USER'S MANUAL FOR ERA'S
COMPOSITE MODEL FOR LANDFILLS (EPACML)
February 1990
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF SOLID WASTE
WASHINGTON O.C. 20460
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TABLE OF CONTENTS
Section
TABLE OF CONTENTS ii
LIST OF FIGURES v
LIST OF TABLES vi
DISCLAIMER viii
ABSTRACT TX
ACKNOWLEDGEMENTS x
1.0 MODEL ACQUISITION AND INSTALLA".3N PROCEDURE 1-1
1.1 Model Acquisition 1-1
1.2 Installation and Testing Procedure 1-1.
1.2.1 Installation on an IBM-PC or Compatible
Microcomputer 1-2
1.2.2 Testing Procedure 1-5
2.0 STRUCTURE OF CODE AND INPUT FILES 2-1
2.1 Introduction 2-1
2.2 The Model Structure 2-1
2.3 Running The EPACML Program 2-4
2.4 Input and Output File Units 2-5
2.4.1 Input Files .. 2-5
2.4.2 Output Files 2-5
2.5 Common Blocks 2-8
2.6 Parameter Statements 2-8
2.7 Structure of the Input Files 2-14
2.7.1 COMMENT CARDS 2-17
2.7.2 DATA GROUP/SUBGROUP SPECIFICATION CARD,
END CARD, AND DATA CARDS 2-17
2.7.3 Specification of Parameter Values 2-18
3.0 FORMAT FOR THE INPUT DATA 3-1
3.1 Introduction 3-1
3.2 The Array Subgroup 3-1
3.3 The Empirical Distribution Subgroup 3-3
3.4 Format of the Input File (User-Specified Name) 3-5
3.4.1 General Data Group 3-5
3.4.2 Source Data Group 3-8
11
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TABLE OF CONTENTS (continued)
Section Page
3.4.3 Chemical Data Group 3-12
3.4.3.1 The Overall Decay Coefficient 3-14
3.4.3.2 Distribution Coefficient 3-16
3.4.4 Unsaturated Zone Flow Data Group 3-16
3.4.4.1 Unsaturated Zone Flow Control Data
Subgroup 3-17
3.4.4.2 Unsaturated Zone Flow Spatial
Discretization Subgroup 3-19
3.4.4.3 Unsaturated Zone Flow Material Data
Subgroup 3-21
3.4.4.4 Unsaturated Zone Flow Material
Allocation Subgroup 3-24
3.4.4.5 Unsaturated Zone Flow Moisture
Data Subgroup 3-26
3.4.5 Unsaturated Zone Transport Data Group 3-29
3.4.5.1 Unsaturated Zone Transport Control
Data Subgroup 3-29
3.4.5.2 Unsaturated Zone Transport Properties
Subgroup 3-29
3.4.5.3 Unsaturated Zone Time Steps Data
Subgroup 3-35
3.4.6 Aquifer Data Group 3-35
3.4.6.1 Computation of Particle Diameter and
Porosity 3-39
3.4.6.2 Computation of Hydraulic Conductivity
and Seepage Velocity 3-40
3.4.6.3 Computation of Source Thickness, Spread,
and Maximum Source Concentration 3-42
3.4.6.4 Computation of the Longitudinal,
Transverse, and Vertical D1spers1v1t1es 3-46
3.4.6.5 Specifying Location of the Receptor Well 3-48
4.0 COMBINING REGIONAL DISTRIBUTIONS TO ESTIMATE THE NATIONWIDE
DISTRIBUTION 4-1
4.1 Introduction 4-1
4.2 Input and Output Files for CMPCDF 4-1
4.3 Input Data Required and Format 4-2
4.4 Computation of Composite Distribution 4-2
REFERENCES 5-1
APPENDIX A LIST OF SUBROUTINES INCLUDED IN THE EPACML MODEL ป-l
APPENDIX B EXAMPLE OF INPUT DATA AND OUTPUT 8-1
111
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TABLE OF CONTENTS (concluded)
Section Page
EXHIBIT 1 MAIN INPUT DATA FILE FOR EXAMPLE 1 B-4
EXHIBIT 2 MAIN OUTPUT FILE FOR EXAMPLE 1 B-7
APPENDIX C EXAMPLE OF INPUT DATA AND OUTPUTS FOR CMPCDF C-l
APPENDIX D DESCRIPTION OF VARIABLES IN OUTPUT FILES 0-1
1v
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LIST OF FIGURES
Figure Page
1-1 Subroutine Organization Tree for EPA's Composite
Landfill Model (EPACML) 1-3
2.1(a) Flowchart of the EPA's Composite Landfill Model 2-2
2.1(b) Flowchart of the Simulation Options 1n the
EPA's Composite Landfill Model 2-3
2.2 Structure of the Input-Data File, Data Groups and
Subgroups 2-15 \
3.1 A Schematic of the Well Location 3-49
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LIST OF TABLES
Table
2.1
2.2
2.3
2.4
3.1
3.2
3.3A
3. 38
3.4A
3.4B
3.5A
3. SB
3.6A
3.6B
3.6C
3.60
3.6E
Description of Common Blocks Contained 1n the EPACML
Model
List of Variables Defined by Parameter Statements
Input Data Groups and Subgroups for the EPACML Model
Distributions Available and Their Codes
Contents and Format for a Typical Array Subgroup
Contents and Format for a Typical Empirical
Distribution Subgroup
Contents and Format for the General Data Group
Default Values for the Variables 1n the
General Data Group
Contents and Format for Source-Specific Data Group
Default Values for the Source-Specific Variables
Contents and Format for the Chemical -Specific
Data Group
Default Values for the Chemical -Specific Variables
Contents and Format for the Unsaturated Zone Flow
Module Control Data Subgroup
Contents and Format for the Unsaturated Zone Flow
Module Spatial Discretization Subgroup
Contents and Format for the Unsaturated Zone Flow
Module Material Subgroup
Default Values for the Unsaturated Zone Material Parameters
Contents and Format for the Unsaturated Zone Flow
Page
2-9
2-11
2-16
2-19
3-2
3-4
3-6
3-9
3-10
3-11
3-13
3-15
3-18
3-20
3-22
3-23
Module Material Allocation Subgroup 3-25
VI
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Table
3.6F
3.6G
3.7A
3.7B
3.7C
3. 70
3.8A
3.8B
3.8C
3.80
3.8E
3.8F
4.1
LIST OF TABLES
Contents and Format for the Unsaturated Zone Flow
Module Moisture Data Subgroup
Default Values for the Unsaturated Zone Moisture
Subgroup Data
Contents and Format for the Unsaturated Zone Transport
Module Control Subgroup
Contents and Format for Unsaturated Zone Transport
Module Data Properties Subgroup
Default Values for the Unsaturated Zone Transport
Data Subgroup
Contents and Format for the Unsaturated Zone Transport
Module Time Stepping Data
(concluded)
Page
3-27
3-28
3-30
3-33
3-34
3-36
Contents and Format for the Aquifer-Specific Data Group 3-37
Default Values for the Aquifer-Specific Variables
Options Available to Compute Particle Diameter,
Porosity, Hydraulic Conductivity, and Seepage Velocity
Computation of Source Thickness and Spread
Computation of Longitudinal, Transverse, and
Vertical 01spers1v1t1es
Options Available for Specifying the Well Location
Contents and Format for the Input Data File Required
3-38
3-41
3-43
3-47
3-51
to Combine Regional CDFs to Yield Composite Nationwide
COF/Spec1f1c Percentlles 4-3
vii
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DISCLAIMER
The work presented 1n this document has been funded by the United
States Environmental Protection Agency. It has not been subject to the
Agency's peer and administrative review, and has as yet not been approved
as an EPA document. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use by the U.S. Environmental
Protection Agency.
vm
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ABSTRACT
The Environmental Protection Agency's Composite Model for Landfills
(EPACML) simulates the movement of contaminants emanating from a hazardous
waste disposal facility. The Composite Model for Landfills consists of a
steady-state, one-dimensional numerical model that simulates flow in the
unsaturated zone. The output from this module, seepage velocity as a
function of depth, is used as input by the unsaturated zone transport
module. The latter simulates one-dimensional (vertical) transport in the
unsaturated zone and includes the effect of longitudinal dispersion, linear
adsorption, and first-order decay. Output from the unsaturated zone
modules--i.e., contaminant flux at the water tableis used to couple the
unsaturated zone module with the semi-analytical saturated zone transport
module. The latter includes one-dimensional uniform flow, three-
dimensional dispersion, linear adsorption, first-order decay, and dilution
due to direct infiltration into the groundwater plume for the case of a
Gaussian source.
The fate and transport of contaminants in the various media depends on
the chemical properties of the contaminants as well as a number of medium-
and environment-specific parameters. The uncertainty and spatial
variability in these parameters is quantified using the Monte Carlo
simulation technique.
This Users' Manual provides Information and detailed guidance on setting
up input data files for the EPACML model. It also includes two sample input
data sets and the corresponding outputs to further assist the user in
setting up the data files. Finally, the manual Includes details of a
program called Composite Cumulative Distribution Function (CMPCDF) that can
be used to combine regional cumulative distribution functions with specified
weights to yield the nationwide composite cumulative distribution function.
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ACKNOWLEDGEMENTS
This report has been prepared by Woodward-Clyde Consultants for the
office of Solid Waste (OSW). U.S. Environmental Protection Agency (EPA).
Dr. Zubalr Saleem was the project manager for EPA and Dr. Atul M. Salhotra
served as project manager for Woodward-Clyde Consultants.
A number of individuals were Involved in the actual development of the
computational codes and provided assistance to OSW. Mr. Doug Marder of
DPRA Inc. made modifications for Implementing the model on various computer
architectures and also provided helpful suggestions for optimizing the
code. Dr. Zubair Saleem provided the overall guidance and technical
advice. Other key individuals and companies involved in the implementation
of the code include Dr. Jan Kool of HydroGeologic Inc.; Barry Lester of
GeoTrans Inc.; Dr. Michael Ungs of Tetratech, Inc.; Phil Mineart of
Woodward-Clyde Consultants; Dr. Carlos Marin, Amblotech; Dr. Ed Sudicky,
University of Waterloo; and Charles Dankwah of Technology Applications,
Inc.
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SECTION 1
MODEL ACQUISITION AND INSTALLATION PROCEDURE
l.l MODEL ACQUISITION
The EPACML [EPA's Composite Model for Landfills!, the CMPCOF (Composite
Cumulative Distribution Function) codes, as well as example data sets and
outputs, can be obtained by contacting:
Or. Zubair Saleem
U.S. Environmental Protection Agency
Office of Solid Waste (OS-331)
401 "M" Street, S.W.
Washington D.C. 20460
^
,.^
Telephone: (202) 382-4761 ^ฐ
1.2 INSTALLATION AND TESTING PROCEDURE
The current version of the EPACML code 1s shipped on 360 K or 1.2 M
byte floppy disks. The code consists of the FORTRAN 77 algorithms, include
files (labeled *.CMN), and sample input and output files. A copy of the
code can also be shipped on an unlabeled magnetic tape written to user
specifications (block size, ASCII or EBCDIC).
A utility program, named CMPCDF, is also Included with EPACML. This
program can be used to aggregate regional COFs (cumulative distribution
functions) of a given variable to estimate nationwide composite CDF of the
variable based on the total probability theorem. Further details of this
program are Included in Section 4.
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8820087TC CON-12
1.2.1 Installation on an IBM-PC or Compatible Microcomputer
The code has been developed and tested on the PC using the following
configuration:
640 K byte RAM
40 M byte hard disk drive
360 K byte or 1.2 M Byte floppy drive
A DSI Co-Processor Board with the SVS Fortran 77 compiler V, 2.8
The size of the executable code is greater than 640 K byte, so if a DSI
board or equivalent 1s not available, additional resources would be
needede.g., extended or expanded memory and a FORTRAN compiler capable of
utilizing this memory. Alternatively, the code can be restructured and
compiled using overlays in which case the model can be run on an AT-
compatible machine. Figure 1-1 gives the subroutine organization tree to
aid in restructuring the program.
The source code provided on floppy diskettes can be copied directly
onto a hard disk. To create an executable version of the model, the source
code needs to be compiled and linked using a FORTRAN compiler. Because of
the large number of files required to compile the program and the potential
for a large number of output files when the model 1s run, it 1s recommended
that the EPACML code be maintained in Us own subdirectory on the hard
disk.
For computers running DOS 3.3 the code can be Installed using the
following procedures:
1) Boot computer
2) Put EPACML source diskette Into drive A
3) 'MD EPACML1 - Create directory EPACML
4) 'CD EPACML1 - Change directory to EPACML
5) 'XCOPY A: C: /S' - Copy files from diskette to hard drive. This
will copy all the files from the diskette and create three
directories, CODE, TEST1, and CMPCDF containing the code, test data
Information, and the CMPCDF program.
1-2
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MAIN
OPENF
SOPEN
COUNT
MODCHK
RANSET
PRTOUT
OUTFOR
DEFGW
DEFVF
DEFVT
UNCPRO
PRINTIN
|- PRNEMP
PRINTO
FRQTAB
FRQPLT
T- AQMOD
HSOMOD
L CHMOD
VFMOD
VTMOD
INITGW
INITVF
-LAYAVE
TMGEN1
-TMGEN2
rLEFTJT
- CHKEND
-READ2
-READ3
FACTR
CALLS
ICHECK
TRNLOG
-TRANSB
-EXPRND
-NORMAL
-LOGNOR
-EMPCAL
EXPRN i
ANRMRN -
UNIFRM
UNIFRN
Figure 1-1. Subroutine Organization Tree for EPA's Composite
Landfill Model (EPACML)
1-3
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MAIN
'CONV02
GW3DPT
-GW3DPS
- VTCALC -r-
ADVECT
ADISPR
COEFF
STEHF
SOLAY1
VFCALC T- RAPSON
L
GW3DPT
GW2DFT
QROMB
TRAPZD
j
FUNCT1
DERFC
EVAL
LAGRNG
SOLAY1
EXPERF
DERFC
EXPO
-DGAUSS
FPSI1
WCFUN
Figure 1-1. Subroutine Organization Tree for EPA's Composite
Landfill Mode! (EPACML) (concluded)
1-4
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For computers running DOS 3.2 (or lower), the following procedure can be
used to Install the EPACML code:
1) Boot computer
2) Put EPACML source diskette Into drive A
3) MD EPACML - Create directory EPACML
4) CO EPACML - Change directory to EPACML
5) MD CODE - Create directory for source code
6) MD TEST1 - Create directory for first test data set
7) MD CMPCDF - Create directory for CMPCDF Program
8) Copy A:\CODE\*.* C:\EPACML\CODE - Copy source code from diskette
9) Copy A:\TEST1\*.* C:\EPACML\TEST1 - Copy test data set one and
results
10) Copy A:\CMPCDF\*.* C:\EPACML\CMPCOF- Copy CMPCDF program
In order to run the EPACML program, the CONFIG.SYS file should have
FILES and BUFFERS set to at least the following values:
FILES = 25
BUFFERS = 15
Information required to adjust system configuration 1s available in the DOS
manual.
1.2.2 Testing Procedure
A sample Input data file for EPACML and for CMPCOF and corresponding
output files are supplied with the disks/tape. The sample input files are
named:
TEST1.DAT
CDF1.OAT
The corresponding output files (generated on unit IOUT; refer to Section
2.4.2 for details) are named:
1-5
-------
TEST1.0UT
CDF1.0UT
Note that the files COF1.DAT and CDF1.0UT are for testing the program
CMPCDF.
Additional details of these sample Input and output files are presented
In Appendices 8 and C. It Is recommended that the user run these two
sample data sets and compare the outputs generated with the above
(supplied) output files to ensure the correct Installation of the code.
1-6
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SECTION 2
STRUCTURE OF CODE AND INPUT FILES
2.1 INTRODUCTION
This chapter provides an overview of the structure of the code and the
input files required to run the model. The model consists of a number of
modules, the theoretical details of which are described in WCC (1988a
and b) of this report.
2.2 THE MODEL STRUCTURE
Figures 2.1(a) and 2.1(b) show the flowchart of the EPACML model. The
major functions currently performed by this model include:
Allocation of default values to input parameters/variables.
Reading of the Input data files.
Echo of Input data to output files.
Generation of random numbers for Monte Carlo simulations.
Calculation of contaminant degradation rates from hydrolysis rate
constants, retardation coefficient, hydraulic conductivity, and
other parameters 1f they are not read 1n as Input variables.
2-1
-------
ERAS LANDFILL MODEL
SET DEFAULT VALUES
READ INPUT DATA
ECHO INPUT DATA
DETERMINISTIC
OR
MONTE CARLO
DETERMINISTIC
MONTE CARLO
DO 1.1 .MONTE
GENERATE RANDOM NUMBERS
RUN OPTIONS
SEEFK3.2.1 (b)
RUN OPTIONS
SEE FIG. 2.1 (b)
WRITE RANDOMLY
GENERATED VARIABLES
PRINT RESULTS
PRINT RESULTS
PRINT PLOTS AND
STATISTICAL ANALYSIS
Figure 2.1 (a). Flowchart of the EPA's Composite Landfill Model
2-2
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1
RUN OPTIONS
UNSATURATEDZONE
FLOW
UNSATURATEDZDNE
TRANSPORT
SATURATED
TRANSPORT
SATURATED
TRANSPORT
Figure 2.1(b). Flowchart of the Simulation Options In the
EPA's Composite Landfill Model
2-3
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Depending on user-selected option:
- simulation of unsaturated zone flow and transport followed by
saturated zone transport
- simulation of saturated zone transport only
In the Monte Carlo mode, the cumulative frequency distribution
(printer plots), selected percentiles and user-specified confidence
intervals for the percentile of receptor-well concentrations.
For each Monte Carlo run, the values of randomly generated input
parameters and the computed receptor concentration values can be
printed.
The code consists of a number of subroutines. Each subroutine includes
several comment statements that describe the function of the subroutine.
Should the user need to edit the code, the location of the anticipated
change can be easily identified. The arguments of each subroutine are
divided into three categories: (1) arguments that are passed to the
subroutine by the calling program, (2) arguments that are modified within
the subroutine, and (3) arguments returned by the subroutine to the calling
program. A list of all the subroutines, the calling subroutine/program, as
well as a brief description of the subroutines are included in Appendix A.
2.3 RUNNING THE EPACML PROGRAM
The model can be run in either the batch or the interactive mode. When
running the model in the batch mode, it is necessary to create the input
file EPA.ST. This process is described below. The absence of the file
EPA.ST causes the code to be implemented in the Interactive mode.
When the EPA.ST file exists, the model will not request any information
from the user. EPA.ST contains two lines: the first line contains the
name of the data input file; the second line contains the name of the
output file. This method can be used to run the model in the background on
computers where this is possible.
2-4
-------
When running the model 1n the Interactive mode, the model will prompt
the user for the name's of the Input and output files.
2.4 INPUT AND OUTPUT FILE UNITS
Within the main program, there are 7 open statements that are used to
open up to 5 files, depending upon the run option chosen. In addition,
subroutine SOPEN contains 9 open statements to open 9 files and subroutine
SATIN contains 1 open statement used to open 1 file. Thus there are 15
files in all. Depending upon the options chosen all 15 files may not be
opened during a particular run.
2.4.1 Input Files
To run the EPACML program, various input files are necessary depending
upon the option chosen. The open statements for these files, the
associated unit numbers, file names, location of the contents are given
below:
Opened In
EPACML
(MAIN)
EPACML
(MAIN)
Unit
Name
EPA.ST
Description
Contains the name of the
main Input file required for
running the model and the
name of the main output
file. Required to run in
batch mode.
user-specified Main Input file.
2.4.2 Output Files
The successful execution of the model generates a number of output
files. The open statements for these files, the associated default unit
numbers, file names, and a brief description are given below:
2-5
-------
Opened In
EPACML
(MAIN)
SOPEN
SOPEN
SOPEN
SOPEN
SOPEN
BAT IN
SOPEN
SOPEN
SOPEN
EPACML
(MAIN)
SOPEN
Unit
Name
Description
user-specified
8 AQUIFER.VAR
13 CHEMICAL.VAR
14 SOURCE.VAR
16 VFLOW1.VAR
17 VTRNSPT.VAR
19 BATCH.ECH
20 VFLOW.OUT
21 VTRNSPT.OUT
22 SAT.OUT
25 STATS.OUT
26 VFLOW2.VAR
Output file. For ANSI
compilers Unit 6 1s preconnected
to "Standard Output", the
computer monitor. Program output
has been redirected to Unit 3.
Values of aquifer variables
generated for Monte Carlo
simulations.
Values of chemical variables
generated for Monte Carlo
simulations.
Values of source variables
generated for Monte Carlo
simulations.
Values of unsaturated zone
material variables generated for
Monte Carlo simulations.
Values of unsaturated zone
transport variables generated for
Monte Carlo simulations.
Echo of the batch input file and
list of any errors in the input
data.
Results from the unsaturated zone
flow module.
Concentrations at the water table
computed by the unsaturated zone
transport module.
Downgradlent well concentrations
computed by saturated zone
transport module.
Summary statistics of the
receptor well concentrations.
Values of functional parameters
for the unsaturated zone
generated for Monte Carlo
simulations.
2-6
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8820087TC CON-19
EPACML 27 SAT1.0UT Downgradient well
(MAIN) concentrations sorted in
ascending order (CDF of
concentrations).
The main output file contains an echo of the input data, printer plots,
and selected statistical parameters of the results of the Monte Carlo
simulations. In addition, a summary output file is created on unit
ISTAT. This file, named STATS.OUT, contains a table of selected
statistical parameters of the receptor-well concentrations from the
saturated zone model, and the surface water model. These summary
statistics are also included in the main output file. In the event that
the Monte Carlo option 1s not selected (i.e., the model 1s run 1n the
deterministic mode), the main output file contains an echo of the input
data and the concentrations in the saturated zone.
If the model is run in the Monte Carlo mode, two additional types of
files may be generated. These are designated as the *.VAR and *.OUT files,
where the '*' refers to a specific type of data for the VAR files and to
the specific module for the case of OUT files. Note that 1f this detailed
information is not required, the user may avoid the generation of these
files altogether. This option is specified by the user 1n the General
Group Data.
The *.VAR files contain the randomly-generated variables, derived
variables used for each Monte Carlo simulation run, and the value of any
deterministic variables. Thus, for example, 1f the saturated zone
transport model 1s run 2000 times* with the value of porosity specified as
a distribution, the file AQUIFER.VAR will contain the 2000 randomly-
generated values of porosity (and any other derived variable that 1s a
function of the porosity) for each Monte Carlo simulation. In addition,
the deterministic or constant values of other aquifer variables (whose
values may be specified as constants rather than as a distribution) will be
included in this file.
*The value of NARRY has been set to 2000 1n order for the program to run
in 640K. The SVS and NDP-FORTRAN compilers permit NARRY = 5000. The
IBM 3090-600E VS FORTRAN compiler permits NARRY = 10000.
2-7
-------
The *.OUT files..contain the model results for each Monte Carlo
simulation. For example, if the model is run with the unsaturated zone
transport simulated 5000 times, the file VTRNSPT.OUT will contain the 5000
simulated values of concentration at the bottom of the unsaturated zone.
Similarly, the file SAT.OUT will contain the 5000 values of the receptor
well concentrations. Results of statistical analysis (mean, median, and
selected percentiles) of these values will be included in the main output
file and in file STATS.OUT.
When the model is run, an echo of the input data file is written to the
file BATCH.ECH. This file contains a record of all data in the input file,
including any error messages generated while reading the data. Errors in
reading the data will stop execution of the program.
2.5 COMMON BLOCKS
Most variables are passed between routines through the use of common
blocks. There are a total of 34 common blocks each containing a related
set of variables. The common blocks are contained 1n files which are
accessed by the code through the use of INCLUDE statements located at the
beginning of each subroutine. The files and the common blocks they contain
are listed in Table 2.1.
2.6 PARAMETER STATEMENTS
Parameter statements are used to define all I/O (Input/Output) unit
numbers and array dimensions in the model. Table 2.2 lists all the
variables which are defined by parameter-statements, their value, location
and description.
In the event that any dimensions or I/O unit numbers need to be changed
this can easily be done by changing the value of the appropriate variable
in the parameter statement.
2-8
-------
Table 2.1. DESCRIPTION OF COMMON BLOCKS CONTAINED IN THE EPACML MODEL
File Name
Common
Blocks -.
Contents
CAQPRM.CMN
CCHPRM.CMN
CSOPRM.CMN
CVFPRM.CMN
CVTPRM.CMN
CAQPRM Distribution parameters and bounds for Monte Carlo
simulation of the aquifer specific data.
CAQNAM Character variables which describe the aquifer specific
data.
CCHPRM Distribution parameters and bounds for Monte Carlo
simulation of the chemical specific data.
CCHNAM Character variables which describe the chemical
specific data.
CSOPRM Distribution parameters and bounds for Monte Carlo
simulation of the source specific data.
CSONAM Character variables which describe the source speciffc
data.
VF1PRM Distribution parameters and bounds for Monte Carlo
simulation of the unsaturated zone flow module material
properties.
VF1NAM Character variables which describe the unsaturated zone
flow module material properties.
VF2PRM Distribution parameters and bounds for Monte Carlo
simulation of the unsaturated zone flow functional
coefficients.
VF2NAM Character variables which describe the unsaturated zone
flow module functional coefficients.
CVFPRM Control parameters used 1n I/O routines for the
unsaturated zone flow module.
CVFNAM Character variables describing unsaturated zone flow
module control parameters.
AD ISC Coordinate data for the unsaturated zone flow module.
CONTR Control parameters for the unsaturated zone flow
module.
VELEM Unsaturated zone flow model results calculated for each
Monte Carlo Simulation.
FLTOTR Parameters for the unsaturated zone flow module
calculated for each simulation.
UNSMAT Material properties generated for each case.
VT1PRM Distribution parameters and bounds of the contaminant
source data used for Monte Carlo simulation of the
unsaturated zone transport module.
2-9
-------
Table 2.1. DESCRIPTION OF COMMON BLOCKS CONTAINED IN THE EPACML MODEL
(concluded)
File Name
Common ฐ'
Blocks
Contents
VT1NAM Character variables which describe the unsaturated zone
transport module contaminant source data.
VT2PRM Distribution parameters and bounds for Monte Carlo
simulation of the unsaturated zone transport module
data.
VT2NAM Character variables which describe the unsaturated zone
transport module parameters.
CVTPRM Control parameters for the unsaturated zone transport
module. Used by the I/O routines.
CVTNAM Character variables which describe the unsaturated zone
transport module control parameters.
WORKS Source data used by the unsaturated zone transport
module.
WORKE Parameters assigned to each layer of the unsaturated
zone transport model. v
VTPARM Control data for the unsaturated zone transport model.
Titles for various output files.
DATA.CMN
GENERAL.CMN
GWATER.CMN
GENRL Variables contained in the general data group.
GENRL2 Character data contained 1n the general data group.
GVARAQ Aquifer parameters used by the saturated zone module.
GVARCH Chemical parameters used by the saturated zone module.
GVARSO Source parameters used by the saturated zone module.
WORKA Intermediate values of concentration used by the
saturated zone module.
WORKC Parameters used by the saturated zone model.
STPARM Counters for saturated zone model.
2-10
-------
Table 2.2. LIST OF VARIABLES DEFINED BY PARAMETER STATEMENTS
Variable
Value
Location of
Statement
Description
Statements for Defining I/O Unit Numbers
TERROFL 6
IOUT
IUNT8
IUNT14
IUNT16
IUNT17
BATOUT
VFOUT
VTOUT
STOUT
ISTAT
3 MAIN (also out-
put variations)
8
IUNT9 9
IUNT13 13
14
16
17
19
20
21
22
26
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
MAIN
Unit number used to write the screen
Unit number used to write to the
main output file
Unit number used to print aquifer
variables generated for Monte Carlo
simulations
Unit number to read from EPA.ST file
Unit number used to print chemical
data generated by Monte Carlo \
simulation
Unit number used to print source
data generated by Monte Carlo
simulation
Unit number used to print
unsaturated zone material data
generated by Monte Carlo simulations
Unit number used to print transport
data generated by Monte Carlo
simulations
Unit number used to echo batch input
data
Unit number used to print
unsaturated zone flow model results
Unit number used to print
unsaturated zone transport model
results
Unit number used to print saturated
zone model results (downgradlent
well concentrations)
Unit number used to print summary
statistical results
2-11
-------
Table 2.2. LIST OF VARIABLES DEFINED BY PARAMETER STATEMENTS (continued)
Location of
Variable Value Statement
Description
IUNT26
26
MAIN
IUNT27
27
MAIN
Statements Used to Dimension Arrays
NARRY
NEQ1
NCH1
NS01
NVF1
NVF2
NNMAT
NPARM
NLAYER
NVT1
NVT2
NNLAY
2000
18
19
10
4
4
20
4
200
2
5
20
MAIN
CAQPRM.CMN
CCHPRM.CMN
CSOPRM.CMN
CVFPRM.CMN
CVFPRM.CMN
CVFPRM.CMN
CVFPRM.CMN
CVFPRM.CMN
CVTPRM.CMN
CVTPRM.CMN
CVTPRM.CMN
Unit number used to print
unsaturated zone flow model
functional parameter data generated
for Monte Carlo simulations
Unit number used to print sorted
saturated zone results (downgradient
well concentrations)
Maximum number of Monte Carlo
simulations allowed
Number of aquifer specific variables
\
Number of chemical specific
variables
Number of source specific variables
Number of material property
variables for the unsaturated zone
flow module
Number of functional coefficients in
the unsaturated zone flow module
Maximum number of materials allowed
by the unsaturated zone flow module
Number of control parameters in the
unsaturated zone flow module
Maximum number of nodes for the
unsaturated zone flow module
Number of unsaturated zone transport
source variables
Number of unsaturated zone transport
layer parameters
Maximum number of layers in the
unsaturated zone transport module
2-12
-------
Table 2.2. LIST OF VARIABLES DEFINED BY PARAMETER STATEMENTS (concluded)
Location of
Variable Value - Statement
Description
NNFLAY
MAXTIM
200
20
CVTPRM.CMN
CVTPRM.CMN
Miscellaneous Statements
JMAX 13 QROMB
JMAXP
JMAX+1
QROMB
QROMB
Maximum number of nodes 1n the
unsaturated zone flow module (should
be > NLAYER)
Maximum number of time steps allowed
for computation of concentration in
the unsaturated zone
Maximum number of Iterations in the
Romberg Integration routine
Dimension of the solution array used
by Romberg Integration
Order of Romberg Integration. K = 2*
1s Simpson's Rule
2-13
-------
2.7 STRUCTURE OF THE INPUT FILES
The overall structure of the main input file is shown in Figure 2.2.
The first two cards allow the user to input the title of the simulation.
The remaining cards in the file contain the data necessary to run the
EPACML model. These data are clustered into a number of groups, each of
which contains a specific type of data that is input using one or more DATA
CARDS. The data groups are divided into subgroups, with each subgroup con-
taining a set of data specific to the group within which the subgroup is
located. In addition to the DATA CARDS, the input file contains DATA
GROUP/SUBGROUP SPECIFICATION CARDS, an END CARD, and if desired, one or
more COMMENT CARDS. The structure of each data group/subgroup is also
illustrated in Figure 2.2. The contents, and format, of each of these
groups/subgroups is discussed in Section 3.
The data for the model are divided into six major groups. These groups
are listed in Table 2.3 along with the group specification code. Each data
group is read in as a unit, with the beginning identified by the GROUP
SPECIFICATION CARD and the end by the END CARD. The data cards are
sandwiched between these two cards. Further, the data group may contain
one or more subgroups that are also listed in Table 2.3. Note that the
structure of a subgroup is exactly the same as that for a group--i.e., a
subgroup is identified by a SUBGROUP SPECIFICATION CARD and terminated by
an END CARD, with the subgroup data sandwiched between the two cards.
The preparation of the batch input data file is significantly
facilitated by the fact that the data file need contain only those data
groups (and subgroups within a data group) that are necessary to run the
options selected by the user. For example, if the user decides to run the
default options with the default data (defined in Section 3.4), none of the
data groups are necessary. In this case, the input data file would contain
only three cards. The first two cards would contain the user-specified
simulation title, and the third card would be the END CARD. If the user
needs to run non-default options and/or use non-default variable values,
2-14
-------
STRUCTURE OF
INPUT DATA FILE
STRUCTURE OF
EACH GROUP OR SUBGROUP
Title Card
Continuation of
Title Card
Group 1 Data
Group 2 Data
Group
N'Data
End Card
Group/Subgroup
Specification Card
Data Card 1
Data Card 2
Data Card M*
End Card
* M depends upon data group
* N varies from 0 to 8 depending upon
Run Options and data values
Figure 2.2. Structure of tne input-data file, data groups, and subgroups
2-15
-------
Table 2.3. INPUT DATA GROUPS AND SUBGROUPS FOR THE EPACML MODEL
Data Group Group Specification Code
1. General Data GEN
2. Source Data SOU
3. Chemical Data CHE
4. Unsaturated Zone Flow Data VFL
5. Unsaturated Zone Transport Data VTP
6. Aquifer Data AQU
Subgroups Subgroup Specification Code
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Array Data
Empirical Distribution Data
Unsaturated Zone Flow Control Data
Spatial Discretization Data
Unsaturated Zone Material Property Data
Material Specification Data
Unsaturated Zone Moisture Data
Unsaturated Zone Transport Control Data
Unsaturated Zone Transport Properties Data
Unsaturated Zone Time Stepping Data
ARR
EMP
CON
SPA
SAT
MAT
SOI
CON
TRA
TIM
2-16
-------
the General Run Data Group will be required. The contents and format of
this group are discussed 1n Section 3.
The options selected by the user and Indicated 1n the General Run Data
Group will determine which additional groups of data are necessary. For
example, 1f the user specifies within the General Run Data Group to run the
saturated zone transport module only, the Unsaturated Zone Flow and
Transport Data Groups (VFL, VTP) will not be necessary. Also note that the
structure of the Input file allows the user to Input the required data
groups In any order.
Within each data group all the data cards need not be Included. Only
the cards with values of variables that are different from the default
variable values need be Input. The default options and data are described
in Sections 3.4.1 to 3.4.6. This aspect of the data groups significantly
reduces the effort necessary to set up the data file for running the model.
2.7.1 COMMENT CARDS
COMMENT CARDS are Indicated by the presence of three asterisks,
'***'. The group of '***' can be Input starting at any column of the card
but must be the first three non-blank characters. The COMMENT CARDS are
useful for separating data types and can be used to Include other helpful
comments. Note that there are no restrictions as to the location and
number of COMMENT CARDS.
2.7.2 DATA GROUP/SUBGROUP SPECIFICATION CARD. END CARD, and DATA CARDS
The DATA GROUP/SUBGROUP SPECIFICATION CARD Indicates the beginning of a
specific data group and Includes the Group (Subgroup) Specification Code
(Table 2.3) 1n colunns 1 to 3 with the format A3. For example, 1f the DATA
GROUP SPECIFICATION CARD contains the letters 'AQU' 1n columns 1 to 3, it
2-17
-------
Implies that the following cards, up to and Including the 'END* card,
contain aquifer data.
With the exceptions discussed below, each data card contains
Information about one variable only. Typically the card will contain the
variable specification Index, variable name, distribution type,
distribution parameters, and permissible maximum and minimum values. To
facilitate the preparation of the Input file, consistent formats for the
data cards have been maintained (amongst the different data groups) to the
extent possible.
The termination of a data group and/or a subgroup 1s Indicated by the
END CARD, which contains the word END 1n the first three columns.
2.7.3 Specification of Parameter Values
Within each group except the General Data Group there are a number of
variables whose value can be specified 1n one of three ways: (1) the
variable may be assigned a constant value, (11) the variable may be derived
within the code using functional relationsfor example, the aquifer
porosity may be derived from the particle diameter, or (111) the variable
may be assigned a distribution and the value randomly generated 1n the
Monte Carlo simulation. Alternatively, 1f the value of a variable is not
specified, the model assigns a default value to the variable. The
available options for distributions as well as a few special cases are
listed 1n Table 2.4. Depending on the distribution selected for a
particular variable, the Input data required to generate the random
variable will vary.
If the variable follows a normal or lognormal distribution, both the
mean and standard deviation are required. For the lognormal distribution
the Inputs Include the mean and standard deviation of the untransformed
data. The transformation to the mean and standard deviation in
the logarithmic (normal) space is performed by the code. For the
2-18
-------
Table 2.4. DISTRIBUTIONS AVAILABLE AND THEIR COOES
Distribution Type Distribution Code
Constant 0
Normal 1
Lognormal 2
Exponential 3
Uniform 4
Log10 uniform 5
Empirical 6
SB Distribution4 7
GELHAR Distribution0 8
AREA Transformation0 9
Dispersivityd 10
Derived Variable -1
Derived Variableฎ -2
Derived Variablef -3
Note: For the lognormal distribution, the mean and standard deviation
are the mean and standard deviation of the data (arithmetic space). The
transformation to the mean and standard deviation in lognormal space is
performed by the code.
a For details of the SB distribution, see McGrath et al. (1973) and
Appendix E of WCC (1988a).
D Gelhar's distribution applies only to saturated zone dispersivities. For
details see Section 4.5.2.5 of WCC (1988a).
c Refer to Section 4.3 of WCC (1988a) on saturated zone transport module
for a description of the transformation. This option 1s available only
for the area of the waste facility.
d Refer to Section 4.5.2.5 of WCC (1988a) for details.
e Value of -2 applies to the computation of source-specific variables
only. For details see Table 3.80. For all other variables, -1 and -2
are Interchangeable.
f Value of -3 applies to the computation of the x and the y coordinates
from the radial distance to the well and the angle. Refer to Table 3.8F
and Section 3.4.6.5.
2-19
-------
exponential distribution, only the mean of the data is required. For a
variable with a uniform distribution, the model requires both the lower and
the upper bounds. For loglO uniform distribution, these bounds are
transformed within the code by taking the logorlthms. For the empirical
distribution, the coordinates (cumulative probability and the value of the
variable) of the cumulative frequency distribution curve are input. The
model allows up to 20 pairs, with the lowest probability specified as 0.0
and the highest as 1.0. Note that the probability coordinates as well as
the corresponding variable values have to be input in strictly increasing
order.
For the SB distribution the following procedure is used to determine
the inputs.
\
1. The mean and standard deviation of the transformed (normal) data
are determined (see Volume 1 for transformation)
2. The mean and standard deviation calculated in Step 1 are
transformed using the equation below:
v . fB exp(Y) + Al ,? n
* ' 1 + exp(Y) K'1'
where
Y = the mean or standard deviation of the transformed data from Step 1
X = the value for the mean or standard deviation Input to the model
A = the minimum value of the untransformed data
8 = the maximum value of the untransformed data
Data for each variable Include an upper and a lower bound. When the
model 1s used 1n the Monte Carlo mode, the value of the randomly generated
variable 1s compared with these bounds. If the generated variable does not
He within the bounds, the value of the variable 1s discarded and a new
value is generated. Note that the input value of the mean should lie
2-20
-------
within the lower and the upper bounds. If this 1s not the case, model
execution stops and an error message Is printed In the file BATCH.ECH.
2-21
-------
SECTION 3
FORMAT FOR THE INPUT DATA
3.1 INTRODUCTION
This section describes in detail the format for the input data required
by the EPA's Composite Model for Landfills. As described in Section 2, the
data are input in groups. These groups may be input in any order.
Further, depending on the run options selected, all the data groups need
not be included.
Information (parameters of the distributions and the bounds) for each
variable within a group is input using the Array Subgroup and the Empirical
Distribution Subgroup. Since these subgroups can be included in a number
of groups and their format is the same throughout, the details of these
subgroups are presented before discussion of specific data groups.
Input line formats are given- as FORTRAN edit descriptions. Note that
all numeric values must be right-justified in their fields (i.e., padded
with leading blanks when necessary).
3.2 THE ARRAY SUBGROUP
The contents and format for the Array Subgroup are shown in Table 3.1.
The first card 1s the SUBGROUP SPECIFICATION CARD, with the code ARR in the
first three columns. The next set of cards contain Information about the
values/distributions, and lower and upper bounds, of the variables specific
to the group within which the Array Subgroup 1s Included. Thus, when the
ARR subgroup 1s Included within the Aquifer Group Data, the subgroup will
3-1
-------
Table 3.1. CONTENTS AND FORMAT FOR A TYPICAL ARRAY SUBGROUP
Card Contents Format
Al 'ARR' A3
A2 I, NAM(I), NOST(I), PAR(I.l), PAR(I.2) 12. IX, A50, 7X.
