM card
is removed and the program may be restarted using the new data.
The new data give values to the TC, D, BS, 0, 10, 101, DINT, BT,
01, KSINT, OINT, CIST arrays as shown.
Common Areas Referenced
COMMON/ZER/MNS, BT
CCMMON/NEX/MNOS, MHO, NS, ED, D, INT, DINT, BS, PLT, HFN, 1FS, PN, PI,
Q., P, KL, KQ, KBW, KLA
CCMMON/TCO/OT, PT, AP, API, CALT, CT, VC, APN
COMMON/PTT/PNT, MAXMU, KFN
CCMMON/TOF/OI, CIST, KBINT
COMMON/TONN/NSO, RALT, 10, 101
COMMON/DIS/NDIS, P01DIS, P02DIS, PJ1DIS, PJ2DIS, MDIS
338
-------
Subroutines Required
Subroutine CONO - determines whether sufficient input pollution values
to a confluence node have been determined to specify the maximum output
from the node that is less than or equal to a specified upper limit.
If so, the maxijnum node output less than the specified upper limit is
calculated.
Subroutine ERROR - used to abort a run when undesirable conditions
occur, and ERROR generates a traceback calling sequence.
Subroutine NEXFES - determines the next feasible solution.
Function HOW - returns a one if node (l,J,K) is upstream of node (IM,
JM,KM), and a zero otherwise.
Subroutine PTMAX - attempts to resolve an uncertain maximum at the node
(IS,JS,KS) by determining the maximum flow less than or equal to HJ. If
another uncertain maximum is encountered, processing is stopped. PTMAX
only examines the flow along the stream (JS,KS).
Subroutine PTMX - computes the maximum pollution flow rate past a given
node which is less than or equal to PLTMAX. PTMX resolves uncertain
maxima.
Subroutine STORE - stores confluence node pollution distribution values
in array PDIS.
Function TCOST - computes the total resource cost.
Subroutine TOFF - processes upstream decision and status variables when
an instream treatment processor is deleted.
Subroutine TON - processes upstream decision and status variables when
an instream treatment processor is implemented.
Subroutine ZO - zeroes out all decision variables that are lower order
than node (l,J,K).
339
-------
Program ALCOT
KU =
3,
KL =
1
Read input data
Read KS(L), NS(2), HS(3), VC, MNO,
MNS, QS, MUST, MHIST, KOUT
Yes
Is NS(1) ^ 0?
Are there level
1 streams?
Is US(2) ^ 0, i.e.,
are there level 2 streams?
KBW = KU - KL + 1
KLA = KL + 1
Figure C.lk Program ALCOT
3^0
-------
Set K = KL
KK = NS(K)
Read ffl)(J,K), J= 1,...KK
K = K + 1
Is K= KU ?
Yes
|Yes
Is KL = 3, i.e.,
are there no level
1 and 2 streams?
INO
Set
K =
KL
M =
Set
J =
1
Figure G.l4 Program ALCOT
-------
L = ND(J,K+I)
Read JN(l,J,K), I = 1,-"L
J = J + 1
No
Is J = M ?
.Yes
KTT -1- 1
No /C
p 9 J
.- 21J
Yes
Compute constants and initial values
MHOS = MNO.MWS, NSO = 3'MNOS, mk = MWO + k,
MIOI = ffllST-MNIST, MIO = MNIST-NSO
It is assumed that there are no more than k-
instream treatment sites per stream.
Initialize variables
TC = 1030, CFAC = 3.6 x 106
DOUT = .TRUE., LOUT = 0
TC is used to record the minimum pollution
control cost for solutions satisfying the
quality standard. DOUT is true -when the
next solution vector will be printed.
LOUT is used to count the number of solu-
tion vectors computed since the last out-
put of a solution vector.
Figure C.lU Program ALCOT
-------
Initialize MDIS and EDIS
arrays
Set 1=1
Set K = 1
MDIS(I, K) = 30
Set J = 1
KDIS(I,J,K) = 0
J = J + 1
No
< "u ( Is J = MNS ?
Yes
K = K + 1
No
Is K = 2 ?
No
Is 1=2?
-Yes
Set K = KL
Figure C.lk Program ALCOT
-------
NS1 = MS(K)
Set J = 1
MD1 = HD(J,K)
Read input data for" node (l,J,K).
Eead P(l,J,K), PA(l,J,K) AP(l,J.K),
APA(I,J,K), Q(I,J,K), EN(I,J,K),
APN(I,J,K), IBT(I,J,K),
C(2,I,J,K)
Convert stream flow from cubic meters
per second to kilograms per hour
Q(I,J,K) = CFAC.Q(I,J,K)
No
J = J + 1
No
Is I = ND1 ?
Yes
Is J = NB1 ?
Yes
Figure C.l^ Program ALCOT
-------
50
K = K + 1
No
Is K = KU ?
Lies
Read input data for the instrearn
treatment sites
Read Cl(NT), NT = 1,
Yes
Is KL = 3 ?
Are there no level 1 and
2 streams?
No
Set K = KLA.
NS1 = NS(K)
Compute values for KM
and NFS arrays
Set J = 1
ND1 = ND(J,K)
Set 1=1
Figure C.l^ Program ALCOT
-------
G
m = OT(I,J,K-I)
No
Is IF > 0, i.e.,
is (l,J,K) a confluence node?
Yes
KFN(NF,K-l) = I
Yes
Is K / 2 ?
Is this a level 3 stream
No
HPS(NF) = J
- I + 1
J =
J +
1
No
No
Is I = KD1 ?
JYes
Is J = E31 ?
K =
K +
1
,,Yes
No
Is K = KU ?
Figure C.lU Program ALCOT
-------
Convert QS from parts per million
to a decimal fraction
QS = QS 10-6
QS - QS/(1.-QS)
Compute the maximum allowable pollutant
quantities at each node and determine
the decision alternatives for each source
by the following procedure.
Set K = KL
RSI =
RS(K)
Set
J =
1
Figure C.l^ Program ALCOT
-------
EDI = HD(J,K)
HJ = 0.0
HJL =0.0
Set 1=1
TQ = Q(I,J,K) QS
Q(I,J,K) = TQ
By the following procedure, convert input
incremental natural pollutant flow to total
natural pollutant flow under the assumption
that all instream treatment processors are
used. Value computed for node (l,J,K) is
flow just upstream from the node, and HJ is
used to accumulate this value. HJL is the
total natural pollutant flow assuming in-
stream treatment processors not used.
Figure C.lk Program ALCOT
-------
No
Is NT > 0 and HJ > 0, i.e.,
is the upstream node a potential
instream treatment site and is j
the natural pollutant input to
that node positive?
Yes
HJ = 0.0
Yes
Is K = KL ?
,,No
m = JU(I,J,K-I)
No
Is HP > 0, i.e.,
Is this a confluence node?
,,Yes
HI = HJ -f- PT(lilF,K-l)
PUL = PUL + EEL(KF,K-l)
Figure C.lk Program ALCOT
-------
TPN = PW(I,J,K)
FU = TPN + PU
PUL = TPN + PUL
PN(I,J,K) - PU
PNT(I,J,K) = PUL
NT = INT(I,J,K)
No
Yes
No
Is I = HD1 ?
,Yes
Is K = HJ ?
,No
PT(J,K) = PN(I,J,K)
Store the natural pollutant out-
put from this stream.
Is NT > 0 and PU > 0, i.e., is
(l,J,K) a potential instream treat-
ment site and is PU > 0 ?
PT(J,K) = 0.0
Figure C.lk Program ALCOT
350
-------
AAPA = Max(0.0,APA(l,J,K))
Is
Yes / C(1,I,J,K) > VC-(AP(I,J,K) -AAPA), i.e.,
is abatement cost greater than variable cost
of treatment?
No
Site alternative 2 will involve both treatment
and abatement
EALT(2,I,J,K) = 3
GALT(1,I,J,K) = C(1,I,J,K) + C(2,I,J,K)
+ VC-AAPA
Site alternative 2 will involve
treatment only.
RALT(2,I,J,K) = 2
CALT(2,I,J,K) - C(2,I,J,K)
+ VC'AP(I,J,K)
Figure C.lU Program ALCOT
351
-------
Yes
Is C(1,I,J,K)
-------
Record the natural pollutant output
of this stream (assuming no instream
processors implemented)
FTL(J,K) = PUL
' K
K +
1
No
Is K = HI ?
Yes
Read KOPT, BUT,
KNTLIM
Yes/ is this a restart case, i.e.,
is KIT 4 0 ?
No
Set
K =
KL
BS1 =
HS(K)
Set J = 1
HD1 = ND(J,K)
Figure C.lU Program ALCOT
353
-------
Set
I =
1
Initialize stopping vector
DL(I,J,K) = o
I =
I H
- 1
J
J +
1
No
Is I = ND1 ?
Yes
Is J = NS1
? j
Yes
K = K +
1
jo/:
Is K = HJ ?
Yes
Determine the last feasible solution
that needs to be considered by the
following procedure. This solution
is known as the stopping vector.
DL(l,J,K) is the mine source deci-
sion at node (l,J,K) for the stopping
vector. Similarly, DIMTL(MT) is the
instream processor decision for pro-
cessor NT. Initialize variables.
FINITY = 103°
MAXMU = 0
MAXMU is the maximum number of entries
in the uncertain maximum list.
Figure C.lk Program ALCOT
-------
PLTMAX is the
allowable upper
limit on pollu-
tion flow.
lo
No
Set K = 3
WS1 = WS(K)
J = MSI
MD1 = KD(J,K)
I = HD1
Is K = 3 ?
Yes
PL5MAX = FIKCTT
Is K <3 ?
Yes
PLTMAX - PTL(J,K)
Figure C.l4 Program ALCOT
355
-------
PLTMAX = minjPLTMAX, Q(l,J,K) - PNT(l,J,K)j
NODE = .FALSE.
NODE is used to communicate to subroutine
PTMX that (I,J,K) is a confluence node
Yes
I
Is K < KL ?
NF = J₯(I,J,K-1)
1
Is node (l,J,K) a confluence node, i.e.,
is NF > 0?
Yes
NODE = .TEUE.
NT = INT(I,J,K)
/
is NT > 0, i.e.,
is (l,J,K) a potential in-
stream processor site?
Yes
Figure C.lk Program ALCOT
356
-------
POUT =0.0
No
Yes
Is
No
Call PTMX(I-1,J,K,FINITY5POUT)
POUT is the maximum possible flow
past (I-1,J,K)
Is POUT >PLTMM, i.e.,
will maximum flow merit activating
the instream processor?
Yes
DINTL(NT) = 1
DL(I,J,K) = EALT(2,I,J,K)
NT = 1, PLTMAX = FINITY
- 2
DINTL(NT) =
NT = 0
0
POUT =
0.0
Figure C.lU Program ALCOT
35T
-------
Call PmK(l-l,J,K,PLTMAX,POUT)
POUT is the maximum flow past (l-l,J,K)
that is less then or equal to PL3MAX
PCK = PLTMAX-POUT
PO = P(I,J,K)
Yes
Is PCK < PO, i.e.,
is difference between upper bound
at (l,J,K) and maximum admissible
flow at (l-l,J,K) less than un-
controlled pollution at mine from
No
DL(I,J,K) = 0
No action required in the stopping
vector
PLTMM = PLTMAX-PO
Decrease upper bound by PO
pp =
;Is PCK < PP, i.e.,
Ls PCK less than flow with moderate
:ost treatment alternative?
Figure C.l^ Program ALCOT
358
-------
DL(I,J,K) = 1
Is RALT(l,I,J,K) > 1), i.e.,
does the moderate cost alternative
involve treatment?
PLTMAX = PLTMAX-PP
Figure C.lU Program ALCOT
359
-------
Yes
Is NF > 0, i.e.,
is (l,J,K) a confluence
node?