BNDS(I.l), BNDS(I,2) 110, 5X, 4G10.2
A3 'END' A3
Note: Card/line A2 is repeated for each variable within the group that is
being updated from the default values.
Definition of Contents
'ARR1 SUBGROUP SPECIFICATION CARD Indicating start of the
Array Subgroup.
I Integer which Identifies the variable being Input. (See
Individual data group tables for values of I for
specific variables.)
NAM(I) Name of variable I. (Used to Identify variables 1n
output files. Note I 1s not a counter. See Individual
data group tables for names of specific variables, e.g.,
Tables 3.4A and 3.46 for source-specific variables.)
NDST(I) Integer which Identifies the type of distribution used
for Monte Carlo simulation for variable I. (See
Table 2.4.) If NOST(I) 1s equal to zero, PAR(I.l) 1s
the value of the variable.
PAR(I.l) Mean for variable I. Note this value should He within
the minimum and maximum value for the variable.
PAR(I,2) Standard deviation for variable I.
BNOS(I.l) Minimum allowed value (lower bound) for variable I.
BNDS(I,2) Maximum allowed value (upper bound) for variable I.
'END' END CARD Indicating end of Array Subgroup.
3-2
-------
contain Information about the aquifer-specific variables such as porosity,
dispersivitles, etc. The specific variables within each group are
discussed 1n Section'3.4.
Note that the number of cards within the Array Subgroup would vary for
two reasons. First, the various groups (General Data Group cannot have any
Array Subgroups) and subgroups have different numbers of input variables,
and second, only those variables with non-default values need to be
input. The variable being input is identified by the value of the index I.
For a specific example, see Tables 3.4A and 3.48 for source-specific
variables.
The value of the integer variable NDST(I) indicates the type of
distribution chosen for the variable identified by the index I. The
available options and values of the integer variable NDST(I) are listed in
Table 2.4. If any of the variables are specified to have an Empirical
distribution (NDST(I) = 6), then it is necessary to include the Empirical
Subgroup, the details of which are described 1n Section 3.3. Note if the
variable is specified to be a constant (NOST(I) = 0), the value input as
mean for the corresponding variable (PAR(I,1)) is used 1n the
simulations. The end of the Array Subgroup 1s indicated by an END CARD.
3.3 THE EMPIRICAL DISTRIBUTION SUBGROUP
The contents and format for the Empirical Distribution Subgroup are
shown in Table 3.2. The first card 1s the SUBGROUP SPECIFICATION CARD,
with the code EMP In the first three columns. The next card Identifies the
variable (using the Index I) that has an empirical distribution and the
number of coordinates of the empirical cumulative distribution function
that are being Input.
A maximum of 20 coordinates, with the lowest probability of zero and
the highest probability of unity (1.0), are allowed. The next set of
3-3
-------
Table 3.2. CONTENTS AND FORMAT FOR A TYPICAL EMPIRICAL DISTRIBUTION SUBGROUP
(required for each variable which 1s being updated from Us
default value and has an empirical distributionI.e., NDST(I) * 6
1n the Array Subgroup)
Card
El
E2
E3
E4
E5
Contents
'EMP'
I, I COUNT
EMPPRM(J,2,I), J ซ 1, ICOUNT
EMPPRM(J.l.I). J ป 1. ICOUNT
'END1
Format
A3
2110
10(68.3,
10(G8.3,
A3
2X)
2X)
Notes: Cards/lines E3 and E4 are repeated twice 1f more than 10 coordinates
are Input.
Cards/lines E2, E3 and E4 are repeated 1f more then one variable has
an empirical distribution.
Definition of Contents
'EMP1
I
ICOUNT
EMPPRM(J,2,I)
EMPPRM(J.l.I)
'END1
SUBGROUP SPECIFICATION CARD Indicating start of the
Empirical Distribution Subgroup.
Integer which Identifies the variable being Input. (Note I
1s not a counter. See Individual data group tables for
values of I for specific variables.)
Number of coordinates of the empirical cumulative frequency
distribution.
Cumulative probability (coordinate) values for the
empirical distribution for variable I.
Corresponding variable values associated with the above
probabilities.
END CARD Indicating end of the Empirical Distribution
Subgroup.
3-4
-------
8820087-S3 CON-3
cards, either two cards or four cards (1f more than 10 coordinate pairs are
input), contain the probabilities (in ascending order) and the cor-
responding values of tht variable. Note that all the cumulative
probability coordinate values are first input, followed by an equal number
of the corresponding variable values. The above procedure is repeated for
each of the variables that have empirical distributions. The end of the
subgroup is indicated by the END CARD.
3.4 FORMAT OF THE INPUT FILE
The format of each data card is described below.
DATA CARDS 1 AND 2
Title of the run that appears on all output files. Format for each
card (80A1).
DATA CARDS 3 THROUGH END
Data cards 3 through the end contain data specific to one or more
groups/subgroups.
The specific formats for each data group are described below. As
mentioned above, the data groups do not have to be input in the order in
which they are discussed. They can be input in any order.
3.4.1 General Data Group
The contents and formats for the General Data Group are shown in
Table 3.3A. This group can contain up to five cards in all. The first
card is the GROUP SPECIFICATION CARD and includes the code GEN in the first
three columns. The second card contains the name of the chemical being
simulated. Card three contains a number of variables that enable the user
3-5
-------
Table 3.3A. CONTENTS AND FORMAT FOR THE GENERAL DATA GROUP
Card Data Format
Gl 'GEN1 A3
G2 Chemical name 80A1
G3 OPTION, ISOURC, OPTAIR, 315, 5X, A13, 2X, 715, F5.0
RUN, MONTE, ROUTE, ISTEAD,
NT, IOPEN, IYCHK, IZCHK,
PALPH
G4 TPSTN(I), I = 1, NT 10(F8.2,2X)
G5 'END1 A3
Definition of Contents
GEN GROUP SPECIFICATION CARD Indicating the start of the General
Data Group.
Chemical Name Name of chemical being simulated.
OPTION Integers defining which scenario to run. Options are:
1 Saturated zone transport model only;
2 Unsaturated and saturated zone models;
ISOURC Dummy integer variable
OPTAIR Dummy integer variable
RUN Indicates the type of run. Options are:
DEFAULT
DETERMINISTIC
MONTE
MONTE The number of Monte Carlo simulations to be performed. MONTE
must be an Integer between 1 and 5000 (500 for Default case).
ROUTE Dummy real variable
3-6
-------
Table 3.3A. CONTENTS AND FORMAT FOR THE GENERAL DATA GROUP (concluded)
Definition of Contents (concluded)
ISTEAO Flag indicating unsteady- or steady-state simulation of
unsaturated and saturated zone transport. Options are:
0 Unsteady state
1 Steady state (Default option)
NT Number of time steps for which unsteady-state saturated zone
transport results are required. (1 for Default case.)
IOPEN Integer flag indicating the information to be output (i.e. the
files to be opened) in addition to the main ouput file and
summary statistics STATS.OUT.
0 Opens all *.VAR and *.OUT files, i.e., writes the Monte Carlo\
variables for each simulation and the corresponding output.
1 Opens the main output file, STATS.OUT and SAT1.0UT.
2 Opens the main output file and STATS.OUT.
IYCHK 0 Rejects the receptor well location y-coordinate values when
this is located outside the approximate width of the plume
(default option).
1 Does not reject any generated y-coordinate values.
IZCHK 0 Rejects all z-coordinate values of the downgradient well
location outside the approximate depth of the plume.
1 Does not reject any generated z-coord1nate values (default
option).
RALPH The selected confidence level for the percentiles.
TPSTN(I) Times at which unsteady-state transport results are required.
Necessary only if ISTEAD * 0 (not required for Default case).
END END CARD Indicating the end of the General Run Data Group.
3-7
-------
to select ttfe model options. The next card is necessary only if the model
is run in tt^ unsteady state and contains the time values at which the
saturated zone results are to be computed. Details of these variables and
options are included 1n Table 3.3A and B. The fifth card 1s the END CARD
that indicates the termination of this set of data. Table 3.3B shows the
default values of the variables included 1n the General Data Group.
3.4.2 Source Data Group
The contents and formats for the Source Data Group are shown in
Table 3.4A. This group describes the contaminant source-specific data.
The first card is the GROUP SPECIFICATION CARD, with the code SOU in the
first three columns. This is followed by the Array Subgroup, which is
indicated by the SUBGROUP SPECIFICATION CARD with the code ARR in the first
three columns. Details of the Array Subgroup were presented in Table 3.1
and Section 3.2. This subgroup contains an array of information about the
values and/or the distributions, and lower and upper bounds, of (up to) ten
source-specific variables. The variable associated with the index I and
their default values are listed in Table 3.4B. Note that of these ten
variables, only the ones with non-default values need to be input, with the
variable being input identified by the value of the Index I. For example,
a data card with I * 5 Indicates that the card contains Information about
the recharge rate.
Of the ten variables Included in this group, only three can be
derived. These are the spread of Input source, a length scale, and a width
scale of tht facilityI.e.. only NOST(4), NOST(8), and NOST(9) can have
values less than zero. The specific relationship used to derive the spread
of the source 1s discussed 1n Section 3.4.6.3. If the 'derived1 option is
used for the length and/or the width scale of the facility, they are
computed as the square root of the area. The tenth variable in this group,
the near field mixing factor, 1s always derived. The relationship used to
derive 1t 1s discussed in Section 3.4.6.3.
3-8
-------
Table 3.3B. DEFAULT VALUES FOR THE VARIABLES IN THE GENERAL DATA GROUP
to
I
o
GENERAL DATA
**ป CHEMICAL NAME FORMAT(80A1)
DEFAULT CASE
200 MONTE 25 1 1 1 0 0 1 90.0
END GENERAL
-------
Table 3.4A.- CONTENTS AND FORMAT FOR THE SOURCE-SPECIFIC DATA GROUP (only
.--required when a parameter 1n this data group Is being updated
'=from Us default value).
Card
SI
A1-A3
E1-E5
S2
Contents
'SOU1
Array Subgroup
Empirical Distribution Subgroup
'END1
Format
A3
(See Table
(See Table
A3
3.1)
3.2)
Definition of Contents
SOU
Array Subgroup
Empirical
Distribution Subgroup
END
GROUP SPECIFICATION CARD Indicating start of the
Source Data Group.
Subgroup defining the source variables being
updated from their default values. See Table 3.46
for default values.
Subgroup defining any empirical distributions used
to update a source variable from its default value.
END CARD indicating end of the Source Data Group.
3-10
-------
Table 3.4B. DEFAULT VALUES FOR THE SOURCE-SPECIFIC VARIABLES
SOURCE SPECIFIC VARIABLE iU A
ARRAY VALUES
*** SOURCE SPECIFIC VARIARI.KS
ป**
**
ป
VARIABLE NAME
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaainant source
5 Recharge rate
6 Source decay constant
7 Initial concentration at landfill
8 Length scale of facility
9 Width scale of facility
END ARRAY
UNITS
/yr
m"2
yr
/yr
1/yr
g/1
DISTRIBUTION
f,
9
0
-1
6
0
0
1
-1
PARAMETERS
MEAN STD DEV
LIMITS
NIK MAX
.700E-02 .700E-02 .254E-04 .688
4.21
.100E+31
50.0
.760E-02
.OOOE*00
1.00
100.
100.
2.16
3.00
.OOOE'OO
.7GOE-02
.OOOE'OO
. lOOE-01
1.00
1.00
-.884
.100
. 100E-02
.254E-04
OOOE'OO
. OOOE+00
1.00
1.00
12.3
.100E*31
.600E+05
.668
10.0
10.0
. 100E+06
. 100E+06
EMPIRICAL DISTRIBUTIONS
I ICOUNT
1 12
.OOO .569 .571 .640
.991 1.000
.254E-04 .762E-02 .330E-01 .508E-01
.246 .688
* I ICOUNT
5 12
.000 .569 .571 .640
.991 1.000
254E-04 762E-02 330E-01 508E-01
246 688
END EMPIRICAL DISTRIBUTIONS
END
.729 .731 .890 .930 .960 .989
.787E-01 .991E-01 .129 .152 .191 .211
.729 .731 .890 .930 .960 .989
.787E 01 .99JE-01 129 .152 .191 .211
-------
The default distribution type 9 Is unique to the area of the landfill
and is based on an analysis of the data collected by the Agency. When this
distribution is used, a normally distributed variable, AT, with a mean of
4.21 and standard deviation of 2.16 and minimum and maximum bounds of -.886
and 12.3 1s generated. This variable 1s then back-transformed to calculate
the area of the landfill using:
Aw = [(1 + 0.08AT)1/0'08+ 0.6] 4047 (3.1)
where
Aw = the area o* the facility [m2!
AT = the normally distributed variable
If any of the variables are specified to have an empirical distribution
(NOST(I) = 6), then it is necessary to Include the Empirical Distribution
Subgroup that contains the coordinates of the empirical cumulative
distribution function. The details of this subgroup are discussed in Table
3.2 and Section 3.3. For the default case shown 1n Table 3.4B, variables 1
and 5 each have an empirical distribution for which 12 coordinate values
are input. Note that 1f none of the source-specific variables have an
empirical distribution, then this subgroup 1s not necessary.
An END CARD Indicates the end of the Source Data Group.
3.4.3 Chemical Data Group
The contents and formats for the Chemical Data Group are shown in
Table 3.5A, which also contains the relevant chemical properties of the
contaminant being simulated. The first card 1s the GROUP SPECIFICATION
CARD, with the code CHE 1n the first three columns. The second card is the
3-12
-------
Table 3.5AV. CONTENTS AND FORMAT FOR THE CHEMICAL-SPECIFIC DATA GROUP (only
-e required when a parameter in this data group is being updated
"... from its default value)
Card
Cl
A1-A3
E1-E5
C2
Contents
'CHE'
Array Subgroup
Empirical Distribution Subgroup
'END1
Format
A3
(See Table
(See Table
A3
3.1)
3.2)
Definition of Contents
CHE GROUP SPECIFICATION CARD Indicating start of the .
Chemical Data Group.
Array Subgroup Subgroup defining the chemical variables being
updated from their default values. See Table 3.SB
for default values.
Empirical Subgroup defining any empirical distributions used
Distribution Subgroup to update a chemical variable from its default
value.
END END CARD Indicating end of the Chemical Data Group.
3-13
-------
SUBGROUP SPECIFICATION CARD, with the code ARR 1n the first three
columns. Thfs- subgroup contains the array of Information about the values
and/or the distributions, and upper and lower bounds, of up to 10 chemical-
specific variables. Of these 10 variables, only the ones with non-default
values need to be Input. The variables being Input are Identified by the
value of the Index I. The variable associated with the Index I as well as
the default values are shown 1n Table 3.56. For example, a data card with
I = 6 Indicates that the card contains Information about the base catalyzed
hydrolysis rate constant for the chemical being simulated.
If any of the variables are specified to have an empirical distribution
(NDST(I) = 6), then it is necessary to include the second subgroup that
contains the coordinates of the empirical cumulative distribution
function. Details of this subgroup are discussed in Table 3.2 and Section
3.3. Note that if none of the chemical-specific variables have an
empirical distribution, then the second subgroup 1s not necessary.
Of the 10 chemical-specific variables, the saturated and unsaturated
zone transport codes use only 3 variables. These are the overall decay
coefficient (I ป 3), the distribution coefficient (I ป 9), and the
biodegradation coefficient (I * 10). The other variables are used to
derive these 3 variables.
3.4.3.1 The Overall Decay Coefficient
The overall decay coefficient 1s computed based on the solid and liquid
phase decay coefficients. Each one of these 1s 1n turn computed using the
three hydrolysis rate constants, the reference temperature, and the
temperature and pH of the aquifer. (The last two are aquifer-specific
variables I ป 13 and 14, respectively.) Thus 1f the value of both the
liquid and solid phase decay coefficients 1s specified by the user (a
constant or a distribution), then the model does not use (hence the user
need not input) the values of the hydrolysis rate constants, reference
temperature, pH, and temperature of the aquifer. Similarly, 1f the value
3-14
-------
Table 3.5B. DEFAULT VALUES FOR THE CHEMICAL-SPECIFIC VARIABLES
CHF.MICAI. SI'K IM( VAKIABLE DATA
ARRAY VALUES
* CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
*ซซ
1 Solid Phase Decay Coefficient
2 Dissolved phase decay coefficient
3 Overall chemical decay coefficient
4 Acid catalyzed hydrolysis rate
5 Neutral hydrolysis rate constant
6 Base catalyzed hydrolysis rate
<*> 7 Reference temperature
ฃ a Normalized distribution coefficient
9 Distribution coefficient
10 Uiodegradation coefficient (sat. zone)
END ARRAY
UNITS
1/yr
1/yr
l/yr
I'M-yr
1/yr
1/M yr
C
1/g
1/yr
|)ISIKIIU;TIO\
PAKAMLTEKS
MEAN STD DEV
LIMITS
MIN MAX
ป
1
1
(I
0
0
0
0
2
0
.OOOE -00
.OOOE* 00
OOOE 00
OOOE+00
.OOOE* 00
.OOOE 00
25.0
.OOOE -00
.219
.OOOE* 00
OOOE'OO
OOOE -00
.OOOE -00
.OOOE-00
. OOOE + 00
OOOE-00
.OOOE* 00
.OOOE* 00
.OOOE* 00
.OOOE +00
OOOE -00
OOOE* 00
.OOOE* 00
.OOOE* 00
.OOOE* 00
.OOOE*OO
.OOOE*00
.OOOE* 00
.OOOE* 00
.OOOE*00
.352E*05
-22IK-09
.358L Of.
370.
280.
. 250E'08
40.0
. 331E'06
. 166E-05
100.
END CHEMICAL SPECIFIC
-------
of the overall decay coefficient 1s specified by the user, as a constant or
a distribution, the model does not use the values of the liquid and solid
phase decay coefficients (as well as the variables used to derive these, as
discussed above).
3.4.3.2 Distribution Coefficient
The distribution coefficient (I ซ 9) for the saturated zone transport
1s computed as the product of the normalized distribution coefficient
(I ป 8) and the fractional organic carbon content 1n the aquifer (aquifer-
specific variable, I ป 15). For the case of unsaturated zone transport,
the distribution coefficient is computed using the normalized distribution
coefficient and the percent organic matter (Unsaturated Zone Transport
Properties Subgroup 1n Table 3.7C, I ซ 3). Note that the relationship
between the percent organic matter and fractional organic carbon is:
* orc /t t\
foc T7I4 <3-2)
where:
foc ป fractional organic carbon content
fom * Percent organic matter content
1.724 conversion factor from organic matter content to organic carbon
content
An END CARD Indicates the end of the Chemical Data Group.
3.4.4 Unsaturated Zone Flow Data Group
This group contains data required by the unsaturated zone flow module
and consists of five subgroups. Note that only those subgroups which
contain variables with values different from the default values need to be
Input. The subgroups and the associated codes are listed below:
3-16
-------
V Subgroup
Subgroup ; Specification Code Refer to Table
Control data CON 3.6A
Spatial discretization SPA 3.66
data
Unsaturated zone material SAT 3.6C
property data
Material allocation MAT 3.6E
data
Soil moisture data SOI 3.6F
The first card of this group 1s the GROUP SPECIFICATION CARD and
Includes the code VFL 1n the first three columns. The next card 1s the
subgroup specification card and Includes the code of the subgroup for which
the data are being Input. Data for each of these subgroups are described
below.
3.4.4.1 Unsaturated Zone Flow Control Data Subgroup-
Table 3.6A describes the unsaturated zone flow control data. Data
in the other subgroups vary depending on the options specified 1n the
Control Data Subgroup. For example, the value of VFCP(4) determines the
Input data required to set up the vertical discretization as explained
below. Note that 1f the depth of the unsaturated zone 1s specified as a
distribution, i.e., Us value 1s generated randomly for each run, the value
of VFCP(4) 1s Ignored. (The depth of the unsaturated zone 1s specified 1n
the Unsaturated Zone Material Subgroup, Section 3.4.4.3.) Also for this
case the value of VFCP(2) should be 1, I.e., the unsaturated zone 1s
considered homogeneous and composed of only one material. The termination
of this subgroup of data Is Indicated by the END CARD.
3-17
-------
Table 3.6A.- CONTENTS AND FORMAT FOR THE UNSATURATED ZONE FLOW MODULE
^CONTROL DATA SUBGROUP
Card
Data
Format
VI
'VFL1
A3
C02
C03
C04
CON'
VFCP(I), I = 1,4
'END1
A3
4110
A3
Definitions of Contents
VFL GROUP SPECIFICATION CARD indicating the start of the
Unsaturated Zone Flow Module Data Group.
CON SUBGROUP SPECIFICATION CARD indicating the start of the
Unsaturated Zone Flow Control Data Subgroup.
VFCP(l) Number of nodes 1n flow model. (Note that VFCP(l) = the
number of layers plus one.)
VFCP(2) Number of different porous materials (also see Table
3.6E). Maximum permissible is 20. If depth of the
unsaturated zone is generated (see Table 3.6C and D),
VFCP(2) must equal 1.
VFCP(3) Parameter Indicating the type of relationships of relative
permeability versus saturation, and pressure head versus
saturation (also refer to Table 3.6F).
1 van Genuchten's functional parameters are to be supplied.
2 Brooks/Corey functional parameters to be supplied.
VFCP(4) Parameter Indicating the method of generating vertical
discretization (also see Table 3.68) when the depth of the
unsaturated zone 1s constant.
0 Vertical discretization Input by user.
1 Vertical discretization generated by the program.
This variable 1s ignored 1f the depth of the unsaturated
zone 1n Table 3.6C 1s randomly generated.
END END CARD Indicating the end of data for this subgroup.
3-13
-------
3.4.4.2 Ur&aturated Zone Flow Spatial Discretization Subgroup--
Table 3.68 describes the Spatial Discretization Subgroup data
identified by the code SPA. This describes the two options available to
set up the spatial discretization for the unsaturated zone flow simulation
when the depth is specified as a constant value. (See Section 3.4.4.3 for
the case when the depth 1s randomly generated.)
If VFCP(4) is set equal to 0 in the Unsaturated Zone Control Data
Subgroup, the coordinates for each node are input in increasing order, with
distance measured downwards from the top of the unsaturated zone.
When VFCP(4) is set equal to 1, the discretization 1s set up by the
code oased on user-input data that consist of five variables shown in Table
3.6B. The steps involved in the discretization are:
(i) The thickness of each of the VFCP(l) number of layers is set at
the minimum of
DXMAX and DXfXFAC)"'1
where n = the ntn layer from the top. Note that n varies from 1 to
VFCP(l) - 1.
(11) The (pseudo) coordinates for the bottom of each layer are
calculated with the origin (zero value of coordinate) at the top of the
unsaturated zone.
(111) The coordinate of the bottom of the last layer gives the
computed (pseudo) depth OP of the unsaturated zone which in general 1s not
equal to the depth of the unsaturated zone input by the user. This user-
specified depth 1s computed as:
D - XO - XSTART (3.3)
3-19
-------
Table 3.6Br- COHTENTS AND FORMAT FOR THE UNSATURATED ZONE FLOW MODULE
tSPATIAL DISCRETIZATION SUBGROUP
Card Data -. Format
SP1 'SPA' A3
SP2 CORD(I). I ป 1, VFCP(l)a 8G10.3
or
XSTART, XO, DX, XFAC, OXMAX 5G10.3
SP3 'END' (subgroup) A3
Definition of Contents
SPA SUBGROUP SPECIFICATION CARD Indicating start of the
Unsaturated Zone Spatial Discretization Subgroup.
If VFCP(4)a* 0
CORO(I) z-coordinate values of nodes 1 through VFCP(l).
Data must be In increasing order.
If VFCP(4) * 1
XSTART Starting z-coordinate of the first node.
XO Ending z-coordinate of the last node.
DX Spacing between the first and second nodes.
XFAC Nodal spacing adjustment factor.
DXMAX Maximum nodal spacing allowed.
END END CARD Indicating the end of data for this subgroup.
a Refer to Table 3.6A for values of VFCP(l) and VFCP(4).
3-20
-------
Note XO and XSTART are both Input variables.
(1v) A depth adjustment factor 1s computed as the ratio of 0 and OP
and used to adjust (normalize) the pseudo coordinates of the various layers
of the unsaturated zone. This ensures that the total depth of the
unsaturated zone equals the depth input by the user.
The termination of this subgroup is Indicated by the END CARD.
3.4.4.3 Unsaturated Zone Flow Material Data Subgroup--
The unsaturated zone can consist of a number of different materials
(the number specified by the value of VFCP(2) 1n Table 3.6A) with different
hydrogeological properties. The properties for each of the materials are
Included In the Unsaturated Zone Material Property Subgroup Identified by
the code SAT. Details of the contents and formats of this subgroup are
shown 1n Table 3.6C. The variables Included in this subgroup as well as
their Transport Model Group default values are shown in Table 3.60. Note
that none of these variables can be derived. Thus, none of these variables
can have a distribution type of -1 or -2.
The depth of the unsaturated zone can be specified as a constant value
or generated from a specified distribution. In the former case, numerical
discretization for the flow computations can be performed in one of two
ways, as explained earlier 1n Section 3.4.4.2. If the depth 1s randomly
generated, the user cannot specify the discretization. In this case, the
code uses the following rules for numerical discretization for the flow
computations:
If the depth 1s less than or equal to 50 m, the number of nodes is
set equal to 50.
3-21
-------
Table 3.6C.- CONTENTS AND FORMAT FOR THE UNSATURATED ZONE FLOW MODULE
MATERIAL SUBGROUP (only required when a parameter in this
rgroup is being updated from its default value)
Card
SA1
A1-A3
E1-E53
SA2
SA3
Note: Cards
i.e., VFCP(2)
Contents
'SAT'
Array Subgroup
Empirical Distribution Subgroup
'END1 (material)
'END1
A1-A3 and/or E1-E5 need to be repeated
number of times.
Format
A3
(See Table 3.1)
(See Table 3.2)
A3
A3
for each material,
Definition of Contents
SAT
Array Subgroup
Empirical
Distribution Subgroup
END
END
SUBGROUP SPECIFICATION CARD indicating start of
Unsaturated Zone Material Data Subgroup.
Subgroup defining the unsaturated zone material
variables being updated from their default
values. See Table 3.60 for default values. This
subgroup 1s repeated for each material.
Subgroup defining any empirical distributions used
to update an unsaturated zone material variable
from its default value. This subgroup may be
repeated for each material depending on the choice
of distribution type for the parameter.
END CARD Indicating end of data for a material (one
such end card 1s required for each material).
END CARD Indicating end of Unsaturated Zone
Material Property Data Subgroup.
4 Necessary only 1f one or more of the variables 1n the Array Subgroup is
input using an empirical distribution.
3-22
-------
Table 3.60. DEFAULT VALUES FOR THE UNSATURATEO ZONE MATERIAL PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
SAT. MATERIAL VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION
***
PARAMETERS
MEAN STD DEV
LIMITS
MIN '' MAX
u>
i
ro
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
4 Depth of the unsaturated zone
END ARRAY
EMPIRICAL DISTRIBUTIONS
I ICOUNT
4 20
.000 .050 .100
.600 .650 .700
.100E-01 .910 1.22
12.2 15.2 16.8
END EMPIRICAL DISTRIBUTION
END MATERIAL 1
END
ivity cซ/hr
ne
.200 .250 .300
. 750 . 800 . 850
1.83 2.74 3.05
21.3 30.5 34.8
7 . 170E-01
0 .430
0 .OOOE+00
6 6.10
. 350 . 400
.900 .950
3 . 60 -J . 75 6 . 09
61.0 107. 183.
2.92 .OOOE+00
.200E-01 .200
.OOOE+00 .OOOE+00
1.00 .610
450 . 500
980 1 . OOO
6.10
366.
3.50
.700
1.00
366.
-------
If the generated value of depth lies between 50 m and 200 m, the
number of nodes 1s obtained by rounding up of the depth. Thus, if
the generated value of the depth 1s 98.4 m, the number of nodes 1s
99. The nodes are all evenly spaced at 1-meter Intervals except
for the distance between the first and second, which equals a
distance necessary to obtain the proper depth. Thus, 1n the above
example, the distance between nodes 1 and 2 would be 0.4m. The
minimum nodal spacing 1s 0.1 meter. If the distance between nodes
1 and 2 1s less than this, then the number of nodes 1s decreased
by one and the distance between nodes 1 and 2 1s Increased by 1 m.
If the depth 1s greater than 200 m, the number of nodes 1s set
equal to 200.
When the unsaturated zone consists of more than one material,
information about each material 1s Input using an Array Subgroup. Thus, 1n
all there are VFCP(2) (Table 3.6A) number of Array Subgroups. These
materials are subsequently Identified by the order 1n which the Array
Subgroups appear. Thus, material number 4 would refer to the material that
has properties Included 1n the fourth Array Subgroup (after the Subgroup
Specification Card). The termination of data for each material 1s
Indicated by an END CARD. The end of saturated materials data 1s also
Indicated by an END CARD.
3.4.4.4 Unsaturated Zone Flow Material Allocation Subgroup
When the unsaturated zone consists of more than one material, a
specific material has to be assigned to each node within the unsaturated
zone. This 1s done by the Material Allocation Subgroup Identified by the
code MAT, the contents and formats of which are Indicated 1n Table. 3.6E.
This subgroup 1s not required 1f the unsaturated zone 1s homogeneous. I.e.,
there 1s only one material (VFCP(2) ซ 1 1n Table 3.6A). The termination of
this subgroup 1s also Indicated by an END CARD.
3-24
-------
Table 3.6E._ CONTENTS AND FORMAT FOR THE UNSATURATED ZONE FLOW MODULE
4; MATERIAL ALLOCATION SUBGROUP (required only 1f VFCP (2) > 1 in
"~_, Table 3.6A, i.e., more than one material)
Card
Ml
M2
M3
Data
'MAT'
IPROP(I),
'END'
Format
A3
I - 1, VFCP(l) 1615
A3
Definition of Contents
MAT SUBGROUP SPECIFICATION CARD for the Unsaturated Zone Flow
Material Allocation Subgroup.
IPROP(I) Material numbers corresponding to nodes 1 through VFCP(l).
For definition of VFCP(l). refer to Table 3.6A. For material
properties corresponding to material numbers, refer to
Table 3.6C.
END END CARD Indicating end of this subgroup.
3-25
-------
3.4.4.5 Unsjrturated Zone Flow Moisture Data Subgroup
In order7to solve., the unsaturated zone flow problem, the relationship
between the relative hydraulic conductivity and water content and pressure
head versus water content need to be specified for each material (refer to
Volume 1 section on unsaturated zone flow module). This Information 1s
Included 1n the Unsaturated Zone Moisture Data Subgroup, Identified by the
code SOI. The contents and format of this subgroup are described in
Table 3.6F.
The above relationships can be Input In one of two ways, depending on
the option selected 1n the Unsaturated Zone Flow Control Data Subgroup
(Table 3.6A, value of VFCP(3)). If VFCP(3) 1s set equal to 1, the
relationships are Input using the empirical coefficients developed by van
Genuchten, and if VFCP(3) is set equal to 2, the relationships by Brooks
and Corey are used (refer to Background Documents on unsaturated zone
module for details). In all, data need to be input for VFCP(2) number of
materials, as discussed in Section 3.4.3.3 and Table 3.6A.
The subgroup specification card 1s followed by VFCP(2) number of the
Array Subgroups (refer to Section 3.2 and Table 3.1), one subgroup for each
material. Table 3.66 presents the definitions and default values of the
variables included 1n the Array Subgroup. None of the variables 1n this
group can be derivedI.e., none of the variables can have a distribution
type of -1 or -2.
Note that the data for each material are read in the same sequence as
1n Table 3.6C (also refer to Section 3.4.4.3). An END card 1s Inserted
after the data for each material. Finally, the end of the subgroup 1s also
Indicated by an END CARD.
After all the required subgroups within the Unsaturated Zone Flow Data
Group have been Input, the termination of this group 1s Indicated by an END
CARD.
3-26
-------
Table 3.6F--. CONTENTS AND FORMAT FOR THE UNSATURATED ZONE FLOW MODULE
v MOISTURE DATA SUBGROUP
Card Data -. Format
SI1 'SOI1 A3
A1-A3 Array Subgroup (See Table 3.1)
'END' (subgroup) A3
Repeat Cards 1-3 VFCP(2) number of times. I.e., once for each material.
Definition of Contents
SOI SUBGROUP SPECIFICATION CARD for Unsaturated Zone Moisture
Data Subgroup.
Refer to Table 3.6G for definition and default values of
variables in the Array Subgroup.
END END CARD indicates end of data for the material. One end
card is necessary for each material.
END END CARD indicating end of this subgroup.
3-27
-------
Table 3.6G. DEFAULT VALUES FOR THE UNSATURATED ZONE MOISTURE SUBGROUP DATA
SOIL MOISTURE PARAMETERS
** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
** FUNC. COEF. VARIABLES
** VARIABLE NAME UNITS
*
*ปes*ป*ซปปปป*ป*ป*ป*ปปปป*ป*ป***ปป*ป#ป*ป*ปปปป***ปป*ปปปปปป<
1 Residual Mater content
2 Brook and Corey exponent. EN
3 ALFA coefficient --
4 Van Gcnuchtซn exponent, ENN
DISTRIBUTION PARAMETERS
MEAN*
ป**ปปป**ปปปป*ปปปปปปปซปปป*ปป*ปปi
1 880E-01
0 .500
7 .900E-02
1 1.23
STD DEV
k * * * * t ** * *
. 900E-02
. 100
.970E-01
.610E 01
I '
LIMITS
MIX .
**%**<***
.OOOE-00 .
.OOOE+00 1
.OOOE'OO .
1.00 1
'i i/.'.j.,
MAX
ฃ ^ ฃ ]
115
.00
150
.50
END ARRAY
V ENB MATERIAL 1
w END
-------
3.4.5 Unsaturated Zone Transport Data Group
The data required for the Unsaturated Zone Transport module are divided
into three subgroups. Note that only those subgroups which contain data
different from the default values need to be Input. Each subgroup Is
handled as 1n the Unsaturated Zone Flow Data Group--1.e., the beginning of
each subgroup is defined by a SUBGROUP SPECIFICATION CARD and the end by an
END CARD. The subgroups included in the Unsaturated Zone Transport Data
Group are listed below:
Subgroup
Subgroup Specification Code Refer to Table
Control data CON 3.7A
Transport properties TRA 3.78
Time steps data TIM 3.70
The first card of this group 1s the GROUP SPECIFICATION CARD and
includes the code VTL in the first three columns. The next card is the
SUBGROUP SPECIFICATION CARD and Includes the code of the subgroup for which
the data are being input. Data contents and the formats for each of these
subgroups is described below.
3.4.5.1 Unsaturated Zone Transport Control Data Subgroup
The Control Data Subgroup 1s Identified by the SUBGROUP SPECIFICATION
CARD with the code CON 1n the first three columns. The contents and
formats are shown 1n Table 3.7A. Note that VTCP(l) 1s set equal to 1 1f
the depth of the Unsaturated zone (see also Section 3.4.4.3) 1s generated
from a distribution. Following the convention established here, the end of
this subgroup data 1s Indicated by the END CARD.
3.4.5.2 Unsaturated Zone Transport Properties Subgroup--
The second subgroup contains the Unsaturated zone transport data and is
identified by the code TRA in the first three columns of the SUBGROUP
3-29
-------
Table 3.7A.-- CONTENTS AND FORMAT FOR THE UNSATURATED ZONE TRANSPORT MODULE
-CONTROL SUBGROUP
Card
Data
Format
VI
'VTL1
A3
TCI .
TC2
TC3
TC4
'CON'
VTCP(I), I - 1, 10
WTFUN
'END1
A3
10 1 10
F10. 2
A3
Definition of Contents
VTCP(l)
VTL GROUP SPECIFICATION CARD indicating the start of the
Unsaturated Zone Transport Group.
CON SUBGROUP SPECIFICATION CARD indicating the start of the *
Unsaturated Zone Transport Control Subgroup.
Number of layers used to represent the unsaturated transport
zone. Note that VTCP(l) < VFCP(l) 1n Table 3.6A (I.e.. number
of layers in the transport model must be less than or equal to
the number of nodes 1n the flow model). VTCP(l) is set equal
to unity if the depth of the unsaturated zone is specified as a
Monte Carlo distribution.
Number of time values when concentration 1n the unsaturated
zone 1s to be evaluated. When running the unsaturated and the
saturated zone, this corresponds to the number of control
points 1n the convolution Integral for coupling the unsaturated
and saturated zones. For this case suggested values are:
20 for nondecaylng continuous source
40 otherwise
Dummy Integer. Not presently used.
VTCP(2)a
VTCP(3)
VTCP(4)
Type of scheme used to evaluate transport 1n the unsaturated
zone
1 Stehfest numerical Inversion algorithm
2 Convolution Integral approach
The use of Stehfest algorithm 1$ recommended when the ratio of
layer thickness to longitudinal d1spers1v1ty 1s less than 20.
3-30
-------
Table 3.7AV CONTENTS AND FORMAT FOR THE UNSATURATED ZONE TRANSPORT MODULE
.-* CONTROL SUBGROUP (concluded)
Definition of Contents (concluded)
VTCP(5) For VTCP(4) = 1, the number of terms governing the accuracy of
the Stehfest algorithm. (Must be a positive even integer. A
value of 18 is suggested as an initial trial value.
For VTCP(4) * 2, the number of increments used in the temporal
discretization of convolution integral approach (value of 10 is
recommended).
VTCP(6) Number of points in the Lagrangian scheme used for
interpolating concentration values (value of 3 is recommended).
VTCP(7) Number of Gauss points used in Gauss-Legendre numerical
integration of the convolution integral (value of 104 is
recommended).
V7CP(8) Number of segments for the numerical approximation of the
convolution integral (value of 2 1s recommended).
VTCP(9) Type of source boundary condition
1 nondecaying continuous source
2 nondecaying pulse source
3 exponentially decaying continuous source
VTCP(10)a Parameter indicating if time values for computing concentration
in the unsaturated zone are to be generated
1 yes
0 no
When running both the saturated and unsaturated zones,
recommended value is 1.
WTFUN Value of weighting factor used to generate time step values for
evaluating concentration in the unsaturated zone. Value of 1.2
1s recommended.
END END CARD Indicating the end of this subgroup.
a These variables are not used when running the model 1n the steady state.
The user may Input any value.
3-31
-------
SPECIFICATION CARD. Following this card 1s the Array Subgroup that
contains tjw values of the unsaturated zone transport variables. The
contents and format "of this subgroup are described 1n Table 3.78. Note
that data for only those variables that have a value different from the
default value need be Input.
If any of the variables are specified to have an empirical
distribution, then It 1s necessary to Include the Empirical Distribution
Subgroup (for details see Table 3.2 and Section 3.3) that contains the
coordinates of the empirical distribution function. This subgroup is
repeated for each layeri.e., VTCP(l) number of layers, as specified in
Table 3.7A. As mentioned before, the multiple layers option 1s available
only when the depth of the unsaturated zone is specified as a constant
value. An END CARD Indicates the end of the Transport Data Subgroup.
The specific variables that comprise this subgroup are shown 1n
Table 3.7C. In the event that there 1s more than one transport layer, the
sum of the depths of Individual layers must be equal to the total depth of
the unsaturated zone.
Of the five variables shown, only the longitudinal dlspersivity of the
soil can be derived. The longitudinal dispersivity 1s computed as a linear
function of the total depth of the unsaturated zone using:
az ป .02 * .0220 (3.4)
where:
0 the total depth of the unsaturated zone [m]
<ป2ป the longitudinal dlspersivity [ml
If Equation 3.4 results 1n a dlspersivity outside of the bounds
specified for dlspersivity, then oz 1s set equal to 1. Once the data for
3-32
-------
Table 3.7B. - CONTENTS AND FORMAT FOR UNSATURATEO ZONE TRANSPORT MODULE DATA
< PROPERTIES SUBGROUP (only required when a parameter in this
; subgroup 1s being updated from its default value)
Card
Tl
A1-A3
E1-E5
T2
T3
Content:
'TRA1
Array Subgroup
Empirical Distribution Subgroup
'END' (Layer)
'END1 (Subgroup)
Format
A3
(See Table
(See Table
A3
A3
3.1)
3.2)
Definition of Contents
TRA .
A1-A3
E1-E5
END
END
SUBGROUP SPECIFICATION CARD Indicating start of Unsaturated Zone
Transport Data Subgroup.
Array Subgroup defining the unsaturated zone transport variables
being updated from their default values. See Table 3.7C for
default values.
Empirical Subgroup defining any empirical distributions used to
update an unsaturated zone transport variable from its default
value.
END CARD Indicates end of data for the layer. One such end card
is necessary for each layer.
END CARD Indicating end of this subgroup.
3-33
-------
Table 3.7C.
DEFAULT VALUES FOR THE UNSATURATED ZONE TRANSPORT MODULE
PROPERTIES SUBGROUP
TRANSPORT PARAMETER
ARRAY VALUES
* UNSATURATED TRKSPT
VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION
**
PARANETKRS
MEAN STO DEV
LIMITS
MIN MAX
i
t*>
1 Thickness of layer
2 Longitudinal dispersivity of layer
3 Percent Organic Natter
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
g/cc
1/yr
0
0
7
0
0
6. 10
.400
. 2GOE 01
1.67
.OOOE'OO
1.00
.400E-01
7.77
.200E-01
.200E-01
.OOOEซ00
.OOOE*00
.OOOE+00
.795
.OOOE+00
500.
10.0
11 .0
2. 12
5.00
-------
the required subgroups have been Input, the termination of the Unsaturated
Zone Transport Property Data Group 1s Indicated by an END CARD.
3.4.5.3 Unsaturated Zone Time Steps Data Subgroup
This subgroup 1s required when running the Unsaturated zone transport
module in the unsteady mode--I.e., when the value of VTCP(IO) (refer to
Table 3.7A) 1s zero.
The Unsaturated Zone Time Steps Data Subgroup 1s Identified by the
SUBGROUP SPECIFICATION CARD with the code TIM 1n the first three columns.
This subgroup allows the user to input time values at which concentrations
at the bottom of the unsaturated zone are to be computed. The contents and
formats are shown in Table 3.70. Following the convention established
here, the end of the subgroup is indicated by the END CARD.
3.4.6 Aquifer Data Group
The contents and formats for the Aquifer Data Group are shown in
Table 3.8A, which describes the data required by the saturated zone
module. The data in this group are used by the saturated transport module
only, except for the source thickness, which is used to satisfy the mass
balance between the unsaturated zone or the source (landfill) and the
saturated zone transport modules. The first card 1s the GROUP
SPECIFICATION CARD, with the code AQU Included 1n the first three
columns. Following this 1s the Array Subgroup, which contains Information
about the values/distributions of up to 18 aquifer-specific variables. The
variables Included 1n this subgroup and their default values are shown in
Table 3.88. Also, of these 18 variables, only the ones with non-default
values need to be Input.
If any of these variables are specified to have an empirical
distribution (NOST(I) ป 6), then 1t 1s necessary to Include the Empirical
Distribution Subgroup (for details see Section 3.3 and Table 3.2) that
3-35
-------
Table 3.70. CONTEHTS AND FORMAT FOR UNSATURATED ZONE TRANSPORT MODULE TIME
-" STEPPING DATA (use only 1f VTCP(IO) - OJ
Card
TM1
TM2
TM3
"Data
'TIM1*
TCO(I), I - 1, VTCP(2)
'END1
Format
A3
8G10.3
A3
Definition of Contents
TIM SUBGROUP SPECIFICATION CARD indicating the start of the Time
Stepping Data Subgroup.
TCO(I) Time values corresponding to time steps 1 through VTCP(2),
used to compute concentrations in the unsaturated zone.
(See Table 3.7A for value of VTCP(2).
END END CARD indicating the end of Time Stepping Data Subgroup.
a Use only 1f VTCP(IO) - 0.
3-36
-------
Table 3.8A; CONTENTS AND FORMAT FOR THE AQUIFER-SPECIFIC DATA GROUP
=5 (required when a parameter 1n this data group 1s being
v updated from Its default value)
Card
Ql
A1-A3
E1-E5
Q2
Contents
'AQU1
Array Subgroup
Empirical Distribution Subgroup
'END1
Format
A3
(See Table
(See Table
A3
3.1)
3.2)
Definition of Contents
AQU
Array Subgroup
Empirical
Distribution Subgroup
END
GROUP SPECIFICATION CARD Indicating start of the
Aquifer Data Group.
Subgroup defining the Aquifer-Specific variables
being updated from their default values. See
Table 3.86 default values.
Subgroup defining any empirical distributions used
to update an aquifer variable from its default
value.
END CARD indicating end of Aquifer-Specific Data
Group.
3-37
-------
Table 3.8B. DEFAULT VALUES FOR THE AQUIFER-SPECIFIC VARIABLES
i
CJ
00
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** AQUIFER SPECIFIC VARIABLES
***
***
VARIABLE NAME
UNITS
i***********************
1 Particle dianeter en
2 Aquifer porosity
3 Bulk density 9/cc
4 Aquifer thickness m
5 Source thickness (Mixing zone depth)
6 Conductivity (hydraulic) ป/yr
7 Gradient (hydraulic)
8 Groundwater seepage velocity ซ/yr
9 Retardation coefficient
10 Longitudinal dispersivity ป
11 Transverse dispersivity n
12 Vertical dispersivity
13 Temperature of aquifer C
14 pH
15 Organic carbon content (fraction)
16 Hell distance froซ site
17 Angle off center degree
IB Hell vertical distance
END ARRAY
DISTRIBUTION
0
2
-1
0
-2
-2
0
0
-1
0
0
0
0
0
0
0
0
0
PARAMETERS
MEAN STD DEV HIM MAX
.172E-02
.OOOE+00
1.64
135.
6.00
.758E+05
.453E-01
300.
l.OO
131.
16.4
.819
13.9
7.92
.294E-02
100.
.OOOE+00
.OOOE+00
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
.OOOE+00
. 400E-03
.300
1.16
3.-OO
2.OO
31.6
. 1OOE-04
. 100E-01
1.00
.100
.1OO
. 38O
5.0O
.300
. 100E-O2
15.2
.OOOE+00
.OOOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0
250.
30.0
14.0
.100E-01
.160E+04
90.0
1.
EMPIRICAL DISTRIBUTIONS
*** I ICOUNT
16 20
.000 .030 .040 .050
.400 .500 .600 .700
.600 13.7 19.8 45.7
366. 427. 610. 805.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
.100
.800
104.
914.
.150
.850
152.
.116E+04
.200
.900
183.
.122E+04
.250
.950
244.
.137E+04
.300
.980
305.
.152E+04
.350
1.000
305.
.161E+04
-------
contains tht coordinates of the empirical cumulative distribution
function. Note thaf'lf none of the aquifer-specific variables listed 1n
Table 3.8A have an empirical distribution, then the empirical distribution
subgroup 1s not necessary.
The end of the subgroup 1s Indicated by an END CARD. A second END CARD
Indicates the end of the Aquifer Data Group.
A number of aquifer-specific variables can either be derived or
directly Input. These Include the particle diameter, porosity, source
thickness, hydraulic conductivity, seepage velocity, and the longitudinal,
lateral, and vertical dispersivities. The available options and the
algorithms for each of them are explained below.
3.4.6.1 Computation of Particle Diameter and Porosity
The particle diameter and porosity of a porous formation have been
related using empirical relationships. One such relationship (refer to
Volume 1 section on saturated zone transport module for details) is
included in this model. If the distribution type for the particle diameter
is set less than or equal to -1 in the Array Subgroup, then the value is
calculated using the Input value of porosity that may be constant or
randomly generated using the relationship:
d exp[(0.261 - 9)/0.0385] (3.5)
Similarly, 1f the distribution type for porosity 1s set less than or equal
to -1, tht porosity 1s calculated using the value of the particle diameter
using the relation:
e 0.261 - 0.0385 ln(d) (3.6)
where:
e the porosity [d1mens1onless]
3-39
-------
d tht mean particle diameter [cm]
These options are Indicated 1n Table 3.8C. Note that 1f both the
distribution types for porosity and particle diameter are less than or
equal to -1, the model will stop and an error message will be printed out.
3.4.6.2 Computation of Hydraulic Conductivity and Seepage Velocity
The hydraulic conductivity of the porous formation can be computed from
known values of particle diameter and the porosity using the relationship:
(3<7)
- e)z
where:
K * the hydraulic conductivity [cm/sec]
o the density of water [kg/m3]
g ป acceleration due to gravity [m/sec2]
u * the dynamic viscosity of water [N-sec/m2]
e ซ porosity [d1mens1on1ess]
d ป mean particle diameter [cm]
In the event that the user specifies the value of the distribution type for
the hydraulic conductivity to be less than or equal to -1, the hydraulic
conductivity 1s calculated using the constant or randomly generated values
of the particle diameter and porosity. Water density and viscosity are
calculated from temperature using relationships presented 1n CRC Manual
(1981).
Similarly, 1f the value of the distribution type for the seepage
velocity 1s specified as less than or equal to -1, the seepage velocity
will be computed using Oarcy's law and value of the porosity I.e.:
(3.8)
3-40
-------
Table 3.8C. OPTIONS AVAILABLE TO COMPUTE PARTICLE DIAMETER, POROSITY,
r HYDRAULIC CONDUCTIVITY, AND SEEPAGE VELOCITY
Variable -
Specification
Index T
1
1
2
2
Variable
Name
Particle
diameter
Particle
diameter
Aquifer
porosity
Aquifer
porosity
Distribution
Code
0-7
1 -1
0-7
1 -1
Value Used for
Computations
User-defined constant or
randomly generated
value from the specified
distribution.
Calculated from
porosity.
User-defined constant
or randomly generated
value.
Calculated from
particle diameter.
Hydraulic
conductivity
0-7
Hydraulic < -1
conductivity
Groundwater 0-7
seepage
velocity
Groundwater < -1
seepage
velocity
User-defined constant
or randomly generated
value.
Calculated from
porosity and particle
diameter, fluid density,
and viscosity using Karman-
Cozney relationship.
User-defined or
randomly generated
value.
Calculated from
hydraulic gradient,
hydraulic conductivity,
and porosity using
Oarcy's law.
3-41
-------
where:
K ป the hydraulic conductivity of the formation [m/yr|
S ซ the hydraulic gradient [ra/ml
9 ซ porosity [dlmenslonless]
These options are also shown 1n Table 3.8C.
3.4.6.3 Computation of Source Thickness, Spread, and Maximum Source
Concentration--
The source thickness (or depth of penetration), the standard deviation
of the gaussian contaminant distribution (spread), and the maximum gausslan
source concentration are related by the mass balance equation, as discussed
1n the Volume 1 section on the saturated zone transport module. Thus, all
three of these variables cannot be Independently defined. The various
options that can be used to estimate these variables are shown 1n Table
3.80 and discussed below.
There are three different ways 1n which the value of the depth of
penetration of the source can be specified. These Include (1) specifying a
constant value or a probability distribution for the depth of penetration,
(11) Independently computing Us value based on assumptions regarding the
development of the plume below the facility. For the latter case:
LIf
+ 8(1 - txp(- ^-ฃ5)) (3.9)
where:
H * the depth of penetration of the source (m)
y ซ the vertical d1spers1v1ty [m]
L the dimension of the facility parallel to the flow
direction [m]
3-42
-------
Table 3.8&*, COMPUTATION OF SOURCE THICKNESS (I ป 5) AND SPREAD (1-7)
Source Thickness. H
Source Spread
Computed
Independently
(-11
Specified
fO - 7]
Computed from a
and Cla [-21
Computed NMFb * 1
Independently (Default Case)
[-1]
NMF ซ 1
NMF ป 1
Specified NMF * 1
[0-7|
Computed from NMF = 1
H and Cl
[-21
NMF * 1
NMF * 1
(Fed. Register,
Jan. 14, 1986.
case)
NMF = 1
Infeaslble
combination
a Cl: Source concentration value specified in the Source Data Group.
b NMF: Near-field mixing factor.
Note: Values in [ ] are distribution codes.
3-43
-------
B * the thickness of the saturated zone [m]
1^ ป Infiltration rate through the facility [m/yrl
Vs ป seepage velocity [m/yr]
e = porosity [dlmenslonless]
and (111) computing the depth of penetration based on the value of the
spread of the source:
A I
H ป - rr-^ - (3.10)
(2*)* Vs9ocn
where:
cQ = factor that accounts for the effect of dispersion on mass
entering the saturated zone [dimension! ess 1
Aw = area of the facility (m2]
o = standard deviation (spread) of the gausslan source [m]
The value of NDST(5) 1n the above three cases 1s ranging from 0 to 7, -1
(as shown in Table 3. 80), and -2, respectively.
Similarly, the spread of the source can be specified 1n three different
ways. These include (1) specifying a probability distribution for the
spread, (11) independently computing the spread of the source. I.e.:
o - U (3.11)
where W - the width of the facility [m].
and (111) computing the spread of the source from values of source
thickness using:
(3-12>
3-44
-------
The value of NDST(7)"in the above three cases is Banging from 0 to 7, -1
(as shown in Table 2.2), and -2, respectively.
The above set of values collectively yield nine combinations, of which
one combination is infeasible, as indicated in Table 3. 80. Note that the
value of the initial source concentration is read in as part of the Source
Data Group. For details, refer to Tables 3.4A and 3. 48. Further, if the
length and/or the width of the facility are not specified, they are
computed as the square root of the area of the facility.
In each of the above eight feasible combinations, the maximum gaussian
source concentration is related to the concentration either at the bottom
of the landfill or the bottom of the unsaturated zone using:
AJf
C0 -- ^ - C (3.13)
0 (2ป)*Ve H o C *
or
CQ = (NMF) Ca (3.14)
where:
CQ = the maximum gaussian source concentration (mg/1)
C = leachate concentration at the bottom of the unsaturated zone
or at the bottom of the facility if the unsaturated zone is
not present (mg/L) '
NMF a near-field mixing factor (dimensionless) given by
AJr
NMF * r-2-1- (3.15)
(2.)Ve H a cn
3-45
-------
Note that 1n the event that the spread of the source 1s computed from
the thickness of source or vice versa, the computed value of the near-field
mixing factor would be equal to unity (refer to Table 3.80). For the other
four combinations, the near-field mixing factor nay not be equal to
unity. From purely physical arguments, this factor should be less than, or
at most equal to, unity. Thus 1n the four cases shown 1n Table 3.8D for
which NMF ^ 1, the model checks to satisfy the constraint (NMF < 1). In
the deterministic mode a warning 1s printed out 1n the main output file.
For the case of a Monte Carlo simulation, the specific set of randomly
generated Input parameters 1s abandoned and a new combination of parameters
1s generated.
3.4.6.4 Computation of the Longitudinal, Transverse, and Vertical
01spers1v1t1es
The value of longitudinal, transverse, and vertical d1spers1v1t1es can
be specified as a constant or as a probability distribution, using the
distribution type codes 0 to 7 shown 1n Table 3.8E. Two additional options
are available for computing the d1spers1v1t1es 1n the saturated media (for
details refer to the Volume 1 section on saturated zone module). One of
these options can be used by specifying a value of 8 for the transverse
and/or the vertical d1spers1v1ty distributions (I.e., NDST(ll) and/or
NDST(12) =8). In this case the Input mean value of these variables (the
value of PAR(I,1) in the Array Subgroup) 1s deemed to be the ratio of the
longitudinal d1spers1v1ty to the transverse and/or the vertical
d1spers1v1ty. Thus this value 1s computed as the longitudinal d1spers1v1ty
divided by the user-specified mean value. This option allows the user to
define different constant values for the ratios of the longitudinal
d1spers1v1ty to the transverse d1spers1v1ty and the ratio of the
longitudinal d1spers1v1ty to the vertical d1spers1v1ty. Note that 1n this
case, the longitudinal d1spers1v1ty can still be defined as a constant or
as a distribution. This option is further Illustrated 1n Table 3.8E.
3-46
-------
Table 3.8E. COMPUTATION OF LONGITUDINAL, TRANSVERSE, AND VERTICAL
DISPERSIVITIES
Variable
Specification Distribution User-Specified
Index Variable Name Type Value Value Used
I NAME(I) NDST(I) ARRPRM(I,l)a 1n the Model
10
11
12
Longitudinal
D1spers1v1ty
Transverse
D1spers1v1ty
Vertical
01spers1v1ty
0-7
8
8
V!
V2
V3
Vl
VV2
V1/V3
a User Input values. Note that V^ may be a generated value.
3-47
-------
D1spers1v1t1es can also be calculated as a fraction of the distance to
the downgradlent receptor well. If NOST(IO) - 10, the longitudinal
d1spers1v1ty 1s set equal to one-tenth the distance to the well. If
NDST(ll) = 10, then the transverse d1spers1v1ty 1s set equal to 0.0333
times the distance to the well, I.e.:
ซL - 0.1Xw (3.16)
aT * 0.0333Xw (3.17)
where:
OL = the longitudinal d1spers1v1ty [m]
aT = the transverse d1spers1v1ty [m]
X,. ป distance to the well [m]
Under this option the vertical d1spers1v1ty may be specified as a constant
or as a distribution.
3.4.6.5 Specifying Location of the Receptor Well-
Figure 3-1 1s a schematic showing how the location of the well is
determined. The coordinates of the well location (xr, yr) are computed
based on user specified values of the radial distance to the well and the
angle 1> shown 1n Figure 3-1. The radius to the well and the angle of the
radius from the plume centerline are calculated based on user input. If
the distribution type for the radial distance to the well 1s -3, then the x
coordinate of the well location 1s set equal to the user specified mean
radial distance. If the distribution type for the angle i> (Figure 3-1) is
-3, then the mean value of 4* is Interpreted as the y coordinate of the well
1n meters. If the distribution type for the radial distance to the well
and the angle from the centerline are both greater than or equal to zero,
then the coordinates of the well location are compiled using:
xr ซ Rcos* (3.18)
3-48
-------
Well Location
WASTE
FACILITY
yr R sin
PLAN VIEW
Waste Facility
SECTION VIEW
Figure 3-1. A Schematic of the Well Location
3-49
-------
(3.19)
If the distribution type for the angle 1s specified as -3 and the
distance to the well has a distribution type of 0-7, then the x coordinate
of the well location 1s estimated using
xr * / R2 - yp2 (3.20)
Table 3.8F lists all of the available options that have been discussed
above.
3-50
-------
Table 3.8F. OPTIONS AVAILABLE FOR SPECIFYING THE WELL LOCATION
Distribution Type
Angle from
Distance to Plume Centerline
Well R 4>
Method to Calculate Coordinates
x-coord1nate y-coord1nate
x.. y..
-3
-3
0-7
0-7
-3
0-7
-3
0-7
user-defined
constant
user defined
constant
user-defined
constant
user-defined
constant
3-51
-------
8720123-S4 CON-1
SECTION 4
COMBINfNG REGIONAL DISTRIBUTIONS TO ESTIMATE
THE NATIONWIDE DISTRIBUTION
4.1 INTRODUCTION
As discussed in the background document for EPACML, it may at times be
necessary to run the EPACML model for a number of different regions or
hydrogeological settings and then to combine the results to yield a
nationwide distribution using specified weights for each region. This
aggregation of distributions is based on the total probability theorem and
is performed by a separate FORTRAN program CMPCDF that is also included
with the EPACML software package. Details of the input to this program are
discussed in Section 4.2 and 4.3.
A typical example where the above procedure may be necessary is
discussed below and also 1n Appendix C. This example is for the case where
the soils of the unsaturated zones of the nation are divided Into three
classes with relative distributions of 0.3, 0.4 and 0.3 respectively. This
results in three different environmental scenarios. The EPACML model can
be run for each of these three cases to yield three regional CDFs
(cumulative distribution functions) for the downgradient well
concentration. The program CMPCDF then combines these individual CDFs to
yield specified percentlles of the dilution/attenuation factor.
4.2 INPUT AND OUTPUT FILES FOR CMPCDF
At the start of execution, the user 1s asked to type 1n the (user-
specified) names of one Input file (on Unit 7) and one output file (on
Unit 8) directly onto the terminal screen. Writing to the screen 1s done
using "*" unit. The contents and format of this Input file (on Unit 7) are
discussed in Section 4.3. Note that these Input/output unit numbers are
independent of the unit numbers in the program EPACML.
4-1
-------
In addition to the above two files, the program opens a number of other
files each of which contain the cumulative distribution function of the
regional downgradlent well concentration. These files are similar to the
SAT1.0UT file created by EPACML containing concentrations sorted 1n
ascending order. The number of these files 1s equal to the number of
regional data to be combined (I.e., NFIL 1n Table 4.1). The Input unit
number for these files ranges from 9 to (9 + NFIL).
4.3 INPUT DATA REQUIRED AND FORMAT
The contents and format of the Input data required by this program are
shown in Table 4.1. The Input data consists of:
the regional CDFs of downgradlent concentrations
the percentlles to be computed
the number of data points (number of Monte Carlo simulations), and
the weight to be assigned to each region.
Note that regional CDFs are Included 1n NFIL number of files. These
files would be Identical to the SAT1.0UT files created by EPACML. An
example Input and output data file for CMPCDF are presented 1n Appendix C.
4.4 COMPUTATION OF COMPOSITE DISTRIBUTION
Having read the above data, the code CMPCDF performs the calculations
1n two steps. In the first step, dilution/attenuation factors are computed
as the reciprocals of the downgradlent well concentration values. In the
final step, a dilution factor 1s selected and Us composite (nationwide)
cumulative probability 1s computed using the total probability theorem.
This computed probability value 1s compared with the desired quantHe value
(PCTIL(I)) and a new dilution factor selected. This step 1s repeated and
the Iteration continued until the computed probability 1s within +.001 of
4-2
-------
Table 4.1. CONTENTS AND FORMAT FOR THE INPUT DATA FILE REQUIRED TO
COMBINE REGIONAL CDFs TO YIELD COMPOSITE NATIONWIDE
CDF/SPECIFIC PERCENTILES
Card
Wl
W2
W3
W4*
W5*
W6*
Data
TITLE (user specified)
NFIL, NPCT
PCTIL(I), I- l.NPCT
FILIN
MONTE
WGTS
Format
A80
215
8F10.0
A16
15
8F10.0
* Note: Cards W4-W6 are repeated NFIL number of times.
Definition of Contents
TITLE Any user specified title.
NFIL The number of files containing the (regional) data.
NPCT The number of percentHes of the composite nationwide
distribution of dilution factors that are to be computed.
PCTIL Actual values of the desired NPCT number of percentiles.
FILIN Name of file containing data sorted in ascending order i.e.
the regional CDF of downgradient well concentrations. Note
this file would be equivalent to the file SAT1.0UT generated
when EPACML is run with 10PEN * 0 or 1 in the General Data
Group.
MONTE The number of data in this file equal to the number of Monte
Carlo simulations. Note this number may vary for each
region.
WGTS The weight assigned to this region.
4-3
-------
the desired value. Once convergence 1s achieved, the value of the
dilution/attenuation'factor and the corresponding quantlle value are output
on Unit 8 (user specified name). Note this unit number 1s Independent of
the unit number 1n the EPACML code.
The program CMPCOF repeats the above steps NPCT number of times. For
further clarification refer to Appendix C that presents an example Input
and output data file.
4-4
-------
5.0
REFERENCES
CRC (1981), Handbook of Chemistry and Physics. 62nd edition, CRC Press.
McGrath, E.J., and D.C. Irving (1973), Techniques for Efficient Monte Carlo
Simulation, Volume II. Random Number Generation for Selected
Probability Distributions. Report Prepared for Office of Naval
Research. Project No. NR 366-076/1-5-72, Code 462.
Woodward-Clyde Consultants (1988a), Background Document for EPA's Composite
Landfill Model (EPACML). Report Prepared for U.S. Environmental
Protection Agency, Office of Solid Waste, Washington, D.C.
Woodward-Clyde Consultants (1988b), Background Document for Unsaturated
Zone Flow and Transport Module of EPACML. Report Prepared for U.S.
Environmental Protection Agency, Office of Solid Waste, Washington,
D.C.
5-1
-------
APPENDIX A
LIST OF SUBROUTINES INCLUDED IN THE EPACML MODEL
A-l
-------
Subroutine Called By
Input /Output Routines-'-
BATIN MAIN
CHKENO BATIN
FRQPLT OUTFOR
FRQTAB
MODCHK
OUTFOR
PRINTO
PRNEMP
PRNTIN
PRTOUT
OUTFOR
FUNCTION
LEFJJT PRTINP
MAIN
MAIN
MAIN, PRTOUT
PRTOUT
MAIN, PRTOUT
MAIN
REA02 BATIN
READ3 BATIN
Description
The batch-run Input processor that reads
from a user-specified file the values of
variables and parameters updated from
their default values.
Checks for the end of a data group.
Prints a CDF and/or PDF to the output
file.
Prints a table of statistics to the
output file.
Left justifies character variables.
Flags which modules are to be run for
Monte Carlo simulations.
Outputs single statistics, frequency
distribution tables, CDF tables, and
printer plots.
Outputs the distribution type, mean,
standard deviation, and maximum and
minimum allowed values for all the
variables which can be generated by
Monte Carlo routines.
Prints empirical distributions to output
file.
Writes out General Data Group to the
output file.
Outputs Monte Carlo Input information to
output file.
Reads in array values as part of the
batch input preprocessor.
Reads in empirical distributions as part
of the batch Input preprocessor.
A-2
-------
Subroutine Called By
SOPEN MAIN
Saturated Zone Module
Description
CONV02
CPCAL
GWCALC
CONV02
FUNCT1 GW2DFT, QROMB,
TRAPZD
GWCALC
MAIN
GW20FS
GWCALC, GW3DPS
GW2DFT
GWCALC, CPCAL,
GW3DPT
GW30PS
GWCALC
GW3DPT
QROMB
GWCALC, CPCAL
GW20FT
Opens output files containing Monte
Carlo output. These are the *.VAR and
*.OUT files.
Couples unsaturated zone and saturated
zone models using the convolution
approach.
Evaluates saturated zone concentrations
at time 'T minus tau' for the
convolution integral approach.
Evaluates the integrand in the
analytical solution.
Main calling routine for saturated zone
model. Sudlcky's analytical solution
for three-dimensional mass transport
problem with a gauss1an-d1str1buted
source.
Analytic solution to the saturated
steady-state, two-dimensional, transport
model with a continuous gaussian source
using the Gauss-Legendre quadrature
Integration scheme.
Analytic solution to the saturated,
unsteady-state, two-dimensional,
transport model with a continuous
gaussian source using the Gauss-Legendre
quadrature Integration scheme.
Evaluates saturated, steady-state,
three-dimensional transport from a
continuous gaussian source. Allows for
the effects of partial penetration.
Evaluates saturated, unsteady-state,
three-dimensional transport from a
continuous gaussian source. Allows for
partial penetration effects.
Performs Integration using Romberg's
method of order 2K (e.g., K ป 2 1s
Simpson's rule).
A-3
-------
Subroutine Called By
TRAPZD QROMB --
Unsaturated Zone Transport Module
AOISPR VTCALC
COEFF
CONV01
DDERFC
OGAUSS
EVAL
EXPERF
VTCALC
VTCALC
EXPERF
SOLBT, GW2DFS
SOLBT
SOLAY1
LAGRNG SOLBT
SOLAY1 VTCALC, SOLBT
SOLBT VTCALC, CONV01
STEHF VTCALC
VTCALC MAIN
Description
Computes the nth stage of refinement of
an extended trapezoidal rule.
Computes concentrations based on the
steady-state, advectlve dispersive
equation with first-order decay.
Generates coefficients of transformed
solution for each layer.
Evaluates layered unsaturated zone
transport solution by the convolution
method.
Computes complementary error function
with real arguments.
Computes the first N roots and weight
factors for the Gauss-Legendre
quadrature integration scheme.
Evaluates functional values at Gauss
integration points.
Evaluates the product of an exponential
function and the complementary error
function with real arguments.
Lagrangian interpolation scheme.
Analytical unsaturated zone transport
solution for layer 1.
Evaluates unsaturated zone
concentrations at the bottom of each
layer at specific time intervals.
Evaluates the Inverse of the Laplace
transform for solute transport in
layered media.
The main calling routine for the
analytical solution of transport through
the unsaturated zone.
A-4
-------
Subroutine Called By
Unsaturated Zone Flow Module
FPSI1 RAPSON
RAPSON
VFCALC
WCFUN
INITGW
VFCALC
MAIN
VFCALC
MAIN
INITVF
MAIN
INITVT
MAIN
LAYAVE
LINV
INITVT
INITVT
Description
Evaluates pressure head based upon
relationship between pressure head and
hydraulic conducting and water content.
Determines pressure head corresponding
to specific flux using modified Newton-
Raphson iteration.
Main calling routine for the one-
dimensional unsaturated zone flow model.
Evaluates the water content-pressure
head relation
Assigns the input variables or values
generated by Monte Carlo routines to the
variable names used in the saturated
zone model. Calculates aquifer,
chemical, and source constants.
Assigns the Input variables or values
generated by the Monte Carlo routines to
the variable names used in the
unsaturated flow model. The initial
conditions and coordinate system for the
unsaturated flow model are defined here.
Assigns the input variables or values
generated by Monte Carlo routines to the
variable names they have in the
unsaturated transport model.
Retardation, calculated here, and
saturations calculated in the flow
model, are assigned to the transport
variables here.
Evaluates average saturation and
porosity for each layer 1n the
unsaturated transport model.
Evaluates coefficients for Stehfast
algorithm.
A-5
-------
Subroutine Called By
TMGEN1 INITVT .
TMGEN2
INITVT
TMGEN3
INITVT
Subroutines to Set Default Values
AQMOO
CHMOO
OEFGW
DEFVF
OEFVT
OEFGW
DEFGW
MAIN
MAIN
MAIN
SOMOO
VFMOO
DEFGW
DEFVF, MAIN
VTMOO DEFVT, MAIN
Monte Carlo Routines
ANRMRN
NORMAL
LOGNOR
Description
Evaluates times used in convolution
integral to couple the unsaturated zone
and saturated zone transport solutions
(for constant source).
Evaluates times used in the convolution
integral to couple the unsaturated zone
and saturated zone transport solutions
(for pulse source).
Evaluates times used in the convolution
integral to couple the unsaturated zone
and saturated zone transport solutions
(for decaying source).
Sets aquifer-specific parameters to
their default values.
Sets chemical-specific parameters to
their default values.
Sets the default values for the aquifer,
chemical, and source variables.
Sets the default values for the
unsaturated zone flow model variables.
Sets the default values for the
unsaturated zone transport model
variables.
Sets source-specific parameters to their
default values.
Sets unsaturated flow-specific
parameters to their default values.
Sets unsaturated zone transport module
variables to their default values.
Generates a (0,1) normally distributed
random number.
A-6
-------
Subroutine Called By
CALLS UNCPRCT
COUNT
EMPCAL
MAIN
CALLS
EXPRN
EXPRNO
EXPRND CALLS
LOGNOR CALLS
IOG10U
NORMAL
RANSET
TRANSB
TRNLOG
CALLS
CALLS
MAIN
CALLS
CALLS
Description
Calls the prescribed random number
generator for each parameter which 1s
used 1n the Monte Carlo simulation.
Counts the number of parameters which
are to be Monte Carloed.
Generates a random number from an
empirical distribution. EMPCAL
generates a uniform random number
between 0-1 and uses it to interpolate
for a value using the piecewise linear
cumulative frequency distribution input
by the user.
Generates an exponentially distributed
random number with a mean of 1.
Generates an exponentially distributed
random number with a specified mean.
Generates a lognormally distributed
random number with a specified mean and
standard deviation. The input mean and
standard deviation are in arithmetic
space.
Generates uniformly distributed log 10
numbers between 0-1, then transforms
them to a range specified by the user.
Generates a (x,o)normally distributed
random number when x is the mean and
-------
Subroutine Called By
UNCPRO MAIN
UNFRN ANRMRN, LOGI0U
UNIFRM, EXPRN
UNIFRM CALLS, EMPCAL
Description
Generates random values for the model
parameters. It also writes to the
output file If any errors occur when
generating the random values.
Generates a (0,1) uniformly distributed
random number.
Generates a uniformly distributed random
number between a user-specified minimum
and maximum.
A-8
-------
APPENDIX B
EXAMPLE OF INPUT DATA AND OUTPUT
The model described 1n this report has been tested for a number of
different data sets. An example data set and model output is briefly
discussed below. rhese input and output files are included on the
diskette/tape that contains the FORTRAN 77 code and can thus be used to
verify the correct installation, compilation and operation of the code.
EXAMPLE
The sample data set (TEST1.DAT) is for a run that simulates the
following:
Steady-state flow and steady state transport in the unsaturated
zone
Steady-state transport in the saturated zone
Exhibit 1 shows the Input data file TEST1.DAT. This file contains
COMMENT CARDS, GROUP/SUBGROUP SPECIFICATION CARDS. DATA CARDS, and END
CARDS. These are discussed below.
As mentioned 1n Section 3.4, the first two cards Indicate the title of
the run. The next card 1s the General Data GROUP SPECIFICATION CARD and is
followed by cards that contain the data 1n this group. The contents and
format for the General Data Group are discussed 1n Table 3.3A. The
termination of this group of data is indicated by the END CARD.
B-l
-------
The next card 1s a GROUP SPECIFICATION CARD and Indicates the beginning
of the chemical data group, the contents and format for which are discussed
1n Table 3.5. This group, 1n general, consists of two subgroups, the Array
subgroup and the Empirical Distribution subgroup. Since none of the
chemical variables are specified to have an empirical distribution, it Is
not necessary to Include the empirical distribution subgroup. The two END
CARDS thus Indicate the end of the Array Subgroup and the Chemical Data
Group, respectively.
Following the Chemical Data Group, the Unsaturated Zone Flow Data Group
is input that in general consists of five subgroups. Since the unsaturated
zone is assumed to be homogenous (i.e., NMAT = 1), it is not necessary to
Include the Material Allocation Subgroup. Further, since the depth of the
unsaturated zone 1s randomly generated, the Spatial Discretization Subgroup
is not necessary. The specific spatial discretization used for flow
computations when the depth 1s a random variable has been explained in
Section 3.4.4.3. The format and contents of the Unsaturated Zone Flow Data
Group are discussed in Tables 3.6A to 3.6F.
The Unsaturated Zone Flow Data Group is followed by the Unsaturated
Zone Transport Data Group that consists of two subgroups. Data and formats
for each of these subgroups have been described 1n Section 3.4.5 and
Tables 3.7A through 3.70. Since the thickness of the unsaturated zone is
specified as a distribution in the unsaturated material property subgroup,
the specification of thickness of transport layer 1s Ignored. In this case
the thickness of the (transport) layer 1s set equal to the generated value
of the unsaturated zone depth. Also, since a steady-state case 1s being
simulated, data for the Time Specification Subgroup 1s not necessary.
Following the Unsaturated Zone Transport Group is the Source Data
Group, the contents and format for which are described 1n Table 3.4. This
data group also consists of two subgroups, the Array and the Empirical
Distribution subgroup. Since the infiltration rate and the recharge rate,
B-2
-------
Identified by a value of Index, I ซ 1 and I * 5, are selected to have an
empirical distribution, 1t 1s necessary to Include the Empirical
Distribution Subgroup. Note that this subgroup consists of ICOUNT (-20)
pairs of coordinates of the cumulative frequency curve for the Infiltration
rate and the recharge rate.
This data set 1s followed by the Aquifer Data Group described 1n
Section 3.4.6 and Table 3.8A.
Finally, the completion of the entire data set 1s Indicated by an
END CARD.
The above computations are performed in the Monte Carlo mode for 1000
simulations. Statistical analyses of the downgradlent well concentrations,
printer plots of the probability density function and the cumulative
distribution function are included 1n the output file TEST1.0UT. A copy of
this output file attached as Exhibit 2.
8-3
-------
EXHIBIT 1
MAIN INPUT DATA FILE FOR EXAMPLE 1
B-4
-------
SOIL TYPE; SANDY LOAM
COVER TYPE; SILT LOAM
GENERAL DATA
CHEMICAL NAME
CHEMICAL TY?E; nondegrader
*
"ON STYP OPTAIR RUN
200 MONTE
MONTE ROUTE I STEAD NT IOPEN YCK ZCK PALPNA
1000 111101 90.0
END GENERAL
CHEMICAL TYPE;
CHEMICAL SPECIFIC
ARRAY VALUES
CHEMICAL SPECIFIC
NONOEGRAOER
VARIABLE DATA
VARIABLES
** VARIABLE NAME
ซ
4 Acid catalyzed hydrolysis
5 Neutral rate constant
6 Base catalyzed hydrolysis
rate
rate
8 Normalized distribution coefficient
END ARRAY
UNITS
l/M-yr
1/yr
l/M-yr
ml/9
DISTRIBUTION PARAMETERS
MEAN STD DEV
0
0
0
0
fWWWW
0
0
0
0
.OOE+00
.OOE-00
.OOE+00
.OOE+00
0
0
0
0
.OOE+00
.OOE+00
.OOE+00
.OOE+00
0
0
0
0
LIMITS
MIN MAX
.OOE+00
.OOE-00
.OOE+00
.OOE+00
0
0
0
0
.OOE+00
.OOE-00
.OOE+00
.OOE+00
END CHEMICAL SPECIFIC
SOIL TYPE; SANDY LOAM
VFL VADOSE FLOW MODEL PARAMETERS
SATURATED MATERIAL PROPERTY DATA
ARRAY VALUES
** SATURATED MATERIAL VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
MEAN STD DEV
I
MIN
1 Saturated hydralic conductivity
2 Vadose zone porosity
END ARRAY
END MATERIAL 1
END SATURATED MATERIAL DATA
m/yr
7
0
2.296
0.41
24.65
0.00
O.OOE+00
0.00
MAX
30.0
0.50
SOIL MOISTURE PARAMETER DATA
FUNCTIONAL COEFICIENTS
ARRAY VALUES
VARIABLE NAME
1 Residual water saturation
3 ALPHA coefficient
4 BETA coefficient
END ARRAY
END MATERIAL 1
END SOIL MOISTURE DATA
END VADOSE FLOW
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD OEV MIN MAX
>***ป************ซ************
7
7
2
0.065
0.070
1.891
0.074
0.171
0.155
O.OOE+00
0.00
1.35
0.11
0.25
3.00
B-5
-------
VTP VAOOSE TRANSPORT MODEL PARAMETERS
TWUBPORT PARAMETERS
VALUES
VAOOSE TRANSPORT VARIABLES
VARIABLE NAME
3 Fractional organic carbon ratter
4. Bulk density
QtO ARRAY
EDO LATER 1
END VAOOSE TRANSPORT OATA
END TRANSPORT MODEL
UNITS
9/CC
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
>*
7
0
0.25
1.60
7.538
0.00
O.OOE+00
0.00
11.0
2.00
SILT LOAM
VARIABLE OATA
" COVER TYPE;
SOURCE SPECIFIC
ARRAY VALUES
SOURCE SPECIFIC VARIABLES
** VARIABLE NAME
T Infiltration rate
5 Recharge rate
ฃN0 ARRAY
EMPIRICAL DISTRIBUTIONS
" 1 ICOUNT
~ INFILTRATION RATE FOR SILT LOAM SOIL
^ 1
^p.ooo
0.801
0.000
0.127
** I
* RECHARGE
5
.000
.590
.000
.229
20
0.260
0.851
0.001
0.147
ICOUNT
RATE FOR
20
.030
.650
.018
.295
0.310
0.865
0.003
0.175
SANDY LOAM
.080
.700
.038
.310
0.498
0.871
0.005
0.185
.130
.755
.066
.366
UNITS
m/yr
m/yr
0.548
0.901
0.010
0.216
.260
.803
.071
.401
DISTRIBUTION PARAMETERS LIMITS
MEAN STD OEV MIN MAX
0.624
0.905
0.053
0.231
.290
.833
.076
.475
6
6
0.674
0.914
0.089
0.251
.400
.880
.104
.495
0.51E-01 0.50E-02 0.10E-04 1.00
0.51E-01 0.50E-02 0.10E-04 1.00
0.726
0.964
0.102
0.267
.478
.930
.142
.638
0.746
0.980
0.109
0.274
.498
.980
.147
.729
.771
1.00
0.124
0.787
.540
1.000
.211
1.064
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC
AQUIFER SPECIFIC VARIABLE OATA
ARRAY VALUES
*" AQUIFER SPECIFIC VAtlASLES
" VARIABLE NAME
UNITS
DISTRIBUTION
PARAMETERS
MEAN STD OEV
LIMITS
MIN MAX
*****'
17 Angle off center
18 Well vertical distance
END ARRAY
**
degree
in
4 .OOOE+00 .OOOE-00 .OOOE*00 90.0
4 .100E+00 .050E+00 .OOOEป00 1.