JYes
Is NT > 0, i.e.,
is (l,J,K) an active in-
stream treatment site?
No
PTL(NF,K-1)
= FINITY
No
PTL(EF,K-I) = POD
PLTMAX = PJD
POD and PJD are determined by subroutine
PTMX if NODE is true to specify the split
in pollution reaching (l,J,K) that comes
from, the tributary and upstream on stream
(J,K)
Figure C.lU Program ALCOT
360
-------
Write out MMMU and the NDIS array
Read the DL and DINTL arrays
Write out the stopping vector,
i.e., the DL and DIWTL arrays
Write out KOPT, KNT, KNTLIM
Yes
Is this a restart case,
i.e., is KHT ^ 0 ?
IWo
Initialize decision arrays if starting
from scratch
D(I,J,K) = 0; BS(I,J,K) = 0; 0(l,J,K)
K= 1,3; J= 1,...MHS; 1= 1,»
= 0
J =
IO(I,J,K,NT) =0; !=!, MHO
; K= 1,2,3; MT = 1,»««MHIST
IOI(NT,I) = 0; I
NT = 1,'"MNIST
= l,-«-MNIST;
Figure C.lU Program ALCOT
361
-------
Initialize decision variables for instream
treatment sites
DINT(NT) = 0, BT(NT) = 0, CIST(HT) = TC
OINT(NT) = o, OI(NT) = o, KSINT(NT) = o for
IT = I,"'MUST
Read interim solutions from cards. Cards are
obtained as output from previous run of the
program in case an optimal solution has not been
achieved. A new value of KNTLIM must be punched
on the first card of the output of the previous
run. The new value of KNTLIM gives the last
value of KMT for the succeeding run.
Read TC
Read D(l,J,K), BS(l,J,K), 0(l,J,K) for
I = 1,"'MWO; J = 1,'"MNS; K = 1,2,3
Read IO(I,J,K,NT) for I = 1,...MWO
J = 1,'"MNS; K = 1,2,3 NT = 1,' * 'MNIST
Read IOl(KT,l) for I = 1,.. .JOUST;
NT = 1,'"M]\IIST
Read DINT(MT), BT(MT), 01(NT), KSINT(NT),
OIKT(NT), CIST(KT) for
FT = 1,'"MKIST
Figure C.lh Program ALCOT
362
-------
Determine whether the stopping
vector has been reached by the
following procedure.
Set KB = 1
K = h - KB
NS1 = E3(K)
NS2 = NS1 + 1
Set JB = 1
J = NS2 - JB
HD1 = KD(J,K)
Set IB = 1
ID = D(ND1-IB+1,J,K)
IL = DL(ND1-IB+1,J,K)
Figure C.I1!- Program ALCOT
363
-------
Yes
Is IL < ID, i.e.,
is the value of the stopping
decision vector at (l,J,K)
less than the value of the
allocation alternative selected
for (I,J,K) or has the stopping
syector been passed?
.No
Yes
m
IB+1
No ,
(
JB = JB+1
No
KB = KB+1
No
Is ID < IL ?
fNo
Is IB = ND1
Yes
Is JB = NS1 ?
Yes
Is KB = KBW ?
Increment the count of the number
of rotation vectors evaluated
KNT = KNT + 1
Is KNT > KNTLIM, i.e., \
has the number of times the criterion
function has been evaluated exceeded
the maximum permitted for this run? J
Figure C.lk Program ALCOT
36U
-------
Call MXFES
to find the next feasible solution.
HEXFES records the solution in the D
and DIM arrays
Compute
total
TTC =
resource
TCOST(X)
i
cost
Is TTC < TC, i.e.,
is the cost of this solution less
than the previous minimum cost?
Yes
Record the new optimal solution
TC = TTC, KOPT = KNT, DOUT = .TRUE.
DOUT being set to .TRUE, forces this
solution to be written out
Write out that solution KMT is optimal
0(1,J,K) = D(I,J,K) for I = I,...MNO;
J = 1,..«ME3; and K = 1,2,3
Figure C.lh Program ALCOT
365
-------
OINT(NT) = DINT(BT)
NT = 1,»"MMIST
Determine whether a lower cost
upstream solution to an in-
stream processor has been found
by the following procedure.
Set FT = 1
Is 01(MT) = 0 and DINT(NT) - 1, i.e.,
is an optimal upstream cost for this
instream processor being computed?
J, Yes
is TTC < CIST(HT), i.e.,
is this solution lower cost than pre-
viously recorded?
Yes
Figure C.lU Program ALCOT
366
-------
Write out KNT, NT
Record this lower cost solution
CIST(NT) = TTC
DOUT = .TRUE.
IO(I,J,K,MTJ.= D(I,J,K) for
I = 1,'"MNO J = 1,...MNS
and K = 1,2,3
IOI(NT,I) = DINT(I) for
I = 1,-"NINST
TOT1
IMJ- -
- 1\TTU-1
-------
No
Is LOUT >KOUT or DOUT = .TRUE.?
This is an output test which guarantees that
every KDUT^k solution vector will be written
out, as well as the next vector when DOUT is
.true.
Yes
Write out the solution vector. DIM values
are noted in the program printout by the
symbols TO, Tl; D values by the symbols MO,
Ml, M2, // separates streams of different
levels; / separates streams of the same level
Write KNT, TTC
DOUT = .FALSE.
Is LOUT > KOUT ?
Yes
Reset the counter of solution
vectors computed since the last
KOUT**1 vector was written
LOUT = 0
Figure C.lk Program ALCOT
368
-------
Skip to the next solution vector
which may have lower cost than
TTC by the following procedure.
ZERO =
.TRUE.
Set K = KL
HS1 = NS(K)
Set J = BS1
BD1 = KD(J,K)
Set I = 1
7esf Is ZERO = .FALSE., i.e., has a nonzero
Yes
decision been encountered?
. No
Is this mine source decision free to
vary and is the current decision specify'
ing some pollution control action, i.e.,
is
D(I,J,K) ^ 0 and BS(l,J,K) ^ 1?
Figure C.l4 Program ALCOT
369
-------
NT = INT(I,J,K)
No
Is NT > 0, i.e.,
is node (l,J,K) a potential
instream treatment site?
Yes
is DINT(NT) = o or BT(NT) = i ?
Is treatment not to be performed at site
NT, or is the decision variable for in-
stream processor NT frozen as part of an
optimal upstream solution?
No
ZERO = .FALSE.
The first nonzero decision has been encountered
DINT(NT) = 0
Call TOFF(NT,I,J,K)
to perform necessary bookkeeping on upstream
variables since HT is deactivated.
Figure C.lk Program ALCOT
370
-------
No
Yes
Is BS(I,J,K) - -1, i.e.,
is some form of pollution con-
trol required at (l,J,K)?
Yes
Is D(I,J,K) = 1 ?
Is the lowest cost alternative
to be implemented at (l,J,K)?
[NO
D(I,J,K) = 1
ZERO = .FALSE.
First nonzero decision
has been encountered
D(I,J,K) = 0
ZERO = .FALSE.
First nonzero decision
has been encountered
Figure G.lh Program ALCOT
371
-------
First nonzero decision variable has already
been found.
I
Yes
./Is BS(I,J,K) = 1 ? J
I No
Yes
-/Is BS(I,J,K) 4 -1 ? J
No
/ Is D(I,J,K) = 1, i.e.,
No I j_s lowest cost control alterna-
V tive to be performed?
D(I,J,K) = 1
D(I,J,K) is equal
to its maximum
value. Set
D(I,J,K) to low-
est possible value
Yes
D(I,J,K) = 2
D(I,J,K) is not equal to its
maximum value. Increase
D(I,J,K) by one
Is D(I,J,K) ^ 2 1
Is control alternative involving treatment to
be implemented?
Figure C.lk Program ALCOT
372
-------
D(I,J,K) =
Use the decision alternative with the next
highest value
No
Is D(I,J,K) = 1 and
RALT (1,I,J,K) >1
Does the lowest cost alter
native involve treatment?
Yes
D(1,J,K) = 2
D(I,J,K) =
0
m =
IHT(I,J,K)
No
Is NT > 0? Is node (I,J,K) a
potential treatment site?
Yes
Figure C.l^ Program ALCOT
373
-------
Yes
Is BT(NT) = 1, i.e.,
is the decision variable for in-
stream processor NT frozen as
part of an optimal upstream solu
tion?
No
Yes
:Is DINT(NT) / O ?
Is instream treatment to be per-
formed at site NT?
DINT(NT) = o
Call TOFF(NT,I,J,K)
TOFF performs book-
keeping on upstream
variables required
since NT is deacti-
vated
No
DINT(NT) = i
Call TON(NT,I,J,K)
TON performs book-
keeping on upstrea
variables required
since NT is activated
Figure C.l^ Program A1COT
37^+
-------
Write KOPT
All feasible solutions have
been evaluated, and the optimal
solution is printed out.
Punch solution onto cards to enable pickup
from this point.
Write KDPT, KNTLIM, TC
Write DIHTL(NT), NT = 1, 'HINST
Write DL(I,J,K), D(l J,K), BS(l,J,K),
0(I,J,K) for I = !,,MHO; J = 1,»««,MNB;
and K = 1,2,3.
Write IO(I,J,K5NT) for I = 1,...,MNO;
J = 1,'"MKB; K = 1,2,3; NT = 1,-"MEIST
Write IOI(HT,I) for I = !,,MKIST; and
NT = 1,"*MWIST
Write DIIiT(KT), BT(HT), 01 (IT),
KSINT(NT), OIMT(lilT), CIST (NT) for
NT = 1,-"MNIST
Figure C.lh Program ALCOT
375
-------
Write out optimal solu-
tion vector. Calculate
and write out optimal
decision at each node and
resulting stream quality.
Set K = KL
NS1 = WS(K)
Set J = 1
EDI = UD(J,K)
Set I =
AY
Figure C.l^ Program ALCOT
376
-------
No
Is 1=1?
lYes
HI will be used to accumulate
stream flow
HJ = 0.0
Initialize HJ
Yes
HJ = HJ + P(I,J,K)
HJ = HJ + P1(I,J,K)
Yes
Is K = KL ?
No
KF = J₯(I,J,K-1)
Is (l,J,K) a confluence
i.e., is W > 0 ?
Yes
A
)
Figure C.l4 Program ALCOT
377
-------
INSIND = OINT(NT)
OINT(NT) is the
value of the
optimal decision
vector at site NT
L
Yes
HI = PU + PT(NF,K-1)
Add in natural pollution
POUT = PU + PN(I,J,K)
NT = INT(l,J,K)
Is NT > 0, i.e.,
is there an instream treatment
site at this node?
Is INSIND = 0, i.e., \
is the instream treatment site )
not active?
No
Figure C.lk Program ALCOT
378
-------
No
positive
pollution
1
possible
.
Yes
Is POUT < 0 ?
LWo
POUT =0.0
1
Is PN(I,J,K)< 0 ?
Yes ( Is natural pollutant load
sat (l,J,K) negative?
HJ=min|pU,-PN(l,J,K)|
COMMENT
PU = 0.0
All natural pollutants were previously
accumulated under the assumption that
all instream processors were turned on.
Must now retrieve the natural pollu-
tion quantity which was zeroed at the
instream processor.
Yes
is PN(I,J,K)< o?
tNo
PU = POUT
Figure C.l^ Program ALCOT
379
-------
Yes
Is I ^ EDI or K = 3 ?
No
Store the accumulated pollution
at the end of the stream
PT(J,K) - POUT
Convert from allowable pollutant flow to
pollutant stream flow in ppm
QT = Q(I,J,K)/QS
QUAL = (POUT 10°)/(POUT + QT)
Find optimal MS values at
each node by the following
procedure
Is IOD >0 ?
MS = RALT(1,I,J,K)
MS =
0
Figure C.lk Program ALCOT
380
-------
MS = RALT(2,I,J,K)
Write out optimal MS value
and quality at the node (l,J,K)
= 1+1
No
J = J + 1
No
K = K + 1
No
Is I = HD1 ?