END AQUIFER SPECIFIC
ALL DATA
i
B-6
-------
EXHIBIT 2
MAIN OUTPUT FILE FOR EXAMPLE 1
B-7
-------
U. S. ENVIRONMENTAL PROTECTION AGENCY
EXPOSURE ASSESSMENT
COMPOSITE LANDFILL MODEL
VERSION 4.0. FEBRUARY 1990
Developed by Phillip Mineart and Atul Salhotra of
Woodward-Clyde Consultants, Oakland, California
In cooperation with:
Hydrogeologic, Inc., Herndon, Virginia,
Geotrans, Inc., Herndon, Virginia,
and
Aqua Terra Consultants, Mountain View, California
1
Run options
SOIL TYPE; SANDY LOAM
COVER TYPE; SILT LOAM
Option Chosen Saturated and unsaturated zone models
Run was MONTE
Number of monte carlo simulations 1000
s steady-state
runs if Y coordinate outside plume
Do not reject runs if Z coordinate outside plume
B-8
-------
CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
Solid phase decay coefficient
Dissolved phase decay coefficient
Overall chemical decay coefficient
Acid catalyzed hydrolysis rate
Neutral rate constant
Base catalyzed hydrolysis rate
Reference temperature
Normalized distribution coefficient
Distribution coefficient
Biodegradation coefficient (sat. zone)
UNITS
1/yr
1/yr
1/yr
l/N-yr
1/yr
l/N-yr
C
ml/9
--
1/yr
DISTRIBUTION
DERIVED
DERIVED
DERIVED
CONSTANT
CONSTANT
CONSTANT
CONSTANT
CONSTANT
DERIVED
CONSTANT
PARAMETERS
MEAN STO DEV
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
LIMITS
MIN MAX
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.35it-05
.221Eป09
.358E*05
.OOOE-00
.OOOE-00
.OOOE-00
40.0
.OOOE-00
.166E-05
100.
B-9
-------
SOURCE SPECIFIC VARIABLES
VARIABLE NAME
Inf i Itration rate
Area of waste disposal unit
Duration of pulse
Spread of contaminant source
Recharge rate
Source decay constant
Initial concentration at landfill
Length scale of facility
width scale of facility
UNITS
m/yr
m'2
yr
m
m/yr
1/yr
mg/l
m
m
DISTRIBUTION
EMPIRICAL
NORM. TRANSF.
CONSTANT
DERIVED
EMPIRICAL
CONSTANT
CONSTANT
DERIVED
DERIVED
PARAMETERS
MEAN STD DEV
.510E-01
4.21
.100E+31
50.0
.510E-01
.OOOE-00
1.00
100.
100.
.500E-02
2.16
3.00
.0006*00
.500E-02
.OOOE*00
.100E-01
1.00
1.00
LIMITS
MIN MAX
.100E-04
-.884
.100
.100E-02
.100E-04
.OOOE*00
.OOOEป00
1.00
1.00
1.00
12.3
.100E-31
.600E-05
1.00
10.0
10.0
.100E-06
.100E-06
EMPIRICAL CUMULATIVE DISTRIBUTIONS
Inf i Itration rate
PROBABILITIES
.801 .851
VALUES
.127 .147
Recharge rate
^PROBABILITIES
.590 .650
VALUES
.229 .295
.000
.865
.OOOE-00
.175
.000
.700
.OOOE-00
.310
.260
.871
.100E-02
.185
.030
.755
.180E-01
.366
.310
.901
.300E-02
.216
.080
.803
.380E-01
.401
.498
.905
.500E-02
.231
.130
.833
.660E-01
.475
.548
.914
.100E-01
.251
.260
.880
.710E-01
.495
.624
.964
.530E-01
.267
.290
.930
.760E-01
.638
.674 .726
.980 1.000
.890E-01 .102
.274 .787
.400 .478
.980 1.000
.104 .142
.729 1.06
.746
.109
.498
.771
.124
.540
.147
.211
B-10
-------
UNSATURATED ZONE FLOW MODEL PARAMETERS
(input parameter description and value)
NP Total ranter of nodal points 7
NMAT Number of different porous materials 1
KPROP - van Genuchten or Brooks and Corey 1
IMSHGN Spatial discretization option 1
OPTIONS CHOSEN
Van Genuchten functional coefficients
User defined coordinate system
MATERIAL NUMBER FOR EACH LAYER
111111
1
B-ll
-------
DATA FOR MATERIAL 1
VADOSE ZONE MATERIAL VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION
PARAMETERS
MEAN STO OEV
LIMITS
MIN
MAX'
Saturated hydralie conductivity
Vadose zone porosity
Air entry pressure head
Depth of the unsaturated zone
ffl/yr
m
m
SB
CONSTANT
CONSTANT
EMPIRICAL
2.30
.410
.OOOE+00
6.10
24.7
.OOOE*00
.OOOE*00
1.00
.OOOEป00
.OOOEป00
.OOOEป00
.610
30.0
.500
1.00
366.
EMPIRICAL CUMULATIVE DISTRIBUTIONS
Depth of the unsaturated zone
PROBABILITIES .000 .050 .100 .200 .250 .300 .350 .400 .450 .500
.600 .650 .700 .750 .800 .850 .900 .950 .980 1.000
VALUES .100E-01 .910 1.22 1.83 2.74 3.05 3.66 4.75 6.09 6.10
12.2 15.2 16.8 21.3 30.5 34.8 61.0 107. 183. 366.
DATA FOR MATERIAL 1
VADOSE ZONE FUNCTION VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION
PARAMETERS
MEAN STO DEV
LIMITS
MIN
MAX
Residual water saturation
Brook and Corey exponent,EN
ALPHA coefficient
BETA coefficient
SB
CONSTANT
SB
LOG NORMAL
.6SOE-01 .740E-01
.500 .100
.700E-01 .171
1.89 .155
.OOOEป00 .110
.OOOE-00 1.00
.OOOE'OO .250
1.35 3.00
UNSATURATED ZONE TRANSPORT MODEL PARAMETERS
NLAT - Number of different layers used 1
NTSTPS - Nuitoer of time values concentration calc 20
IADV - Type of transport solution 1
[SOL Type of scheme used in vadose zone 1
N - Stehfest terms or nuaber of increments 18
NTEL Points in Lagrangian interpolation 3
NCPTS Number of Gauss points 104
NIT - Convolution integral segments 2
I SOUND Type of boundary condition 1
ITSGEN - Time values generated or input 1
TMAX - Max simulation time 10.0
WTFUN weighting factor -- 1.2
(IONS CHOSEN
Stehfest numerical inversion algorithm
Nondecaying continuous source
Computer generated times for computing concentrations
B-12
-------
DATA FOR LAYER 1
VAOOSE TRANSPORT VARIABLES
VARIABLE NAME
Thickness of layer
Longitudinal dispersivity of layer
Fractional organic carbon matter
Bulk density
Biological decay coefficient
VARIABLE NAME
Particle diameter
Aquifer porosity
Sulk density
Aquifer thickness
Source thickness (mixing zone depth)
Conductivity (hydraulic)
Gradient (hydraulic)
Groundwater seepage velocity
Retardation coefficient
Longitudinal dispersivity
Transverse dispersivity
Vertical dispersivity
Temperature of aquifer
PH
Organic carbon content (fraction)
Well distance from site
Angle off center
Well vertical distance
UNITS
m
m
g/cc
1/yr
AQUIFER
UNITS
cm
--
g/cc
m
m
m/yr
m/yr
--
m
m
m
C
--
m
degree
m
DISTRIBUTION
CONSTANT
CONSTANT
SB
CONSTANT
CONSTANT
SPECIFIC VARIABLES
DISTRIBUTION
LOG10 UNIFORM
DERIVED
DERIVED
EXPONENTIAL
OERIV60
DERIV6D
EXPONENTIAL
DERIVED
DERIVED
GELHAR
RATIO
RATIO
NORMAL
NORMAL
LOG NORMAL
EMPIRICAL
UNIFORM
UNIFORM
PARAMETERS
MEAN
6.10
.400
.250
1.60
.OOOE+OO
STD DEV
1.00
.4006-01
7.54
.OOOE+OO
.200E-01
PARAMETERS
MEAN STD DEV
.6306-03
.OOOE+OO
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.
.OOOE+OO
.100
.630E-04
.OOOE+OO
.OOOE+OO
78.6
.600
.758E+04
.310E-01
.OOOE+OO
.100
.700
.OOOE+OO
.950E-01
5.29
1.28
.3006-03
.OOOE+OO
.OOOE+OO
.500E-01
LIMITS
MIN
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
MAX
500.
10.0
11.0
2.00
5.00
LIMITS
MIN MAX
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+OO
.OOOE+OO
.100
.560
1.80 ป
560.
10.0
.151E-06
.100
.925E-C4
.352E-:6
324.
41.0
250.
30.0
14.0
.100E-01
.1606-34
90.0
1.00
EMPIRICAL CUMULATIVE DISTRIBUTIONS
Well distance from sita
PROBABILITIES
.400 .500
VALUES
366. 427.
.000 .030
.600 .700
.600 13.7
610. 805.
.040 .050 .100 .150 .200 .250 -.300 .350
.800 .850 .900 .950 .980 1.000
19.8 45.7 104. 152. 183. 244. 305. 305.
914. .116E+04 .1226+04 .137E+04 .152E+04 .1616+04
B-13
-------
1931 Values generated which exceeded the specified bounds.
SATURATED ZONE
NOT LOAM
I IT LOAM ...
N
MEAN
STANDARD DEVIATION
COEFFICIENT OF VARIA1
MINIMUM VALUE
MAXIMUM VALUE
80th PERCENT I LE
85th PERCENT I LE
90th PERCENT! LE
95th PERCENT I LE
VALUE X OF TIME EQUALLED
OR EXCEEDED
.OOOE+00 100.000
.821E-01 3.200
.164 1.300
.246 .800
.329 .500
.411 .500
.493 .300
.575 .300
.657 .100
.739 .100
.821 .100
>
TRANSPORT
90.
1000
ซ .101E-01
.502E-01
riON > 4.99
> .0006+00
ซ .821
ป .176E-02
ซ .517E-02
ป .123E-01
ซ .484E-01
X OF TIME IN INTERVAL
96.800
1.900
.500
.300
.000
.200
.000
.200
.000
.000
PERCENT CONFIDENCE INTERVAL
.133E-02 .295E-02
.372E-02 .687E-02
.944E-02 .193E-01
.352E-01 .634E-01
B-14
-------
100 + *' * * * + * * + * ป
i !
! !
i i
flft + .... + ป+**+**++*ป+*+ป+<+*ป+
F ! !
R ! !
E ! * '"' I
0 60 ป--+ # ป *
(1 !
E !
N !
r 40 *.---.* * + 4
I
,.-..*......ซ......ซ......*......*......ซ......*......*......ซ......ซ
Y ! !
j j
X ! I
20 ป*-+ * + + + ซ......*. ป-..ซ......*
! ' I
i |
! ' I
Q ป.-...+...ป.-ป..-..+..-..ป-....ป--...ป...ป..ป.....ป.....+...*..ซ
.000 .082 .164 .246 .329 .411 .493 .575 .657 .739 .821
.1E+01
CONCENTRATION
1
M !
U !
A !
T !
I !
E !
i
F !
E !
0 t
U !
N !
C !
Y !
.000 .082 .164 .246 .329 .411
,
1
1
,
j
'
,
;
i
1
1
!
1
1
1
.493 .575 .657 .739 .821
CONCENTRATION
B-15
-------
LOWING GRAPHS ARE FOR THE TOP 20X OF THERESULTS
~100 * * *
i ซ
F !
R !
E !
U !
E !
N !
Y !
i
X !
1 *
| *
1 * *
1
1
i
1
1
1
1
1
1
.002 .084 .166 .248 .330 .412 .494 .576 .657 .739 .821
ซ .1E+01
CONCENTRATION
1
C 100 * * *
U j .......
M !
U !
I 80 * *ป * ซ + + + * * * +
A ! !
T ! * !
I ! !
E ! !
! !
F ! I
R CO +-*ป-*-----+-*-+..+...+.....+.-...*+.*..-+*.**+
E ! !
0 ! I
U ! I
E 20 + + * * * * * * * * ป
N ! !
C ! !
Y ! !
Q ป......*......ซ......*......*......+......+......+.......+......+......ซ
.002 .084 .166 .248 .330 .412 .494 .576 .657 .739 .821
.16*01
CONCENTRATION
B-16
-------
APPENDIX C
EXAMPLES OF INPUT DATA AND OUTPUTS FOR CMPCDF
C-l
-------
APPENDIX C
EXAMPLE OF INPUT DATA AND OUTPUT FOR
COMBINING REGIONAL CUMULATIVE DISTRIBUTION FUNCTIONS
This section presents an example that Illustrates the use of the
program CMPCDF described 1n Section 4.0 of the report. Example Input data
as well as the output obtained using the program are discussed. Note that
the example presented 1n this Section 1s for Illustration only and 1s not
directly related to the output obtained using the EPACML model.
EXAMPLE 1
This example combines the cumulative distribution functions of
downgradlent well concentrations obtained from three Individual runs of
EPACML to estimate specific quantlies of the composite/nationwide CDF of
the dilution/attenuation factor. Details of the Input formats have been
discussed earlier 1n Section 4.0.
Table C.I lists the three Individual Monte Carlo runs as well as the
name of the file that contains the sorted concentrations 1n ascending order
for each run. These files are the SATI.OUT files generated on Unit 27 when
the EPACML model 1s run with the flag IOPEN 0 or 1 In the General Run
Data Group. Table C.2 contains the sample Input data. The first date line
(after the title card) Indicates that 3 Regional COFs are to be combined
and 12 qualities fro* the composite nationwide CDF are to be estimated.
This card Is followed by two data lines containing the 12 quantHes. The
next data 11nt Indicates the name of the file that contains (one of the
three) CDF of normalized downgradlent well concentrations. The next two
data cards Indicate the number of sorted data In the file and the weight to
be assigned to this region. This set of three data lines 1s repeated three
times, I.e., once for each region.
C-2
-------
Table C.I. .DETAILS OF THE THREE REGIONAL RUNS TO BE COMBINED
v7
Run Weight File Name
1 0.3 SAT1.0UT
2 0.4 SAT2.0UT
3 0.3 SAT3.0UT
C-3
-------
TEST CASE OP COMPOSITING PROGRAM; 3 PRE-SORTED DATA SETS
3 12
5. 10. 15. 20. 40. 50.0 60.0 80.
85. 90. 95. 100.
SAT1.0UT ;:..
500
0.3000
SAT2.0UT
500
0.4000
SAT3.0UT
500
0.3000
Table C.2. INPUT DATA SET FOR EXAMPLE 1 FOR PROGRAM COFCMP
C-4
-------
Table G.3 contains the sample output data. After echoing the data, the
output prints the d1>ut1on/attenuat1on factors. Note that since the
dilution/attenuation factors are the Inverse of concentration, the V
percentlle of the dilution/attenuation factor Is equivalent to the (100-p)
percent11e of normalized downgradlent well concentration value.
C-5
-------
PROGRAM COFCMP Program for combining regional
concentration values using
specified weights to yield
composite nationwide COP of
dilution factors
TEST CASE OP COMPOSITING PROGRAM; 3 PRK-SORTED DATA SETS
*********ECHO OP INPUT DATA:
Files from which data are read:
sATI.OUT
SAT2.0UT
SATS.OUT
File has 500 rows of data
weighting factor - .3000
File has 500 rows of data
Weighting factor .4000
File has 500 rows of data
Weighting factor - .3000
********COMPOSITE NATIONWIDE CDF:
Percentile Dilution
5.00 1.095
10.0 1.370
15.0 1.641
20.0 1.933
40.0 5.393
50.0 9.786
60.0 19.63
80.0 128.5
85.0 252.5
90.0 547.0
95.0 2236.
100. .10001+11
Table C.3. OUTPUT FOR EXAMPLE 1 FOR PROGRAM COFCMP
C-6
-------
APPENDIX 0
DESCRIPTION OF VARIABLES IN OUTPUT FILES
D-l
-------
8720123APd CON-2
APPENDIX 0
DESCRIPTION OF VARIABLES IN OUTPUT FILES
Title (units) 1n
*.VAR Files
FORTRAN Name
Variable
AQUIFER.VAR
01AM (en)
THETAS
RHOB (g/cc)
BAQFR ()
HSOURC (m)
OKS (m/yr)
SS mm/im
VEL (m/yr)
RETARD
ALFAL (ซ)
ALFAT (m)
ALFAZ (m)
TEMP (8C)
pH
FOC (fraction)
XI (m)
Yl (m)
Zl (m)
SOURCE.VAR
QC (m/yr)
AW (m2)
TS (yr)
SIGMA ()
QO (m/yr)
00
THETAS
RHOB
BAQFR
HSOURC
OKS
SS
vw
R
ALFAL
ALFAT
ALFAZ
T
PH
FOC
XPSTN
YPSTN
ZPSTN
QC, UIFR, SINFL
AW
TOFF
S
RECR6
Particle diameter
Aquifer porosity
3ulk density
Aquifer thickness
"hlckness of source
iydraullc conductivity
- jraullc gradient
)undwater seepage velocity
cardatlon coefficient
.ong1tud1nal d1spers1v1ty
Transverse d1spers1v1ty
Vertical d1spers1v1ty
Aquifer temperature
pH of aquifer
Organic carbon content
Distance to monitoring point
1n x-d1rect1on
Distance to monitoring point
1n y-d1rect1on
Distance to monitoring point
1n z-direction
Infiltration rate
Area of waste disposal
Duration of pulse
Spread of Input source
Recharge rate
unit
D-2
-------
Title (units) 1n
*.VAR/OUT Files
FORTRAN Name
Variable
SOURCE.VAR (continued)
GAM (1/yr) GAM
CSOURC (mg/1) C0
L (m) LENGTH
WIO (m) WIDTH
OF DF
CHEMICAL.VAR
GLAM2 (1/yr)
GLAM1 (1/yr)
GLAM (1/yr)
OKAO
OKNO
OKBO
TR (
OKOC
(1/m-yr)
(Vyr)
(1/m-yr)
'C)
(inl/g)
KD
BLAM (1/yr)
VFLOW1.VAR
SHC (cm/hr)
VOZ
AEPH
DEPTH ()
GLAM2
GLAM1
K
OKAO
OKNO
OKBO
TR
DKOC
KD
BLAM
PMKSAT
WCS
HCRIT
OTHIK
Source decay constant
Initial concentration at
landfill
Length scale of facility
Width scale of facility
Near-field mixing factor
Solid-phase decay coefficient
Dissolved-phase decay coefficient
Overall chemical decay
coefficient
Add catalyzed hydrolysis rate
Neutral hydrolysis rate
Base catalyzed hydrolysis rate
Reference temperature
Normalized distribution
coefficient
Distribution coefficient
Blodegradation coefficient for
the saturated zone
Saturated hydraulic conductivity
Unsaturated zone porosity
A1r entry pressure head
Depth of the unsaturated zone
0-3
-------
Title (units) 1n
*.VAR/OUT Files
FORTRAN Name
Variable
VFLOH2.VAR
RWC
EN BETA
ALFA (I/cm) ALPHA
ENN ENN
VTRNSPT.VAR
MID (m) WID
A (m) A
FOCV AK
RHO (g/CC) RHO
DECAY (1/yr)
Residual water content
Brook and Corey exponent, EN
ALPHA coefficient
Van Genuchten exponent
Thickness of layer
Longitudinal dlsperslvlty of
layer
Percent organic matter
Bulk density of soil layer
Biological decay coefficient In
unsaturated zone
0-4
-------
EPACML-S0002.A
BACKGROUND DOCUMENT FOR ERA'S
COMPOSITE MODEL FOR LA5WiL? (EPACML)
February 1990
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF SOLID WASTE
WASHINGTON O.C. 20460
-------
DISCLAIMER
The work presented in this document has been funded by the United
States Environmental Protection Agency. It has not been subject to the
Agency's peer and administrative review, and has as yet not been approved
as an EPA document. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use'by the U.S. Environmental
Protection Agency.
11
-------
ABSTRACT
The Environmental Protection Agency's Composite Landfill Model (EPACML)
simulates the movement of contaminants (through the unsaturated and
saturated zones) leaching from a hazardous waste landfill. The composite
model consists of a steady-state, one-dimensional numerical module that
simulates flow in the unsaturated zone. The output from this module,
seepage velocity as a function of depth, is used as input by the unsaturated
zone transport module. The latter simulates transient, one-dimensional
(vertical) transport in the unsaturated zone and includes the effects of
longitudinal dispersion, linear adsorption, and first-order decay. Output
from the unsaturated zone modules--!,e., contaminant flux at the water \
tableis used to define the gaussian-source boundary conditions for the
transient, semi-analytical saturated zone transport module. The latter
includes one-dimensional uniform flow, three-dimensional dispersion, linear
adsorption, lumped first-order decay, and dilution due to direct
infiltration into the groundwater plume.
The fate and transport of contaminants in the unsaturated and the
saturated zones depends on the chemical properties of the contaminants as
well as a number of medium- and .environment-specific parameters. The
uncertainty in these parameters is quantified using the Monte Carlo
simulation technique.
The model can be used to back-calculate the allowable concentration of
a chemical constituent at the point of release (I.e., below a landfill)
such that the receptor well concentration does not exceed a health-based
(maximum) threshold level.
This report provides details of the fate and transport modules, the
Monte Carlo simulation technique and values of the Input parameters that
the Agency has compiled based on nationwide surveys of waste disposal
facilities.
-------
TABLE OF CONTENTS
Section
DISCLAIMER
ABSTRACT
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
ACKNOWLEDGEMENT
1 OVERVIEW OF THE LANDFILL MODEL
1.1 Introduction
1.2 EPACML - An Overview
1.3 Report Organization
2 THE UNSATURATED ZONE FLOW MODULE
2.1 Introduction
2.2 Governing Equations and Solution Techniques
2.3 Limitations and Assumptions of the Unsaturated
Zone Flow Module
2.4 Data Required
3 UNSATURATED ZONE TRANSPORT MODULE
3.1 Introduction
3.2 Governing Equations
3.2.1 Unsteady-State Transport
3.2.2 Steady-State Transport
3.3 Limitations and Assumptions of the Unsaturated
Zone Transport Module
3.4 Data Required
3.4.1 Contaminant Source-Specific Parameters
3.4.2 Chemical-Specific Parameters
3.4.2.1 The Chemical Transformation Rate
3.4.2.2 The Distribution Coefficient
3.4.2.3 3ercent Organic Carbon Matter
Page
ii
111
i v
v i i i \
X
xii
1
1
2
5
7
7
7
12
13
15
15
15
15
20
21
22
22
22
22
24
24
IV
-------
TABLE OF CONTENTS (continued)
Section
4 THE
4.1
4.2
4.3
4.4
4.5
3.4.3 Unsaturated Zone-Specific Parameters
3.4.3.1 Longitudinal Dispersion Coefficient
SATURATED ZONE MODULE
Introduction
Governing Equations
Assumptions and Limitations of the Saturated Zone
Transport Module
Coupling of the Unsaturated and the
Saturated Zone Modules
4.4.1 Steady-State Coupling
4.4.2 Unsteady-State Coupling
Parameters Required by the Saturated Zone
Transport Module
4.5.1 jource-Spedfic Parameters
4.5.1.1 Depth of Penetration of Source
4.5.1.2 The Spread of the Gaussian Source
4.5.1.3 Maximum Source Concentration
4.5.1.4 Other Parameters Required
4.5.2 Aquifer-Specific Parameters
.5.2.1 Porosity
.5.2.2 Bulk Density
.5.2.3 Seepage Velocity
.5.2.4 Hydraulic Conductivity
.5.2.5 Dispersion Coefficients
4.5.2.6 Recharge Rate into the Plume
4.5.3 Chemical-Specific Parameters
4.5.3.1 Hydrolysis Rates
4.5.3.2 The Distribution Coefficient
4.5.4 Receptor Well Location-Specific Parameters
5 UNCERTAINTY ANALYSIS
5.1
5.2
5.3
Introduction
Statement of the Problem and Technical Approach
The Monte Carlo Analysis Technique
Page
24
24
27
27
27
34
35
35
37
38
38
42
44
44
45
45
45
45
46
46
47
49
49
50
51
52
54
54
54
58
-------
TABLE OF CONTENTS (continued)
Section Page
5.4 Uncertainty in the Input Variables 60
5.5 The Random Number jenerator 64
5.6 Analysis of the Model Output 72
5.7 Implementation of the Monte Carlo Simulation
Procedure 73
6 DEFAULT INPUT DATA FOR EPACML 77
6.1 Introduction 77
6.2 Chemical-Specific Data Group 77
6.2.1 Decay Coefficient 77
6.2.2 Chemical Specific Hydrolysis Rate Constants 79
6.2.3 Distribution Coefficient 79
6.2.4 Biodegradation Coefficient 79
6.3 Source-Specific Data Group 79
6.3.1 Infiltration Rate 79
6.3.2 Area of Facility 84
6.3.3 Duration of Pulse 84
6.3.4 Spread of the Contaminant Source 84
6.3.5 Recharge Rate 84
6.3.6 Source Decay Constant 85
6.3.7 Initial Concentration at Source 85
6.3.8 Length Scale of the Facility 85
6.3.9 Width Scale of the Facility 85
6.4 Unsaturated Zone Flow Data Group 85
6.4.1 Control Parameter Subgroup 85
6.4.2 Material Variables Subgroup 88
6.4.3 Functional Variables Subgroup 88
6.5 Unsaturated Zone Transport Data Group 88
6.5.1 Control Parameter Subgroup 88
6.5.2 Vadose Transport Variable Subgroup 93
6.6 Aquifer-Specific Data 93
6.6.1 Temperature 93
6.6.2 Groundwater pH 93
6.6.3 Fractional Organic Carbon Content 96
6.6.4 Particle-Size Distribution 96
6.6.5 Hydraulic Gradient 96
6.6.6 Thickness of the Saturated Zone 96
6.6.7 Dlspersivities 96
6.6.8 Receptor Well Location-Specific Data 97
-------
TABLE OF CONTENTS (concluded)
Section Page
7.0 REFERENCE CASE AND SENSITIVITY ANALYSES 102
7.1 Reference Case 102
7.2 Sensitivity Analysis 102
7.2.1 Infiltration Rate 102
7.2.2 Location of Well 102
7.2.3 Area of Landfill 106
NOTATION 111
REFERENCES 115
APPENDIX A - DERIVATION OF THE ADVECTIVE AND DISPERSIVE FLUX
EMANATING INTO THE AQUIFER AT THE SOURCE x ป 0
FOR STEADY-STATE CONDITIONS A-l
APPENDIX B - SIMPLIFIED ESTIMATION FOR DEPTH OF PENETRATION B-l
vu
-------
LIST OF TABLES
Table
2-1
3-1
3-2
4-1
4-2
4-3(a)
4-3(b)
5-1
5-2a
5-2b
6-1
6-2
6-3
6-4
INPUT PARAMETERS REQUIRED FOR UNSATURATED ZONE
FLOW MODULE
INPUT PARAMETERS REQUIRED FOR THE UNSATURATED ZONE
TRANSPORT MODULE
COMPILATION OF FIELD DISPERSIVITY VALUES (GELHAR ET AL.
1985)
INPUT PARAMETERS REQUIRED FOR THE SATURATED ZONE
TRANSPORT MODULE
ADDITIONAL DATA REQUIRED TO COMPUTE INPUT PARAMETERS FOR
THE SATURATED ZONE TRANSPORT MODULE
ALTERNATIVES FOR INCLUDING DISPERSIVITIES IN THE
GROUNDWATER MODEL
PROBABILISTIC REPRESENTATION OF LONGITUDINAL DISPERSIVITY
FOR DISTANCE OF 152.4 m
QUALITATIVE COMPARISON OF UNCERTAINTY-PROPAGATION METHODS
RESULTS OF RANDOM NUMBER GENERATOR TEST FOR 500 VALUES
RESULTS OF RANDOM NUMBER GENERATOR TEST FOR 1000 VALUES
PARAMETERS INCLUDED IN THE CHEMICAL-SPECIFIC DATA GROUP
OF EPACML MODEL
CHEMICAL-SPECIFIC PROPERTIES USED IN SIMULATIONS
PARAMETERS INCLUDED IN THE SOURCE-SPECIFIC DATA GROUP
OF EPACML MODEL
EMPIRICAL DISTRIBUTIONS USED TO REPRESENT INFILTRATION
RATE fm/vH THROUGH SUBTITLE D LANDFILL
Page
14
23
26
39
41
48
48
57
65
66
78
80
81
82
-------
LIST OF TABLES (concluded)
Table
6-5
6-6
6-7
6-8
6-9
6-10
6-11
7-1
7-2
7-3
7-4
7-5
PARAMETERS INCLUDED IN THE UNSATURATED ZONE FLOW DATA
GROUP OF EPACML MODEL
UNSATURATED ZONE FLOW MODEL PARAMETERS FOR DIFFERENT
SOIL TYPES
EMPIRICAL DISTRIBUTION USED TO REPRESENT THE THICKNESS
OF THE UNSATURATED ZONE
PARAMETERS INCLUDED IN THE UNSATURATED ZONE TRANSPORT
DATA GROUP OF EPACML MODEL
VALUES OF BULK DENSITY AND FRACTIONAL ORGANIC CARBON
MATTER USED IN THE UNSATURATED ZONE TRANSPORT MODEL
PARAMETERS INCLUDED IN THE AQUIFER-SPECIFIC DATA GROUP
OF EPACML MODEL
EMPIRICAL DISTRIBUTIONS USED TO REPRESENT THE DISTANCE
TO WELL
WEIGHTS USED TO ESTIMATE THE COMPOSITE NATIONWIDE
DISTRIBUTION OF DAFs FOR LANDFILL SCENARIOS
DILUTION/ATTENUATION FACTORS FOR DIFFERENT SCENARIOS
FOR REFERENCE CASE
EFFECT ON OAF OF RESTRICTING ANGLE OFF PLUME CENTERLINE.
TO 45 DEGREES (WELL RESTRICTED TO PLUME)
EFFECT ON OAF OF NOT RESTRICTING WELL TO PLUME
EFFECT ON OAF OF CHANGING AREA OF LANDFILL
Page
86
89
90
92
94
95
99
102
104
107
108
109
-------
LIST OF FIGURES
Figure Page
l-l(a) FLOWCHART OF THE EPA's COMPOSITE LANDFILL MODEL 3
l-l(b) FLOWCHART OF THE SIMULATION OPTIONS IN THE EPA's
COMPOSITE LANDFILL MODEL 4
2-1 A SCHEMATIC OF THE WASTE FACILITY AND LEACHATE MIGRATION
THROUGH THE UNSATURATED AND SATURATED ZONES 8
3-1 A SCHEMATIC OF TRANSPORT THROUGH THE LAYERED UNSATURATED
ZONE 19
4-1 A SCHEMATIC DIAGRAM OF THE SOURCE BOUNDARY CONDITIONS
FOR THE SATURATED ZONE TRANSPORT MODULE 30
4-2 A SCHEMATIC OF THE WASTE FACILITY AND LEACHATE MIGRATION
THROUGH THE UNSATURATED AND SATURATED ZONES 43
4-3 A SCHEMATIC OF THE WELL LOCATION 53
5-1 A SCHEMATIC DESCRIPTION OF THE MONTE CARLO METHOD
OF UNCERTAINTY ANALYSIS 59
5-2 SELECTING A JOHNSON DISTRIBUTION FROM SKEWNESS AND KURTOSIS 63
5-3 COMPARISON OF THE EXACT AND THE GENERATED CUMULATIVE
FREQUENCY DISTRIBUTION FOR A NORMALLY DISTRIBUTED VARIABLE 67
5-4 COMPARISON OF THE EXACT AND THE GENERATED CUMULATIVE FRE-
QUENCY DISTRIBUTION FOR A LOG NORMALLY DISTRIBUTED VARIABLE 68
5-5 COMPARISON OF THE EXACT AND THE GENERATED CUMULATIVE
FREQUENCY DISTRIBUTION FOR AN EXPONENTIALLY DISTRIBUTED
VARIABLE 69
5-6 COMPARISON OF THE EXACT AND THE GENERATED CUMULATIVE FRE-
QUENCY DISTRIBUTION FOR AN EMPIRICALLY DISTRIBUTED VARIABLE 70
5-7 COMPARISON OF THE EXACT AND THE GENERATED CUMULATIVE
FREQUENCY DISTRIBUTION FOR A UNIFORMLY DISTRIBUTED VARIABLE 71
-------
LIST OF FIGURES (concluded)
Figure
5-8
6-1
6-2
6-3
6-4
7-1
7-2
TYPICAL RESULTS OBTAINED USING EPACML IN THE MONTE
CARLO MODE
EMPIRICAL DISTRIBUTION USED TO REPRESENT THE INFILTRATION
RATE FOR INFILTRATION THROUGH A SUBTITLE D LANDFILL
EMPIRICAL DISTRIBUTION USED TO REPRESENT THE THICKNESS
OF THE UNSATURATED ZONE
SCHEMATIC OF THE WELL LOCATION
EMPIRICAL DISTRIBUTION USED TO REPRESENT THE DISTANCE
TO WELL
SENSITIVITY OF EPACML RESULTS TO INFILTRATION RATE
DILUTION ATTENUATION FACTOR AS A FUNCTION OF AREA OF
Page
74
83
91
98
100
105
110
LANDFILL
-------
ACKNOWLEDGEMENT
This report has been prepared by Woodward-Clyde Consultants for the
Office of Solid Waste (OSW), U.S. Environmental Protection Agency. Or.
Zubair Saleem was the project manager for EPA and Dr. Atul M. Salhotra
served as the project manager for Woodward-Clyde Consultants.
A number of individuals were involved in the actual development of the
computational codes and provided assistance to OSW. Key individuals
include Dr. Peter Huyakorn of HydroGeoLoglc Inc.; Barry Lester of Geotrans
Inc.; Dr. Michael tings of TetraTech, Inc.; Phil Mlneart of Woodward-Clyde
Consultants; Dr. Carlos Marin, Ambiotech; Dr. Ed Sudlcky, University of
Waterloo; and Lee Mulkey and Bob Carsel of EPA's Athens Environmental
Research Laboratory.
-------
SECTION 1
OVERVIEW OF THE LANDFILL MODEL
1.1 INTRODUCTION
This chapter provides an overview of the U.S. Environmental Protection
Agency's Composite Model for Landfills (EPACML). The model simulates the
fate and transport of contaminants released from a hazardous waste disposal
facility into the environment. Release to soil, including the unsaturated
and the saturated zone, are included in the model.
The physical scenario being simulated by the model is that of a
hazardous waste land disposal facility that releases pollutants into the
unsaturated soil, and groundwater. In response to a number of complex
physical, chemical, and biological fate and transport processes, the
pollutants move in the subsurface environment.
Several factors are considered, in the model, including the toxicity,
mobility, and persistence of constituents 1n the waste. The toxicity of a
constituent is considered by specifying an allowable health-based
concentration level at the point of measurement and back-calculating the
maximum acceptable waste leachate concentration that can be released from a
land disposal unit (landfill) and not exceed the specified concentration
level. The mobility of constituents is considered through incorporation of
sorption as a delay mechanism to travel in groundwater. The persistence of
organic constituents is incorporated into the groundwater model by
considering hydrolysis. Details of the modeling approach were provided in
the Federal Register notices of January 14, 1986 (51 FR 1602), June 13,
1986 (51 FR 21648), and August 1, 1988 (53 FR 28892).
-------
1.2 EPACML - AN OVERVIEW
Figure 1-1(a,b) shows a flowchart of the landfill model. The major
functions currently performed by this model include:
Allocation of default values to input parameters/variables.
Reading of the input data files.
Echo of input data to output files.
Generation of random numbers for Monte Carlo simulations.
Calculation of contaminant degradation rates from hydrolysis rate
constants, retardation coefficient, and soil conductivity (from
particle diameters) if it is not read in as an input variable.
Depending on user-selected options:
- simulation of unsaturated zone flow and transport
- simulation of saturated zone transport only
- combinations of the above
In the Monte Carlo mode, the cumulative frequency distribution
(printer plots) and selected percent!les of concentrations at
receptors located in the saturated zone are output.
For each Monte Carlo run, the values of randomly generated input
parameters and the computed concentration values can be-printed.
The fate and transport of contaminants in the subsurface environment
critically depends on a number of unsaturated- and saturated-zone-specific
parameters. Typically a number of these parameters exhibit spatial and
-------
c
EPA'S LANDFILL MODEL
DETERMINISTIC
RUN OPTIONS
SEE FIG. 1-1 (b)
PRINT RESULTS
ฑ
SET DEFAULT VALUES
READ INPUT DATA
ECHO INPUT DATA
DETERMNST1C
CR
MONTE CARLO
WRITE RANDOMLY
GENERATED VARIABLES
RUN OPTIONS
SEE FIG. 1-1 (b)
1
PRINT RESULTS
ป"->
10
PRINT PLOTS AND
STATISTICAL ANALYSIS
i
Figure 1-1 (a). Flowchart of the EPA's Composite Landfill Model
-------
1
RUN OPTIONS
UNSATURATEDZONE
FLOW
UNSATURATEDZONE
TRANSPORT
SATURATED
TRANSPORT
SATURATED
TRANSPORT
Figure l-l(b).
Flowchart of the Simulation Options In the
EPA's Composite Landfill Model
-------
temporal variability as well as variability due to measurement errors. The
Landfill Model has the capability to analyze the Impact of uncertainty and
variability in the model inputs on the model outputs, i.e., concentrations
at specified points in the aquifer. The current version treats such
variability using the Monte Carlo simulation technique and 1s discussed 1n
detail in Chapter 5.
Further, since the model would typically be used in the Monte Carlo
mode to address the implications of model parameter uncertainties, it was
considered necessary to include a post-processing module. This module
performs statistical analysis and produces printer plots of the cumulative
frequency distributions (CDFs). This uncertainty post-processor also has
the capability to combine a number of regional CDFs to yield a composite
nationwide CDF of the receptor concentration, as well as to compute
confidence bounds for the estimated percentile values.
Finally, the model can be used to 'back-calculate' the concentrations
(for steady-state infinite contaminant source case) of the chemical at the
source, given a concentration level at a specified distance downgradient
from the source. This implies that given a potential point of human
exposure and a concentration deemed to be protective of human health and/or
the environment, the model can be used to back-calculate the maximum
constituent concentration in the leachate immediately beneath or adjacent
to the land disposal unit that will ensure that the specified protective
level of contaminant concentration is not.exceeded at the potential
exposure point. The concentration deemed to be protective of human health
is termed the RfD (Reference Dose) value.
1.3 REPORT ORGANIZATION
The EPACML model (EPA's Composite Model for Landfills), consists of
three modules. These include the unsaturated zone flow and transport
module, the saturated zone transport module, and an uncertainty analysis
-------
(Monte Carlo) pre- and post-processing module. Technical details of the
saturated zone module are presented in Section 4 of this report. The
uncertainty analysis module is discussed in Section 5, and Section 6
contains the default (generic nationwide) values of the data used for the
current regulatory implementation of the model. Details of the unsaturated
zone flow and transport modules are discussed in Sections 2 and 3
respectively.
-------
SECTION 2
THE UNSATURATEO ZONE FLOW MODULE
2.1 INTRODUCTION
In the event that the bottom of the hazardous waste disposal unit 1s
located above the water table, the leachate would migrate through the
unsaturated zone and Into the saturated zone. A schematic diagram of the
leachate migration 1s shown in Figure 2-1. In such situations it 1s
important to include the unsaturated zone in the analysis of contaminant
fate and transport.
This chapter presents details of the semi-analytical unsaturated zone
flow module included in the landfill model. Additional details are
presented in Huyakorn et al. (1988). The flow module computes the water
saturation values within the unsaturated zone which are used by the
unsaturated zone transport module to compute seepage velocities.
Theoretical details of the flow module and the underlying assumptions and
data requirements are presented below.
2.2 GOVERNING EQUATIONS AND SOLUTION TECHNIQUES
The unsaturated zone flow module simulates steady downward flow to the
water table. The governing equation is given by Darcy's law:
"rw ( - 1) ' 'f
-------
PLAN VIEW
SECTION VIEW
Monitoring
-.Well
Ground Surface
Water Table
Aquifer
B
PWVWWWWVWVWWVW^
Figure 2-1. A Schematic of the Waste Facility and Leachate Migration
Through the Unsaturated and Saturated Zones
-------
where
4i = the pressure head [ml
z = the depth coordinate which is taken positive downward [m]
Ky = the saturated hydraulic conductivity [m/yr]
k^ = the relative hydraulic conductivity [dimensionless)
If = the infiltration rate [m/yr]
The boundary condition at the water table is:
*U) = 0 (2-2)
where L is the thickness of the unsaturated zone [m].
To solve the above problem, it is necessary to specify the relation-
ships between the relative hydraulic conductivity (k^) and water
saturation (Sw), and between the pressure head (
-------
a = soil-specific parameter [1/m]
ill. = the air entry pressure head, which is subsequently assumed zero |m]
a
Se = the effective saturation (dimenslonless)
Further, the parameters e and -r are related through
t - 1 - 1/e (2-6)
and hence only the parameter B is specified.
Alternatively, the kfw(Sw) relationship presented by Brooks and Corey
(1966) may be used. The relationship between the relative hydraulic
conductivity and effective saturation 1s given by:
krv ' se <2-7' .
Note that the relationship between the saturation water content and the
suction pressure head is the same as in Equation 2-4.
As a first step in the solution of Equations 2-1 and 2-2, the soil
constitutive relations Equations 2-3 and 2-4 are combined. Using van
Genuchten's constitutive equations and assuming iii = 0, this leads to the
following expression for k (iiป):
i W
<|i > 0
-lfi A / .xBa/B-l^ (2"8)
[1 + (-a40 1 } 4, < 0
(-a*i)Bl(l|~*B'
Next, Equation 2-8 1s substituted into Equation 2-1 and the derivative
i*
32 replaced by a backward finite difference approximation. This yields,
after some rearranging:
10
-------
AZ
- o.
> 0
p.
(2-9)
where i is the representative pressure head for the soil layer between z
and z - AZ.
If Brooks and Corey's (1966) relationship 1s used, the expression for
relative hydraulic conductivity becomes:
rw
1,
tl-
ili > 0
\ * < o
(2-10)
Substituting Equation 2-10 into Darcy's law (Equation 2-1), the resulting
expression equivalent to Equation 2-9 is:
AZ
> 0
(2-11)
In Equations 2-9 and 2-10, 5 can be written as a weighted average of
*_ and HI, ._:
Z Z-AZ
(2-12)
where u is a weighting coefficient (0 < u < 1). A value of u equal to
unity was found to give accurate results.
Using Equations 2-9 or 2-11 and 2-12 together with the lower boundary
condition Equation 2-2 allows the solution for 4>. = 4ป, . This value
11
-------
for -41. is then used in place of * in Equations 2-9 or 2-11 and 2-12 and
the equation is solved for the pressure head at the next desired distance
upward from the water table. In this sequential manner, the pressure head
at any depth in the unsaturated zone is computed. The Newton-Raphson
method is used to solve the nonlinear root-finding problem (Equation 2-9 or
2-10). In the event that the Newton-Raphson method does not converge, the
bisection method is used. The latter method 1s computationally slower but
ensures convergence.
After the pressure-head distribution 1n the unsaturated zone has been
found, the corresponding saturation distribution, Sw(z), is computed using
Equation 2-4. In principle, the saturation distribution can be found
without first solving for iii(z) by substituting Equation 2-3 or 2-7 rather
than Equation 2-8 or 2-10 into Equation 2-1. The disadvantage of this
approach is that it becomes more difficult to accommodate nonuniform
material properties. Whereas the iii-profile is continuous in the
unsaturated zone, the Sw-profile is discontinuous at the interface of soil
layers with contrasting hydraulic properties.
2.3 LIMITATIONS AND ASSUMPTIONS OF THE UNSATURATED ZONE FLOW MODULE
The major assumptions on which the flow module is based include:
(i) Flow of the fluid phase is considered isothermal, one-
dimensional, and governed by Darcy's law.
(11) The flow field is considered to be steady.
(ii1) The simultaneous flow of the second phase (i.e., air) .can be
disregarded.
(iv) Hysteresis effects are neglected in the specification of the
characteristic curves.
12
-------
2.4 DATA REQUIRED
The data required by the unsaturated zone flow module are listed 1n
Table 2-1. Note that either the van Genuchten's or Brooks and Corey's
relationship is required. The current version of the landfill model does
not have a source module to estimate the vertical infiltration through the
facility and the Infiltration is a user-specified variable. The actual
values of the data used are presented in Section 6.
13
-------
Table 2-1. INPUT PARAMETERS REQUIRED FOR UNSATURATED ZONE FLOW MODULE
Parameter
Unit
van Genuchten's Constitutive Relationship
Soil-specific parameter, 6
Soil-specific parameter, a
Air entry pressure head, v
Residual saturation, Swr
Brook and Corey's Constitutive Relationship
Soil-specific parameter, n
Infiltration Rate through the Facility
Saturated Hydraulic Conductivity of the Soil
Thickness of the Unsaturated Zone
[dimensionless]
[I/ml
[m]
[dimensionless]
[dimensionless]
If [m/yr]
Kv [m/yr]
L [m]
14
-------
SECTION 3
UNSATURATED ZONE TRANSPORT MODULE
3.1 INTRODUCTION
This section presents the details of the unsaturated zone transport
module included in the landfill model. As mentioned above* transport
within the unsaturated zone is important only in the event that the bottom
of the waste disposal unit is located well above the water table.
This chapter presents the theoretical basis of the unsaturated zone
transport module as well as the underlying assumptions. The data
requirements for this module are also discussed below.
3.2 GOVERNING EQUATIONS
3.2.1 Unsteady-State Transport
The transport of contaminants within the unsaturated zone is treated as
a one-dimensional problem. Important fate and transport mechanisms
considered by the module Include longitudinal dispersion, linear
equilibrium adsorption and first-order decay of the contaminant. With
these assumptions, the transport equation can be expressed as:
Rv Hi" ' ฐv -4- - Vv -if - W . <3-"
d Z
15
-------
where
C = the dlssolved-phase contaminant concentration 1n the unsaturated
zone (mg/a)
Dv = the longitudinal dispersion coefficient 1n the unsaturated zone
[m2/yr]
xy = the first-order degradation rate within the unsaturated zone
Il/yr]
Rv = the unsaturated zone retardation factor
Vy = the steady-state unsaturated zone seepage velocity [m/yr]
t = time (yr]
z = the vertical coordinate which 1s positive downwards (m)
In Equation 3-1, the retardation factor 1s computed using:
% 1 * ^v (ซ).
where
ฐbv = the bu1k dens1ty of tne unsaturated zone (g/cc)
K^y = the contaminant distribution coefficient for the unsaturated zone
[cc/g]
e = the porosity of the unsaturated zone [cc/cc]
Sw = the fractional saturation within the unsaturated zone [cc/cc]
The overall first-order degradation rate, xy, Includes the effect of both
blodegradatlon ar? chemical transformation, primarily hydrolysis
reactions. The latter 1s discussed 1n detail 1n Section 6.2.
Further in Equation 3-1, the unsaturated zone seepage velocity 1s
computed using:
16
-------
where If is the steady-state infiltration rate within the unsaturated
zone. Note that in the landfill model, If is assumed to be steady. Also,
the saturation, Sw, is computed by the unsaturated zone flow module, as
discussed above.
Solution of the above differential equation requires two boundary
conditions. The first boundary condition describes the source
concentration and may be of the following form:
C(O.t) = C0 (3-4a)
or
C(0,t) = CQ exp(-At) (3-4b)
or
C(0,t) = CQ[1 - s(t - T)] (3-4c)
where
A = the source concentration decay rate [1/yr]
s(t-T) = the unit step function with a value of unity for t > T and
zero for t < T [t and T are 1n years]
CQ = the initial (or steady-state) concentration at the top of the
unsaturated zone [mg/i]
Note that Equation 3-4(a) represents a constant source concentration
condition, Equation 3-4(b) an exponentially decaying source boundary
concentration, and Equation 3-4(c) a finite (constant concentration) pulse
source condition. The second boundary condition, which applies at a large
distance from the source, is
C(-,t) = 0 . (3-5)
The Initial condition is
C(z,0) = 0 (3-6)
17
-------
The analytical solution for the unsteady-state transport problem has been
presented by Marino (1974) and van Genuchten and Alves (1982). Using the
constant concentration boundary condition, Equation 3-4(a), the solution
can be expressed as:
c 1 (Vy - r)z Ryz - rt j (Vy + r)z Ryz + rt
Co * 20v 2/DlTt 2 ^T 2/077
Using the exponentially decaying concentration boundary condition, the
solution to Equation 3-1 becomes:
R z - r,t
r 1 zlvu " riJ Kuz ' ri
^- = i exp (-At) {exp [^ i-1 erf el v 1
^*^* ' ^^*.j o^nn^
2'finrt
z(v.+ MJ R,z + :it
+ exp [ %, 1 ) erfc [ v i ]} (3-8).
where : is given by:
The effect of varying degradation rates, dispersion coefficient and
seepage velocity (computed by the flow module) is accounted for by dividing
the unsaturated zone into a number of horizontal layers, each one of which 1s
assumed to be homogeneous. This is schematically shown in Figure 3-1.
Equation 3-1 1s sequentially solved for each layer. For the first layer, any
one of the source boundary conditions, Equation 3-4, can be specified. For
the remaining layers, the following source boundary condition, which ensures
continuity of concentration, is applied:
C^.t) = C.+1(0,t) (3-10)
18
-------
Flow
I
V,
ll
Layer 1
Layer 2
Layer 3
C/Co
1
z=0
C/Co
2= I
C/CQ
1
Z= In-I 2
c/Co
1
Z= \ +\
Figure 3-1. A Schematic of Transport Through the Layered
Unsaturated Zone
19
-------
where i is the thickness of a layer and the subscripts 1 and 1+1 refer to
successive layers. Equation 3-10 Implies that the source concentration at the
top of any layer 1+1 is set equal to the concentration computed at the bottom
of the previous layer i. Note that the layers can be of different thickness.
The solution to the layered unsaturated zone 1s derived using Laplace
transform techniques to transform the governing partial differential equation
(Equation 3-1) and the boundary conditions to an ordinary differential
equation in the Laplace domain. The ordinary differential equation is solved
in the Laplace domain and then inverted using either the convolution theorem
or the Stehfest algorithm (Stehfest 1970; Moench and Ogata 1981). The latter
is a numerical inversion scheme. Both these solution schemes are included in
the model. In general, the Stehfest algorithm is computationally faster.
However, at very high Peclet numbers there is a possibility that this \
numerical solution may not converge. For such cases, the convolution
integration method may be used. Details of the solution scheme are presented
by Shamir and Harleman (1967) and Haderman (1980).
3.2.2 Steady-State Transport
For the case of a steady-state continuous contaminant source, the
governing Equation 3-1 can be simplified to yield:
Dv a2C Vv 3C .
For this case the boundary conditions are:
C(Z-O) = C0 (3-12a)
|f (zป.) = 0 (3-12b)
The analytical solution to the above system of equations 1s:
20
-------
C(z) = C exp (jfr- - 2(\ R /D + VV40')*} (3-13a)
o *uv
or
C(2) = CQ exp <ฃ. - j|- (1 + -Y*-)*} (3-13b)
Z 2 V
In the event that dispersion within the unsaturated zone 1s neglected, the
above equation reduces to:
-ง = exp Hp-) (3-14)
0 S
where L = the depth of the unsaturated zone (ml.
For a layered unsaturated zone, Equation 3-14 can be expressed as: v
C , n xv1*K
-ฃ- = exp (-z -^Y-4 (3-15)
o 1=1 vi
where n 1s the number of homogenous layers within the unsaturated zone.
3.3 LIMITATIONS AND ASSUMPTIONS OF THE UNSATURATED ZONE TRANSPORT MODULE
The major assumptions on which the unsaturated zone transport module 1s
based are:
(1) The flow field within the unsaturated zone 1s at a steady state.
(11) The seepage velocity as well as other model parameters (dispersion
coefficient, partition coefficient, etc.) are uniform In each
layer. I.e., each layer 1s homogeneous and 1sotrop1c.
(111) Transport 1s assumed to be strictly one dimensional. Lateral and
transverse advection and dispersion are neglected.
21
-------
(iv) Adsorption and decay of the solute may be described by a linear
equilibrium isotherm and a first-order decay constant,
respectively. The daughter products of chemical and biochemical
decay are neglected.
(v) Each layer is approximated as being Infinite in thickness. This
assumption is valid and introduces negligible errors if the ratio
of longitudinal dispersivity to the layer thickness 1s small
3.4 DATA REQUIRED
Table 3-1 lists the parameters required by the unsaturated zone transport
module. The actual values of these parameters are presented 1n Section 6. \
3.4.1 Contaminant Source-Specific Parameters
The unsaturated zone transport module requires three source-specific
parameters. These are listed in Table 3-1. Note that the module is linear
with respect to the source concentration so that if the source concentration
is set to unity, the module computes normalized downgradient well
concentrations.
3.4.2 Chemical -Specif ic Parameters
Table 3-1 lists the four chemical-specific parameters required by the
module. These may either be directly input or computed using other parameters
as discussed below.
3.4.2.1 The Chemical Transformation Rate
The chemical decay coefficient is computed using the hydrolysis rate
constants as discussed in Section 6.2. The overall decay rate is then
computed by adding the biological decay rate to the chemical decay rate.
22
-------
Table 3-1. INPUT PARAMETERS REQUIRED FOR THE UNSATURATED ZONE TRANSPORT
MODULE
Parameter Unit
Contaminant Source-Specific Parameters
Source decay constant (for unsteady-state simulation only) A (1/yr)
Source concentration at top of unsaturated zone CQ (mg/il
Pulse duration (for unsteady-state simulation only) T [yr)
Chemical-Specific Parameters
Chemical transformation rate (computed using
hydrolysis rate constant and pH as in the
saturated zone transport module) x [1/yr)
i
Biodegradation rate xfa [1/yr]
Percent organic carbon matter (to compute
partition coefficient) foin
Distribution coefficient Kdv [cc/gj
Unsaturated Zone-Specific Parameters
Number of layers and thickness of each for n,i. [m]
transport module
2
Longitudinal dispersion coefficient Dy [nr/yr]
Bulk density of the soil obv (g/cc)
Porosity of the unsaturated zone e [dimensionlessl
Seepage velocity (computed by the flow module) V$ (m/yr)
Temperature of the unsaturated zone layers Ty [ฐC]
pH of the unsaturated zone layers . pH
23
-------
3.4,2.2 The Distribution Coefficient
In the absence of user-specified values of the distribution coefficient,
the latter is computed as the product of the normalized distribution
coefficient for organic carbon and the fractional organic carbon content.
3.4.2.3 Percent Organic Carbon Matter
The value of the fractional organic carbon content is required to compute
the distribution coefficient. The former is computed using (Enfield et al.
1982):
f ฐ
oc 00 x.724
where
foc = fractional organic carbon content [dlmensionless]
fom = percent organic matter content [dimensionlessl
3.4.3 Unsaturated Zone-Specific Parameters
Table 3-1 lists the unsaturated zone specific transport parameters. Of
these, the seepage velocity is computed using Equation 3-3, with the
saturation values computed by the unsaturated zone flow module. All other
values are user-specified input except for the longitudinal dispersion
coefficient, which is computed as discussed below.
3.4.3.1 Longitudinal Dispersion Coefficient
The longitudinal dispersion values are computed using the relationship:
(3-17)
where
5
Dv = the longitudinal dispersion coefficient (nr/yrl
Vv = the seepage velocity in the unsaturated zone [m/yr]
24
-------
a = the longitudinal d1spersiv1ty (m]
The disperslvity values used 1n the models are based on an analysis of the
data presented by Gelhar et al. (1985) shown 1n Table 3-2. Using regression
analysis, the following relation was developed:
ay = .02 + .022L, R2 = 66% (3-18)
where L 1s the depth of the unsaturated zone. To avoid excessively high
values of disperslvity for deep unsaturated zones, a maximum disperslvity of
1.0 m 1s used. Thus, for all depths greater than 44.5 m, a will be set equal
to 1.0 m.
o
5
-------
Table 3-2. COMPILATION OF FIELD DISPERSIVITY VALUES (GELHAR ET AL. 1985)
Author
Yule and Gardner
(1978)
Hlldebrand and
Himmelblau (1977)
Kirda et al.
(1973)
Gaudet et al.
(1977)
Brissaud et al.
(1983)
Warrick et al.
(1971)
Van de Pol et al.
(1977)
Biggar and Nielsen
(1976)
Kies (1981)
Jury et al. (1982)
Andersen et al.
Type of
Experiment
Laboratory
Laboratory
Laboratory
Laboratory
Field
Field
Field
Field
Field
Field
Field
Vertical Scale
of Experiment [m]
0.23
0.79
0.60
0.94
1.00
1.20
1.50
1.83
2.00
2.00
20.00
Longitudinal
Dispersivity
av (ml
0.0022
0.0018
0.004
0.01
0.0011,
0.002
0.027
0.0941
0.05
0.168
0.0945
0.70
(1968)
Oakes (1977)
Field
20.00
0.20
26
-------
SECTION 4
THE SATURATED ZONE MODULE
4.1 INTRODUCTION
This chapter presents details of the module used to simulate
contaminant fate and transport within the saturated porous zone. Recall
that the contaminant can enter the saturated formation by direct leaching
from the waste disposal unit (1n the absence of an unsaturated zone) or by
percolation through the unsaturated zone. The composite model allows the
user to specify either of the above options. Note that 1n both cases the
governing equations, and hence the semi-analytical solution for transport
in the saturated zone, is the same.
The following sections describe the governing equations, boundary and
initial conditions, model limitations, and the parameters required to solve
the equations.
4.2 GOVERNING EQUATIONS
The three-dimensional solute transport equation on which the model 1s
based can be written as:
(4-1)
27
-------
where:
x, y, z ป spatial coordinates 1n the longitudinal, lateral and vertical
directions, respectively [ml
C ป dissolved concentration of chemical [mg/i, g/m ]
Dy. Ou, 07 = dispersion coefficients in the x, y and z directions,
respectively (nr/yr)
one-dimensional,
direction [m/yr]
V = one-dimensional, uniform seepage velocity 1n the x
RS = retardation factor in the saturated zone [dimenslonlessl
t = elapsed time [yr]
x = effective first-order decay coefficient in the saturated zone
U/yrl
q = net recharge outside the facility percolating directly into
and diluting the contaminant plume [m/yr] \
B = the thickness of the saturated zone [ml
In Equation 4-1, the retardation factor and the effective decay
coefficient are defined as:
Rs
and
where:
Pb ซ bulk density of the porous media [g/cc]
Kd ซ distribution coefficient [cc/g]
e = effective porosity for the saturated zone [cc/ccj
\l = first-order decay constant for dissolved phase [1/yr]
x- = first-order decay constant for the sorbed phase [1/yrJ
28
-------
x. = first-order lumped biodegradation rate in the saturated
zone [1/yr]
The flow domain is regarded as semi-Infinite 1n the x direction
(0 < x < ป) , infinite in the y-d1rect1on ( < y < ป) and finite 1n the
z-direction (0 < z < B).
Solution of Equation 4-1 requires initial and two-boundary conditions
in the x, y, and z directions. At the source (downstream edge of the waste
disposal unit) the contaminant concentration is assumed to be a gaussian
distribution in the lateral direction and uniform over the vertical mixing
or penetration depth, H. A schematic description of the flow domain and
the source boundary condition is shown 1n Figure 4-1. Mathematically, the
.above-stated assumptions can be expressed as:
C(x, y, z, 0) = 0 (4-4a)
Cn exp(-y2/(2o2)], 0 < z < H (4-4b)
C(ฐ'y*2't)= 0ฐ ,H
-------
Figure 4-1. A Schematic Diagram of the Source Boundary Conditions for the
Saturated Zone Transport Module
30
-------
Huyakorn et al. (1987) have presented analytical solutions for the
system of Equations 4-1 to 4-4. The general solution can be expressed as:
C(x, y, 2, t) = ง Cf(x, y, t) + ACp(x. y, 2, t) (4-5)
where Cf and &C are functions given by:
t
Cf(x, y, t) = 5 J F(x, y, T) exp(-nt) dt (4-6)
*Cp(x, y. z, t) 25. I I cos () sin
I F(x. y, T) exp (-Bnt) dr (4-7)
in which
* v
exp (- -2 - *- *) (4-8a)
4D*7 4D*t * Za
x y
*
Cox V x
exp () (4-8b)
*2
V
n - 4^* + X (4-8c)
31
-------
an = " + -J-* <4-8o>
where:
* * *
D , D . and D, = the retarded dispersion coefficients (Dy/R., DV/R_,
A y z * * jr *
DZ/RS) 1n the x, y and z direction
Vs* = the retarded solute (seepage) velocity (Vs* = VS/RS1
T = the variable of integration
Note that 1n the event that H = B, i.e., the source fully penetrates the
saturated formation, AC = 0 in Eq. 4.5. At any distance, x, from the
source, maximum contaminant concentration would occur at the centerline of \
the plume and can be represented as:
C(x, 0, 0. t) - {J Cf(x, 0, t) + ACp(x, 0, 0, t) (4-9)
where Cf (x, 0, t) and.AC (x, 0, 0, t) are given by Equations 4-6 and 4-7
with arguments y and z set equal to zero, and the function F(x, 0, T)
defined as:
exp (-x2/4D*T)
F(x, 0, T) = -372 2~* T72 (4-10)
T3/Z (2oZ + 4DJi)1/Z
As t approaches Infinity, a steady-state condition 1s reached. The steady-
state concentration along the plume centerline can be expressed as:
C*(x. 0. 0) - g C*(x, 0) * ACJ(x, 0, 0) (4-11)
where:
32
-------
n n iin*
Cf (x. 0) = 5* J exp [- S-Sj- - x (-^ * jj) ]du (4-12a)
,Cj(x, 0, 0) - sin ()
2 2 u2D* B
J exp [- S- x (-=-ฃ + ซ) 1 du (4-12b)
0 x x
2C_o V*x
2
The above solution for the transient state, I.e., Equations 4-5 to 4-
8d, was earlier programmed 1n FORTRAN 77 1n the code named EPATMOD.
Similarly, the steady-state solution, Equations 4-11 and 4-12, has been
programmed In the code named EPASMOD. In these codes, the Integrals in
Equation 4-7 and Equation 4-12 are computed numerically using the Gauss-
Quadrature scheme (Carnahan et al. 1969). Note that for large time, t,
EPATMOD yields the steady-state solution that 1s Identically equal to
EPASMOD. However, the code EPASMOD 1s significantly faster than EPATMOO
and should be used for steady-state computations. Finally, note that the
model uses the principle of superposition, to compute the plume
concentration for a pulse source, I.e., a contaminant source of finite
duration, TS. Both these codes have been incorporated Into the composite
code, EPACML, and constitute the saturated zone transport module of this
code.
The concentrations computed by the saturated zone model at a down-
gradient location (e.g., receptor well) can be used 1n a back calculation
33
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mode as explained in Section 5.6 to estimate the maximum allowable leachate
concentration at the waste disposal facility.
4.3 ASSUMPTIONS AND LIMITATIONS OF THE SATURATED ZONE TRANSPORT MODULE
Following are the 11st of assumptions Inherent 1n the saturated zone
transport module:
1) The saturated, porous medium properties are 1sotrop1c and
homogeneous. The module cannot be used to simulate transport 1n
fractured media unless the fractured medium is represented as an
equivalent porous formation.
ii) The groundwater flow velocity is steady and uniform. This Implies
that the recharge through the facility and Into the groundwater
plume is small compared to the natural (regional) flow.
iii) Contaminant degradation/transformation follows the first-order rate
law and is restricted to biodegradatlon and hydrolysis. The latter
is a second-order process from which the first-order rate is
obtained using existing environmental conditions. I.e., pH. This
assumption is conservative since it neglects degradation due to
other mechanisms such as oxidation, reduction, etc. Further, the
by-products of degradation are neglected.
1v) Contaminant sorption follows a linear adsorption Isotherm.
Adsorption takes place instantaneously and the adsorbed phase is in
local equilibrium.
v) Assumptions regarding the source boundary conditions and the extent
of the formation have been discussed in Section 4.2.
34
-------
4.4 COUPLING OF THE UNSATURATED AND THE SATURATED ZONE MODULES
In the event that the transport of contaminants through the unsaturated
and the saturated zones are considered, an Important requirement 1s that
the principle of conservation of mass be satisfied, I.e., the mass flux
that leaches out of the facility (1n the absence of an unsaturated zone or
from the bottom of the unsaturated zone) be equal to the mass flux that
enters the saturated zone. This mass flux consists of the sum of advectlve
and dispersive mass fluxes.
4.4.1 Steady-State Coupling
The mass that leaches out of the facility can be expressed as:
ML Au I, C, (4-13)
where:
M|_ = the mass that leaches out of the facility [g/yr)
Aw = the area of the facility [m2]
If = infiltration rate through the facility [m/yr]
Ca = concentration in the leachate from the facility [g/m3] 1f
attenuation within the unsaturated zone 1s neglected or the
unsaturated zone 1s absent. Alternatively, C 1s the estimated
concentration at the bottom of the unsaturated zone.
The mass flux that 1s advected Into the saturated zone 1s calculated by
integrating the source concentration 1n the y direction from -ซ to +ซ and
over the depth z = 0 to z = H. Thus the mass flux advected into the
aquifer is:
H +-
M - J J C(x = 0, y, z) V e dydz (4-14)
a 2=0 y=-ซ 5
where:
35
-------
Ma = mass flux advected into the aquifer [g/yr]
C(x = 0, y, z) = concentration as a function of y and 2 at the source
[g/m3, mg/i] as expressed by Eq. 4-4b
Vs - the seepage velocity in the saturated zone [m/yrj
e = effective porosity of the saturated zone (cc/cc)
Similarly, the mass flux that enters the saturated zone due to dispersion
can be expressed as:
H +-
M - J J e 0
2=0 y=-
3X
dy dz (4-15)
x=0
Integrating Equation 4-14, with CQ assumed uniform over the source
depth H, yields:
Ma = (2 i)* a Vs 6 H CQ (4-16)
Ungs (1987) (attached as Appendix A) has evaluated the integral in Equation
4-15 to yield:
4 x R D
Md = (2 ,)% o Vs e H CQ [-% + % (1 ซ s * x] ) (4-17)
Vs
where:
x ซ the overall first-order decay coefficient [1/yr]
Rs ซ the linear retardation factor [dimensionless]
DX = the longitudinal dispersion coefficient [wr/yr]
Note that in the event that Dx = 0, the dispersive flux, Md, is zero. Thus
the total flux into the saturated zone is given by the sum of advective
(Equation 4-16) and dispersive (Equation 4-17) fluxes:
MT = (2*)1* o Vs 0 H CQ C|J (4-18)
36
-------
where:
1 1 4 x< R< ฐ* *
'D^I + lt1* I 2S X) 1 (4-19)
s
Note that 1f ;D 1s set equal to unity, 1t Implies that the dispersive flux
is neglected.
Equating Equations 4-13 and 4-19 yields the following expression of the
mass balance:
Aw If C^ = (2 ,)* o Vs e H CQcD (4-20)
The above equation is used to couple the unsaturated and the saturated zone
models under steady-state conditions.
4.4.2 Unsteady-State Coupling
For the case of unsteady-state transport in the unsaturated zone, the
mass flux at the water table varies in time, and the above approach for
coupling the unsaturated and the saturated zone 1s no longer valid. In the
unsteady state, concentrations 1n the saturated zone are determined using
the convolution Integration approach that superimposes the effects of
source changes over time as follows:
C(x,y.z,t) = J |f I f(x,y,z,t - T) dT (4-21)
Q 3T T
where:
C*(t) * the concentration at the water table at time t [mg/il
f(x,y,z,t) = the normalized (with respect to source concentration)
solution of the saturated zone analytical solution
[mg/a]
37
-------
In Equation 4-21, the value of f(x,y,z,t) is the solution to the saturated
zone transport equation ."1th the gausslan source boundary condition. In
the computer code program, the above Integral 1s numerically evaluated
using the trapezoidal rule.
4.5 PARAMETERS REQUIRED BY THE SATURATED ZONE TRANSPORT MODULE
Table 4-1 lists the input parameters required to compute the
contaminant concentrations in the saturated zone. These parameters can be
classified into the following four groups:
(1) Contaminant source-specific parameters
(2) Aquifer-specific parameters
(3) Chemical-specific parameters
(4) Receptor well location-specific parameters
Important qualitative and quantitative aspects of each of these input
parameters are discussed below.
Note that in the event that values of the parameters listed in Table 4-
1 are not available, the EPACML code includes the option of deriving these
using other variables (presented in Table 4-2) and using a set of
empirical, semi-empirical or exact relationships as discussed below. The
specific parameter values and the empirical relationships used while imple-
menting the code for the current regulation are described 1n Section 6.
4.5.1 Source-Specific Parameters
For steady-state analysis, the model requires three source-specific
parameters. These parameters are estimated based on the mass balance
Equation 4-20 and consideration of other physical/empirical Information as
explained below.
38
-------
Table 4-1. INPUT PARAMETERS REQUIRED FOR THE SATURATED ZONE TRANSPORT
MODULE*
Parameter Unit
Contaminant Source-Specific Parameters
Steady-State
Leachate concentration at the CQ [mg/i, g/m ]
waste facility
Standard deviation of the source o [m]
Thickness of gaussian source H (m]
Unsteady State (additional parameter)
Duration of the pulse TS (yr)
Aquifer-Specific Parameters
Porosity 0 [cc/cc]
Bulk density pfa [g/cc]
Thickness of the aquifer B (m]
Seepage velocity Vs (rn/yr]
Longitudinal dispersion coefficient Dx (nr/yr]
Lateral dispersion coefficient Dy [nr/yr]
Vertical dispersion coefficient DZ Im2/yr]
Aquifer temperature T [ฐC1
Recharge rate into the plume q [m/yr]
Chemical-Specific Parameters
Effective first-order decay coefficient x$ (1/yr)
Distribution coefficient Kd (cc/g)
Biodegradation rate x [1/yr]
39
-------
Table 4-1. INPUT PARAMETERS REQUIRED FOR THE SATURATED ZONE TRANSPORT
MODULE* (concluded)
Parameter Unit
Receptor Well Location-Specific Parameters
Coordinates with respect to the source xp, yr, zr [m]
Time value at which concentration is
required tr (yr]
*A few of the parameters are derived from variables shown in Table 4-2.
40
-------
Table 4-2. ADDITIONAL DATA REQUIRED TO COMPUTE INPUT PARAMETERS FOR THE
SATURATED ZONE TRANSPORT MODULE
Parameter
Unit
Input Variables to Compute Source-Specific Parameters
Area of the land disposal facility
Infiltration rate through the facility
Input Variables to Compute Aquifer-Specific Parameters
Mean particle diameter of the porous medium
The hydraulic gradient
Longitudinal dispersivity
Transverse dispersivity
Vertical dispersivity
Input Variables to Compute Chemical-Specific Parameters
Reference temperature
Second-order acid-catalysis hydrolysis rate constant
at reference temperature
Second-order base-catalysis hydrolysis rate constant
at reference temperature
Neutral hydrolysis rate constant at reference
temperature
\ [m2]
If lm/yr]
d [cm]
S (m/ml
oL(m]
aT(m]
Trrc]
K/ U/mole-yr]
a
Kbr U/mole-yr]
T
pH of the aquifer
Normalized distribution coefficient for organic carbon
Fractional organic carbon content
Input Variables to Compute Receptor Uell Location-Specific Parameters
Radial distance to well
Angle to the well location
pH [log 10 mole/i]
fQC (dimensionlessl
R 1m]
* (degrees]
41
-------
4.5.1.1 Depth of Penetration of Source-
Infiltration of water through the facility results 1n the development
of a plume below the facility. This 1s shown 1n Figure 4-2. The thickness
of this plume depends on the vertical d1spers1v1ty of the media. An
estimate of 'H' can thus be obtained using the following relationship:
, LI.
H = (2av L)* + B(l - exp (- y^J)) (4-22)
where:
a., = the vertical dispersivity [m]
L = the length scale of the facility i.e., the dimension of the
facility parallel to the flow direction [m] (if L is not known,
an estimate can be obtained from Equation 4-23)
B = the thickness of the saturated zone [m]
In Equation 4-22 the first term represents the thickness of the plume due
to vertical dispersion and the second term represents the thickness of the
plume due to the vertical velocity below the facility resulting from
infiltration. The detailed derivation of the second term is presented in
the attached document (Appendix B). While implementing this alternative,
it is necessary to specify that in the event that the computed value of H
is greater than B, the thickness of the source, H, 1s set equal to B.
If L is not known, an estimate can be obtained by taking the square
root of the area, i.e.,
(4-23)
The above assumes that the waste disposal facility has a square shape.
42
-------
PLAN VIEW
Contaminant Plume
SECTION VIEW
Monitoring
-.Well
Ground Surface
Water Table
Aquifer
B
,?9W?9WWW?99Sซ^^
Figure 4-2. A Schematic of the Waste Facility and Leachate Migration
Through the Unsaturated and Saturated Zones
43
-------
4.5.1.2 The Spread of the Gaussian Source--
The standard deviation of the gausslan source 1s a measure of the
spread of the source and can be estimated as:
o = W/6 (4-24)
where:
W = the width scale of the facilityI.e., the dimension of the
facility orthogonal to the groundwater flow direction (m)
Dividing by 6 implies that 99.86 percent of the area under the gausslan
source is flanked by the width, of the facility. Note that 1f the
orientation of the facility with respect to the groundwater flow direction \
is not known, then a measure of width of the facility can be obtained by
taking the square root of the area, as in Equation 4-23.
4.5.1.3 Maximum Source Concentration-
Having obtained both H and o (using Equations 4-22 and 4-24,
respectively) based on physical considerations, the mass balance equation
can be used to compute CQ, i.e.,
A I.
Z - C , (4-25)
(20* Vs e H o
or
CQ = (NMF) Cl (4-26)
In Equation 4-26 the factor NMF can be thought of as representing a near-
field dilution effect or the effect of mixing below the facility; this
factor, based on purely physical considerations, should be less than or at
most equal to unity to ensure that C < C . Note that the use of
44
-------
Equation 4-26 presents the problem of estimating C . A conservative
maximum value of C& would be the solubility of the contaminant in water.
4.5.1.4 Other Parameters Required-
Computation of the source-specific parameters using the above method,
Equations 4-22, 4-24, and 4-26, requires knowledge of the area of the
facility; the infiltration rate through the facility; aquifer-specific
variables including seepage velocity, porosity, longitudinal dispersivity
and depth of the aquifer; and chemical-specific adsorption coefficient.
These are discussed in the following section.
4.5.2 Aquifer-Specific Parameters
The model requires nine aquifer-specific parameters listed in Table 4-
1. These can be input directly or computed using the variables listed in
Table 4-2 and the relationships presented below.
4.5.2.1 Porosity
In the absence of user-specified distribution for porosity, it can be
calculated from the particle diameter using the following empirical
relationship (Federal Register Vol. 51, No. 9, pp. 1649, 1986):
9 = 0.261 - 0.0385 ln(d) (4-27)
where d = the mean particle diameter [cm].
4.5.2.2 Bulk Density
The soil bulk density directly influences the retardation of solutes
and is related to the soil structure. An exact relationship between the
soil porosity, particle density and the bulk density can be derived (Freeze
and Cherry 1979). Assuming the particle density to be 2.65 g/cc, this
relationship can be expressed as:
45
-------
Pb = 2.65(1 - e) (4-28)
where ob the bulk density of the son (g/cc).
4.5.2.3 Seepage Velocity
The seepage velocity 1s related to the aquifer properties through the
Carey's law. Assuming a uniform, saturated porous medium, the magnitude of
the seepage velocity can be expressed as:
Vs = -*f- (4-29)
where:
K = the hydraulic conductivity of the formation [m/yr]
S = the hydraulic gradient [m/m]
Note that in general, the hydraulic gradient 1s a function of the local
topography, groundwater recharge volume and location, and the volume and
location of groundwater withdrawals. Further, it may also be related to
the porous media properties.
4.5.2.4 Hydraulic Conductivity
In the absence of site-specific measurements, the hydraulic conduc-
tivity can be calculated using approximate functional relationships. One
such relationship included in the model, the Karman-Cozney equation (Bear
1979), can be expressed as:
a3 2
6 d (4-30)
M9x2 IA
where:
46
-------
K = the hydraulic conductivity [cm/s]
o = the density of water [kg/m3]
g = acceleration due to gravity (m/s^l
7
u = the dynamic viscosity of water [N-s/nr]
d = mean particle diameter [cm]
In Equation 4-30 the constant 1.8 Includes a unit conversion factor. Both
the density of water (p) and the dynamic viscosity of water are functions
of temperature and are computed using regression equations presented 1n CRC
(1981). Note that at 15ฐC, the value of log/I.8vl 1s about 478.
4.5.2.5 Dispersion Coefficients
The model computes the longitudinal, lateral and vertical dispersion
coefficients as the product of the seepage velocity and longitudinal (a.),
transverse (a,) and vertical (a..) dispersltles. A literature review
Indicated generalized theory to describe dispersities, although a strong
dependence on scale has been noted (Gelher et al. 1985). In the absence of
user-specified values, the model allows two alternatives.
Alternative 1, shown in Table 4-3(a), 1s based on the values presented
in the Federal Register, Vol 51, No. 9, pp. 1652 (1986). These are:
aL = 0.1 xf (4-31)
<4'32>
where xr ป the distance to the recepter well [m]. Under this option, ov is
assumed to be uniformly distributed in the range of .0125 to .1 of the
longitudinal dlspersivityi.e., in the range of 0.38 to 1.52 m.
Alternative 2 allows a probabilistic formulation for the longitudinal
dispersivity as shown in Tables 4-3(a) and 4-3(b) (personal communication
to Or Zubair Saleem, Gelhar (1986)]. The longitudinal dlspersivity is
47
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Table 4-3(a). ALTERNATIVES FOR INCLUDING DISPERSIVITIES ?.N THE
GROUNDWATER MODEL
DispersivHy
Alternative 1
Existing Values
Alterna iv'a 2
Gelhar' , Recommendation
aL (m)
OT (m)
av (m)
aL/aT
ฐL/aV
15.24*
5.07*
0.38-1.52
3
10-40
(uniform
distribution)
ProbablMs
(see TabU
aL/8
aL/160
8
160
tic Formulation
4-3(b))
* Assumes xr = 152.4 m (500 ft). Also see Equation 4-33.
Table 4-3(b). PROBABILISTIC REPRESENTATION OF LONGITUDINAL DISPERSIVITY
FOR DISTANCE OF 152.4 m
Class
1
aL (m)
Probability
Cumulative
Probability
0.1-1
0.1
0.1
1-10
0.6
0.7
10-100
0.3
1.0
48
-------
assumed to be uniform within each of the three intervals shown in Table 4-
3(b). Note that these values of longitudinal dlspersivity shown are based
on a receptor well distance of about 152.4 m. For other distances, the
following equation is used:
aL(x) = OL(X = 152)(x/152.4)ฐ'5 (4-33)
The transverse and vertical dispersivity are assumed to have the
following values:
ay = oL/8 (4-34)
av = aL/160 (4-35)
4.5.2.6 Recharge Rate into the Plume--
Recharge rate into the plume can be calculated by a variety of ways.
One possibility is to use the HELP (Hydrologlc Evaluation of Landfill
Performance) model without any engineering controls (leachate collection
system or a liner) to simulate the water balance for natural conditions.
Results of such an analysis have been presented by E.G. Jordon Co. (1985
and 1987), and are included as default values in the model. This recharge
1s assumed to have no contamination and hence dilutes the groundwater
plume.
4.5.3 Chemical-Spedfie Parameters
The model requires three chemical-specific parameters (see Table 4-1)
that can be computed from the variables listed In Table 4-2. Note that
chemical degradation within the saturated zone 1s limited to hydrolysis,
and the by-products of hydrolysis are assumed to be non-hazardous.
49
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4.5.3.1 Hydrolysis Rates
The acid-catalysed, neutral and base-catalysed hydrolysis r are all
Influenced by groundwater temperature. This effect 1s often quantified
using the Arrhenius equation, which yields:
KI.n.b ' i.
where:
T = temperature of the groundwater [ฐC1
Tr = reference temperature [ฐC]
Tr T
Karb and K^ b = the second-order acid- and base-catalysis hydrolysis
rate at temperature Tr and T respectively U/mole-yr)
Tr T
Knr and Kn * the neutral hydrolysis rate at temperatures Tr and T
respectively [1/yr]
Rg ป universal gas constant [1.987E-3 kcal/deg-mole]
Ea = Arrhenius activation energy (kcal/mole)
Note that, using the generic activation energy of 20 kcal/mole
recommended by Wolfe (1985), the factor Ea/Rg has a value of about 10,000.