Yes
Is J = MSI ?
Yes
Is K = HI ?
Yes
Figure C.lk Program ALCOT
381
-------
Subroutine CONO(QST, PO, PI, NDIS, P01DIS, PJ1DIS,
NREP, PLOM, PUS, QSN, CHO)
CONO determines whether sufficient input pollu-
tion values to a confluence node have been de-
termined to specify the maximum output from the
node that is less than or equal to a specified
upper limit. If so, the maximum node output
less than the specified upper limit is calcu-
lated.
Calculate the lowest possible pollutant flow
to the node from the main stream.
CHK = QST - QSN
Yes
Is QSN < 0, i.e.,
is upper limit on pollution flow
from (l,J,K) with maximum control
exerted upstream negative?
LNo
PP = PO
PO is pollutant flow without abatement
SMALL = 103°
Yes
Is PP < QSN, i.e.,
can the source at this conflu-
ence node emit pollutants
without control and still
satisfy the upper limit QST?
PP =
PI
Figure C.15 Subroutine CONO
382
-------
Is PP < QSN, i.e.,
can the source at this confluence
node emit pollutants with lowest
cost control alternative and still
satisfy the upper limit on flow from
from the node,
WO = KDIS(l)
EfU = EDIS(2)
NO = number of values tabulated in array P01DIS
for stream RF
P01DIS is an array of input pollutant flow to
the node from the tributary
Ml = number of values tablulated in the array
PJ1DIS for stream HF
PJ1DIS is an array of pollutant input flows to
the node from sources upstream of the main
stream
PCK = QST - PP
PCK is the max pollutant flow to the confluence
node from the main stream and/or the tributary
QJ3T = upper limit on pollution flow from conflu-
ence node (l,J,K)
Figure C.15 Subroutine COWO
3Q3
-------
Yes
Yes
Is POIDIS(NO) < CHO, i.e., is
the NO admissible output pollutant
flow from the tributary no greater
than lowest possible output for
the tributary? If so, all possible
values of flow from the tributary
have been computed.
No
Is POIDIS(NO) + PJLDIS(l) 5 PCK,i.e.,
is a lower value of P01DIS unnecessary?
Note that a lower input pollution value to the
confluence node from the tributary is needed.
KFN = 1
Calculate the upper limit on the required value
PUS = POIDIS(NO) - EPSN
Set flag to note that additional inputs to the
confluence node are required
NREP = 1
Note: the arrays P01DIS
ordered so that
larger values
appear first
Figure C.15 Subroutine CONO
38k
-------
Yes
Yes
Is
PJIDIS(MJ) < CHK, i.e.,
have all possible values of flow
from the main stream been computed?
No
Is
PJIDIS(NU) + POlDIS(l) 2 PCK, i.e.,
is a smaller value for PJ1DIS unnecessary?
,No
Note that a lower input pollution value to the
confluence node from the main stream is required.
KFN = 2
Compute the upper limit on the required value
PUS = PJIDIS(NU) - EPSN
Set flag to note that additional inputs to the
confluence node are required
HREP = 1
PLTM = SMALL
SMAX = SMALL
Set
IA =
1
Set IB = 1
Figure C.-15 Subroutine CONO
385
-------
No
SUM = POIDIS(IB) + PJIDIS(IA)
,
Is
SUM < PCK and SUM > SMAX, i.e.,
does a larger upper bound satis-
fying PCK exist?
lYes
SMAX = SUM
No
Is COH = .TRUE., i.e, is this
confluence node the node being
analysed by the main program to
determine the stopping vector
value?
__
Record the input from the tributary
POD = PCIDIS(IB)
Record the input from the main stream
PJD = PJIDIS(IA)
(Note that the last values recorded for
these inputs will be when
PP = 0)
IB =
IB+1
±
IA =
IA+1
No
No
Is IB = NO
fYes
Is IA = Ml ?
Yes
Figure C.15 Subroutine CONO
386
-------
No
Is SMAX = SMALL ?
,,Yes
There are no flow values downstream
of the confluence node less than PCK
Gall ERROR
SMAX = SMAX + PP
Is SMAX >PLTM ?
Is the current value of SMAX greater than
the previously calculated maximum output
from the confluence node?
Yes
Record the new maximum
PLTO = SMAX
Figure C.15 Subroutine CONO
387
-------
Set the flag to indicate
maximum output from this
node has been determined
KREP = 0
Yes
ReturnX
o
Is PP < 0 ?
No
Is PP > PI ?
Is this the no pollution
control case?
Yes
PP = PI
PCK = QST - PP
Figure C.15 Subroutine
-------
Subroutine ERROR
Error is used when logical inconsistencies are
discovered in the program execution. An error
message is generated and the run is terminated.
Write
ERROR DETECTED II EXECUTION
Call ERRTRA
Write ten times
BUFFERS ARE CLEARED
J = 600000
L = K(J)
Figure C.l6 Subroutine ERROR
-------
Subroutine EEXFES
HEXFES determines the next feasible solution.
If the current solution specified by the D
and DINT arrays is feasible, that solution is
obtained. ZERO is true when all lower order
decisions are to be set to zero.
ZERO = .FALSE.
Set K = 3
ESI = ES(K)
J = MSI
EDI = ED(J,K)
I = EDI
Figure C.17 Subroutine EEXFES
390
-------
No
Is ZERO = .TRUE. ?
Yes
Call ZO(I,J,K)
Zero out decisions at (l,J,K)
and all lower order decisions
ZERO = .FALSE.
PC = PN(I,J,K)
NT = INT(I,J,K)
PE is the additional pollutant that would be
released if a stream treatment site were not
used. Only natural sources are used in cal-
culating PE.
PE = 0.0
No
r
Is NT > 0, i.e.,
4 is (l,J,K) a potential instream
V treatment site?
Figure C.I? Subroutine NEXFES
391
-------
Is PC > 0 and DINT(HT) = 1 ?
.Yes
PC = 0.0. Instream treatment is to
be performed at site (l,J,K).
Natural pollutant load becomes zero.
No
Is PC > 0 and DINT(lT) = 0 ?
Yes
PE = PC
Instream treatment not to be performed
at site (I,J,K)
PLT(I,J,K) = PC
PLT(l,J,K) is total pollutant load just down-
stream of the site, but PH(l,J,K) is the
natural pollutant load just upstream. Initi-
alize PLT(l,J,K) to account for natural
pollutant flow
Figure C.I? Subroutine NEXFES
392
-------
Yes
Is BS(I,J,K) = 1
or is D(I,J,K) = 2, PE = 0, _...,
is site (l,J,K) not being examined, J
or is no additional pollutant to
emitted by (l,J,K)?
), i.e., \
ed,
be /
QMAX = 10:
I
/Is K = 1 ? J
Yes
The arrays II and JJ
define a path from
(l,J,K) to the basin
outlet.
JJ(1)
JJ(3)
11(2) =
J, .JJ(2) = EFS(J),
1, 11(1) = I,
,1), 11(3) = HM(JJ(2),2)
No
Is K = 2 ?
Yes
Figure C.I? Subroutine NEXFES
393
-------
JJ(2) - J, JJ(3) = 1,
11(2) = I, I
JJ(3) = 1, 11(3) = I
Determine maximum allowable pollution load
from this site and record the result in
. Start at the basin outlet.
KK - 4
KK = KK - 1
IH - HD(JJ(KK),KK)+1, MI
= IH - II(KK)
Figure C.17 Subroutine NEXFES
-------
Set IM = 1
NZ = INT(IH-IM, JJ(KK), KK)
QE = PLT(IH-IM, JJ(KK), KK)
QE is the total pollutant flow
just downstream of (IH-IM,JJ(KK),
KK)
No
No
Is this node an instream treatment site,
i.e., is NZ > 0?
Yes
Is instream treatment being performed at
this site, i.e., is DINT(NZ) = 1?
Yes
Yes
Is QE > 0 ?
No
QE =
-QE
Figure C.I? Subroutine NEXFES
395
-------
Yes
Is QMAX < QE ?
J.NO
QMAX = 103°
QF = Q(IH-IM,JJ(KK),KK) -
Yes
Is
< QF ?
LNo
Q)V[AX = QF
IM = Bl+1
No
Is IM = HI '?
Yes
Figure C.I? Subroutine HEKFES
396
-------
No
Is KK - K ?
jYes
Yes
Yes
Is PE = 0 ?
LNo
/Is QMAX > PE ?"\
Call TON(HT,I,J,K) to process upstream
variables as a result of implementing an
instream treatment facility.
DINT(NT) = i
Zero out all lower order decision variables
so that intervening feasible solutions are
not skipped.
ZERO = .TRUE.
No
Is BS(I,J,K) = 0 ?
Yes
Abatement or treatment is not required
at this site
D(I,J,K) = 0
= QMAX - PE
Figure C.I? Subroutine NEXFES
397
-------
Yes
Yes
Is D(I,J,K) > 0 ?
No
PL = P(I,J,K)
\
Is
> PL ?
No
PL = P1(I,J,K)
ZERO = .TRUE.
Zero out all lower order decision
variables to avoid skipping a
feasible solution
Yes
Is QKAX > PL ?
LNo
D(I,J,K) -
2
D(I,J,K) = 1
(
is RALT(1,I,J,K)
Yes
>E = 0 ? j
fNo
0.0
D(I,J,K) = 2
>
t
Figure C.l? Subroutine NEXFES
-------
Is D(I,J K) = 2 ?
ZERO = .TRUE.
Zero out all lower order decision
variables to avoid skipping a
feasible solution
D(I,J,K) = 2
Yes
Is PE = 0 ?
No
PL = 0.0
Adjust downstream pollutant load for
this decision
PLE = PL + PE
Figure C.17 Subroutine NEXFES
399
-------
81
No
Set KK = K
IL = II(KK)
IH = ND(JJ(KK),KK)
Set IM = IL
PCK = PLT(IM,JJ(KK),KK)
NT = INT(IM,JJ(KK),KK)
Is NT > 0, i.e., \
is node (IM,JJ(KK),KK) an instream treatment )
site? J
,, Yes
: ^___._ f __ \ ___ i -10
X a lAl-iN J_ ^ 1>I JL y JLy X * C» ?
Is instream treatment being performed at
this site?
less than 0
fYes
Is PCK \ Sweater than 0 f call ERROR
Ccall ERROR J
equal 0
Figure C.I? Subroutine NEXFES
-------
AD
A
PLE = min{pLE5-PCK]
PLT(IM5JJ(KK),KK) = PCK + PLE
IM =
UYB-1
KK = K+l
No
No
Is IM = IE ?
,Yes
Is KK = 3 ?
Yes
I = 1-1
No
J
J-l
No
K =
K-l
No
Is 1=1?
. Yes
Is J = 1 ?
Yes
Is K = KL ?
c
Yes
Return
Figure C.17 Subroutine NEXFES
-------
Function NON(l,J,K,IM,JM,KM)
WN returns a one if the node I,J,K is up-
stream of the node (IM,JM,KM); otherwise,
a zero is returned
IS = IABS(IM)
js = IABS(JM)
KS = IABS(KM)
II = I, JJ = J, KK= K
Yes
Is KK = KS ?
Yes
No
Is KK = 1 ?
Increment to the third level stream
II = EFW(JJ,KK)
J J = 1
Is KS = 2 ?
, No
JJ = NFS(JJ), KK = 2
Figure C.l8 Function NON
-------
Increment to the second level stream
II = NFN(JJ,KK)
JJ = IFS(JJ)
Stream levels are now the same
No
Yes
Is JJ = JS ?
,Yes
Is II > IS ?
WON = 1
c
Return
NOW =
0
c
Return
Figure C.l8 Function NON
-------
Subroutine FfflAX(IS,JS,KS,II,JJ,KK,LS,HJ,Fm,
PTMO, QST,QCK,<9SN,PZ,PU1)
Subroutine PMAX attempts to resolve an uncertain maximum a% the node
(IS,JS,KB) by determining the maximum flow less than or equal to PU.
PWAX only examines the flow along the stream (JS,KS). If another un-
certain maximum is encountered, processing is stopped, IS is set to
one, and (II,JJ,KK) is set to the node coordinates where the uncertain
maximum occurred. QCK is the admissible pollution at that point, QST
is the minimum of QCK and HJ, PZ is the source pollution being evalu-
ated at the uncertain maximum and PU1 is the new upper pollution limit
to resolve the uncertain maximum, PB4 is the maximum pollution less
than or equal to PU. IS is zero when PTM applies to node (IS,JS,K3).
Both (IS,JS,KB) and (II,JJ,KK) are coded to show where the uncertain
maxima occurred. If IS is less than zero or II is less than zero, then
alternative zero caused the uncertain maximum. Similarly, JS less than
zero or JJ less than zero implies alternative one, and KS less than
zero or KK less than zero implies alternative two. If all node coor-
dinates are positive, the uncertain maximum is at a confluence node.
IE = IS , 1=1
JE = uS , J = | JE|
KE = KS K = |KE|
jo. = | KE| - i
PUL = HJ
PMAX = 0.0
PHT1 = PNT (I,J,K)
QC = Q(I,J,K) - FUT1
0,3 = min(QC,FU)
QS is the maximum allowable pollu-
tion flow at this node
qn = QS + PMT1 - PN(I,J,K)
QN is the maximum permissible load-
ing at this node with complete up-
stream control
Yes
Yes
-T Is Kl< KL >. J
THO
| NF = JH(I,J,K1) |
/ Is MF < 0 1 J
No
Confluence node reached.
PO = P(I,J,K)
PA = P1(I,J,K)
IL = KD(HF,KL)
CHO= PN(IL,HF,K1) - PHT(IL,HF,K1)
Yes
{ Is KL = 2 >. j
No
0
Figure C.3_9 Subroutine PTMAX
koh
-------
Call COHO(Q£, PO, PA, HDIS(1,HF,KL), P01DIS(l,HF),
PJ1DIS(1,JSF), HREP, PLTO, PU2, QN, CHO)
PLTM will be the maximum flow past the con-
fluence node if HREP = 0
Call COHO(QS, PO, PA, FDIS(l,NF,KL), P02DIS(l,NF),
PJ2DIS(1,HF), HREP, PLTM,, HJ2, QJI, CHO)
NEEP will be the maximum flow past the con-
fluence node if HREP = 0.
Uncertain maximum at the confluence node
LS = 1, PTM = PMAX
HJ1 = PU2, II = I.
JJ = |JS|, KK= [KB |
I
( Return J
Figure C.19 Subroutine EEMAX
-------
Yes
Has the uncertain maximum at (IS,JS,KS) been
encountered, i.e., is
-I = IE ?
No
Is
P(I,J,K) > QN, i.e.,
does pollutant loading with no control imply
that the upper limit will be exceeded regard-
less of upstream flow?
LNo
Yes
PCK = P(I,J,K) + IMAX
Yes
Is PCK > QS, i.e.,
has another uncertain maxi-
mum been encountered?
>
No
EMAXO = PCK
110 U-
the uncertain maximum at (IS,JS,KS) been
encountered, i.e., is
I = IE and -J = JE ?
No
P = P1(I,J,K)
Evaluate low cost alternative by the follow-
ing procedure
Figure C.19 Subroutine POMAX
-------
Can the upper limit Qg be satisfied with
maximum upstream control, i.e., is
P < QH ?
No
Yes
PCK = P + H4AX
Has another uncertain maximum been
encountered, i.e., is
PCK > QS ?
, No
Determine the maximum flow satisfying the
upper limit QS
PMAXO = min{pCK,BMAXO[
Has the uncertain maximum at (IS,JS,KS) been
reached, i.e.,
I = IE and -K = KE ?
Has another uncertain maximum been encountered,
i.e., is
PMAX
Yes
K = -K
Record the necessary variables for
the uncertain maximum
II * I, JJ = J, KK = K
LS = 1, PTM = MAX
PB40 = PMAXO, QpT = QS
QCK = QC, QgN = QP
PZ = P, PU1 = OS - P
t
( Return J
Figure C.19 Subroutine PEMAX
i+OT
-------
Record the necessary variables for resolving
the uncertain maximum
LS = 0, EM = PMAX
ETMO = FMAXO
Return
Figure C.19 Subroutine PTMAX
-------
Subroutine PTMX(lJ,JJ3KK,PLTMM,POUT)
PTMX computes the maximum pollution flow rate past node (II,JJ,KK)
which is less than or equal to PI/MAX. PTMX resolves uncertain maxima.
KCW(J,K) = Value of WE for confluence node being fed by stream (J,K).
KCW(J,K) = 0 if admissible pollution values for the confluence
node are not being calculated.
1 if admissible pollution flow to a confluence node from a lower
level stream is being calculated.
KFW =
2 if admissible pollution flow to a confluence node from the
node's stream is being calculated.
0 if pollution flow to a node that is not a confluence node is
being calculated.
MDIS(I,K) = Maximum number of pollutant flows which can be stored for
confluence nodes receiving flow from level K streams. Set 1=1
for output from level K stream, 1 = 2 for upstream output on
level K+l stream receiving flow from level K streams.
MU = Number of entries on the uncertain maximum list.
(MUl(l),MUJ(l),MUK(l)) = Objective node coordinates for the Ith entry
on the uncertain maximum list.
WDIS(I,J,K) = lumber of admissible pollutant flows calculated for con-
fluence node receiving flow from level K stream J. Set 1=1
for level K stream J output and 1=2 for upstream output on
level K+l stream receiving flow from level K stream J.
PJ1DIS(I,J) = Ith admissible output pollutant flow gust upstream from
confluence node receiving flow from level 1 stream J. (Note that
PJ1DIS(I,J)> PJ1DIS(I+1,J).
PJ2DIS(I,J) = Level 2 analogue of PJ1DIS(I,J).
PMAL(l) = Maximum pollution flow rate at the time the ith entry on
uncertain maximum list was encountered.
PMAX = Maximum flow rate less than or equal to PLTMAX. (PMAX is used
in determining POUT).
POUT = Pollution flow rate returned as maximum value at node (II,JJ,KK)
less than or equal to PLTMAX.
i
U09
-------
P01DIS(I,J) = Ith admissible output pollutant flow from level 1 stream
J. (Note that P01DIS(l,J3) is greater than or equal to
P02DIS(I,J) = Level 2 stream analogue of P01DIS(l,J).
PTM = Maximum pollution flow rate less than or equal to PU. (FEM
is used in resolving uncertain maxima).
PU = Upper limit on pollution flow rate currently being used.
PUM(l) - Upper limit on pollution flow rate at time i**1 entry on un-
certain maximum list was encountered.
UlO
-------
No
10
Initialize variables
KCN(J,K) =0, J = 1,---MNS, K= 1,2
KFN = 0, IM = II, JM = JJ,
KM = KK, HJ = PLTMAX, MU = 0
Is the main program evaluating a
confluence node, i.e., does
NODE = .TRUE. ?
lYes
3M = IM+1
K ~ KL? J Xj I 1
NSl = HS(K)
ND1 = ND(J,K)
No
Is MU =
= 0 ? )
Yes
H4AX = 0
No
Is MU
0 ? J
, Yes
PTM = 0
Figure C.20 Subroutine PTMX
Ull
-------
Is (I,J,K) upstream of IM, JM, KM, i.e., is
NON(I,J,K,IM,JM,KM) = 1 ?
Yes
FNT1 = ENT(I,J,K)
QCK= Q(I,J,K) - PNT1
QST = min QCK,HJJ
QST is the upper limit on pollution
flow at this node
QgN = QST + PNT1 - PN(I,J,K)
QSN is the maximum pollution input
from this node when complete control
is implemented upstream
Yes
/Is K = KL ? J
Ho
KL = K - 1
m = JU(I,J,K1)
39 )/° f Is this a confluence node, i.e.,
is NF > 0 ?
Yes
Yes
Have admissible flows been previously computed
at this node, i.e., is
NDIS(2,NF,KL) J 0 ?
No
No
BDIS(2,NF,K1) =
1
Is KL = 1 ?
>
, Yes
PJ1DIS(1,NF) = MAX
Figure C.20 Subroutine PIMX
U12
-------
Ho
C
Is KL = 2
Yes
PJ2DIS(1,NF) = PMAX
No
Is I = IM and J = JM and K = KM, i.e.,
has an objective node been reached?
Yes
Is the uncertain maximum list
empty, i.e., is
MU < 0 ?
___
KFN = KCN(HF,KL)
Maximum uncertainty node has been reached
IM = MUI(MU), JM = MUJ(MU)
KM = MUK(MU), HJ = HJL(MU)
MU = MU - 1
KCN(KF,KL) = o
|No
520 )< Ies ( Is KM = 2 ? J
\ No
Call STORE(FM,P01DIS(l,NF), MDIS(l,l),
KDIS(1,NF,1))
Enter the value FEM into the array P01DIS
Figure C.20 Subroutine PTMX
U13
-------
Call STORE(PTM,PJ1DIS(1,NF),
MDIS(2,1), NDIS(2,NF,1))
Enter the value PTM into the array PJ1DIS
Yes
Call
Enter
(V
v_
STORE (PTM
MDIS(1,2)
the value
KFN - 2
J. No
0
,P02DIS(1,NF),
, NDIS(1,NF,2))
PTM into the array
P02DIS
Call STORE(PTM,PJ2DIS(l,KF),
MDIS(232), KDIS(2,NF,2))
Enter the value PTM into the array PJ2DIS
KFN = 0
IL = ND(NF,K1)
CHO = PN(IL,WF,KL) - PNT(IL,NF,K1)
CHO is the decrease in natural pollu-
tion at the tributary outlet due to
the use of instream processors
Figure C.20 Subroutine PTMX
-------
Yes
Is this node the confluence node being examined
by the main program, i.e., is
NODE = .TRUE, and MU = 0 and I = IM and
J = JM and K = KM ?
iNo ' '
CON = .TRUE.
PO = 0.
PA = 0.
1
PO = P(I,J,K)
PA = P1(I,J,K)
CON = .FALSE.
Yes
Is KL = 2 ?
I
No
Call CONO(Qj3T,PO,PA,NDIS(l,NF3Kl),
P01DIS(1,NF), PJ1DIS(1,NF),
HREP, P1TM, HJ2, QSN, CHO)
to determine the maximum output from this
confluence node less than Q£T. The desired
value is returned in PLTM
Figure C.20 Subroutine PTMX
-------
Call CONO(QST,PO,PA,HDIS(1,HF,K1),
P02DIS(1,KF), PJ2DIS(l,UF),
NREP, PLTM, PU2, QSU, CHO)
to determine the maximum output from
this confluence node less than QST.
The desired output is returned in PI/M
Was COWO unable to determine PLTM
because of insufficient known pollu-
tion distribution values at the node,
i.e.. is HREP = 1?
,. Yes
Create another maximum uncertainty
entry to obtain another distribution
value by the following procedure
MCI = MU
Ho
Is MU >MAXM0 ?
0
\
MAXMU =
t
Yes
Mil
No
:Is MO > KMU ?
SMU is the maximum length of the
uncertain maximum list.
I Yes
Can
EEROR
Figvire C.20 Subroutine PTMX
-------
PMAL(MU) = MAX
KCN(NF,KL) = KM
KFN is determined by subroutine GONO
MUI(MU) = IM
MUJ(MU) = JM
MUK(MU) = KM
Yes
No
N°
-f Is MU < 1 ? J
, No
PMAL(MU) = POM
HJL(MU) = HJ
PU = HJ2
IM = I
JM = J
KM = K
<;
Is MU = 0
Yes
PMAX = PLTM
Is MU >0 ?