The acid-catalyzed, base-catalyzed and neutral hydrolysis rate
constants can be combined (Mill et al. 1981) to yield the composite, first-
order, dlssolved-phase hydrolysis rate:
xl
where:
[H*] = the hydrogen 1on concentration (mole/i]
[OH") = the hydroxyl Ion concentration (mole/il
50
-------
Note that (H*) and [OH~] can both be computed from the pH of the aquifer,
I.e.,
IH+] = 10-PH (4-38)
[OH-] ซ 10~(14-PH) (4-39)
For the case of sorbed-phase hydrolysis, evidence suggests that base-
neutralized hydrolysis can be neglected and that the acid-neutralized
hydrolysis rate 1s enhanced by a factor of a. Thus, the effective sorbed-
phase decay rate can be expressed as:
X2 a'^lH+l + Kj (4-40)
I
where a = acid-catalysis hydrolysis rate enhancement factor for sorbed
phase with a typical value of 10.0.
4.5.3.2 The Distribution Coefficient
The relationship most suited for relating the chemical distribution
coefficient, K
-------
4.5.4 Receptor Uell Location-Specific Parameters
Figure 4-3 1s a schematic of the receptor well location relative to tht.
waste facility. The location of the well 1s determined by specifying the
radial distance to the well, angle between the plume centerline and the
radial location of the well measured counterclockwise, and the depth of
penetration of the well. Thus knowing these, the cartesian coordinates of
the well location are computed as:
xr = R cos * (4-42)
yr = R sin * - (4-43)
where:
R = the radial distance to the well [m]
iiป = the angle measured counterclockwise from the plume center line
(degrees)
*r. yr = the cartesian coordinates of the well location {m]
In addition to the x and y coordinates, the z coordinate 1s specified
as an input parameter and the well is assumed to have a single slot at that
depth.
52
-------
WASTE
FACILITY
PLAN VIEW
Waste Facility
VVVVVVVVV9VVQ<^^
SECTION VIEW
Figure 4-3. A Schematic of the Well Location
53
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SECTION 5
UNCERTAINTY ANALYSIS
5.1 INTRODUCTION
As described in Section 1, EPACML simulates the movement of
contaminants emanating from a waste disposal facility to a downgradient
receptor well. The model includes algorithms that simulate the movement of
the contaminant within the unsaturated zone and the saturated zone based on \
a number of user-specified parameters. These Include chemical-specific,
aquifer-specific, source-specific and receptor well location-specific
parameters.
Typically the values of these parameters are not known exactly due to
measurement errors and/or Inherent spatial and temporal variability.
Therefore, it is often more appropriate to express their value in terms of
a probability distribution rather than a single deterministic value and to
use an uncertainty propogation model to assess the effect of the
variability on the model output.
This section presents the uncertainty propagation method Implemented in
the composite model. The method allows a quantitative estimate of the
uncertainty 1n the downgradient receptor well location due to uncertainty
in the model Input parameters.
5.2 STATEMENT OF THE PROBLEM AND TECHNICAL APPROACH
The objective of the uncertainty analysis/propagation approach is to
estimate the uncertainty in the receptor well concentration given the
54
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uncertainty 1n the input parameters. Alternatively, the objective is to
estimate the cumulative probability distribution of the downgradient well
concentration given the probability distribution of the input parameters.
Thus if Cw represents the downgradient well concentration and X represents
the vector of all model inputs:
Cw - g(X) (5-1)
where g represents the semi -analytical, composite model. Note that some or
all of the components of X may vary in an uncertain way, i.e., they are
random variables defined by cumulative probability distribution
functions. Thus the goal here is to calculate the cumulative distribution
function F- (C'w) given a probabilistic characterization of X. Note that
' ) iswdefined as:
w
Fc (C'J Probability (Cw < C'J (5-2)
where C1 is a given downgradient well concentration.
To our knowledge, five main methods have been proposed to evaluate
Fr (C1 ). These include:
Lw w
1. First-Order and First-Order-Second-Moment Analysis (FO, FOSM);
2. Monte Carlo Simulation (MC);
3. Discretization of Probability Distributions (DPD);
4. Response Surface Analysis (RS); and
5. Rackwitz-Fiessler Method and its variants (RF).
55
-------
These methods were evaluated by U.S. EPA in order to select the most
appropriate method for uncertainty analysis using the composite model. The
selection criteria included:
1. Computation efficiency, measured by the number of response
calculations required to achieve a given level of precision in
estimation of the output statistic (in this case, the 85th
percentile of the output distribution).
2. Accuracy in evaluation of the output statistice.g., a specified
percentile value.
3. Generality of application, so that a number of modules and input
conditions, and all sources of uncertainty, can be accommodated by
the same uncertainty-propagation method.
4. Simplicity of usage, measured by the number of parameters that must
be specified by the user for each application.
5. Completeness of the information produced, which may include only the
mean and variance of the output distribution or may be the whole
distribution, and which may or may not contain information useful
for uncertainty decomposition.
6. Flexibility with respect to input distributions, so that the method
would be able to accommodate a number of different Input
distributions.
Using the above criteria, a qualitative comparison of the various
uncertainty-propagation methods is included in Table 5-1.
With the above criteria in mind and knowledge of the composite model,
the Monte Carlo Analysis method was selected. This approach is simple,
55
-------
Table 5-1. QUALITATIVE COMPARISON OF UNCERTAINTY-PROPAGATION METHODS
UNCERTAINTY PROPAGATION METHOD
Criterion FO, FOSM MC
Computational *** **
Efficiency
Accuracy * *
Generality ** ***
Simplicity *** ***
Information Produced ** *
Variation of FX ** **
DPD RS RF
** *
* ** **
* * *
*** ** *
*+ ** ***
** **+ *
\
no star - criteria not satisfied
* - criteria partially satisfied
** - criteria satisfied in general
*** - criteria satisfied
57
-------
unbiased and completely general. Also, the method 1s especially attractive
when there are many Input variables that are randomly distributed, because
the efficiency does not depend on the dimensionality of the Input vector.
Further, since the composite model 1s analytical, 1t would not be very
expensive to run a large number of independent executions of the model to
achieve satisfactory confidence limits on the downgradlent well
concentration. Details of this method are discussed below.
>- \
5.3 THE MONTE CARLO ANALYSIS TECHNIQUE
Figure 5-1 illustrates the Monte Carlo method used in this analysis.
Given a set of deterministic values for each of the input parameters, Xj,
X2, . . . ,Xn, the composite model computes the downgradlent receptor well
concentration Cw, i.e.:
Cw = g (Xlf X2. X3 Xn) (5-3)
Application of the Monte Carlo simulation procedure requires that *t
least one of the input variables, Xj, . . . ,Xn, be uncertain and the
uncertainty represented by a cumulative probability distribution. The
method involves the repeated generation of pseudo-random values of the
uncertain input variable(s) (drawn from the specified distribution and
within the range of any imposed bounds) and the application of the model
using these values to generate a series of model responses, I.e., values of
Cw. These responses are then statistically analyzed to yield the
cumulative probability distribution of the model response. Thus,
various steps Involved in the application of the Monte Carlo sim
technique Involve:
1) Selection of representative cumulative probability dlstr-s-::-
functions for the relevant input variables
58
-------
Model Paramaters/Data
EPACML Model
Cw=g(x)
Model Output
2
EE
o
INPUT VALUES
2
cc
LL
2
O
INPUT VALUES
O
LLJ
CC
INPUT VALUES
2
cc
o
Cw
OUTPUT VALUES
INPUT VALUES
INPUT DISTRIBUTIONS
OUTPUT DISTRIBUTION
Figure 5-1. A Schematic Description of the Monte Carlo Method
of Uncertainty Analysis
59
-------
ii) Generation of a pseudo-random number from the distributions
selected 1n (1). These values represent a possible set of
values for the Input variables
111) Application of the model to compute the derived Inputs and
output(s)
1v) Repeated application of step: (11) and (111)
v) Presentation of the series of output (random) values generated
in step (iii) as a cumulative probability distribution function
(CDF)
vi) Further analysis and application of the cumulative probability
distribution as a tool for decision making
5.4 UNCERTAINTY IN THE INPUT VARIABLES
The variables required by the composite model can be broadly classified
into two different sets that exhibit different uncertainty characteris-
tics. These are:
i) Variables that describe the chemical, biochemical, and
toxicological properties of the hazardous constituent. Examples
of these variables include the octanol-water partition
coefficient; add-, neutral, and base-catalyzed hydrolysis rate;
soil adsorption coefficient; etc.
ii) Variables that describe the environmental properties of .the
various media and impact the fate and transport of the pollutant
within each medium. Examples of these variables Include the
groundwater velocity, soil porosity, organic carbon content,
dispersivity values, etc.
60
-------
Uncertainty in the first set of variables primarily arises due to
laboratory measurement errors or theoretical analysis used to estimate the
numerical values. In addition to experimental precision and accuracy,
errors may arise due to extrapolations from controlled (laboratory)
measurement conditions to uncontrolled environmental (field) conditions.
Further, for some variables, semi-empirical methods are used to estimate
the values. In this case, errors 1n using the empirical relationships also
contribute to variability 1n the model outputs.
Uncertainty 1n the second set of variables, Identified above, may
Include both measurement and extrapolation errors. However, the dominant
source of uncertainty 1n these 1s the inherent natural (spatial and
temporal) variability. This variability can be Interpreted as site-
specific or within-site variation in the event that the model is used to
analyze exposure due to a specific land-disposal unit. Alternatively it
can represent a larger-scale (regional/national) uncertainty 1f the model
is used to conduct exposure analysis for a specific chemical or specific
disposal technology on a generic, nationwide or regional basis. Note that
the distributional properties of the variables may change significantly
depending upon the nature of the application.
Whatever the source of uncertainty, the uncertainty preprocessor
developed for the composite model requires that the uncertainty be
quantified by the user. This implies that for each Input parameter deemed
to be uncertain, the user select a distribution and specify the parameters
that describe the distribution.
The current version of the preprocessor allows the user to select one
of the following distributions:
i) Normal
11) Lognormal
i11) Uniform
61
-------
iv) Log uniform
. v). Exponential
\1) Empirical
vi1) Johnson SB
1. _i
The first two distributions require the user to specify the mean and
the variance. The third and the fourth require minimum and maximum
values. The fifth distribution requires only one parameter: the mean of
the distribution. For the empirical distribution, the user is required to
input the coordinates of the cumulative probability distribution function
(minimum 2 pairs, maximum 20 pairs), which is subsequently treated as a
piece-wise linear curve. Finally, the Johnson SB distribution requires
four parameters: mean, variance, the lower and upper bounds.
Of the above seven distributions, the characteristics of the first six
are readily available in literature (Benjamin and Cornell 1970). However
details of the Johnson SB distribution may not be as readily available.
Consequently a brief description of this distribution 1s presented below.
This distribution represents a transformation applied to the random
variable such that the transformed variable 1s normally distributed. The
specific transformation is:
SB: Y = tn(ig'jjj) (5-5)
where:
in = natural logarithm transformation
X = untransformed variable with limits of variation from A to B
Y = the transformed variable with a normal distribution
Selection of the Johnson SB distribution for a sample data set is
accomplished by plotting the skewness and kurtosis of the sample data as
shown in Figure 5-2. The location of the sample point indicates the
62
-------
Surface Imp. Area Distributions (in sq. meters) for Selected Waste Volumes
Percentiles
1E-03
1
5
10
15
25
40
50
60
75
85
90
95
99
100
Waste Volumes (in cubic yards)
20,000
1124
1547
2856
4044
4517
5480
7216
8213
9404
1.116E+04
1.319E+04
1.445E+04
1.708E+04
2.115E+04
2.502E+04
25,000
1369
2037
3671
4613
5510
6757
8575
1.005E+04
1.152E-I-04
1.348E+04
1.595E+04
1.803E+04
2.236E+04
2.721E-f-04
4.194E+04
30,000
1801
2101
4180
5349
6335
7912
9873
1.172E+04
1.330E+04
1.580E+04
1.901E+04
2.129E+04
2.524E+04
3.113E+04
4.926E+04
40,000
2321
3511
5814
7249
8632
1.073E+04
1.290E+04
1.468E-f04
1.717E+04
2.104E+04
2.459E+04
2.744E+04
3.252E+04
4.140E+04
5.220E+04
50,000
3080
4672
6949
9189
1.076E+04
1.265E+04
1.603E+04
1.879E+04
2.116E-f04
2.536E+04
3.006E+04
3.397E+04
3.964E+04
4.665E+04
7.734E+04
60,000
3321
5268
8451
1.110E-f04
1.248E+04
1.542E+04
1.953E+04
2.227E+04
2.600E+04
3.126E+04
3.627E+04
3.938E+04
4.578E+04
6.124E+04
9.085E+04
80,000
3823
5137
1.051E+04
1.314E+04
1.570E+04
1.882E-I-04
2.377E+04
2.758E+04
3.184E-I-04
3.833E+04
4.561E-f04
5.186E+04
6.003E+04
7.349E+04
9.627E+04
90,000
4242
6469
1.074E+04
1.524E+04
1.743E+04
2.090E+04
2.654E+04
3.047E+04
3.399E+04
4.278E+04
5.233E+04
6.044E+04
6.937E+04
8.988E+04
1.300E-ป-05
Percentiles
1E-03
1
5
10
15
25
40
50
60
75
85
90
95
99
100
100,000
4656
6349
1.265E+04
1.602E+04
1.908E+04
2.281E+04
2.943E+04
3.400E+04
3.823E+04
4.721E-f04
5.728E + 04
6.568E + 04
7.313E+04
9.423E+04
1.143E-f-05
Waste Volumes (in cubic
150,000
6660
8172
1.755E+04
2.413E+04
2.791E-f04
3.459E+04
4.403E+04
5.097E-ป-04
5.739E+04
6.909E+04
8.179E + 04
9.044E+04
1.046E-f-05
1.289E-f05
1.677E+05
f 200,000
8587
1.491E+04
2.490E+04
3.050E+04
3.591E+04
4.459E+04
5.569E-I-04
6.453E+04
7.259E+04
8.560E+04
1.031E+05
1.136E+05
1.320E+05
1.678E-f05
[ 2.630E-f 05
250,000
1.046E+04
1.804E+04
2.793E+04
3.794E-f04
4.412E-ป-04
5.426E+04
6.874E+04
8.065E+04
9.083E+04
1.104E+05
1.283E+05
1.428E+05
1.629E+Q5
2.112E+05
i\531E+05
300,000
1.228E+04
1.799E+04
3.508E+04
4.248E+04
5.090E+04
6.046E+04
7.905E+04
9.194E+04
1.042E+05
1.244E+05
1.504E+05
1.719E+05
2.024E+05
2.369E+05
3.093E+05
yards)
400,000
1.584E+04
2.707E+04
4.371 E+ 04
5.697E+04
6.656E+04
7.849E+04
1.036E+05
1.226E+05
1.379E+05
1.670E+05
2.041E+05
2.298E+05
2.587E+05
3.066E+05
4.851E+05
500,000
2.233E+04
2.655E+04
4.748E+04
6.856E+04
7.960E+04
9.492E+04
1.205E+05
1.385E+05
1.609E-f05
1.918E+05
2.303E+05
2.545E+05
2.974E+05
3.810E+05
4.856E+05
-------
SJ
J2
to
|ซ4
x:
<ป<:
Line for
student t
distribution
Region for Johnson
SQ Distribution
Normal
Distribution
0,. SKEWNESS
Source: McGrath at al. 1973
Figure 5-2. Selecting a Johnson Distribution from Skewness and Kurtosis
62
-------
distribution fซr the sample data. For additional details of the Johnson
distribution, ;ht reader 1s referred to McGrath and Irving (1973) and
Johnson and Ko .z (1970).
5.5 THE RANDOM MJMBER GENERATOR
Having selected the distribution for the various Input parameters, the
next step 1s the generation of random values of these parameters. This
requires the use of pseudo-random number generating algorithms. There
exist numerous non-proprietary subroutines that can be used to generate
random numbers. A number of these are comparable in terms of their
computational efficiency, accuracy and precision. The specific routines
Included 1n the composite code are those described by McGrath and Irving
(1973). The performance of these algorithms has been checked to ensure
that they accurately reproduce the parameters of the distributions that are
being sampled as described below.
In order to test the algorithms, two sets of runs were made. For Run
1, 500 random numbers were generated; for Run 2, 1000 random numbers were
generated. For the five distributions tested, the Input parameters and the
results are shown in Tables 5-2(a) and (b). In each case, the output
statistics for the randomly generated variables closely match the Input
values. Additional testing using the bootstrap method has been performed
by the Agency to estimate the number of runs.
For Run 2, the randomly generated variables were arranged 1n ascending
order and the cumulative probability distributions of the generated
variable plotted and compared with the theoretically exact/expected
distributions. These are shown in Figures 5-3 to 5-7. Visual inspection
of these figures further testify to the accuracy of these algorithms.
Note that more rigorous statistical tests could be used to further test
the accuracy of the algorithms. However, the above simplified analysis has
provided sufficient proof of the accuracy of the results and Indicated that
these algorithms satisfactorily reproduce the input statistics and
distributions of the variables.
64
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Table 5-2(a). RESULTS OF RANDOM NUMBER GENERATOR TEST FOR 500 VALUES
Normal
LogNormal
Exponential
Empirical1
Uniform
Input Statistics
Observed Output Statistics
mean std. dev.
10.00 1.00
10.00 1.00
10.00 10.00
18.855
10** 25***
mean std. dev. max
10.00 1.05 13.40
9.97 0.98 13.20
9.80 9.67 53.70
18.54 25.54 99.20
17.4 ~ 24.9
min
6.90
7.60
0.00
0.10
10.1
Cumulative Probability
Values
Expected Mean
**Minimum Value
***Maximum Value
0.0 0.1 0.7 1.0
0.1 1.0 10.0 100.0
18.855
65
-------
Table 5-2(b). RESULTS OF [ANDOM -NUMBER GENERATOR TEST FOR 1000 VALUES
Input Statistics
Observed Output Statistics
Normal
LogNormal
Exponential
Empirical1
Uniform
mean std. dev.
10.00 "1.00
10.00 1.00
10.00 10.00
18.855
10** 25***
mean
9.99
9.97
9.77
21.57
17.41
std. dev.
1.00
0.99
10. .04
28.16
4.26
max
13.60
14.50
86.20
99.80
25.00
min
7.25
7.26
0.15
0.11
10.00
Cumulative Probability
Values
Expected Mean
**Minimum Value
***Maximum Value
0.0 0.1 0.7 1.0
0.1 1.0 10.0 100.0
18.855
DC
-------
14
Figure 5-3. Comparison of the Exact and the Generated Cumulative Frequency
Distribution for a Normally Distributed Variable
67
-------
10 11 12 13 14 15
Figure 5-4. Comparison of the Exact and the Generated Cumulative Frequency
Distribution for a Log Normally Distributed Variable
68
-------
75
o
Figure 5-5. Comparison of the Exact and the Generated Cumulative Frequency
Distribution for an Exponentially Distributed Variable
69
-------
ฃ
5
'Is
Figure 5-6. Comparison of the Exact and the Generated Cumulative Frequency
Distribution for an Empirically Distributed Variable
-------
I
T5
.9.
.8
.7
.6
.5
.4,
.3.
.2.
.1.
10
12
14
16 18
Values
20
22
24
Figure 5-7. Comparison of the Exact and the Generated Cumulative Frequency
Distribution for a Uniformly Distributed Variable
71
-------
5.6 ANALYSIS OF THE MODEL OUTPUT
Using the randomly generated parameter values, the imdel 1s used to
estimate values of concentrations at various points 1orated downgradient
from the waste facility. Thus, 1f Cw represents the normalized (with the
leachate concentration at the waste facility) receptor w&ll concentration
calculated by the model assuming that the leachate concentration at the
waste disposal facility is unity, and Cj 1s the (health-based maximum
allowable) threshold concentration for the chemical at the receptor well,
the maximum allowable leachate concentration at the waste facility can be
back-calculated using:
CT
Ca * ^ (5-6)
w
Note that the maximum allowable leachate concentration defined by Equation
5-6 is the leachate concentration for which the downgradient receptor well
concentration does not exceed the threshold concentration. Alternatively,
rsr <5-7>
Lw LT
Equation 5-7 states that the reciprocal of the computed normalized
concentration represents the maximum allowable ratio of leachate
concentration to the threshold concentration. Thus, for example, if the
simulated normalized concentration Cw = 0.05, Equation 5-7 Implies that the
maximum allowable leachate concentration from the landfill could be 20
times the threshold value for the chemical. Note that both Cw and CT are
chemical specific.
The above back-calculation procedure and the Monte Carlo analysis
allows the maximum leachate concentration to be couched 1n a probabalistic
framework. Thus for each chemical, the maximum allowable leachate
concentration is chosen by considering the percentage of feasible
nationwide sites, p, for which the resulting downgradient concentrations
are in compliance with established standards. This is further explained
below.
72
-------
Application of the above Monte Carlo method results 1n an array of
values for the model output (normalized concentration), each representing a
feasible waste disposal facility-environmental scenario. These values are
statistically analyzed to derive the cumulative probability distribution
function as shown 1n Figure 5-8. The cumulative probability distribution,
Fc (C ), together with the allowable threshold value, CT, and the back
w
calculation procedure (Equations 5-6 and 5-7), provide the Information
necessary to calculate the maximum allowable leachate concentration. In
particular the value of leachate concentration C that leads to pfc of the
sites in compliancei.e., the receptor well concentration 1s less than or
equal to the threshold concentrationis:
e, -TJ- <5-8>
where C- 1s the p percentile concentration obtained from the cumulative
distribution function of the downgradient well concentration. Note that
for the current regulation, the maximum allowable leachate concentration
C , is chosen such that at least p = 85% of the sites are 1n compliance.
5.7 IMPLEMENTATION OF THE MONTE CARLO SIMULATION PROCEDURE
The immediate objective of the Agency 1s to run the composite model in
the Monte Carlo mode and develop the chemical-specific cumulative frequency
distribution of the normalized downgradient well concentration that is
representative of nationwide uncertainty 1n the model parameters. For
policy development/analysis purposes, the Agency plans to select a specific
(e.g., 85th) percentile of the normalized concentration and compute the
maximum leachate concentration using Equation 5-8. The percentile is
selected from a cumulative distribution of the normalized concentrations
that are representative of nationwide variation 1n the model input
parameters. This nationwide variation is represented by dividing the
73
-------
J
o
u.
o
u.
O
u
c
u.
u:
K
<
D
O
1.0
0.9-
0.8-
0.7-
0.6-
C.5-
CX-
0.3-
0.2-
C.l-
0 0
CHEMICAL 1
I I I I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7. 0.8 0.9 1.0
NORMALIZED CONCENTRATION, Cw*
Figure 5-8. Typical Results Obtained Using EPACML in the
Monte Carlo Mode
Normalized with respect to source concentration
74
-------
nation into nine hydrogeologic settingseach with a different combination
of unsaturated soil type and infiltration rate. Other Inputse.g.,
aquifer-, chemical-, and receptor well-specific parametersare considered
the same for each of these nine settings.
For each chemical, nine Monte Carlo simulations using the composite
model each representative of a hydrogeologic setting and described above
are conducted. Data used for the saturated zone transport computations are
presented in Section 4. The model results, normalized concentrations at
the downgradient well, were used to derive the cumulative probability
distribution function for each soil type. These Individual distributions
were then combined together using weighting factors for the hydrogeologic
settings (relative nationwide occurrence of each hydrogeologic setting) to
estimate the composite distribution based on the total probability theorem.
Thus, the composite probability of a concentration C' is given by:
9
FC^ <:). I FCC,- C'JDP, (5-9)
1=1
where
C'w = a specified concentration value
Fc (Cw ซ C'w) * probability that the composite (nationwide)
normalized concentration is less than or equal
* C'w
F(CW = C'JI) ป probability that the concentration is less
than or equal to C'w for hydrogeologic setting I
P! ซ probability of occurrence of hydrogeologic setting I
Having thus derived FC(CW)the composite nationwide cumulative
probability distributionthe maximum leachate concentration for a
specified percentile can be obtained and interpreted for regulatory
purposes as described in Section 5.2 and Equation 5-8.
The composite model code, EPACML, Includes an uncertainty post-
processor that can be used to derive the cumulative distribution
75
-------
and specified percent!les of that function. Further, printer plots of the
cumulative frequency distribution of the concentration at the receptor we!
location can also be obtained.
76
-------
SECTION 6
DEFAULT INPUT DATA FOR EPACML
6.1 INTRODUCTION
The EPACML model requires five groups of data; chemical-specific data,
source-specific data, unsaturated zone flow data, unsaturated zone
transport data, and aquifer-specific data. A brief discussion of each data
group and the values used for the base case simulation for each of the
variables within the group is given below.
6.2 CHEMICAL-SPECIFIC DATA GROUP
The chemical-specific data group contains the parameters required to
calculate the overall decay rate and the retardation coefficient of the
chemical being simulated for the unsaturated and the saturated zones.
Table 6-1 shows the parameters in the chemical-specific data group for a
conservative chemical. Each of the parameters 1s discussed below.
6.2.1 Decay Coefficient
The overall decay coefficient for a chemical is the weighted average of
the dissolved and sorbed phase decay coefficients as discussed 1n
Section 4.2. The dissolved and the solid phase decay coefficients are
derived from values of chemical specific hydrolysis rate constants, and the
pH, temperature, bulk density and porosity of the aquifer. (The latter are
included in the aquifer-specific data group and discussed in Section 6.6).
-------
Table 6-1. PARAMETERS INCLUDED IN THE CHEMICAL-SPECIFIC DATA GROUP OF EPACML MODEL
co
VARIABLE NAME
Solid phase decay coefficient
Dissolved phase decay coefficient
Overall cheir.ical decay coefficient
* Acid catalyzed hydrolysis rate
Neutral rate constant
Base catalyzed hydrolysis rate
Reference timperature
Noiralized distribution coefficient
Distribution coefficient
Biodegradation coefficient (sat. zone)
CHEMICAL
UNITS
1/yr
1/yr
1/yr
l/M-yr
1/yr
l/M-yr
C
ml/g
--
1/yr
SPECIFIC VARIABLES
DISTRIBUTION
DERIVED
DERIVED
DERIVED
CONSTANT
CONSTANT
CONSTANT
CONSTANT
CONSTANT
DERIVED
CONSTANT
PARAMETERS
MEAN STD DEV
.OOOEซ00
.OOOEป00
.OOOE'OO
.OOOEป00
.OOOEป00
.OOOE'OO
25.0
.000ฃป00
.219
.OOOE+00
.OOOEป00
.OOOEป00
.OOOE+00
.0006*00
.OOOE+00
.OOOEซ00
.OOOE'OO
.OOOE'OO
.OOOEซ00
.OOOE+00
LIMITS
MIN MAX
.OOOE+00
.OOOE'OO
.OOOEป00
.OOOE*00
.OOOEป00
.OOOEซ00
.OOOE+00
.OOOEป00
.OOOE*00
.OOOE+00
.352E+05
.221Eซ09
.J58E+05
.OOOEป00
.0006*00
-OOOE*00
40.0
.OOOE+00
.166Eป05
100.
* Th.-se values vary depending on the chemical being simulated
-------
6.2.2 Chemical Specific Hydrolysis Rate Constants
Table 6-2 presents the values of the hydrolysis rates for a
conservative chemical, chlordane and chloroform, at a reference temperature
of 25ฐC.
6.2.3 Distribution Coefficient
The distribution coefficient is calculated as the product of the
normalized distribution coefficient and the fractional organic carbon
content in the aquifer. The normalized distribution coefficients used in
the simulations are given in Table 6-2. The value of organic carbon
content of the aquifer is discussed with the aquifer-specific data in
.Section 6.6.
6.2.4 Biodegradation Coefficient
For these simulations, biodegradation as a mechanism was neglected,
I.e., the biodegradation coefficient was set to zero.
6.3 SOURCE-SPECIFIC DATA GROUP
The source-specific data group describes the geometry, leachate rate
and contaminant source characteristics for the landfill. Table 6-3 shows
the parameters included in this group. A description of each parameter is
given below.
6.3.1 Infiltration Rate
Three different empirical cumulative probability distributions for
infiltration rate were used, each corresponding to a different cover soil
type for the landfill. These distributions were derived using the HELP
model (E.C. Jordan 1985 and 1987). Table 6-4 and Figure 6-1 present these
distribution.
79
-------
Table 6-2. CHEMICAL SPECIFIC PROPERTIES USED IN SIMULATIONS
Add
Catalyzed
Hydrolysis
(i/M-yr)
Base
Catalyzed
Hydrolysis
(i/M-yr)
Neutral
Rate
Constant
d/yrj
Normalized
Distribution
Coefficient
(ml/g)
Conservative Chemical
Chloroform
Chlordane
0.0
0.0
0.0
0.0
.21E+04
37.7
0.0
.23E-04
0.0
0.0
39.8
.331E+06
80
-------
Table 6-3. PARAMETERS INCLUDED IN THE SOURCE-SPECIFIC DATA GROUP OF EPACML MODEL
SOURCE SPECIFIC VARIABLES
CD
VARIABLE NAME
* Infiltration rate
* Area of waste disposal unit
Duration of pulse
Spread of contaminant source
* Recharge rate
Source decay constant
Initial concentration at landfill
length scale of facility
Width scale of facility
EMPIRICAL CUMULATIVE DISTRIBUTIONS
UNITS
m/yr
m 2
y
w/yr
1/yr
ปg/ 1
m
M
DISTRIBUTION
EMPIRICAL
NORM. TRANSF.
CONSTANT
DERIVED
EMPIRICAL
CONSTANT
CONSTANT
DERIVED
DERIVED
PARAMETERS
MEAN STD DEV
.510E-01
4.21
.100E+31
50.0
.510E-01
.OOOEป00
1.00
100.
100.
.500E-02
2.16
3.00
.OOOE*00
.500E-02
.OOOE+00
.100E-01
1.00
1.00
LIMITS
MIN
.100E-04
-.884
.100
.100E-02
.100E-04
.OOOE+00
.OOOE+00
1.00
1.00
MAX
1.00
12.3
.100E+31
.600E+05
1.00
10.0
10.0
.1006*06
.1006*06
Infiltration rate for silt loan soil cover
PROBABILITIES .000 .260
.801 .851 .865 .671
310
901
498 .548
905 .914
.624
.964
VALUES .0006+00 .1006-02 .JOOE-02 .5006-02 .100E-01 .530E-01 .890E-01
.127 .U7 .175 .185
Recharge rate for sandy IOM soil type
PROBABILITIES .000 .030
.590 .650 .700 .755
VALUES .OOOE+00 .1806-01 .3806-01
-22V .295 .310 .366
216
080
803
.660E-01
.401
231 .251
130 .260
833 .880
.267
.290
.930
.710E-01 .760E-01 .104
.475 .495
.638
674
980 1
.102
274
400
980 1
.142
.729
.726 .746
.000
.109
.787
.478 .498
.000
.771
124
.540
.147 .211
1.06
Inl 11 ir.it ion and recharge vary depending on cover soil type and unsaturated lone soil type respcctivly (Sections 6.3.1 and 6.3.5)
A:C.I v.irirs (or landfill or surface impoundment scenarios (Sect inn 6.3.?)
-------
Table 6-4. EMPIRICAL DISTRIBUTIONS USED TO REPRESENT INFILTRATION
RATE (m/yr) 'HP.OUGH SUBTITLE D LANDFILL
COVER SOIL TYPE
S1lt Loam
Cumulative
Probability
(*)
0.0
26.0
31.0
49.8
54.8
62.4
67.4
72.6
74.6
77.1
80.1
85.1
86.5
87.1
90.1
90.5
91.4
96.4
98.0
100.0
Rate
0.000
0.001
0.003
0.005
0.010
0.053
0..089
0.102
0.109
0.124
0.127
0.147
0.175
0.185
0.216
0.231
0.251
0.267
0.274
0.787
Sandy
Cumulative
Probability
0.0
3.0
8.0
13.0
26.0
29.0
40.0
47.8
49.8
54.0
59.0
65.0
70.0
75.5
80.3
83.3
88.0
93.0
98.0
100.0
Loam
Rate
(m/yr)
0.000
0.018
0.038
0.066
0.071
0.076
0.104
0.142
0.147
0.211
0.229
" 0.295
0.310
0.366
0.401
0.475
0.495
0.638
0.729
1.064
S1lty Clay
Cumulative
Probability
(*)
0.0
57.0
57.0
64.0
73.0
73.0
89.0
93.0
96.0
99.0
99.0
100.0
Loam
Rate
(m/yr)
2.54E-5
0.00762
0.0330
0.0508
0.0787
0.0991
0.129
0.152
0.191
0.211
0.246
0.688
82
-------
co
CO
s?
X
-s-ป
^~
* -ซ
0
JO
o
l_
Q_
0)
J3
D
|
O
90-
80-
70-
60-
50-
40-
30-
20-
10-
n ,
} u, ^^- "
.rVoa/ ^^^
lr** /
// /A"^^
// X
r ^
y A
j^ /
^*
/ o o silt loam
/ Silty Clay Loam
/ A A Sandy Loam
/
/
f
./
/
ฃ. 1 1 L_ 1 1
0.0
0.2 0.4 0.6 0.8 1.0
Infiltration Rate through Landfill (m/yr)
1.2
Rgure 61. Empirical Distribution Used to Represent the Infiltration Rate
through a Subtitle D Landfill
-------
6.3.2 Area of Facility
A transformed normal distribution was used to represent the area of the
landfill (U.S. EPA 1988). For this case, a normally distributed number
(AT) (with mean - 4.21, standard deviation of 6.16 and minimum and maximum
values of -.884 and 12.3, respectively) is first generated and then
transformed to the actual area using:
AW = ((AT * 0.08 + i)(l/ฐ-08) + Oe6j * 4047 (6>1)
where
AW = the area of the facility {m2]
AT = the normally distributed variable
2
4047 = converts acres to m
6.3.3 Duration of Pulse
All simulations were performed for steady-state, hence the duration of
the pulse was set to a very large number.
6.3.4 Spread of the Contaminant Source
The spread of the contaminant source in the saturated zone was
calculated as one-sixth of the facility width.
6.3.5 Recharge Rate
The ambient recharge rate was estimated using the same distributions as
the infiltration rates (see Table 6-4). Three different distributions were
used depending upon the unsaturated zone soil underlying the facility (also
see Section 6.5).
84
-------
6.3.6 Source Decay Constant
For the steady-state simulations presented 1n this report, the source
decay rate was set to zero.
6.3.7 Initial Concentration at Source
A continuous source with a constant concentration of unity was assumed.
Hence, the model output 1s the normalized concentration of the chemical at
the downgradient well.
6.3.8 Length Scale of the Facility
The length scale of the facility was calculated as the square root of
the area.
6.3.9 Width Scale of the Facility
The width scale of the facility was calculated as the square root of
the area.
6.4 UNSATURATED ZONE FLOW DATA GROUP
The unsaturated zone flow data shown in Table 6-5, consists of three
subgroups that Include the unsaturated zone control parameter group, tne
material variables and the functional variables. Data 1n each of these
groups is discussed below.
6.4.1 Control Parameter Subgroup
Table 6-5 lists the values assigned to the control parameters. !"<-:-
the depth of the unsaturated zone 1s randomly generated (see Section C.:.:,
the spatial discretization required for the numerical solution of t)e
unsaturated zone flow equation, was performed automatically by the mcc-?
85
-------
Table 6-5.
PARAMETERS INCLUDED IN THE UNSATURATED ZONE FLOW DATA GROUP OF
EPACML MODEL
UNSATURATEO ZONE fLOU MODEL PARAMETERS
(input parameter description and value)
NP - Total nuafoer of nodal points
NMAT - Number of different porous materials
KPROP - Van Genuchten or Brooks and Corey
IMSHGM - Spatial discretization option
Co
at
OPTIONS CKOSEN
^ar\ icnuchten functional coefficients
DATA FOR MATERIAL 1
VAOOSE ZONE MATERIAL VARIABLES
VARIABLE NAME
UNITS DISTRIBUTION
PARAMETERS
MEAN STD DEV
LIMITS
MIN
MAX
Saturated hydraulic conductivity
* Vadose zone porosity
* Air entry pressure head
Depth of the unsaturated zone
/yr
--
m
SB
CONSTANT
CONSTANT
EMPIRICAL
2.30
.410
.OOOE+00
6.10
24.7
.0006*00
.0006+00
1.00
.OOOE+00
.OOOE+00
.0006*00
.610
30.0
.500
1.00
366.
EMPIRICAL CUMULATIVE DISTRIBUTIONS
Depth ol the ur-ปซturated zone
Pซu8ABIi:ilCS .000 .050
.600 .6'jO .700 .750
VALUES .100E-01 .910 1.22
15.2 16.8 21.3
.100 .200 .250
.BOO .850 .900
1.8J 2.74 3.05
30.5 34.8 61.0
.300 .350
.950 .980 1
3.66 4.75
101. 183. _.
.400
l.OOO
6.09
366.
.450
.500
6.10
-------
Table 6-5.
PARAMETERS INCLUDED IN THE UNSATURATED ZONE FLOW DATA GROUP OF
EPACML MODEL (concluded)
DATA FOR MATERIAL 1
VADOSE ZONE FUNCTION VARIABLES
VARIABLE NAME
* Residual water saturation
Brook and Corey exponent. EN
* ALPHA coefficient
BEIA coefficient
UNITS DISTRIBUTION
SB
CONSTANT
SB
LOG NORMAL
PARAMETERS
MEAN STD DEV
.650E-01
.500
.700E-01
1.89
.740E-01
.100
.171
.155
LIMITS
MIN MAX
.OOOE+00
.OOOE+00
.OOOEซ00
1.55
.110
1.00
.350
3.00
* these values change depending on the underlying unsaturated lone.
co
-------
using procedures" described in U.S. EPA (1990), Thus the values of
parameters NP ar.'d IMSHGN a^e ignored. Further, the unsaturated zone is
considered to be homogeneous. The value of KPROP = 1 implies that van
Genuchten's soil characteristic relationship 1s to be used.
6.4.2 Material Variables Subgroup
This subgroup includes four variables. The values of the first three--
saturated hydraulic conductivity, vadose zone porosity and the air entry
pressure head are unsaturated zone soil type dependent. The specific
values for three different soils are shown in Table 6-6. The depth of the
unsaturated zone was generated using the empirical distribution presented
in Table 6-7 and Figure 6-2.
6.4.3 Functional Variables Subgroup
This subgroup includes four variables, all of which are unsatjrated
zone soil dependent. The specific values used are listed 1n Table 6-6.
Note that since the van Genuchten's relationship for the characteristic
curves was selected, the value of Brook and Corey exponent, ENN is
neglected by the model.
6.5 UNSATURATED ZONE TRANSPORT'DATA GROUP
The unsaturated zone transport data shown in Table 6-8, consists :' t-o
subgroups the control parameter supgroup and the vadose transport varia3>s
subgroup. The parameters within each group are discussed below.
6,,5.1 Control Parameter Subgroup
When the model is run in the steady-state with the depth of th*
unsaturated zone randomly generated, tne variables within this grw., .
ignored by the model. However, default values are printed in the -ซ. -
output file.
8?,
-------
8820087168 CON-I
Table 6-6. UNSATURATED ZONE FLOW MODEL PARAMETERS FOR DIFFERENT SOIL TYPES
CD
IO
Parameters
Variable Name Units
SILT LOAM
Saturated hydraulic cm/hr
conductivity
Vadose zone porosity
Residual water saturation
ALPHA coefficient
BETA coefficient
Air entry pressure head m
SILT CLAY LOAM
Saturated hydraulic cm/hr
conductivity
Vadose zone porosity
Residual water saturation
ALPHA coefficient
BETA coefficient
A1r entry pressure head m
SANDY LOAM
Saturated hydraulic cm/hr
conductivity
Vadose zone porosity
Residual water saturation
ALPHA coefficient
BETA coefficient
Air entry pressure head m
Limits
Distribution1
LOG NORMAL
CONSTANT
SB
LOG NORMAL
SB
CONSTANT
SB
CONSTANT
NORMAL
SB
NORMAL
CONSTANT
SB
CONSTANT
SB
SB
LOG NORMAL
CONSTANT
Mean
.343
.450
.680E-01
.190E-01
1.41
0
.170E-01
.430
.890E-01
.900E-02
1.24
0
2.30
.410
.650E-01
.700E-01
1.89
0
Std. Dev.