Yes
POM = PLTM
Figure C.20 Subroutine PTMX
1417
-------
= minJQCK,HJJ
Q3T is the upper limit for pollution flow
at this node
QgN = QST + PNT1 - FN(I,J,K)
QSN is the maximum possible pollution to
be emitted from this node with complete
upstream control
PO = P(I,J,K)
No
Is MU < 0 ?
)
\ Yes
PMAXO « PMAX
PMAXO is the temporary recording of the
new maximum flow for PMAX
No
Is MU > 0 ?
Yes
PTMO = PTM
PTMO is the temporary recording
of the new maximum flow form FM
Yes
Yes
Is PO > QSN ?
Is MU J 0 ?
No
< Yes ( Is PO + PMAX > QST ?
1
No
PMAXO = PO + PMAX
Figure C.20 Subroutine PTMX
-------
I = -I
Setting I to a negative value
note that the uncertain maxi-
mum occurred while evaluating
the no control option.
HJ1 = QST - PO
HJ1 is the upper limit on
pollution flow for resolving
the uncertain maximum
Call FMAX(I,J,K,IS,JS,KS,LU,
HJ1, PTM1, PTM10, QPT, QCK,
QSN, PO, HJ2)
Attempt to resolve the uncertain
maximum by calling PTMAX
.Yes
80
Can the uncertain maximum t>e resolved,
i.e., is
EU = 0 ?
Create
No
new entry on
MU = MU +
uncertain max
1
list
No
No
Is MU > MAXMU ?
,Yes
MAXMU = MU
Is MU > WU ?
Maximum length of the uncertain
maximum list in MU
, Yes
Call ERROR
Figure C.20 Subroutine PTMX
-------
MUI(MU) = IM
MUJ(MU) = JM
MUK(MU) i KM
Yes
I
Is MU < 1 ?
IMAL(MU)
PMAX
PMALO(MU) =
PMAXO
I
!NO
PMAL(MU) = POM
B/IALO(MU) = PTMO
PUL(MU) = PU
IM = I, JM=J, KM=K,
I = IS, J = JS, K = KB,
JS = IABS(JS), KB = lABS(KS),
WD1 = HD(JS,KS), WS1 = NS(KS)
PTM = PTM1, PTMO = PTM10
PU = HJ1, HJ1 = PU2
Yes
1
Is I < 0 ?
Yes
Is J < 0 ?
,No
Figure C.20 Subroutine PTMX
-------
Yes
-f Is K < 0 ? J
Resolve the maximum uncertainty
PCK = PO + PTM1
No
Is PCK > QST ?
PTM1 is previously determined
largest value smaller than
QST-PO. Thus adding PO to PTM1
should produce a value smaller
Jbhan QST. Error otherwise
Yes
Call ERROR
No
Is MU = 0 and PCK > PMX ?
Yes
PMAXO = PCK
No
Is MU > 0 and PCK > PTM
Yes
PTMO = PCK
Figure C.20 Subroutine PTMX
1*21
-------
I = -I
Return the coordinate to a positive value
Cases where uncertain maxima exist are
analyzed by the following procedure.
No
Is -I = IK and J = JM and K = KM ?
.Yes
Tne current maximum uncertainty can
now be resolved
PCK = PO + KM
HI = PUL(MU)
QgT = minJQCKjHJ
JM = MUI(MU)
JM = MUJ(MU)
KM = MUK(MU
Yes
Is MU = 1 ?
LNo
PTM = IMAL(MU)
PTMO = FMALO(MU)
MU = MU - 1
Figure C.20 Subroutine PTMX
-------
No
Is PTM < PCK < QgT
FMO = PCK
PMAX = PMAL(l)
PMAXO = PMALO(l)
MU = 0
No
Is PMAX < PCK < QST
X /
1 Yes
PMAXO = PCK
PCK = PO + PHI
Is PCK >QST
D
No
Figure C.20 Subroutine PTMX
-------
Yes
Yes
PTMO = PCK
Evaluate alternative 1
PO = P1(I,J,K)
Is PO
,No
Is MU / 0 ?
No
PCK = PO + PMAX
Is PCK >QgT ?
PMAXO = max PCK.PMAXO
|PCK,3
Yes
J = -J, setting J to a negative value notes that
the uncertain maximum occurred while evalu-
ating alternative i
PU1 = QST - PO, PU1 is the upper limit on pollu-
tion flow for resolving the uncertain
maximum
Figure C.20 Subroutine PIMX
-------
Call mAX(l,J,K,IS,JS,KS,Itf,HJl,Pam,PTM10,
QST, QCK, QgN, PO, HJ2)
Attempt to resolve the uncertain maximum by
calling ECMAX
i Can the uncertain maximum be resolved,
i.e., is
LU = 0 ?
Yes
Resolve the uncertain maximum
PCK = PO + PTM1
No
-c
? J
Yes
Call ERROR
PTM1 is previously computed largest value
smaller than QST-PO. Thus adding PO to
PTM1 should produce a value smaller than
Error otherwise.
No
Is m = 0 and PCK > PMAX ?
I
? J
Yes
PMAXO = max JPCK, PMAXOJ
^
/Is MU >
0 and PCK > PTM
?"\
I Yes
PTMO = maxpCK,PTMo
Figure C.20 Subroutine P1MX
-------
260 H-
No
250 u-
Return the coordinate to a positive value
J = -J
Cases where uncertain maxima exist
are analyzed by the following pro-
cedure.
Is I = IM and -J = JM and K = KM ?
I
Yes
Current maximum uncertainty can
now be resolved
PCK = PO + PTM
PU = PUL(MU)
QST = min (QCK,PUJ
IM = MUI(MU), JM = MUJ(MU),
KKM = MUK(MU)
Yes
Is MQ = 1 ?
I
No
PTM = PMA.L(MJ)
PTMO = PMALO(MU)
MU = MU - 1
Figure C.20 Subroutine PTMX
-------
No
Yes
Is PTM < PCK ^
Yes
PTMO = max|pCK,PTMO
PMAX = PMAL(l)
PMAXO = PMA.LO
MU = 0
PMAXO = max PCK,PMAXO
r300
V_>
S~^
(260
PCK =
PO + PTM
>
t
Is PCK > QST ?
No
PTMO = maxjPCKjPTMOj
Evaluate alternative 2
Figure C.20 Subroutine PTMX
-------
S~~\ Y
^_X
Evaluate alternative 2 or the
treatment alternative
PO = 0
1
23 /*"
j,
")
Io
Is MAX > QST ?
Yes
I
No
BIAX = max{pMAX,PMAXOJ
K = -K, setting K to a negative value notes
that the uncertain maximum occurred
while evaluating alternative 2
PU1 = QgT, FUl is the upper limit on pollu-
tion flow for resolving the uncertain
maximum
Call PmAX(l,J,K,IS,JS,KS,LU,PUl,FTMl,,FTM10,
Q3T,QCK,Q3N,PO,PU2)
Attempt to resolve the uncertain maximum by
calling PTOAX
Yes
Can the uncertain maximum be. resolved?
Is LU = 0 ?
Figure C.20 Subroutine
-------
No
Is PTM1 >
Yes
Call ERROR
PTM1 is determined by PTMAX
to be the largest previously
computed value less than or
equal to QgT
No
i
No
Is MU = 0 ?
Yes
IMAX = EMI
No
Is MU > 0 ?
I
Yes
PTM = POM1
K = -K
Return the coordinate to
a positive value
Figure C.20 Subroutine PMX
1*29
-------
Cases where uncertain maxima exist
are analyzed by the following pro-
cedure
Is I = IM and J = JM and -K = KM?
,,Yes
The current maximum uncertainty can
now be resolved.
HJ = HJL(MU)
QST = MIN(QCK,HJ)
PTM = MAX(PTM,P1MO
c
Is FM > QST ?
-Yes
Call ERROR since upper limit on
pollution was set to prevent this
case in resolving the maximum un-
certainty
IM = MUI(MU)
JM = MUJ(MU)
KM = MUK(MU)
No
>
.No
MU = MU-1
Figure C.20 Subroutine P3MX
-------
:Does an uncertain maximum
exist, i.e., is
PTM > QST
Yes
PTM = MAX(PTM,PTMO)
NT = INT(I,J,K)
1
Does a potential upstream \
processor exist at this \
node, i.e., 1
NT > 0 ? /
I
Process the instream treatment site
PNT1 = -PNT(I,J,K)
Figure C.20 Subroutine PTMX
-------
No
Is MU = 0, BdAX < PMT1 < QST ?
Yes
Implementation of the instream processor
would permit higher pollution flow
EMAX = PHT1
1
No
Is
MU > 0, FTM < PNT1 <
Yes
Implementation of the instream processor
would, permit higher pollution flow
HM = PNT1
Yes
f Are computations complete, i.e., is
A I = IM, J=JM, K=KM, MU = 0 ?
I
No
Yes
/Is I > KD1 1\
I
No
1 = 1 + 1
Yes
1
Is K > KLJ ?
Figure C.20 Subroutine PTMX
-------
Yes
No
No
Is KDIS(1,J,K) =/ 0 ?
No
»
Is K = 1 ?
Yes
P01DIS(l,J) = MAX
No
1
Is K = 2 ?
I
Yes
P02DIS(1,J) = MAX
NDIS(1,J,K) = 1
KFN = KC1(J,K)
I
Is a pollution distribution value from
this stream to its confluence node
being computed, i.e., is KPN = 1?
1 Yes
KG =
K -f
- 1
Figure C.20 Subroutine PTMX
U33
-------
No
Is K = 1 ?
Yes
JC =
HFS(J)
No
Is K = 2 ?
Yes
JC =
1
1C =
I
;is (IC,JC,KC) the objective point currently
being computed, i.e., is
IM = 1C and JM = JC and KM = KC ?
Yes
Skip to the confluence node
NF = J, KL = K, I = 1C, J = JC,
K = KC, MSI = NS(K), ND1 = KD(J,K),
PWT1 = PNT(I,J,K), QCK = Q(l,J,K) - PNT1
Q0T = min QCK,PU
QSN - Q3TM- PNT1 - PN(l,J,K)
Figure C.20 Subroutine PTMX
-------
Yes
Is J > HS1 ?
J = J + i
1 = 1
K = K + 1
J = 1
Call ERROR
All possible nodes have
been investigated and
node (II,JJ,KK) has been
passed
POUT = IMAX
I
Return
Figure C.20 Subroutine PTMX
-------
Subroutine STORE(PLT,PDIS,MDEM,NDIS)
STORE stores confluence node pollution
values in array PDIS. Successive values
in PDIS are nonincreasing. The input
pollution value to be stored is PLT.
PLTM = PLT
NDIS is the current number of values in
PDIS
ND = NDIS
No
No
Is PLTM > PDIS(WD) ?
I
Yes
Call ERROR. Successive values
stored in PDIS must be nonincreasing.
ND = ND + 1
Will the allowable length of the
PDIS array be exceeded, i.e., is
ND >MDEM ?
Yes
Call ERROR
I
Record the new entry
PDIS(ND) = PLTM
NDIS = ND
1
Return
Figure C.21 Subroutine STORE
-------
Function TCOST(x)
Function TCOST computes the total resource
cost for the solution represented by the D
and DINT arrays. This cost is accumulated
in the variable TTC.
TTC = 0.0
Set K = KL
MSI = NS(K)
Set J = 1
1
PTC will be used to accumulate the
annual pollution flow in stream J
PTC = 0
EDI = MD(J,K)
Set
/Is K < KL ? J
< YeS ( Is K < KL ?
Figure C.22 Function TCOST
-------
No
No
NF = JU(l,J,K-l)
Is NF > 0, i.e.,
is node (l,J,K) a confluence node?
Yes
PTC = PTC + PT(EF,K-1)
Add pollutant input from stream
(NF,K-l)
PTC = PTC + APN(I,J,K)
Add in annual natural pollution at
I
ID = D(I,J,K)
PTC = PTC + AP(I,J,K)
Add in annual pollu-
tion with no pollution
control
I
Is ID >0, i.e.,
is pollution control to be
performed at this node?
Yes
Figure C.22 Function TCOST
-------
Yes
Is ID = 1 ?
Is lowest cost alternative to
be implemented?
No
TTC = TTC + CALT(2,I,J,K)
Add in fixed cost of treatment
alternative 2
PTC = PTC + APld.J.K)
Add in pollutant load with lowest
cost alternative implemented
TTC = TTC + CALT(l,I,J,K)
Add in annual cost for lowest cost
alternative
m = INT(I,J,K)
Is NT > 0, i.e., is node (l,J,K)
a potential instream treatment site?
,Yes
No
Is DINT(NT) = 1, i.e., is instream
treatment being performed at this
site?
.Yes
Figure C.22 Function TCOST
^ 39
-------
No
Is PTC > 0, i.e., is the
stream providing any pollu-
tant to treat?
TTC = TTC + CI(NT) + VC*PT1
Increase total cost b"17" fixed and
variable costs of operating in-
stream treatment processor.
/^~~~\JesS X
( 80 ^*(is K > 3 ? J
LNO
PT(J,K)
<
= PTC
Figure C.22 Function TCOST
hko
-------
K = K + 1
Is K = KU ?
TCOST = TTC
( Eeturn J
Figure C.22 Function TCOST
kkl
-------
Subroutine TOFF(NT,II,JJ,KK)
TOFF processes upstream decision and status
variables when an instream processor is de-
activated. IT is the processor number and
(II,JJ,KK) is the node at -which NT is
located. NN is the number of tributary
streams on the tributary list
NN = 0
I = II
U = J J
K = KK
KEEP = KSINT(NT)
No
Is the upstream solution for this
treatment processor frozen at the
optimal value, i.e., is
OI(NT) = 1 ?
Yes
Reset the upstream solution
and allow it to vary by the
following procedure
BS(I,J,K) = 0
D(I,J,K) = 0
HE = IKT(I,J,K)
I
Is this node a potential instream
treatment site, i.e., is MR > 0 ?
Yes
No
Figure C.23 Subroutine TOFF
-------
KBINT(M) = 0
DINT(ER) = o
BT(KE) = 0
Is K < KL ?
I
Yes
No
IF = JN(I,J,K-1)
I
Is this node a confluence node, ^ No
i.e., is IF > 0 ?
Yes
Increase the length of
the tributary list
m = m + i
I
Is M >30 ?
No
I
Yes
Call EEROE to abort- the run
since the tributary list is
limited to 30 entries
Enter the tributary on the
tributary list
PS(M) = HF
PL(M) = K-I
Figure C.23 Subroutine TOFF
-------
Is I =
J =
1-1
h©
Yes
Are there entries on the
tributary list, i.e., is
m > 0 ?
lies
No
Remove an entry
J = PS(OT)
K = PL(EM)
I = ND(J,K)
m = m-i
Is MT upstream of an active instream
processor, i.e., is KEEP >0 ?
Yes
KBINT(NT) = i
OI(MT) = o
Call TON(KT,II,JJ,KK) to perform
necessary bookkeeping since NT is
still upstream of an active in-
stream processor 01(HT) = 1
RETURN
Figure C.23 Subroutine TOFF
kkk
-------
ed \
Has a feasible solution been computed
since NT was activated, i.e., is V
No
CIST(NT) < ,9-103°
J
Yes
Record that the low cost upstream
solution recorded for NT is an
optimal upstream solution
oi(NT) = i
Is NT upstream of an active
instream processor, i.e., is
KSINT(NT) = 1 ?
Yes.
RETURN
i
No
Zero out the upstream solution
up to the next active instream
treatment facility by the follow-
ing procedure. FIRST is true
during the first iteration to
avoid the treatment processor NT.
FIRST = .TRUE.
Is FIRST = .TRUE. ?
No
NR = INT(I,J,K)
Figure C.23 Subroutine TOFF
-------
Has a potential treatment site
been reached, i.e., is
W. > 0 ?
I Yes
KSINT(NR) = o
Yes
No
Is this treatment processor
active, i.e, is
DINT(KR) = 1
No
Zero out the decision at
this node
D(I,J,K) = 0
BS(I,J,K) = 0
FIRST = .FALSE.
Is K £ KL ?
No
WF = JN(I,J,K-1)
Has a confluence node been encountered,
i.e., is NF > 0 ?
I Yes
Increase the length of the
tributary list
HK = MN + 1
Figure C.23 Subroutine TOFF
kk6
-------
Is 1=1?
Yes
Are there any more entries on
the tributary list, i.e., is
m > o ?
Yes
Remove an entry
J = PS(NN)
K = PL(NN)
I = ND(J,K)
m = Ni-i
Figure C.23 Subroutine TOFF
\
, Yes
Call ERROR to abort the run
since the length of the tribu-
tary list has been exceeded
i
i
Enter the tributary on the
tributary list
PS(IH) = HF
PL (UN) = K-l
i
RETURN
-------
Subroutine TON(NT,II,JJ,KK)
TON processes upstream decision and status
variables when an instream processor is
implemented. (II,JJ,KK) is the node at -which
the instream processor is located, and NT is
the processor number. Initialize UN, the
number of upstream tributaries encountered.
NN = 0
I = II
J = JJ
K - KK
Is OI(FT) = 1, i.e., \
has an optimal solution been ob- ]
tained for this instream treatment I
processor? /
Yes
Record optimal upstream solution by the
following procedure.
Figure C.2k Subroutine TON
-------
BS(I,J,K) = 1
Record that the decision is
frozen at this node
Record the optimal upstream solution
for this source
D(L,J,K) = IO(I,J,K,MT)
HR = INT(I,J,K)
I
Is NR > 0, i.e.,
is this node a potential instream
treatment site?
Yes
Record the optimal upstream solution
for this processor
DINT(NR) = IOI(NR,NT)
Note that this processor decision is
frozen
BT(NR) = 1
Record that HR is upstream of an active
instream processor
KSINT(KR) = 1
< YeS ( Is K < KL ?
,
No
f
NF = JTSf(l,J,K-l)
Figure C.2k Subroutine TON
-------
No
Is NF > 0, i.e.,
is this node a confluence node?
Yes
+ 1
No
Is NN > 30 ?
There is only room for
30 tributaries to be
stored by the program
Yes
Call ERROR
Record the tributary on the tribu-
tary list
PS(UN) = NF
PL(NN) = K-I
Is NN > 0 ?
Are tributaries remaining
to be processed?
Yes
Figure C.2k Subroutine TON
1*50
-------
Remove the next tributary from the
tributary list
J = PS(WN)
K = PL(ffl)
I = ND(J,K)
UN = m-I
BT(HT) = o
KBIMT(NT) = o
Treatment site NT is free to vary
Site NT is not upstream of an
active instream processor
Return
CIST(NT) = 103°
FIRST = .TRUE.
FIRST is true when processing
the node containing the newly
implemented processor
Figure C.2k Subroutine TON
-------
No
true
If .NOT. FIRST J
I
false
FIRST = .FALSE.
HR = INT(I,J,K)
Is NR > 0, i.e., is
(l,J,K) a potential treatment node?
Yes
KSINT(NR) = 1
Site HR is upstream of an
active instream processor
I
Is DIMf(HR) = 1, i.e., is instream treatment
to be performed at site NR?
Yes
Figure C.2^ Subroutine TON
U52
-------
No
Is EALT(2,I,J,K) = 3, i.e., is
abatement and treatment cheaper
than treatment alone at this
node?
Yes
D(I,J,K) = 1
BS(I,J,K) = -1
Require some form of pollution control
to be performed at (l,J,K).
Is K < KL ?
m = JW(I,J,K-I)
Is WF > 0, i.e.,
is this a confluence node?
Yes
Figure C.2k Subroutine TOW
-------
C
Increase the number of entries on
the tributary list
HN = M + 1
Ho
Is UN > 30 ?
There is storage capacity for only
30 tributaries in this program
Record the tributary on the tributary list
PS(OT) = NF
PL(NN) = K-l
Are there tributaries left
to be examined, i.e., is
M > 0 ?
110 H-
Yes
Remove a tributary
J = PS(UN)
K = PL(NK)
I = KD(J,K)
m = ra-i
Figure C.2k Subroutine TON
-------
Subroutine ZO(l,J,K)
ZO zeroes out all decision variables that
are lower order than node (l,J,K). Node
(l,J,K) is also zeroed out
KB = K + 1
No
Set KK = KL
KB = KB - 1
JB = NS(KB)
Is KK = KL ?
I
Yes
JH = J
JB = JH + 1
I
Set J J = 1
JB = JB - 1
1D1 = ND(JB,KB)
Figure C.25 Subroutine ZO
-------
©*
No
Is KK = KL and 0, i.e.,
is node (IB,JB,KB) a potential
instream treatment site?
I
Yes
Is DINT(NT) = 1, i.e.,
is the instream processor active?
Yes
Figure C.25 Subroutine ZO
-------
is BT(KT) = o ?
Is treatment site being
examined?
Yes
= 0
Call TOFF(NT,IB,
-------
Yes
(Is NBSC = -1 ?
Must abatement be per-
formed at this site?
D(I,J,K) = 1
No
D(I,J,K) = 0
II = II + 1
No
Is II = EDI ?
JJ = JJ + 1
No
I
Yes
Is JJ = JH ?
KK = KK + 1
No
I
Yes
Is KK = K ?
Yes
Return
Figure C.25 Subroutine ZO
1*58
-------
APPENDIX D
COST OF DRAINAGE TREATMENT
INTRODUCTION
In the allocation of resources for the control of acid mine drainage
effects, the preferred allocation is strongly dependent upon the specific
treatment and abatement methods allowed, as well as the specific costs
involved for each allowable method. At each mine source or instream
treatment site, an engineering analysis will choose the cheapest
(according to an economic criterion and desired effect on acid flow)
treatment or abatement methods. Moreover, the specific treatment or
abatement costs will influence the global or basin-wide selection of
treatment and/or abatement control actions at each site. Realizing
that input cost data will be required at each site to operate the opti-
mization models described in Appendix C, an effort was made to generate
cost functions for several treatment and abatement techniques which
would be representative of observed costs, have relatively high confi-
dence levels, and be amenable to extrapolation beyond the limits of the
data base from which they were derived.
Table D.I is presented to set the context in which these cost functions
must perform. Table D.I describes, in various systems of units, treat-
ment and abatement cost ranges for a variety of techniques. It should
be noted that these data are abstracted from a 1968 publication based
on 1951 to 1966 cost figures. These numbers are presented to show the
relative cost levels on a per gallon basis for treatment methods and
relative cost for abatement methods.
Predesign cost estimates are extremely important for determination of
the feasibility and applications of a proposed treatment project. The
basic costs which are of interest to the designers are the per gallon,
per acre or yearly treatment and abatement costs. To construct
parametric relationships for accurately estimating these costs requires
large amounts of data, since the total product costs are complex func-
tions of a number of variables and the costs are also changed with
locations and time due to different economic conditions. Usually, in
-------
Table D.I. COST AND EFFECTIVENESS OF VARIOUS TECHNIQUES
FOR CONTROLLING ACID MINE DRAINAGE
Technique
Effectiveness
(% acid removal)
Cost
($)
Treatment
Neutralization
Distillation
Reverse Osmosis
Ion Exchange
Freezing
Electrodialysis
At-Source Control
80 to 97
97 to 99
90 to 97
90 to 99
90 to 99
25 to 95
.10
.Uo
.68
.61
.67
.58
.3/kgal
.25/kgal
.57/kgal
53/kgal
,23/kgal
.52/kgal
Water Diversion
Mine Sealing
Surface Restoration
Revegetation
25 to 75
10 to 80
25 to 75
5 to 25
300 -
1000 -
300 -
70 -
2000/acre
2000/acre
3000/acre
350/acre
Note: The above table is outlined from J. Martin and R. D. Hill,
"Mine Drainage Research Program of the Federal Water
Pollution Control Administration," Paper presented at the
Second Symposium on Coal Mine Drainage Research,
Pittsburg, Pennsylvania, May lU-15, 1968.
order to account for time effects upon costs, time correcting cost
indexes should be incorporated.