.989
.OOOE+00
.710E-01
.120E-01
1.63
2.92
.OOOE+00
.900E-02
.970E-01
.610E-01
,
24.7
.OOOE+00
.740E-01
.171
1.55
Min
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
1.00
--
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
1.00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
1.35
Max
15.0
.500
.110
.150
2.00
--
3.50
.500
.115
.150
1.50
-
30.0
.500
.110
.250
3.00
"
1 See Section 5.4 for a description of the distributions.
-------
Table 6-7. EMPIRICAL DISTRIBUTION USED TO REPRESENT THE'THICKNESS OF THE
UNSATURATED ZOi:E
Serial
Number
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
CunuUtive
Prot ability
(*)
0
5
10
20
25
30
35
40
45
50
60
65
70
75
80
85
90
95
98
100
Depth
()
0.01
0.91
1.22
1.83
2.74
3.05
3.66
4-. 75
6.091
6.101
12.20
15.24
16.77
21.34
30.49
34.76
60.98
106.71
182.93
365.85
90
-------
100
160 200 240
Thickness (m).
360 400
Figure 6-2. Empirical Distribution Used to Represent the Thickness of the
Unsaturated Zone
-------
Table 6-8.
PARAMETERS INCLUDED IN THE UNSATURATED ZONE TRANSPORT DATA GROUP
OF EPACML MODEL
VO
f\>
UNSATURATED ZONE TRANSPORT MODEL PARAMETERS
* NLAY
NTSIPS -
IADV
* ISOL
H
NTEL -
NGPTS -
' NIT
' 1 BOUND -
ItSCEN -
IHAX
* UlfUN
OPTIONS
Number of different layers used
Number of time values concentration calc
Type of transport solution
Type of scheme used in vadose zone
Stehfest terms or number of increments
Points in Lagrangian interpolation
Number of Gauss points
Convolution integral segments
Type of boundary condition
Time values generated or input
Max simulation time
Weighting factor
CHOSEN
1
20
1
1
18
3
104
2
1
1
10.0
1.2
Stehfest numerical inversion algorithm
Nondecaying continuous source
Computer generated times for computing concentrations
DATA FOR LATER 1
VADOSE TRANSPORT VARIABLES
VARIABLE NAME UNITS
Thickness of layer m
Longitudinal dispersivity of layer m
Fractional organic carbon matter
Bulk density g/cc
Biological decay coefficient 1/yr
DISTRIBUTION
CONSTANT
CONSTANT
SB
CONSTANT
CONSTANT
PARAMETERS
MEAN
6.10
.400
.250
1.60
.OOOE+00
STD DEV
1.00
.400E-01
7.54
.OOOE+00
.200E-01
LIMITS
MIN
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
MAX
500.
10.0
11.0
2.00
5.00
,i
-------
6.5.2 Vadose Transport Variable Subgroup
This subgroup consists of five parameters shown 1n Table 6-8. These
Include the thickness of the unsaturated zone, the longitudinal
d1spers1v1ty, bulk density, fractional organic carbon matter content, and
biological decay coefficient. For contaminant transport computations, the
unsaturated zone was simulated as a single layer of thickness equal to the
depth of the unsaturated zone generated as part of the unsaturated zone
flow data (Section 6.4.2). The longitudinal d1spers1v1ty and biological
decay coefficient were assigned constant values of 0.40m and 0.00,
respectively. Values of the fractional organic carbon matter content and
the bulk density are soil dependent. For the three soils used in the
simulations, the values are presented in Table 6-9.
6.6 AQUIFER-SPECIFIC DATA
The aquifer-specific input data used 1n the model are shown in
Table 6-10. The specific relationships used to derive porosity (nป), bulk
density (ob), hydraulic conductivity (K), seepage velocity (Vs) and
dispersivitles have been discussed in detail 1n Section 4.5.2. The source
of each of these data are discussed below.
6.6.1 Temperature
The data used for groundwater temperature are the same as used in the
January 16, 1986, Federal Register Notice and are presented 1n Table 6-10.
6.6.2 Groundwater pH
The groundwater pK distribution has been derived based on an analysis
of the STORET data. It is assumed that the groundwater 1s sufficiently
buffered to insure that the pH is not influenced by Input of contaminants
or changes in temperature.
93
-------
Table 6-9. VALUES OF BULK DENSITY AND FRACTIONAL ORGANIC CARBON MATTER USED
IN THE UNSATURATEO ZONE TRANSPORT MODEL
vO
Variable Name Units Distribution1
SANDY LOAM
Fractional organic -- SB
carbon matter
Bulk density g/cc CONSTANT
SILTY CLAY LOAM
Fractional organic -- SB
carbon matter
Bulk density g/cc CONSTANT
SILT LOAM
Fractional organic -- SB
carbon matter
Bulk density g/cc CONSTANT
Parameters
Moan Std.Dev.
.250 7.54
1.60
.26E-01 7.77
1.67
.39E+01 7.74
1.65
Limits
M1n Max
O.OE+0 11.0
O.OE+0 11.0
O.OE+0 11.0
1 See Carsel (1988) 5.3 for a description of the distributions.
-------
Table 6-10. PARAMETERS INCLUDED IN THE AQUIFER-SPECIFIC DATA GROUP OF EPACML MODEL
AQUIFER SPECIFIC VARIABLES
vo
en
VARIABLE NAME UNITS
Particle diameter cm
Aquifer porosity
Bulk density g/cc
Aquifer thickness
Source thickness (mixing lone depth)
Conductivity (hydraulic) ซ/yr
Gradient (hydraulic)
Groundwater seepage velocity M/yr
Retardation coefficient
Longitudinal dispersivity
Transverse dispersivity
Vertical dispersivity
Temperature of aquifer C
nH
Organic carbon content (fraction)
Distance to well
Angle off center degree
Well vertical distance
EMPIRICAL CUMULATIVE DISTRIBUTIONS
Well distance fro* site for landfill
PROBABILITIES .000 .030 .040
.400 .500 .600 .700 .800
VALUTS .600 13.7 19.8 45.7
fe*. *:/. 610 805. 9U.
DISTRIBUTION
LOG 10 UNIFORM
DERIVED
DERIVED
EXPONENTIAL
DERIVED
DERIVED
EXPONENTIAL
DERIVED
DERIVED
GELHAR
RATIO
RATIO
NORMAL
NORMAL
LOG NORMAL
EMPIRICAL
CONSTANT
UNIFORM
.050 .100
.850 .900
104. 152.
PARAMETERS
MEAN STD DEV
.6 JOE -03
.OOOEป00
1.64
78.6
6.00
.758Eป05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.
.OOOEป00
.OOOE+00
.150
.950
183.
.630E-04
.OOOE*00
.OOOE+00
78.6
.600
.758Eป04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOEป00
.500E-01
.200
.980 1.
244.
.116Eซ04 .122Eซ04 .137E*04 .152Eซ04
LIMITS
MIN MAX
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
152.
.OOOE+00
.OOOEป00
.100
.560
1.80
560.
10.0
.151Eป06
.100
.925Eป04
.352Eซ06
324.
41.0
250.
30.0
14.0
.100E-01
152.
90.0
1.00
250 .300 .350
000
305.
.161E+04
305.
ttrnarios
-------
6.6.3 Fractional Organic Carbon Content
The organic carbon content, foc, 1s used to determlre ihe distribution
coefficient, K^. Unfortunately, few if any comprehensive subsurface
characterizations of organic carbon content exist. In general the values
are low, typically less than .01. A low range for fQC was assumed, and the
distribution shape was determined by the distribution of maasured dissolved
organic carbon recorded as entries to EPA's STORE! data base.
6.6.4 Particle-Size Distribution
The data used for the particle-size distribution are the same as used
for the January 14, 1986, Federal Register and are presented in Table 6-10.
6.6.5 Hydraulic Gradient
The hydraulic gradient is a function of the local topography, ground-
water recharge, volumes and locations and the influence of withdrawals.
The probability distribution for the gradient is derived from a survey of
RCRA Part B permit applications.
6.6.6 Thickness of the Saturated Zone
The thickness of the saturated zone determines the maximum depth of the
plume as it moves downgradient. Literature values taken from measurements
and surveys conducted by the Agency were used to derive the distribution
for this parameter.
6.6.7 D1spersiv1ties
The longitudinal dispersivity was estimated using Gelhars empirica1
distribution. The transverse dispersivity was set equal to one-eighth
longitudinal dispersivity, and the vertical dispersivity was set equal to
the longitudinal dispersivity cr^iced by 160.
96
-------
6.6.8 Receptor Well Location-Specific Data
In order to uniquely specify the location of the monitoring point or
the receptor well location, the cartesian coordinates need to be
specified. As discussed 1n Section 4.5.4, the x and y coordinates are
obtained from values of the radial distance to the well and the angle
measured counterclockwise from the plume centerline (y = 0). A schematic
diagram is shown in Figure 6-3. An empirical distribution was used to
estimate the distance to the well. The values are shown in Table 6-11 and
Figure 6-4. This is based on a survey by the Agency.
The angle,
-------
WASTE
FACILITY
PLAN VIEW
R
Well Location
X r = R COS Q
yr =Rsinq
Waste Facility
VvV
SECTION VIEW
Data: R follows an empirical distribution (Table 6.9)
q uniformly varies between Oc and 90ฐ
xr and yr constrained to lie within approximate
dimensions of the plume
zr uniformly distributed within the saturated zone
Figure 6-3. Schematic of the Weil Location
98
-------
Table 6-11. EMPIRICAL DISTRIBUTION USED TO REPRESENT THE DISTANCE
TO WELL
Cumulative
Probability
%
0.0
3.0
4.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
50.0
60.0
70.0
80.0
85.0
90.0
95.0
98.0
100.0
Distance
to Well
(n)
0.6
13.7
19.8
45.7
103.6
152.4
182.9
243.8
304.79
304.81
365.7
426.7
609.6
804.6
914.4
1158.2
1219.1
1371.5
1523.8
1609.3
99
-------
CD
O
&
_>ป
15
o
JQ
0
ol
0>
5
3
E
3
O
iuu -
90-
80-
70-
60-
50-
40-
30-
20-
10-
0 <
^^^
/
/
^^
-s'
^s^
,/^
^ir
f
/
/
y
A
/^
v^
/
. /
S
1 I 1 1 1 1 I I I
P 1 1 1 1 1 1 1 1
0 200 400 600 800 1000 1200 1400 1600
Distance (m)
Figure 64. Empirical DistributiojMsed to Represent the Distance to Well
-------
7.0
REFERENCE CASE AND SENSITIVITY ANALYSES
7.1 REFERENCE CASE
A chemical-specific cumulative frequency distribution of the normalized
downgradient well concentration that is representative of nationwide
uncertainty in the model parameters was developed by running the EPACML
model in the Monte Carlo mode. Data used for this was presented in Section
6. The nationwide variation was obtained by dividing the nation into a
number of relatively homogeneous environmental settings. Each setting was
simulated using EPACML to obtain a cumulative distribution function of the
normalized concentration specific for that setting. These individual
distributions were combined using weighting factors for the environmental
settings (relative nationwide occurrence of each environmental setting) to
estimate the composite nationwide distribution based on the total
probability theorem. Details of the aggregation procedure are discussed in
detail in U.S. EPA (1990).
For the reference case, three different soil types were selected to
represent the nationwide variations in the unsaturated zone soil type.
Each of these soils was used to represent a soil type underlying a landfill
or soil used as the cover material for the landfill. This results in nine
different environmental settings. Further, 1t was assumed that
infiltration through the landfill should be less than the ambient.recharge
(see also EPA 1990). This eliminated three of the nine combinations
resulting in six feasible scenarios that are shown 1n Table 7-1 along with
their assigned weights, i.e., their nationwide occurrence.
101
-------
Table 7-1. WEIGHTS USED TO ESTIMATE THE COMPOSITE NATIONWIDE
DISTRIBUTION OF DAPS FOR LANDFILL SCENARIOS
Weight
Son Type Cover Soil f
Sandy Loam Sandy Loam 2.37
S1H Loam 8.72
S1lty Clay Loam 4.32
S1H Loam S1lt Loam 37.87
Sllty Clay Loam 18.73
S1lty Clay Loam Sllty Clay Loam 28.0
102
-------
Using the data presented in Section 6 and the six environmental
scenarios described above, EPACML simulations were conducted for the
reference case. The EPACML model results are 1n the form of normalized
concentrations. These concentrations are the inverse of the Dilution
Attenuation Factor (DAF). All the results presented in this chapter are in
terms of DAF. Results from the reference case simulations are shown in
Table 7-2.
7.2 SENSITIVITY ANALYSIS
EPACML model runs were conducted to test model sensitivity to
dispersivity, aquifer temperature, infiltration value, landfill area and
well location. Model results were found to be insensitive to aquifer
temperature. The two different dispersivity relationships presented in
Table 4.3a and b were simulated. Alternative 2 described in Table 4.3b
results in generally lower dispersivities and higher DAFs. Model
sensitivities to the value of infiltration, well location and landfill area
are discussed below.
7.2.1 Infiltration Rate
Contaminant transport in the saturated zone is not a direct function of
the infiltration rate. However, as discussed in Section 4.5.1.3, near
field dilution (see equations 4-25 and 4-26) is directly proportional to
infiltration. Since DAF equals the inverse of normalized concentration,
the relationship between Infiltration rate and DAF 1s non-linear. The
relationship between Infiltration rate and DAF 1s presented in Figure 7-1.
7.2.2 Location of Well
The method used to determine the location of the well was described 1n
Section 4.5. Briefly, the coordinates of the well location are computed
based upon user-specified values of radial distance to the well and the
angle iii, off the plume centerllne (the well can be located on either side
of the plume centerline). Two different sets of runs were conducted to
103
-------
Table 7-2. DILUTION/ATTENUATION FACTORS FOR DIFFERENT SCENARIOS FOR
REFERENCE CASE
Serial Unsaturated-
Number Zone Soil
1
2
3
4
5
6
Sandy Loam
Sandy Loam
Sandy Loam
Silty Clay Loam
Silty Clay Loam
Silt Loam
Composite
Cover Soil for
Estimating
Infiltration
Sandy Loam
Silt Loam
Silty Clay Loam
Silt Loam
Silty Clay Loam
Silty Clay Loam
Percentlle2
95 90 85
7.63
20.7
17.2
17.9
12.0
12.0
14.0
16.4
81.3
64.5
51.3
45.2
49.8
51.8
42.4
193
147
159
123
118
130
80
82.6
568
383
383
311
281
325 -x
Also governs the ambient recharge rate.
2 Dilution Attenuation Factor is the inverse of the normalized
concentration output from EPACML.
104
-------
350-
300-
250-1
0.6
Infiltration Rate (m/yr)
08
1.2
Figure 7-1. Sensitivity of EPACML Results to Infiltration Rate.
IPS
-------
test the sensitivity of this method: ii> was restricted to 45 degrees on
either s to 45 degrees results in a decrease in OAF of approximately
20%. At the 95 percentile value, there is only a 7% decrease, however. At
high percent!les the probability that the well is located near the plume
centerline increases, resulting in a decrease in the effect of angle
restriction.
Table 7-4 shows the effect of not restricting the well location to the -v
plume. If this restriction is removed, there is a large increase in DAP
due to the generation of many well locations outside the plume boundary.
This effect decreases for high percentiles, since for high percentiles,
there is a high probability the well is located near the plume centerline.
7.2.3 Area of Landfill
In EPACML, increasing the area of the landfill increases the mass
leaving the landfill. This causes an increase in the down gradient
concentration (or decrease in OAF). EPACML was run in deterministic mode
for six different areas. Table 7-5 and Figure 7-2 present the results from
these simulations. The results indicate that there is a non-linear
relationship between OAF and area as indicated by the approximate straight
line fit to the data on Figure 7-2 (which has log-log scales). Area
affects the downgradient concentrations in two ways, an Increase in area
results in an increase in near field dilution (see equation 4-26) and an
increase in the spread of the gaussian source (Section 4.5.1.2).
106
-------
Table 7-3. EFFECT ON OAF OF RESTRICTING ANGLE OFF PLUME CENTERLINE TO 45
DEGREES (well restricted to plume)
Percentlles
80 85 90 95
45 degrees 264 104 40.6 13.0
90 degrees 325 130 51.8 14.0
107
-------
Table 7-4. EFFECT ON DAF OF NOT RESTRICTING WELL TO PLUME
Percentlles
80 85 90 95
Not Restricted 8280 1580 239. 35.4
Restricted 325 130 51.8 14.0
% Change 2450 1115 361. 152.
108
-------
Surface Imp. Area Distributions (in sq. melcrs) for Selected Waste Volumes
Percentiles
1E-03
1
5
10
15
25
40
50
60
75
85
90
95
99
100
Waste Volumes (in cubic yards)
20,000
1124
1547
2856
4044
4517
5480
7216
8213
9404
1.116E+04
1.319E+04
1.445E+04
1.708E+04
2.115E+04
2.502E+04
25,000
1369
2037
3671
4613
5510
6757
8575
1.005E+04
1.152E+04
1.348E+04
1.595E+04
1.803E+04
2.236E+04
2.721E+04
4.194E+04
| 30,000
1801
2101
4180
5349
6335
7912
9873
1.172E+04
1.330E+04
1.580E+04
1.901E+04
2.129E+04
2.524E+04
3.113E+04
4.926E+04
40,000 1
2321
3511
5814
7249
8632
1.073E+04
1.290E+04
1.468E+04
1.717E+04
2.104E+04
2.459E+04
2.744E+04
3.252E+04
4.140E+04
5.220E+04
50,000
3080
4672
6949
9189
1.076E+04
1.265E+04
1.603E+04
1.879E+04
2.116E+04
2.536E+04
3.006E+04
3.397E+04
3.964E+04
4.665E+04
7.734E+04
60,000
3321
5268
8451
1.110E+04
1.248E+04
1.542E+04
1.953E+04
2.227E+04
2.600E+04
3.126E+04
3.627E+04
3.938E+04
4.578E+04
6.124E+04
9.085E+04
80,000
3823
5137
1.051E+04
1.314E-f04
1.570E+04
1.882E-I-04
2.377E+04
2.758E+04
3.184E+04
3.833E+04
4.561E+04
5.186E+04
6.003E+04
7.349E+04
9.627E+04
90,000
4242
6469
1.074E+04
1.524E+04
1.743E+04
2.090E+04
2.654E+04
3.047E+04
3.399E+04
4.278E+04
5.233E+04
6.044E+04
6.937E+04
8.988E+04
1.300E+05
Percentiles
1E-03
1
5
10
15
25
40
50
60
75
85
90
95
99
100
100,000
4656
6349
1.265E+04
1.602E-I-04
1.908E+04
2.281E+04
2.943E+04
3.400E+04
3.823E+04
4.721E-I-04
5.728E+04
6.568E+04
7.31 3E -1-04
9.423E+04
1.143E+05
Waste Volumes (in cubic
150,000
6660
8172
1.755E+04
2.413E+04
2.791E+04
3.459E+04
4.403E+04
5.097E+04
5.739E+04
6.909E+04
8.179E+04
9.044E+04
1.046E+05
1.289E+05
1.677E+05
200,000
8587
1.491E-I-04
2.490E-I-04
3.050E+04
3.591E+04
4.459E+04
5.569E+04
6.453E+04
7.259E+04
8.560E+04
1.031E+05
1.136E+05
1.320E+05
1.678E+05
2.630E+05
250,000
1.046E+04
1.804E+04
2.793E-I-04
3.794E+04
4.412E+04
5.426E+04
6.874E+04
8.065E+04
9.083E+04
1.104E+05
1.283E+05
1.428E+05
1.629E+05
2.112E+05
2.531 c +05
300,000
1.228E+04
1.799E+04
3.508E+04
4.248E+04
5.090E+04
6.046E+04
7.905E+04
9.194E+04
1.042E+05
1.244E-I-05
1.504E+05
1.719E+05
2.Q24E+05
2.369E+05
3.093E+05
yards)
400,000
1.584E+04
2.707E+04
4.371 E+ 04
5.697E+04
6.656E+04
7.849E+04
1.036E+05
1.226E+05
1.379E+05
1.670E+05
2.041E+05
2.298E+05
2.587E+05
3.066E+05
4.851F+05
500,000
2.233E+04
2.655E+04
4.748E+04
6.856E+04
7.960E+04
9.492E+04
1.205E+05
1.385E+05
1.609E+05
1.918E+05
2.303E+05
2.545E+05
2.974E+05
3.810E+05
4.856E+05
-------
Table 7-5. EFFECT ON OAF OF CHANGING AREA OF LANDFILL
Area
(Acres)
4
12
40
122
280
5250
80
1430
757.
323
149
77.5
13.5
Percent lies
85
709
332
136
56.8
35.5
7.81
90
223
148
51.8
23.9
14.5
4.44
95
67.1
34.6
15.0
7.58
4.85
2.14
109
-------
1000T-
1
o
tt>
^3
o
w 100-t
*"^ -i_
C
V
O
CL
x:
c
o
*3
3
-
10-!
f
4.
i
o"-.
-i41- h-f-f H ปป--+i --I- ii 11 1
10 100
.|J ------- 4 -
1000
1E4
Area (acres)
Rgure 7-2. Dilution Attenuation l^btor as a Function of Area of Landfill
-------
NOTATION
AW = Area of land disposal unit [nr]
B - Thickness of the saturated zone [m]
C * Concentration of the contaminant [mg/i]
Cj = Concentration of the contaminant 1n the leachate from the waste
facility or the bottom of the unsaturated zone [mg/i]
CQ = Maximum gausslan-source concentration [mg/z]
Cy - Health based threshold concentration [mg/il
d = Representative particle size for the porous media (cm]
Du = The longitudinal dispersion coefficient 1n the unsaturated zone
[mz/yr]
Dx, Dy, D2 = Hydrodynamlc dispersion coefficient in the x, y and z
directions in saturated zone [nr/yr]
DX*,D*,DZ* = Retarded hydrodynamic dispersion coefficient 1n the x, y
and z directions 1n the saturated zone [nr/yrl
Ea = Arrhenius activation energy (kcal/mole)
foc = Percent organic carbon in the saturated zone (g/gl
fom s Percent organic matter content [dlmenslonless]
FC(C') = Nationwide Composite Cumulative probability distribution function
w for normalized downgradient well concentration
H - Thickness of source within the saturated zone [m]
If - Infiltration rate through the land disposal facility [m/yrj
k^ = The relative hydraulic conductivity [dlmenslonlessj
K = Hydraulic conductivity for the saturated zone lra/yr]
KH = Distribution coefficient for chemical 1n the liquid and solid phase
[cc/g]
KHU s Tne contaminant distribution coefficient for the unsaturated zone
dV [cc/g]
111
-------
K = Normalized distribution coefficient for organic carbon [u/g]
Kv = The saturated hydraulic conductivity [m/yrj
i = The thickness of a layer
L = Dimension of the waste facility parallelto the direction of ground
water flow [m]
Lv a The thickness of the unsaturated zone (m)
Mfl ป Mass entering the saturated zone due to advection [kg/yr]
Md a Mass entering the saturated zone due to dispersion Ikg/yr]
M|_ = Mass leaching out of the facility [kg/yr]
My a Total mass, sum of advective and dispersive, entering the saturated
zone (kg/yr]
n = The number of homogenous layers within the unsaturated zone
[dimensionless]
Pj a Probability of occurrence of hydrogeologic setting I
q = Infiltration into the contaminant plume outside the waste facility
[m/yr]
Rg = Universal gas constant (1.987E-3 Kcal/8C-mole]
RS = Retardation factor for the saturated zone [dimensionless]
Ry = The unsaturated zone retardation factor [dimensionless]
s(t-T) = The unit step function with a value of unity for t > T and
zero for t < T [t and T are in years]
Se = The effective saturation [dimensionless]
Sw - The fractional saturation within the unsaturated zone [cc/cc]
W
Swr = The residual water saturation [dimensionless]
t = Elapsed time [yr]
T = Temperature of the saturated zone [ฐC]
TS = Duration of pulse source [yr]
Vs = Seepage velocity in the saturated zone [m/yr]
112
-------
V*s = Retarded seepage velocity 1n the saturated zone Im/yr]
Vy = The steady-state unsaturated zone seepage velocity [m/yr]
W = Dimension of the waste facility orthogonal to the direction of
groundwater flow (m)
xr = x coordinate of the receptor well [ml
x - Longitudinal coordinate direction [m]
y = Lateral coordinate direction [ml
yr = y coordinate of the receptor well [ml
z = Vertical coordinate pointing downwards [ml
zr = z coordinate of the receptor well [ml
a = Soil-specific parameter [I/ml
i
o = Acid-catalysis hydrolysis rate enhancement factor for sorbed phase
[dlmensionless]
a. = Longitudinal (x-direction) dlspersivity [ml
OT = Transverse (y-direction) dispersivity [ml
o = The longitudinal dlspersivity [ml
av = Vertical (z-d1rect1on) dlspersivity [ml
B,Y * Soil-specific parameters [dlmenslonlessl
e - Effective porosity of the saturated zone [dlmensionless]
x. = Biological decay coefficient for the chemical in the saturated zone
b U/yr)
x ป Overall decay coefficient within the saturated zone [1/yrJ
x = The first-order degradation rate within the unsaturated zone
v ll/yr]
x. = Liquid-phase chemical decay coefficient [1/yrl
\~ - Solid-phase chemical decay coefficient [1/yrl
A = The source concentration decay rate [1/yrJ
113
-------
p. = Bulk density of the saturated soil [g/ccl
o. - The bulk density of the unsaturated zone [g/cc]
o - Standard deviation of the gaussian contaminant source [m]
4ป = The pressure head (m]
15 = The representative pressure head for the soil layer between z
and z - AZ
-------
REFERENCES
CRC (1981), Handbook of Chemistry and Physics. 62nd edition, CRC Press.
Bear, J. (1979), Hydraulics of Groundwater. McGraw H111, New York.
Benjamin, J.R., and C.A. Cornell (1970), Probability, Statistics, and
Decision for Civil Engineers. McGraw Hill, New York.
Brooks, R.H., and A.T. Corey (1966), "Properties of Porous Media Affecting
Fluid Flow." ASCE J. Irrlg. Drain. D1v. 92(2);61-68.
Carnahan, B., H.A. Luther, and J.O. Wllkes (1969), "Applied Numerical
Methods." John Wiley.
Carsel, R.F., and R.S. Parrish (1988), "A Method for Developing Joint
Probability Distribution of Soil-Water Retention Characteristics."
Water Resources Research 24(5):755-769.
Carsel, R.F., R.S. Parrish, R.L. Jones, J.L. Hansen, and R.L. Lamb (1985),
"Characterizing the Uncertainty of Pesticide Leaching 1n Agricultural
Soils." Draft submitted to J. Env. Qua!.
CRC (1981), Handbook of Chemistry and Physics. 62nd edition, CRC Press.
E.G. Jordan Co. (1985), "Analysis of Engineered Controls of Subtitle C
Facilities for Land Disposal Restrictions Determinations. Revised
Distribution of Leaching Rates." Draft Report ECJ Project No. 4756-01
prepared for Research Triangle Institute, North Carolina and USEPA,
OSW, Washington, D.C.
E.C. Jordan Co. (1987), Technical Memorandums dated June 2, 1987, and
September 1987, submitted to USEPA, OSW, Washington, D.C.
Electric Power Research Institute (1985), "A Review of Field Scale Physical
Solute Transport Processes in Saturated and Unsaturated Porous
Media." EPRI EA-4190. Project 2485-5. Palo Alto, California.
Enfield, C.G., et al. (1982), "Approximating Pollutant Transport to Ground
Water." Ground Water. Vol. 20, No. 6, pp. 711-722.
Federal Register (1986), "Hazardous Waste Management System: Land Disposal
Restrictions." USEPA. Vol. 15, No. 9.
115
-------
8820087REF CON-2
Freeze and Cherry (1979), "Groundwater." Prentice Hall, Englewoods Cliffs,
New Jersey.
Gelhar, L., et al. (1985), "A Review of Field Scale Physical Solute
Transport Processes in Saturated and Unsaturated Porous Media." EPRI
EA-4190. Project 2485-5. Palo Alto, California.
Haderman, J. (1980), "Radionuclide Transport through Heterogenous Media."
Nuclear Technology 47:312-323, February 1980.
Huyakorn, P.S., J.E. Buckley, and J.B. Kool (1988), "Finite Element and
Semi-Analytical Code for Simulating One-Dimensional Flow and Solute
Transport in the Unsaturated Zone." (Report Prepared for U.S. EPA
Office of Solid Waste. Prepared by HydroGeologic, Inc.)
Huyakorn, P.S., M.J. Ungs, L.A. Mulkey, and E.A. Sndicky (1987), "A Three-
Dimensional Analytical Method for Predicting Leachate Migration."
Groundwater Vol. 25 No. 5, September-October 1982.
Johnson, N.L., and S. Kotz (1970), Distributions in Statistics; Continuous
Univariate Distributions. Houghton Mifflin Company, Boston.
Karickhoff, S.W. (1984), "Organic Pollutant Sorptlon in Aquatic Systems."
ASCE J. Hyd. Div.. Vol. 110 (6), pp. 707-735.
Marino, M.A. (1974), "Distribution of Contaminants in Porous Media Flow."
Water Resources Research 10(5):1013-1018.
McGrath, E.J., and D.C. Irving (1973), Techniques for Efficient Monte Carlo
Simulation, Volume II. Random Number Generation for Selected
Probability Distributions. Report prepared for Office of Naval
Research. Project No. NR 366-076/1-5-72, Code 462.
Mill, T., et al. (1981), "Laboratory Protocols for Evaluating the Fate of
Organic Chemicals 1n Air and Water." Final Draft. Prepared for U.S.
EPA Technology Development and Applications Branch under EPA Contract
3JL
27.
No. 68-03-2227. Environmental Research Laboratory, Athens, Georgia.
Moench, A.F., and A. Ogata (1981), "Numerical Inversion of the Laplace
Transform Solution to Radial Dispersion in a Porous Medium." Water
Resources Research 17(l):250-252,
Perrier, E.R., and A.C. Gibson (1980), "Hydrologic Simulation on Solid
Waste Disposal Sites." SW-868. U.S. E.P.A. Cincinnati, OH.
Schroeder, P.R., et al. (1984), "The Hydrologic Evaluation of Landfill
Performance (HELP) Model: Volume 1 - Users Guide for Version 1, and
Volume II - Documentation for Version I." U.S. E.P.A/530-SW-84-009
and -010. U.S.E.P.A. Washington, D.C.
116
-------
Shamir, V.Y., and D.R.F. Harleman (1967), "Dispersion in Layered Porous
Media." Journal of Hydraulics Division. ASCE-HYs, pp. 237-260.
Stehfest, H. (1970), "Numerical Inversion of Laplace Transforms." Commun.
ACM 13(l):47-49.
Ungs, M.J. (1987), attached as Appendix B to "Background Document for EPA's
Composite Landfill Model (EPACML)."
van Genuchten, M. (1976), "A Closed Form Equation for Predicting the
Hydraulic Conductivity of Unsaturated Soils." Soil Sc1. Soc. J.
44(5):892-898.
van Genuchten, M., and W.J. Alves (1982), "Analytical Solutions of the One-
dimensional Convective-Dispersive Solute Transport Equation."
Technical Bulletin No. 1611, United States Department of Agriculture.
Wolfe, N.L. (1985), "Screening of Hydrolytic Reactivity of OSW
Chemicals." USEPA Athens Environmental Research Laboratory, Athens,
Georgia.
Woodward-Clyde Consultants (1990), User's Manual for EPA's Composite
Landfill Model (EPACML), Report Prepared for USEPA, OSW, Washington
D.C. Project No. 68-03-6304.
117
-------
APPENDIX A
DERIVATION OF THE ADVECTIVE AND DISPERSIVE
FLUX EMANATING INTO THE AQUIFER AT THE
SOURCE x = 0 FOR STEADY-STATE CONDITIONS
A-l
-------
De^v^ation of the Advective and Dispersive Flux Emanating Into the Aquifer at the
Source x ซ 0 for Steady-State Conditions
The steady-state concentration can be expressed as:
C*(x,y.z) - ฃ C*(x,y) + ACJ(x.y.z) (A.I)
where Cฃ and AC* are functions given by
C*-(x,y) = l/TQ | F*(x,y,v,B0)dv (A.2)
v=-ซ
\
ซ
ACJ(x,y,z; = if I i cos(^Jsin(^) /^ J F*(x,y.v,Bn)dv (A.3J
nปl
in which
,x
F*(x,y,v,6n) = Kl(Bn( +)) exp(' -) n-0.1.... (A.4J
x y
V*x
DJ. (A.7J
where K.(ซ) is a modified Bessel function of the second kind. The above equations
are the steady-state solution to the partial differential equation given by Eq. 4.1
and boundary conditions given by Eq. 4.4
A-2
-------
The following relationship is given on page 482, 13.914 of Gradshteyn and RyshnB
(1965) for the K, Bessel function.
'
For the special case of yซo and zปo, the Integral of F*(x,o,v,B_) with respect to v
can be performed with the aid of Eq. A.8.
0* ซ 'D* fT
v=-ซ n u=o xx
\
v=.
J cos(uvjexp(- -^7 )dvdu (A.9)
:.ซ
The last right hano side integral of Eq. A.9 can be evaluated as follows
cos(uv)exp(- ^r)dv = o/2n exp(- -=^-) (A.10)
ys~" -"Tป- - >
Substitute Eq. A.10 into Eq. A.9 'rt
F.i..o...ปB)d. - -- txpt- -ซ
" x 8
Substitution of Eq. A. 11 into Eqs. A. 2 and A. 3 will yield the solution shown by Eqs.
4.12a and 4.12b.
/ufD*y B0l
| exp[- -^ -x / ^ * -^]du (A. 12)
-o
A-3
-------
E ls1n(*Si) [ exp[- ^ -
n=1 n
where
2Co V*x
*) (A
x
and where 8Q and Bn are given by Eqs. A. 6 and A. 7.
At any point in the aquifer, the total mass flux density along the x axis is
defined as the sum of advected mass flux and dispersive mass flux densities [kg/(yr
m')].
flux density -fVJC*(x.y.z) -ซDX |-plx.y,z) (A. 15)
In order to compute the total mass flux m [kg/yr], the flux density is integrated
over a specified cross-sectional area. Since we are interested in measuring the
total mass flux that enters the aquifer along the x axis at the x=0 boundary, the
flux density is integrated over the saturated depth of the aquifer B and over the
infinite y axis plane. Hence
. B
m ' 6 J J (flux density)dydz at x - 0 (A. 16)
where 6 is the porosity [cc/cc].
Substitute Eq. A. 15 into Eq. A. 16
B ซ B
mn ซ 9Vi I I C*(o.y,z)dydz -6DV J | |^(o,y.z)dydz (A. 17)
9 s y... 2*0 x y z-0 ax
Substitute Eq. A.I, A. 2 and A. 5 into Eq. A. 17. The integration over the y variable
in C*(x,y,z) will be performed first.
A-4
-------
I C*lx.y,2)dy ป ง J C*(x,y)dy * J AC*(x,y.z)dy (A. 16?
ya.ซ ฐ ys-ซ y=-ซ **
Note the Integrations of Eq. A. 18 will be first done with the variable x not set
^i *^^^
equal to zero. The variable x can only be set to zero after the x dev/ative of Eq.
t* *
A. 16 Is performed.
The only term In C*, and AC* that contains a y variable In Eqs. A. 2 and A. 3 Is
that of SF*(x,y.v,Bn;. Then
J $F*(x,y,v,B)dy
n
%/
'ป -
X y y=-co
The right hano side Integral of Eq. A.19 can be solved as
f .X y-K - .X , _, _.u
I AC*(x,y,z)dy = 2-f- o/^ exp(^) I 1 Cos(iH)s1n(M)
ซ-ซ K x y x n=l D
x' v2
IP *
ป > A-5
xP) (A'20)
y=-ป ^
Substitute Eqs. A.19 ana A.20 into the integral of Ct
/x
_____ x ป ปD* +
I C*f(x,y)dy - C0xo/|p:: exp(^) I K' ฐ X ^ dV (A.21J
- 'Dxฐy x v-. , (xl ^
x y
and the Integral of AC*
P
V*.X
7 *.(/ซ({ฃ*ฃ) )
/T J X H dv (A.22J
-------
The right hand side Integrals of Eqs. A.21 and A.22 can be evaluated (p.705, I
6.596.3; Graoshteyn and Ryzhik, 1965).
? ^ A & F ) J /FD7 /T
| K. / pn x y dv m i / xj. exp{.x /V
' ' * p u
. (A.23)
vป-ซ / x1 . v'v "n
* "5* o*'
x y
Substitute the solution of Eq. A.23 into Eq. A.21 and A.22
V*x
Cr(x,y,)dy = C o/2n expljrrz - x/ *ฃ) (A.24)
y=-ซ x x
In order to evaluate the dispersive flux, we Mill need to evaluate the y integral of
the x derivatives of Ct and AC*. Differentiate Eqs. A. 24 and A. 25 with respect to x
ac*f(x,y) v* /"T v*x /
IT d^ = C00/H (% - /D^'PtlF ' X
ฐ tux x x x
dx * ~* wotv n nfc, n
ya-ซ ncl A A
V*x /T"
exp(^- - x/w) (A.27)
X X
Integrate Eqs. A.24 to A.27 with respect to the z variable between 0 and B
f I ,- V*sx /^
J / Ct(x,y)dydz C o/2ti B exp(^y - x/ 57) (A.26)
zซ0 ys-ซo x x
B
I I ACJ(x,y,z)dyd2 = 0 (A.29)
A-6
-------
? dC*f(x,y) _ V* /T V?x
J I -jjl dydz = Co/H 8(2^7-/^)exp(^- x) (A.30)
2=0 y=-ซ x ux *ux ux
J / |ฃc*p(x,y,z)dydz. 0 (A/31j
2ซ0 y "
The infinite series of Eqs. A.25 and A.27 vanish when integrated with respect to 2
since the integral of cos(nnz/B) is a sine function which vanishes at the limits 0
ana B.
Evaluate tne integral solutions of Equations A.26 to A.31 at x*0 and substitute into
Eq. A.17 in order to compute the total mass flux
B '
where
V* = V^/RS
ฐx = Dx/Rs
Substitute 3 from Eq. A. 6 into Eq^ A. 32 and rearrange to get the final solution for
the total steady state mass flux m [kg/yr].
m ซ H/2rT V^8oClll + mdf) (A. 33)
The first term of Eq. A. 33 represents the contribution of advective flux and the
second term m., 1s the fractional increase in the steady state mass flux due to the
contribution of dispersive flux.
/ ^
/ 1 + n*
(A. 34)
Note that the factor m f is equal to zero in the event that the dispersive flux is
neglected or if there is no decay.
A-7
-------
Reference
Gradshteyn, I.S. ano I.M. Ryzhik. 1965. Table of Integrals, Series ana Proaucts.
Academic Press, New York. 1056 pages.
A-8
-------
APPENDIX B
SIMPLIFIED ESTIMATION FOR DEPTH OF PENETRATION
B-l
-------
Simplified Estimation for Depth of Penetration
The depth of penetration of a solute plume that is developing under a
surface Impoundment can be estimated by separating the contribution of
advection and dispersion during solute transport
H
where H [L] is the depth of penetration. hftdy [L] is the vertically advected
component of the penetration depth and h_ [L] is the vertically dispersed
component of the penetration depth.
The advected depth h B, is the depth that a particle would be
Q Q V
transported under the influence of vertical advection
where V2 [L/T] is the vertical seepage velocity and T [T] is time of travel.
If the vertical seepage velocity is a constant with depth, then
v
However, under impoundments, the vertical seepage velocity varies
linearly with depth, with a maximum value at the top of the water table and
zero at the bottom of the aquifer. A numerical solution for a surface
Impoundment was performed using SEFTRAN, with the vertical velocity
variation under the Impoundment plotted in Figure 1. This variation can be
modeled mathematically as
V2 V20(l-z/B) (4)
where B [L] is the saturated aquifer thickness, z [L] 1s the depth from the
top of the water table and Y2Q [L/T] Is the maximum vertical seepage
velocity. V can be estimated from the net vertical recharge rate.