As suggested by different researchers (12,13), the total treatment
process costs should be divided into manufacturing costs and general
expenses. In order to evaluate each of the items, the total capital
costs should be considered first. For the sake of elucidating the
basic principles of the cost estimates, Tables D.2 and D.3 itemize the
important costs that should be considered in the economic studies.
These two tables are summarized from Reference (12).
TREATMENT COST MODEL
From Table D.I, it could be concluded that neutralization would be the
crucial first target for economic modelling. Accordingly, several cost
model structures are presented and evaluated for this treatment process,
These models are derived from data of the estimated costs of lime
-------
Table D.2. ESTIMATION OF CAPITAL INVESTMENT COST
I. Direct Cost:
Material and labor involved in actual installation of complete
facility, about 70 to 85% of the fixed capital investment.
A. Equipment + Installation + Instrumentation
B. Building + Process + Auxiliary
C. Service Facilities + Yard Improvements
II. Indirect Cost:
Expenses which are not directly involved with material and labor
of actual installation of complete facility
A. Engineering and Supervision
B. Construction expense and Contractor's fee
C. Contingency.
III. Fixed-capital Investment = Direct Costs + Indirect Costs
IV. Working Capital (10 to 20 percent of total capital investment)
V. Total Capital Investment = Fixed-capital Investment + Working
Capital.
-------
Table D.3. ESTIMATION OF TOTAL PRODUCTION COSTS
I. Manufacturing Cost = Direct Production Cost + Fixed Charge +
Plant Overhead Costs
A. Direct Production Costs (about 60f0 of total product cost)
1. Raw Material
2. Operating Labor (10 to 20$ of total product cost)
3. Utilities (10 to 20$ of total product cost)
U. Maintenance and Repairs (2 to 1.0% of fixed capital
investment cost)
5- Laboratory Charges (10 to 20$ of operating labor)
B. Fixed Charges (10 to 20$ of total product cost)
1. Depreciation (about 10$ of fixed capital investment
depends on life periods)
2. Local Tax, Insurance and Rent (about 5 to 10$ of fixed-
capital investment).
C. Plant Overhead Costs (about 5 to 15$ of total production
cost including general plant upkeep and overhead, payroll
overhead, packaging, medical services, recreation, salvage
and so on.
II. General Expenses = Administrative Costs + Distribution and Selling
Costs + Research and Development Costs
III. Total Production Cost = Manufacturing Cost + General Expenses
462
-------
neutralization of acid mine drainage obtained by West Virginia University,
Morgantown, West Virginia in 1967. The original data are shown in
Table D.U. The total costs are assumed to be the sum of plant costs
(except sludge removal), lime costs, labor costs, cost of sludge dis-
posal, maintenance costs, and contingency costs. The cost of hydrated
lime is taken at $2U/ton bagged, $22/ton bulk. The data which are used
for the basis of the model includes the following items:
Description % of Total Costs
A. Direct Production Costs
1. Raw material (lime) 25 - 50
2. Labor costs 8-12
3. Utilities (for sludge disposal) 8-11
k. Maintenance 6-8
B. Fixed Charges and Plant Overhead 12 - 30
C. Contingency and Miscellaneous 5-12
Because of limitations in the data displayed in Table D.k, the cost
model analysis is limited to two independent variables and relatively
simple relationships. A reasonable relationship should show total
treatment costs on a unit volume basis increasing with decrease in
plant size and increase in acidity concentration. Therefore, it was
first proposed that:
T = a(A)a(B)b (D.I)
where A is input acidity concentration in ppm,
B is the plant capacity in gal/day,
T is the treatment cost in cents/kgal, and
a, a, b are constant.
In order to estimate the values for a, a, and b, a plot at log T versus
log B while holding A constant was generated. Since four sets of data
are given in Table D.U, four different values for the slope b using
estimates from a least squares regression analysis, were obtained, and
then these values were averaged to estimate a mean value of b. In the
same manner by holding B constant, and plotting log T versus log A, a
mean value of a was obtained. From the results, Equation (D.l) becomes
T = 0.5293 (A)°-7(B)-°-068 (D.2)
-------
Table D.k. ESTIMATED COSTS OF LIME NEUTRALIZATION OF ACID MINE DRAINAGE
(all costs in cents/1000 gallons)
O\
" Plant Approximate
Capacity acidity
(gal/day) concentration
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
6500
6500
6500
6500
3*100
3^00
3^00
3^00
lUOO
1UOO
lUOO
1^00
650
650
650
650
Appr oximat e
iron
content
2000
2000
2000
2000
1000
1000
1000
1000
650
650
650
650
325
325
325
325
Plant cost
(except sludge
removal) Lime**
12.0
11.2
10. k
9.8
9-5
8,5
7.5
7.25
9-5
8.5
7.75
7.25
8.5
7.5
6.75
6.5
53
51
U9
k8
28.0
26.0
25.5
25.5
12.9
11.5
11.0
11.0
6.1
5.7
5-5
5-5
Labor
lU.O
12.6
11.8
11.0
10.0
5-0
2.5
2.0
8.0
U.o
2.0
1.6
6.0
3.0
1.8
1.0
Sludge
disposal Maintenance
11.0
10.5
10.5*
10.5*
8.0
7.0
7.75*
7.50*
4.0
3.5
3.75*
3.75*
2.0
1.8
1.9*
1.9*
6.0
5.8
5-5
5.3
4.0
3.0
2.5
2.5
3.0
2.5
2.0
2.0
2.5
2.0
1.5
1.5
Sludge
accumulation
Contingencies Total (acre-ft/yr)
5.0
5.0
5.0
5.0
3.0
3-0
3.0
3.0
3.0
3.0
3.0
3-0
2.5
2.5
2.5
2.5
101
96
92
89
62.5
52.5
48.5
47.74
3U. 8
33.0
29.5
28.6
27.60
22.50
19-95
18.90
13
39
117
351
9.8
30.1
91.0
273.0
4.9
15. 4
45.4
136.5
2.8
7.7
23.1
68.6
*These costs allow for excavating some hard rock
**Cost of hydrated lime taken at $24.00/ton bagged, $22.00/ton bulk
-------
However, the problem of solving for the annual treatment cost is always
raised. In order to do so, Equation (D.2) must be converted from
cents/kgal to dollars/yr. This procedure follows:
Since T is in j^/kgal and B is in gal/day,
Hence,
G $/year = ($/lOO cents)(T cents/1000 gal)-(365 days/year)(B gal/day)
G = 365 10-5(T)(B) (D.3)
Substituting Equation (D.3) into Equation (D.2), we obtained
G= 1.9323 10-3 (A)°-7(B)°'93:? (D.U)
The comparative results from the data and the model are tabulated in
Tables D.5 and D.6. Table D.5 shows the treatment costs expressed in
terms of cents per 1000 gallons; whereas Table D.6 indicates the results
of the total annual costs for a given size of plant. The deviations
between model and actual results are less than 25% of actual values,
which is reasonable for predesign cost estimates.
However, in order to pursue a better model, an additional coefficient
was incorporated. Several models were evaluated, and the best fit for
the entire set was determined to be Equation (D.5).
G - 365 x ID"5 (36.5^ + 0.0322A)(B)°-932 (D.5)
Tables D.7 and D.8 present comparisons between data and actual results,
and these tables show a maximum error in predicting the actual results
of 11.6$ of actual values.
In comparing the two models represented by Equations (D.4) and (D.5),
significant improvement is achieved by using Equation (D.5). The maxi-
mum deviation of the predicted results from the data is less than 12%
compared to 25$ deviation obtained by Equation (D-U). A 12$ error in
predicting costs before a detailed system design is performed should
be acceptable is most applications. However, one might note that these
models were derived by finding the best fit to the same data that were
used to estimate predictive errors; thus, a new data set may give larger
errors. Also, the linear relationship between the annual costs and the
acidity seems to fit the data better than using 0.7th power as suggested
by Equation (D.^). The linear relationship is strongly supported by
Figure D.I where lime cost is plotted against acid concentration for the
data listed in Table D.4.
^65
-------
Table D.5. ESTIMATED COSTS OF LIME NEUTRALIZATION OF
ACID MINE DRAINAGE BASED ON EQUATION (D.4)
(all costs in cents/1000 gallons)
Plant capacity Acidity Data Model Deviation
(gal/day) (ppm) result result
300,000 6500 101 104.80 3.76
900,000 6500 96 101.27 5.1*9
2,700,000 6500 92 90.25 -1.90
8,100,000 6500 89 83.75 -5-90
300,000 3400 62.5 66.59 6.54
900,000 34oo 52.5 61.79 17.70
2,700,000 3400 1*8.5 57.34 18.22
8,100,000 3400 47.75 53-21 11.1*3
300,000 1400 34.8 35.78 2.82
900,000 ll*00 33.0 33.21 0.64
2,700,000 11*00 39.5 30.81 U.l*l*
8,100,000 ll*00 28.6 28.56 -0.03
300,000 650 27.6 20-91 -24.2
900,000 650 22.5 19.41 -13-7
2,700,000 650 19.95 18.01 -9.6
8,100,000 650 18.90 16.71 -11.6
466
-------
Table D.6. ESTIMATED COSTS OF LIME NEUTRALIZATION OF
ACID MINE DRAINAGE BASED ON EQUATION (V.k]
(all costs in dollar per year)
Plant capacity
(gal/day)
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
Acidity
(ppm)
6500
6500
6500
6500
3Uoo
3UOO
3^00
3^00
1^00
lUoo
1^-00
1*4.00
650
650
650
650
Data result
($/yr)
110,593
315,360
906,660
2,631,285
68,^37
172A63
^-77,968
1,1+11,729
38,106
108,1405
390,723
8^5,559
30,222
73,913
196,607
558,779
Model result
($/yr)
1114,208
319,^97
889,^95
2,^76,397
72,9H
202,987
565,125
1.573,337
39,179
109,075
303,671
8^3,^35
22,898
63,7to
177,^80
h9k,l!2
Deviation
do]
3.30
1.31
-1.89
-5-87
6.5^
11.08
18.20
11. U5
2.81
0.62
U.U5
-0.01
-2k. 2
-13-75
-9-73
-11.37
-------
Table D-7- ESTIMATED COSTS OF LIME NEUTRALIZATION OF
ACID MINE DRAINAGE BASED ON EQUATION (D.5)
(all costs in cents/1000 gallons)
Plant capacity
(gal/day)
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
Acidity
(ppm)
6500
6500
6500
6500
31*00
31*00
3^00
31*00
lUoo
ii+oo
ll+OO
ll*00
650
650
650
650
Data
result
101
96
92
89
62.5
52.5
1+8.5
^7.75
3U.8
33-0
29-5
28.6
27.6
22.5
19-95
18.90
Model
result
10k. k
96.9
89-93
83-^3
62.02
57-55
53-^0
^9.53
3^.65
32.16
29.81+
27.69
2k. ho
22.6k
21.00
19. U9
Deviation
(fo)
3.26
0.9
-2.250
-6.23
-0.78
-8.620
9.620
3-791
+1.59
-2.5U
+1.15
-3.18
-11.59
0.62
5.26
3.12
14-68
-------
Table D.8. ESTIMATED COSTS OF LIME NEUTRALIZATION OF
ACID MINE DRAINAGE BASED ON EQUATION (D-5)
(all costs in dollars/year)
Plant capacity
(gal/day)
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2,700,000
8,100,000
300,000
900,000
2, -700, 000
8,100,000
Acidity
(ppm)
6500
6500
6500
6500
3400
3400
3400
3400
1400
1^400
i4oo
1400
650
650
650
650
Data
result
110,593
315,360
906,660
2,631,285
60,477
172,463
477,968
1,411,729
38,106
108,405
290,723
845,559
30,222
73,913
196,607
558,779
Model
result
114,323
318,282
886,112
2,466,979
67,897
189,019
526,238
1,465,073
37,938
105,624
294,062
818,685
26,708
74,346
207,010
576,327
Deviation
(*)
3-37
0.93
-2.23
-6.24
-0.76
9.60
10.10
3-75
-0.44
-2,56
1.15
3.18
-11.63
0.60
5.29
3-14
^69
-------
7000
Q. 5000
D.
cc
I-
2
UJ
O 3000
O
Q
<
1000
0
10 20 30 40
LIME COST U/kgal)
50
Figure D.I. A plot of acidity concentration vs. lime cost
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The annual treatment costs are exponentially Increased with plant
capacity. At all levels of acidity, the annual costs increase the most
rapidly in the data set from 1 x 10s to 3 x 10s gallons per day.
In order to apply the model represented by Equation (D.5) to arbitrary
process environments, the following factors which influence the cost
estimates should be considered with great care. As indicated by the
data given in Table D.h, the cost of limestone contributes 25 to 50f0 of
the total cost. Limestone costs may be an essential factor affecting
the determination of the total costs. Limestone costs vary with loca-
tion of the treatment plant with respect to the nearest lime producer,
and they also change from time to time. In order to obtain a reasonable
estimate of the treatment cost, a correction factor for limestone costs
dependent on location and time, should be taken into account. Construc-
tion costs also vary with location and the type of excavation required,
but this factor is hard to predict. Other costs, such as labor costs,
plant costs, costs for sludge disposal, maintenance and contingency
costs are relatively constant with locations, and each of them contrib-
utes only a relatively small percentage to the total costs compared to
the limestone costs. Therefore, only the time effect on the construc-
tion costs should be considered. This can be done simply by incorpo-
rating the cost indexes, which are available in the literature, into
the cost estimates.
EXAMPLE APPLICATION
An example application is presented in order to illustrate the applica-
tion of the cost model and the inclusion of the corrections mentioned
above.
Sample Problem
A treatment plant was built in Morgantown, West Virginia, in 1967.
This plant could handle 300,000 gallons of water with an acid concen-
tration of 6500 ppm per day. The following problems are posed:
(a) If the same plant was to be used in 1970, what would the
annual total cost be?
(b) If a treatment plant which could handle 900,000 gallons
of water with an acid concentration of 3^00 ppm per day
were to be built in Central Ohio, what would the approxi-
mate annual cost be in 1970? The total cost for treating
1000 gallons of water with an acid concentration of
3^00 ppm in Central Ohio is estimated to be $.30.
-------
Solution to the Problems
Problem (a): Choosing 196? as the base year, its cost index is assumed
to be 100. From the literature, the cost index for 1970 is found to be
114 (this is only a hypothetic value).
The annual cost for the plant can be computed from Equation (D.5):
G = 365 x ID'5 (36.54 + 0.0322A)(B)°-93£>
= 365 x 10'5 (36.54 + 0.0322 x 6500)(300000 )°'932>
= $114,188.
The annual cost for the plant in 1970 would be
Cost Index in 1970
4.970 - ^1967 ' Cost Index in 1967
= 114,188 x 1.14
= $130,174.
Problem (b): From Equation (D.5):
G = 365 x 10~5 (36.54 + .0322 x 3400)(900000)°-932
= $188,824
Since the annual cost, G, is the sum of lime cost, labor cost, sludge
disposal cost, plant cost, maintenance cost and contingency cost, all
these costs are based on the data obtained in West Virginia. In order
to correct for the location effect on lime cost, one must calculate:
(l) From Figure D.2, with acid concentration of 3400 ppm,
the treatment cost for 1000 gallons of acid water is
about $0.26 in West Virginia; thus, the difference be-
tween the total lime costs in West Virginia and Central
Ohio is,
(0.3 - 0.26)($/kgal)(365 day/yr)(900 kgal/day) = 0.04 x 365 x 900
= $13,150
-------
7000
E
£ 5000
o
en
LU
O
Z
g 3000
1000
0
10 20 30 40
LIME COST($/kgal)
50
Figure D.2. A plot of acidity concentration vs. lime cost
1967 West Virginia University data
-------
(2) For the treatment plant in Central Ohio, the true annual
cost in 1967 should be corrected to
188,82U + 13,150 = 201,
(3) In 1970, the total annual cost would be
G = 201,97^ x (ll>l/100)
= 230,250
SUMMARY
This type of mathematical analysis permits the estimation of treatment
costs based on information concerning acidity and plant size. The re-
sults predicted by the model should only be used as preliminary cost
estimates. As one may note the original data given in Table D.^4 do not
provide sufficient information for detailed cost estimates that are
sensitive to individual situations. However, by utilizing the cost
model, designers should be able to determine preferred plant sizes and
treatment plant locations.
As pointed out by Peter and Timmerhaus, a "Study Estimate" or "Factored
Estimate" based on the knowledge of major items has a probable accuracy
of ±30$) (12). Based upon this standard, the cost estimating relation-
ship, Equation (D.5), describes the observed results well in that the
maximum error in the predicted result is less than 12.%. Therefore,
this cost estimating relationship should be used by considering how
significant factors affect the individual cases in a particular appli-
cation.
*If the lime cost difference between two locations is less than
the correction for location effect is unnecessary. As shown in the
above case, the correction term'only contributes to less than 5$ of the
total costs.
-------
REFERENCES FOR APPENDIX D
1. E. Martin and R. Hill, "Mine Drainage Research Program of the
Federal Water Pollution Control Administration," paper presented
at Second Symposium on Coal Mine Drainage Research, Pittsburgh,
Pennsylvania, May 1^-15, 1968.
2. C. T. Holland, "Experience in Operating an Experimental Acid Mine
Drainage Treatment Plant," 13, No. 2, 157th National Meeting of
the American Chemical Society, Minneapolis, Minnesota, April 13-18,
___
3. R. D. Hill and R. C. Wilmonth, "Limestone Treatment of AMD,"
A.I.Ch.E. 250, p. 162.
14. "Treatment of Acid Mine Drainage by Ozone Oxidation," Department
of Applied Science, Brookhaven National Lab., Associated University,
Inc . , Dec . , 1972 .
5. "Evaluation of a New Acid Mine Drainage Treatment Process," Water
Pollution Control Research Series, 1^010 DYI 02/71.
6. R. B. Scott, R. Hill and R. Wilmonth, "Cost of Reclamation and
Acid Mine Drainage Abatement," Water Quality Office, Environmental
Protection Agency, Cincinnati, Ohio, ^3226, Oct., 21-23, 1970.
7. J. B. Jone and S. Ruggeri, "Abatement of Pollution from Abandoned
Coal Mines by Means of in situ Precipitation Technique," paper
presented at the 157th National Meeting American Chemical Society,
13, No. 2, April 13-18, 19&9-
8. R. A. Tybout, "Private and Social Costing and Pricing as Decision
Determinants," paper available at The Ohio State University,
Department of Economics.
9. Hoggan, et al., "State and Local Capability to Share Financial
Responsibility of Water Development with Federal Government,"
U. S. Water Resources Council, 1971.
10. "West Virginia Water Pollution Control Program," EPA and FWQA
Dept., 1970.
11. Peters and Timmerhaus, Plant Design and Economics for Chemical
Engineers , McGraw-Hill Book, 2nd edition, 1968.
12. J. P. Gibb, "Cost of Water Treatment in Illinois," Illinois State
Water Survey, Urbana, 1968.
-------
13. Morth, "Acid Mine Drainage: A Mathematical Model," Ph.D. Disserta-
tion, The Ohio State University, 1971.
lU. Chow, K., "Computer Simulation of Acid Mine Drainage," Master's
Thesis, The Ohio State University, 1972.
15. Proc.Second Symposium on Coal Mine Drainage Research, Pittsburgh,
-T ,-N /"" f~l ^ ^ F "--"'"--in mi L....II---L ..
16. Water Pollution Control Research Series, 1^010, DYG, EPA, Aug.,
1972.
17- Water Pollution Control Research Series, 1^010, FQR, EPA, March,
1972.
18. Water Pollution Control Research Series, lUOlO, DYK, EPA, March,
1972.
19. Water Pollution Control Research Series, 12010, EQF, EPA, March,
1971.
20. Water Pollution Control Research Series, 1^010, FNQ, EPA, February,
1972.
21. Lund, H., Industrial Pollution Control Handbook, McGraw-Hill, 1973-
22. Environmental Protection Technology Series, EPA* R2-72-056, Nov.,
1972.
23. Water Pollution Control Research Series, 1^010, EQF, EPA, February,
1971.
2k. Water Pollution Control Research Series, 12010, FNQ, EPA, March,
1Q70.
-------
TECHNICAL REPORT DATA
(f lease read Instructions on the reverse before completing)
. REPORT NO.
EPA-600/2-76-112
2.
3. RECIPIENT'S ACCESSION-NO.
. TITLE AND SUBTITLE
RESOURCES ALLOCATION TO OPTIMIZE MINING BDLLUTION
CONTROL
5. REPORT DATE
November 1976
(Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Kenesaw S. Shumate, E. E. Smith, Vincent T. Ricca,
and Gordon M. Clark
8. PERFORMING ORGANIZATION REPORT NO
RF
9. PERFORMING ORGANIZATION NAME AND ADDRESS
The Ohio State University Research Foundation
131i* Kinnear Road
Columbus, Ohio 1+3212
10. PROGRAM ELEMENT NO.
EHE 623 05-01-Q8A-05
11. CONTRACT/GRANT NO.
68-01-072**
12. SPONSORING AGENCY NAME AND ADDRESS
Industrial Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Final, 6/29/72 - 9/30/73
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
16, ABSTRACT __
A comprehensive model for mine drainage simulation and optimization of resource allo-
cation to control mine acid pollution in a watershed has been developed. The model
is capable of: (a) producing a time trace of acid load and flow from acid drainage
sources as a function of climatic conditions; (b) generating continuous receiving
stream flow data from precipitation data; (c) predicting acid load and flow from mine
drainage sources using precipitation patterns and watershed status typical of "worst
case" conditions that might be expected, e.g., once every 10 or 100 years; and
(d) predicting optimum resource allocation using alternative methods of treatment
and/or abatement for "worst case" conditions during both wet and dry portions of the
hydrologic year. The model is comprehensive and may, therefore, be more detailed
than required. This attention to detail was given in the belief that it will be
easier to simplify the model than to modify it to increase detail. Because of the
detail incorporated in the model as now constituted, a large amount of field data is
required as input. In most cases, the desired field data are not now available.
The model has not been fully tested or compared to real systems, nor has sensitivity
to input data been determined. Therefore reliability of the model, and the necessity
of detailed field data, have not been established. Comparisons with real systems
are necessary to determine the level of simplification that can be permitted before
_the validity or usefulness of the model is impaired.
17,
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Strip mining, Coal mining, Mathematical
models, Drainage, Watersheds, Refuse
Mine drainage, Computer
models, Watershed models,
Deep mines, Refuse piles.
Coal mine drainage, Acid
generation, Acid drainage
treatment
08/1, 08/H
08/G, 08/M
S. DISTRIBUTION STATEMENT
Release to public
19. SECURITY CLASS (ThisReport)'
Unclassified
21. NO. OF PAGES
493
20. SECURITY CLASS (Thispage}
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
1*77
6USGPO: 1977 757-056/5461 Region 5-11
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