B-2
-------
Figure 1. Variation in the vertical seepage velocity with depth
25
50
I
100-
125
0.0 0.5 1.0 1.5 2.0 2.5
Vertical Seepage Vt-loclty, Vz (ft/yr)
3.0
SEFTRAN DATA
I 10 1n/yr
p 0.3
H0 132.5 ft
ML 118.0 ft
L 8000 ft
Kx 36500 ft/yr
KZ 3650 ft/yr
A * 200 ft
& zซ 10 ft
t
Ntt recharge rate
porosity
upstriwn water Ublt tltvitlon
dOMStPtvn MUr Ublt tltvitlon
distance bttMtn boundaries
horizontal hydraulic conductivity
vertical hydraulic conductivity
horizontal el awn t size
vertical element size
steady state
B-3
-------
As written, Eq. 2 cannot be Integrated since V2 Is not an explicit
function of tine. Consider the following differential equation for the
vertical seepage velocity
Tt ' vz(2)
Rearrange terms In Eq. 5 and Integrate to depth h
h.dv
T f(z) ]dt
2*0 V2' t*0
Substitute Eq. 4 Into Eq. 6 and Integrate to get
f8-ln(l-h /B) -T (7)
20
Solve for h dy from Eq. 7
v
The time of travel T [T] can be estimated as the time 1t takes for a
particle to be advected horizontally under an Impoundment of length L [L]
ffc- (9)
x
where Vx [L/Tj 1s the horizontal seepage velocity. Vx 1s assumed to be a
constant.
Prlckett, Naymlk and Lonnqulst (1981) estimate the magnitude of the
effect of dispersion on particle transport as
4loซg
'wrt
B-4
-------
where a, and ay [L] are the longitudinal and vertical d1spers1n1ties; V
[L/TJ 1s the magnitude of the seepage velocity; and A. and Ayert [L] are
the longitudinal and vertical dispersed distances that correspond to one
standard deviation of random transport. If the effect of the "horizontal
seepage velocity Is assumed to be much larger than that of the vertical,
then the dispersed depth Is estimated from Eq. 11 as
Hence, the total depth of penetration Is the sum of the vertically
advected and dispersed components. Substitute Eqs. 8 and 12 Into Eq. 1 to
obtain the total estimated depth of penetration
B(l-e ฐ ) + /&VT (13)
The solution to Eq. 13 needs to be checked when evaluating any
particular case so that a value of H greater than the aquifer thickness B is
not used. If the computed H Is greater than B, set H equal to B.
References
PMckett, T., T. NaymU and C. Lonnqulst. 1981. A random-walk solute
transport model for selected groundwater quality evaluations. Bulletin 65
Illinois State Water Survey, Department of Energy and Natural Resources,
Champaign, Illinois. 103 pages.
B-5
-------
EPACML-S0002.C
SAMPLE*
EPACML INPUT DATA FILES FOR LANDFILLS
*0nly the area distributions change with change in landfill volume
-------
UAIA
WASTE VOLUME = 20,000 cu. yds.
TEST RUN * 1 FOR A NONDEGRAOER
VERSION 3 OF EPACML MODEL
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Silty Clay Loam
*** ISOURC
OPTION- OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE I STEAD IOPEN IZCHK
5000 111001 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
*** CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
***
**
**********ซ******ป**************ป
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
********************************************************************************
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
370.
280.
.250E+08
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
*** SOURCE SPECIFIC VARIABLES
VARIABLE NAME UNITS
***
A***************************************************
DISTRIBUTION PARAMETERS
LIMITS
MEAN STD DEV MIN
************************************************
MAX
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
m/yr
m*2
yr
m
m/yr
1/yr
6 .0076200 .700E-02 .254E-04 .688
6 4.21 2.16 -.884 12.3
0 .100E+31 3.00 .100 .100E+31
-1 50.0 .OOOE+00 .100E-02 .600E+05
6 .760E-02 .760E-02 .254E-04 .668
0 .OOOE+00 .OOOE+00 .OOOE+00 10.0
-------
7 Initial concentration at landfill mg/l
8 Length scale of facility m
9 Width scale of facility m
END ARRAY
0 1.00 .100E-01 .OOOE+00 10.0
-1 100. 1.00 1.00 .100E+06
-1 100. , 1.00 1.00 .100E+06
EMPIRICAL DISTRIBUTIONS
ซ** I ICOUNT
1 12
.000 .570 .570 .640 .730 .730
.990 1.000
.254E-04 .762E-02 .330E-01 .508E-01 .787E-01 .991E-01 .129
.246 .688
*** I I COUNT
2 15
.001 .01 .050 .100 .150 .250
.850 .900 .950 .990 1.000
1292. 1490. 2640. 3356. 4001. 5280.
19675. 2.390E4 3.015E4 4.566E4 1.820E5
** I ICOUNT
5 12
.000 .570 .570 .640 .730 .730
.990 1.000
.254E-04 .762E-02 .330E-01 .508E-01 .787E-01 .991E-01 .129
.246 .688
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
.890 .930 .960 .990
.152 .191 .211
.400 .500 .600 .75
7186. 8538. 10056. 14147.
.890 .930 .960 .990
.152 .191 .211
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
** NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
XSTART XO OX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
* SATURATED MATERIAL VARIABLES
2.00
ปป* VARIABLE NAME UNITS
*
**ปป****ป**ปป*****ปปซป****
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
**********ป*******ซ********ป**ป*********ป*******
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
cm/hr
7
0
0
.170E-01
.430
.OOOE+00
2.921
.200E-01
.OOOE+00
.OOOE+00 3.50
.200 .700
.OOOE+00 1.00
-------
4 Depth of the unsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
*** I ICOUNT
4 20
.000 .050 .100 .200
.600 .650 .700 .750
.100E-01 .910 1.22 1.83
12.2 -15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE. PARAMETERS
*** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
*** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
A***********************************************************************************************************
1 Residual water content
2 Brook and Corey exponent, EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
1 .890E-01 .900E-02 .OOOE+00 .115
0 .500 .100 .OOOE+00 1.00
7 .900E-02 .970E-01 .OOOE+00 .150
1 1.236 .610E-01 1.00 1.50
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
*** NLAY
1
** UTFUN
1.200
NTSTPS
20
IADU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT
2
I BOUND
1
ITSGEN
1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
** UNSATURATED TRANSPOR VARIABLES
VARIABLE NAME
*
**
***************************************
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
A*******************************************************************
1 Thickness of layer
2 Longitudinal dispersivity of layer
3 Percent organic matter
ID
m
6.10
.400
.260E-01
1.00
.400E-01
7.77
.OOOE+00 500.
.OOOE+00 10.0
.OOOE+00 11.0
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
9/cc
1/yr
1.67
.OOOE+00
.200E-01
.200E-01
.795 2.12
.OOOE+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** AQUIFER SPECIFIC VARIABLES
VARIABLE NAME
ป**ซปป******ปซ*****ป*****ซ**
1 Particle diameter
2 Aquifer porosity
3 Bulk density
4 Aquifer thickness
5 Source thickness (mixing zone depth)
6 Conductivity (hydraulic)
7 Gradient (hydraulic)
8 Groundwater seepage velocity
9 Retardation coefficient
10 Longitudinal dispersivity
11 Transverse dispersivity
12 Vertical dispersivity
13 Temperature of aquifer
U pH
15 Organic carbon content (fraction)
16 Well distance from site
17 Angle off center
18 Well vertical distance
END ARRAY
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8
366. 427. 610.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
END ALL DATA
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
***********ป**ปซ*ปป****ซ*ป**************ปป****ป*******ป****
cm
--
g/cc
m
me depth) m
m/yr
:y m/yr
--
m
m
m
C
--
ic t ion)
m
degree
m
.050 .100 .150
.700 .800 .850
45.7 104. 152.
805. 914. .116E+04
5
-2
-1
3
-1
-2
3
-2
-1
8
8
8
1
1
2
6
4
4
.200
.900
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
OOOOE+00
0.50E+00
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00 .OOOE+00
0.50E-01
.250 .300
.950 .980 1.
183. 244. 305.
.122E+04 .
305.
O.OOE+00
350
000
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324,
41.0
250.
30.0
14.0
.100E-01
.160E+04
90.0
1.00
137E+04 .152E+04 .161E+04
ft-
-------
WASTE VOLUME = 20,000 cu. yds.
TEST RUN FOR NONDEGRAOER, SANDY LOAM
VERSION 3 OF EPACML MODEL
GENERAL DATA
*** CHEMICAL NAME FORMAT(80A1)
Sandy Loam SoiI Cover
* ISOURC
***OPTION OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE ISTEAD IOPEN IZCHK
5000 111001 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
*** CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
***
***
*ป******ป*ป****
UNITS DISTRIBUTION PARAMETERS
MEAN STD DEV
*******ปป*****************ป********ป****ซ***ป**ซ
LIMITS
MIN MAX
i************ป************
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/H-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
370.
280.
.250E+08
40.0
.331E+06
.1666+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
** SOURCE SPECIFIC VARIABLES
** VARIABLE NAME UNITS
**
******ป*****ป*ซป****ปป************ปซ***ป****
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
ปป********ปปป*****ซซ***ปป***********ป*********ป*
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
m/yr
wf2
yr
m
m/yr
1/yr
6
6
0
1
6
0
.700E-02 .700E-02 .OOOE+00 1.064
4.21 2.16 -.884 12.3
.100E+31 3.00 .100 .100E+31
50.0 .OOOE+00 .100E-02 .600E+05
.760E-02 .760E-02 .254E-04 .668
.OOOE+00 .OOOE+00 .OOOE+00 10.0
-------
7 Initial concentration at
8 Length scale of facility
9 Width scale of facility
END ARRAY
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
1 20
.000 . .030 .080
.590 .650 .700
.000 .018 .038
.229 .295 .310
** I I COUNT
2 15
.001 .01 .050
.850 .900 .950
1292. 1490. 2640.
19675. 2.390E4 3.015E4
* I I COUNT
5 20
.000 .030 .080
.590 .650 .700
.000 .018 .038
.229 .295 .310
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE
VFL UNSATURATED FLOW MODEL
CONTROL PARAMETERS
landfill
.130
.755
.066
.366
.100
.990
3356.
4.566E4 1
.130
.755
.066
.366
DATA
PARAMETERS
mg/l
m
ro
.260 .290
.803 .833
.071 .076
.401 .475
.150 .250
1.000
4001. 5280.
.820E5
.260 .290
.803 .833
.071 .076
.401 .475
.400
.880
.104
.495
.400
7186.
.400
.880
.104
.495
*** NP NMAT KPROP IMSGN
7 1
1 1
0
-1
1
1.00
100.
100.
.100E-01 .OOOE+00 10.0
1.00 1.00 .100E+06
1.00 1.00 .100E+06
.478
.930
.142
.638
.498
.980
.147
.729
.540
1.000
.211
1.064
.500 .600 .75
8538. 10056. 14147.
.478
.930
.142
.638
.498
.980
.147
.729
.540
1.064
.211
1.064
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50 2.00
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
*** SATURATED MATERIAL VARIABLES
VARIABLE NAME
*********************************
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
UNITS
DISTRIBUTION PARAMETERS
LIMITS
MEAN STD DEV MIN MAX
A**************************************************************************
cm/hr
2.296
.410
.OOOE+00
24.65
.200E-01
.OOOE+00
.OOOE+00 30.0
.200 .700
.OOOE+00 1.00
-------
4 Depth of the unsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
I 20
.000 .050 .100 .200
.600 - .650 .700 .750
.100E-01 .910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
*** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
*** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
**************ป****ซ********ป*ซ*****ซ*******ป****ป******ซ***ซ*ปปป*ซ*********ป******ป***ป***ป*ป*ซป*
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
.065
.500
.070
1.891
.074
.100
.171
.155
.OOOE+00 .11
.OOOE+00 1.00
.OOOE+00 .250
1.35 3.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
NLAY
1
UTFUN
1.200
NTSTPS
20
IAOU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT
2
I BOUND
1
ITSGEN
1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
*** UNSATURATED TRANSPOR VARIABLES
VARIABLE NAME UNITS
ป*ปป***ซ*ป*ป**ซป****ป******
1 Thickness of layer m
2 Longitudinal dispersivity of layer m
3 Percent organic matter
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
ปป*****ป*ป**************************ซ*ป***ซ**ป*
0
0
7
6.10
.400
.25
1.00
.400E-01
7.538
.OOOE+00 500.
.OOOE+00 10.0
.OOOE+00 11.0
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
g/cc
1/yr
1.6
.OOOE+00
.200E-01
.200E-01
.795 2.12
.OOOE+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** AQUIFER SPECIFIC VARIABLES
VARIABLE NAME
UNITS
*********
DISTRIBUTION PARAMETERS
MEAN STD DEV
A***********************************
LIMITS
MIN MAX
***************************
1 Particle diameter cm
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Groundwater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
14 pH
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center degree
18 Well vertical distance m
END ARRAY
5
2
1
3
1
2
3
2
1
8
8
8
1
1
2
6
4
4
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
45.0E+00
.500E+00
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
.500E-01
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
.OOOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324..
41.0
250.
30.0
14.0
.100E-01
. 160E+04
90.0
1.00
EMPIRICAL DISTRIBUTIONS
** I ICOUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8
366. 427. 610.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
.050 .100
.700 .800
45.7 104.
805. 914.
.150 .200 .250 .300 .350
.850 .900 .950 .980 1.000
152. 183. 244. 305. 305.
.116E+04 .122E+04 .137E+04 .152E+04 .161E+04
END ALL DATA
-------
LANDFILL INPUT DATA
WASTE VOLUME = 20,000 cu. yds.
TEST RUN FOR A NONOEGRADER, SILTLOAM
VERSION 3 OF EPACML MODEL
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Silty Loam Soil Cover
*** ISOURC
***OPTION' OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE ISTEAD IOPEN IZCHK
5000 111001 90.0
** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
** CHEMICAL SPECIFIC VARIABLES
** VARIABLE NAME
***
1 Solid phase decay coefficient
2 Dissolved phase decay coefficient
3 Overall chemical decay coefficient
4 Acid catalyzed hydrolysis rate
5 Neutral hydrolysis rate constant
6 Base catalyzed hydrolysis rate
7 Reference temperature
8 Normalized distribution coefficient
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone)
END ARRAY
UNITS
1/yr
Vyr
1/yr
l/M-yr
1/yr
l/M-yr
C
ml/g
--
1/yr
DISTRIBUTION PARAMETERS
MEAN STD DEV
-1
-1
-1
0
0
0
0
0
-2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
LIMITS
MIN MAX
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
. OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.22.1E+09
.358E+05
.000
.000
.OOOE+00
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
*** SOURCE SPECIFIC VARIABLES
ป** VARIABLE NAME
**
ซ*****ป****ป**************ป**
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
UNITS
****ป*ซ********ปป****ป**********
m/yr
yr
m
m/yr
1/yr
! I BUT I ON PARAMETERS
6
6
0
1
6
0
MEAN
.100E-01
4.21
.100E+31
50.0
.760E-02
.OOOE+00
STD DEV
.700E-02
2.16
3.00
.OOOE+00
.760E-02
.OOOE+00
UNITS
MIN
.000
-.884
.100
.100E-02
.254E-04
.OOOE*00
MAX
.787
12.3
.100E+31
.600E+05
.668
10.0
-------
7 Initial concentration
8 Length
9 Width
END ARRAY
EMPIRICAL
*ซ* |
.000
.801
.000
.127
I
.001
.850
1292.
19675.
*** I
.000
.801
.000
.127
at
landfill
scale of facility
scale of facility
DISTRIBUTIONS
I COUNT
1 20
.260
.851
.001
.147
I COUNT
2 15
.01
.900
.310
.865
.003
.175
.050
.950
U90. 2640.
2.390E4 3.015E4
I COUNT
5 20
.260
.851
.001
.147
.310
.865
.003
.175
.498
.871
.005
.185
.100
.990
3356.
4.566E4
.498
.871
.005
.185
mg/l
in
m
.548
.901
.010
.216
.150
1.000
4001.
1.820E5
.548
.901
.010
.216
.624
.905
.053
.231
.250
5280.
.624
.905
.053
.231
0
-1
-1
.674
.914
.089
.251
.400
7186.
.674
.914
.089
.251
1.00
100.
100.
.726
.964
.102
.267
.500
8538.
.726
.964
.102
.267
.
1
1
.746
.980
.109
.274
.600
10056.
.746
.980
.109
.274
100E-01 .1
.00 1
.00 1
.771
1.000
.124
.787
.75
14147.
.771
1.000
.124
.787
.100E+06
.100E+06
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
* NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
* SATURATED MATERIAL VARIABLES
2.00
***
*
VARIABLE NAME
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
UNITS
cm/hr
DISTRIBUTION PARAMETERS
LIMITS
MEAN
STD DEV
MIN
.343
MAX
***********
.989 .OOOE+00 15.0
.450 0.0 .200 .700
.OOOE+00 .OOOE+00 .OOOE+00 1.00
10
-------
4 Depth of the vrtsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
*** I ICOUNT
A 20
.000 .050 .100 .200
.600 .650 .700 .750
.100E-01 .910 1.22 1.83
12.2 *15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
**ป FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
*** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
*** MEAN STD DEV MIN MAX
A*************************************************************************************************************************
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
.068
.500
.019
1.409
.071
.100
.012
1.629
.OOOE+00 .11
.OOOE+00 1.00
.OOOE+00 .150
1.00 2.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
NLAY
1
WTFUN
1.200
NTSTPS
20
IADU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT
2
I BOUND
1
ITSGEN
1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
* UNSATURATED TRANSPOR VARIABLES
*** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
** MEAN STD DEV MIN MAX
ปป******ปซ**ป*ซซ*******ซซ*****ซซ**********a****ป*******ซซ*ป**ป****ป********ซป**ซ***ซ****ซ************ป
1 Thickness of layer m 0 6.10 1.00 .OOOE+00 500.
2 Longitudinal dispersivity of layer m 0 .400 .400E-01 .OOOE+00 10.0
3 Percent organic matter -- 7 .039 7.74 .OOOE+00 11.0
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
9/CC
1/yr
1.65
.OOOE+00
.200E-01
.200E-01
.795
.OOOE+00
2.12
5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
** AQUIFER SPECIFIC VARIABLES
*** VARIABLE NAME
*
*******ซ***********ปซ**ป****ซ
1 Particle diameter
2 Aquifer porosity
3 Bulk density
4 Aquifer thickness
5 Source thickness (mixing zone depth)
6 Conductivity (hydraulic)
7 Gradient (hydraulic)
8 Groundwater seepage velocity
9 Retardation coefficient
10 Longitudinal dispersivity
11 Transverse dispersivity
12 Vertical dispersivity
13 Temperature of aquifer
14 pH
15 Organic carbon content (fraction)
16 Well distance from site
17 Angle off center
18 Well vertical distance
END ARRAY
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
ปป**ป****ซ****ป****ปป******ป*ป**ซป****ปป****ป**ซ*ซซ***ปป*
cm
g/ec
m
m
m/yr
m/yr
m
m
m
C
m
degree
m
5
-2
-1
3
-1
-2
3
-2
1
8
8
8
1
1
2
6
4
4
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
.OOOE+00
.OOOE+00
.630E-04
.OOOE+00
.OOOE+00
78.6
6.00
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
.500E-01
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
.OOOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0.
250.
30.0
14.0
.100E-01
.160E+04
90.0
1.000
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8 45.7
366. 427. 610. 805.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
.050 .100 .150 .200 .250 .300 .350
.700 .800 .850 .900 .950 .980 1.000
152. 183. 244. 305. 305.
104.
914.
.116E+04 .122E+04 .137E+04 .152E+04 .161E+04
END ALL DATA
-------
LANDFILL INPUT DATA
WASTE VOLUME = 20,000 cu. yds
TEST RUN f 1 FOR NONDEGRADER, SCL.SNL
VERSION 3 OF EPACML MODEL
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Silty Clay Loam Cover, Sandy Loam Recharge
*** ISOURC
***OPTION OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE I STEAD I OPEN IZCHK
5000 111001 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
*** CHEMICAL SPECIFIC VARIABLES
*** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS
*** . MEAN STD DEV
A*********************************************************************************************
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
LIMITS
MIN MAX
ป**************ป**
.OOOE+00 .352E+05
.OOOE+00 .221E+09
.OOOE+00 .358E+05
.OOOE+00 370.
.OOOE+00 280.
.OOOE+00 .250E+08
.OOOE+00 40.0
.OOOE+00 .331E+06
.OOOE+00 .166E+05
.OOOE+00 100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
* SOURCE SPECIFIC VARIABLES
* VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
*** MEAN STD DEV MIN MAX
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
*ปป***ซป**ปซปซป*ป****ปปป****ปป**ซป**ป****ปปป**
m/yr
mA2
y
m
m/yr
Vyr
6
6
0
-1
6
0
.0076200
4.21
.100E+31
50.0
.760E-02
.OOOE+00
.700E-02
2.16
3.00
.OOOE+00
.760E-02
.OOOE+00
.254E-04
-.884
.100
.100E-02
.254E-04
.OOOE+00
.688
12.3
.100E+31
.600E+05
.668
10.0
13
-------
7 Initial concentration at landfill mg/l
8 Length scale of facility m
9 Width scale of facility m
END ARRAY
0 1.00 .100E-01 .OOOE+00 10.0
-1 100. - 1.00 1.00 .100E+06
1 100. 1.00 1.00 .100E+06
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
.000
.990
.254E-04
.246
*** I
.001
.850
1292.
19675.
*** I
.000
.59
.000
.229
1 12
.570
1.000
.762E-02
.688
I COUNT
2 15
.01
.900
1490.
2.390E4
I COUNT
5 20
.03
.65
.018
.295
.570
.330E-01
.050
.950
2640.
3.015E4
.08
.70
.038
.310
.640
.508E-01
.100
.990
3356.
4.566E4
.13
.755
.066
.366
.730
.787E-01
.150
1.000
4001.
1.820E5
.26
.803
.071
.401
.730
.991E-01
.250
5280.
.29
.833
.076
.475
.890
.129
.400
7186.
.40
.88
.104
.495
.930
.152
.500
8538.
.478
.93
.142
.638
.960
.191
.600
10056.
.498
.98
.147
.729
.990
.211
.75
14147.
.54
1.00
.211
1.064
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
*** NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
** SATURATED MATERIAL VARIABLES
2.00
*** VARIABLE NAME
*.
ซ*ปปปป**ป*ป*ป**.ปปปปปป*ปป**ซ**ปปป
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
UNITS
cm/hr
m
DISTRIBUTION PARAMETERS
MEAN STD DEV
>...*.............................***
7 2.296 24.65
0 .410 .200E-01
0 .OOOE+00 .OOOE+00
LIMITS
MIN MAX
.OOOE+00
.200
.OOOC+00
JO.O
.700
1.00
-------
4 Depth of the unsaturated zone
EMO ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
*** 1 ICOUNT
4 20
.000 .050 .100 .200
.600 .650 .700 .750
.100E-01 ..910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
* FUNCTIONAL COEFFICIENTS
ARRAY VALUES
*** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
MEAN
STD DEV
MIN
MAX
*ป*******************ปป*************ปซป*******ป*********ปป*********ซ****ป***ปป*ป****
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
.065
.500
.070
1.891
.074
.100
.171
.155
.OOOE+00 .11
.OOOE+00 1.00
.OOOE+00 .250
1.35 3.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
*** NLAY
1
** WTFUN
1.200
NTSTPS
20
IADU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT
2
I BOUND
1
ITSGEN
1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
*** UNSATURATED TRANSPOR VARIABLES
*
***
VARIABLE NAME
UNITS
1 Thickness of layer
2 Longitudinal dispersivity of layer
3 Percent organic matter
m
m
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
in*****************************************************************
0 6.10 1.00 .OOOE+00 500.
0 .400 .400E-01 .OOOE+00 10.0
7 .25 7.538 .OOOE+00 11.0
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
g/cc
1/yr
1.6
.OOOE+00
.2006-01
.200E-01
.795 2.12
.OOOE+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
* AQUIFER SPECIFIC VARIABLES
*** VARIABLE NAME
***
*ป***ป*****ป****ซ********
1 Particle diameter
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Groundwater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
U pN
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center degree
18 Well vertical distance m
END ARRAY
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
ป*ป*****ป***********ป*******************ป**ป******ป*************ป*
cm
5
2
1
3
1
2
3
2
1
8
8
8
1
1
2
6
4
4
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
45.0
0.50E+00
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
0.50E-01
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
O.OOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41. ff
250.
30.0
14.0
.100E-01
.160E+04
90.0
1.00
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8
366. 427. 610.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
.050 .100
.700 .800
45.7 104.
805. 914.
.150 .200 .250 .300 .350
.850 .900 .950 .980 1.000
152. 183. 244. 305. 305.
.116E+04 .122E+04 .137E+04 .152E+04 .161E+04
END ALL DATA
-------
TEST RUN * 1, NCNDEGRADER, SCL.SL
VERSION 3 OF EPACML MODEL
LANDFILL INPUT DATA
WASTE VOLUME = 20,000 cu. yds
GENERAL DATA
*** CHEMICAL NAME FORMAT(80A1)
Silty Clay Loam Cover, Silt Loam Recharge
*** ISOURC
OPTION OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE I STEAD IOPEN IZCHK
5000 111001 90.0
** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
* CHEMICAL SPECIFIC VARIABLES
*** . VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
* MEAN STD DEV MIN MAX
A******************************************************************************************
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
370.
280.
.250E+08
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
** SOURCE SPECIFIC VARIABLES
VARIABLE NAME
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
UNITS
DISTRIBUTION PARAMETERS
MEAN
STD DEV
LIMITS
MIN
MAX
****ป**ป****ปปป******************ซซ*****ป********ป*****
nv/yr
nt*2
yr
m
m/yr
1/yr
6
6
0
1
6
0
. .0076200 .700E-02 .254E-04 .688
4.21 2.16 -.884 12.3
.100E+31 3.00 .100 .100E+31
50.0 .OOOE+00 .100E-02 .600E+05
.760E-02 .7606-02 .254E-04 .668
.OOOE+00 .OOOE+00 .OOOE+00 10.0
-------
7 Initial concentration at landfill mg/l
8 Length scale of facility m
9 Width scale of facility m
END ARRAY
0 1.00 .100E-01 .OOOE+00 10.0
-1 100. , 1.00 1.00 .100E+06
-1 100. 1.00 1.00 .100E+06
EMPIRICAL DISTRIBUTIONS
** I I COUNT
.000
.990
.254E-04
.246
* I
.001
.850
1292.
19675.
** I
1 12
.570
1.000
.762E-02
.688
I COUNT
2 15
.01
.900
1490.
2.390E4
I COUNT
.570
.330E-01
.050
.950
2640.
3.015E4
.640
.508E-01
.100
.990
3356.
4.566E4
.730
.787E-01
.150
1.000
4001.
1.820E5
20
.730
.890
.930
.991E-01 .129
.152
.250
5280.
.400
7186.
.500
.960
.990
.191
.211
.600
8538. 10056.
.75
14147.
.000
.801
.000
.260
.851
.001
.147
.310
.865
.003
.175
.498
.871
.005
.185
.548
.901
.010
.216
.624
.905
.053
.231
.674
.914
.089
.251
.726
.964
.102
.267
.746
.980
.109
.274
.771
1.000
.124
.787
.127
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
*** NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
** SATURATED MATERIAL VARIABLES
2.00
VARIABLE NAME
*************************************ป
UNITS DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
*ปป*ซ**************ป*ป*****ป************ป***ซ************
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
cm/hr
.343
.450
.OOOE+00
.989
.200E-01
.OOOE+00
.OOOE+00 15.0
.200 .700
.OOOE+00 1.00
-------
4 Depth of the unsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
** I ICOUNT
4 20
.000 . .050 .100 .200
.600 .650 .700 .750
.100E-01 ..910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
*** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
.500
1.000
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
6.10
366.
*** VARIABLE NAME UNITS .DISTRIBUTION PARAMETERS LIMITS
*** MEAN STO DEV MIN MAX
*************************************************************************************************************************
1 Residual water content -- 7 .086 .071 .OOOE+00 .11
2 Brook and Corey exponent,EN - 0 .500 .100 .OOOE+00 1.00
3 ALFA coefficient 1/cm 2 .019 .012 .OOOE+00 .150
4 Van Genuchten exponent, ENN -- 7 1.409 1.629 1.00 2.00
END ARRAY
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
** NLAY
1
** WTFUN
1.200
NTSTPS
20
IADU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT IBOUND ITSGEN
2 1 1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
** UNSATURATED TRANSPOR VARIABLES
VARIABLE NAME UNITS
1 Thickness of layer m
2 Longitudinal dispersivity of layer m
3 Percent organic natter
DISTRIBUTION PARAMETERS
LIMITS
MIN
MAX
>***ซ
0
0
7
>*********
6.10
.400
.039
************
1.00
.400E-01
7.74
.oooc+oo
.OOOE+00
.OOOE+00
500.
10.0
11.0
-------
4 Bulk density of soil for .layer
5 Biological decay coefficient
END ARRAY
9/cc
1/yr
1.65
.OOOE+00
.200E-01
.200E-01
.795 2.12
.0006+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** AQUIFER SPECIFIC VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
*ซ*****ป**ป*********ป**********
1 Particle diameter cm
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Groundwater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
14 pH
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center degree
18 Well vertical distance m
END ARRAY
r**ซซ<
5
2
1
3
1
2
3
2
1
8
8
8
1
1
2
6
4
4
ป*ปป***ป*
.630E-03
.OOOE+00
1.64
78.6
6.00
.7586+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
45.0E+00
0.50E+00
*******
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
0.50E-01
ซ****ซ**ซi
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
O.OOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0
250.
30.0
14.0
.100E-01
. 160E+04
90.0
1.00
EMPIRICAL DISTRIBUTIONS
*** I I COUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8
366. 427. 610.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
.050 .100
.700 .800
45.7 104.
805. 914.
.150 .200 .250 .300 .350
.850 .900 .950 .980 1.000
152. 183. 244. 305. 305.
.116E+04 .122E+04 .137E+04 .152E+04 .161E+04
END ALL DATA
-------
TEST RUN i 1, NONdegrader.SL.SNL
VERSION 3 OF EPACML MODEL
LANDFILL INPUT DATA
WASTE VOLUME = 20,000 cu. yds.
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Silty Loam Soil Cover, Sandy Loam Recharge
*** ISOURC
"OPTION OPTAIR RUN
200 MONTE
ROUTE NT IYCHK PALPH
MONTE ISTEAD IOPEN IZCHK
5000 111001 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
*** CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
** MEAN STD DEV
A********************************************************************************************:
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
LIMITS
MIN MAX
***************************
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
.000
.000
.OOOE+00
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
*** SOURCE SPECIFIC VARIABLES
*** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
*** MEAN STD DEV MIN MAX
**************************************************************************************************************************
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
m/yr
m*2
yr
m
m/yr
6 .100E-01 .700E-02 .000 .787
6 4.21 2.16 -.884 12.3
0 .100E+31 3.00 .100 .100E+31
-1 50.0 .OOOE+00 .100E-02 .600E+05
6 .760E-02 .760E-02 .254E-04 .668
-------
6 Source decay constant
7 Initial concentration at
8 Length
9 Width
landfill
scale of facility
scale of facility
1/yr
mg/l
m
m
0
0
-1
-1
.OOOE+00 .
1.00
100.
100.
.
1
1
OOOE+00 .1
100E-01 .!
.00 1
.00 1
END ARRAY
EMPIRICAL
* I
.000
.801
.000
.127
*** I
.001
.850
1292.
19675.
** I
.000
.590
.000
.229
DISTRIBUTIONS
I COUNT
t 20
.260
.851
.001
.147
I COUNT
2 15
.01
.900
U90.
2.390E4 3.
I COUNT
5 20
.030
.650
.018
.295
.310
.865
.003
.175
.050
.950
2640.
015E4
.080
.700
.038
.310
.498
.871
.005
.185
.100
.990
3356.
4.566E4
.130
.755
.066
.366
.548
.901
.010
.216
.150
1.000
4001.
1.820E5
.260
.803
.071
.401
.624
.905
.053
.231
.250
5280.
.290
.833
.076
.475
.674
.914
.089
.251
.400
7186.
.400
.880
.104
.495
.726
.964
.102
.267
.500
8538.
.478
.930
.142
.638
.746
.980
.109
.274
.600
10056.
.498
.980
.147
.729
.771
1.000
.124
.787
.75
14147.
.540
1.000
.211
1.064
.OOOE+00 10.0
.OOOE+00 10.0
.100E+06
.100E+06
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
*** NP NMAT
7 1
KPROP IMSGN
1 1
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
*** COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
** SATURATED MATERIAL VARIABLES
2.00
** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
* MEAN STD DEV MIN MAX
**ซ********ปซซ*ปปซ******ป***************ปปปป**ซ******ป****ป******ป****ป**ป*****ป*********ป*****
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
cm/hr
7
0
2.296
.410
24.65
0.0
.OOOE+00 30.0
.200 .700
-------
3 Air entry pressure head
4 Depth of the unsaturated zone
END ARRAY
m
m
0 .OOOE+00 .OOOE+00 .OOOE+00 1.00
6 6.10 - 1.00 .610 366.
EMPIRICAL DISTRIBUTIONS
** I ICOUMT
4 20
.000 .050 .100 .200
.600 . .650 .700 .750
.100E-01 .910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
*** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
VARIABLE NAME
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
UNITS
DISTRIBUTION
1/cm
7
0
7
2
PARAMETERS
MEAN STD DEV
.065
.500
.070
1.891
.100
.074
9
.171
.155
LIMITS
MIN MAX
.OOOE+00 .11
.OOOE+00 1.00
.OOOE+00 .250
1.35 3.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
* NLAY NTSTPS IADU
1 20 1
*** WTFUN
1.200
I SOL
1
N
18
NTEL NGPTS
3 104
NIT I BOUND ITSGEN
2 1 1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
* UNSATURATED TRANSPOR VARIABLES
*** VARIABLE NAME UNITS
***
ซ****ซ*******ป**********ป*ซ
1 Thickness of layer m
2 Longitudinal dispersivity of layer m
DISTRIBUTION
PARAMETERS
MEAN STD OEV
LIMITS
MIN MAX
0 6.10 1.00 .OOOE+00 500.
0 .400 .400E-01 .OOOE+00 10.0
-------
3 Percent organic matter
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
g/cc
1/yr
.25
1.6 '
.OOOE+00
7.538
.200E-01
.200E-01
.OOOE+00 11.0
.795 2.12
.OOOE+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
** AQUIFER SPECIFIC VARIABLES
***
*
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
1 Particle diameter
2 Aquifer porosity
3 Bulk density
4 Aquifer thickness
5 Source thickness (mixing zone depth)
6 Conductivity (hydraulic)
7 Gradient (hydraulic)
8 Groundwater seepage velocity
9 Retardation coefficient
10 Longitudinal dispersivity
11 Transverse dispersivity
12 Vertical dispersivity
13 Temperature of aquifer
14 pH
15 Organic carbon content (fraction)
16 Well distance from site
17 Angle off center
18 Well vertical distance
END ARRAY
EMPIRICAL DISTRIBUTIONS
* I I COUNT
16 20
.000 .030 .040
.400 .500 .600
.600 13.7 19.8
366. 427. 610.
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
END ALL DATA
MEAN STD DEV MIN MAX
ป*ปซ***********************ปป*ปป*ป*ป**
cm
--
9/cc
m
>ne depth) m
m/yr
:y m/yr
--
m
m
m
C
--
iction)
m
degree
m
.050 .100 .150
.700 .800 .850
45.7 104. 152.
805. 914. .116E+04
5
-2
-1
3
-1
-2
3
-2
-1
8
8
8
1
1
2
6
4
4
.200
.900
183. 244.
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
152.4
45.0
.500E+00
.630E-04
.OOOE+00
.OOOE+00
78.6
6.00
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.OOOE+00
.500E-01
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
.OOOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06.
324.
41.0
250.
30.0
14.0
.100E-01
.160E+04
90.0
1.000
.250 .300 .350
.950 .980 1.000
305.
305.
.122E+04 .137E+04 .152E+04 .161E+04
-------
EPACML-S0002.D
SAMPLE*
EPACML INPUT DATA FILES
FOR SURFACE IMPOUNDMENTS
*Only the area distributions change with change in Surface Impoundment volume
-------
EPACML RUNS FOR SURFACE IMPOUNDMENTS, Silty Clay Loam
VERSION J OF EPACML MODEL
GENERAL DATA
* CHEMICAL NAME FORMAU80A1)
Silty Clay Loam
SURFACE IMPOUNDMENT INPUT DATA
WASTE VOLUME = 20,000 cu. yds.
** ISOURC
***OPTION' OPTAIR RUN
200 MONTE
ROUTE NT IYCHK RALPH
MONTE I STEAD IOPEN IZCHK
5000 111001 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
*** CHEMICAL SPECIFIC VARIABLES
**
*
***
VARIABLE NAME
UNITS DISTRIBUTION PARAMETERS
MEAN STD DEV
*ป***ปซป**************ซ**ป*ซป*ซ*ซ***ปป*ปป**ซ*ป**ซป
LIMITS
MIN MAX
r**************iป*******4***
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
370.
280.
.250E+08
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
** SOURCE SPECIFIC VARIABLES
VARIABLE NAME
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
UNITS
m/yr
m*2
yr
m
m/yr
1/yr
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
rซซซปl
6
6
0
1
6
0
i***********ป
1.10
4060
.100E+31
50.0
.760E-02
.OOOE+00
******
.700E-02
2.16
3.00
.OOOE+00
.760E-02
.OOOE+00
0.001
5.95
.100
.100E-02
.254E-04
.OOOE+00
3.60
6.86E+5
.100E+31
.600E+05
.668
10.0
-------
7 Initial concentration at landfill mg/l
8 Length scale of facility m
9 Width scale of facility m
END ARRAY
0 1.00 .100E-01 .OOOE+00 10.0
-1 100. .. 1.00 1.00 .1006*06
-1 100. 1.00 1.00 .100E+06
EMPIRICAL DISTRIBUTIONS
I
I COUNT
19
.000
.732
.001
1.50
.014
.785
.100
1.70
I COUNT
.061
.835
.300
1.80
.118
.905
.500
2.10
.151
.961
.600
2.40
.271
.971
.800
2.50
.371
.983
.900
2.80
.511
.997
1.10
3.30
.560
1.000
1.20
3.60
15
.001
.850
1124.0
13186.
'* I
.010
.900
1547.
14448.
I COUNT
.050
.950
2856.
17075.
.100
.990
4044.
21146.
.150
1.00
4517.
25021 .
12
.000
.990
.254E-4
.246
*** I
.570
1.000
.00762
.688
I COUNT
.570
.0330
.640
.0508
.730
.0787
.250
5480.
.730
.0991
.400
7216.
.890
.129
.500
8213.
.930
.152
.600
.593
1.30
.750
9404. 11164.
.960
.191
.990
.211
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
** NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
** COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
* SATURATED MATERIAL VARIABLES
2.00
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
*** MEAN STD DEV MIN
****ซป***ป***ป*****ป*******************ซ***ซ**ป********ปป*ป*ป**
MAX
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
cm/hr
7
0
.170E-01
.430
2.921
.200E-01
.OOOE+00
.200
3.50
.700
-------
3 Afp entry pressure head
4 Depth of the unsaturated zone
END ARRAY
m
m
0 .OOOE+00 .OOOE+00 .OOOE+00 1.00
6 6.10 - 1.00 .610 366.
EMPIRICAL DISTRIBUTIONS
** I ICOUNT
4 20
.000 .050 .100 .200
.600 - .650 .700 .750
.100E-01 .910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
*** VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
* MEAN STD DEV MIN MAX
*************************************************************************************************************************
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
1 .890E-01 .900E-02
0 .500 .100
7 .900E-02 .970E-01
1 1.236 .610E-01
.OOOE+00 .113,
.OOOE+00 1.00
.OOOE+00 .150
1.00 1.50
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
* NLAY NTSTPS IADU
1 20 1
*** WTFUN
1.200
I SOL
1
N
18
NTEL NGPTS
3 104
NIT IBOUND ITSGEN
2 1 1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
** UNSATURATED TRANSPOR VARIABLES
**
***
****
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
ป**ป***ซป***********ป*
MEAN STD DEV MIN MAX
************ซ******************ป*****ซ*ป**********ป*ป********ป*
1 Thickness of layer
2 Longitudinal dispersivity of layer
m
m
6.10
.400
1.00
.400E-01
.OOOE+00 500.
.OOOE+00 10.0
-------
3 Percent organic matter
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
9/cc
1/yr
7
0
0
.260E-01
1.67
.OOOE+00
7.77
.2006-01
.200E-01
.OOOE+00 11.0
.795 2.12
.OOOE+00 5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
** AQUIFER SPECIFIC VARIABLES
* VARIABLE NAME UNITS
***
**ป******ป*************ป****ซ***ซ
1 Particle diameter cm
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Grounduater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
U pH
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center - degree
18 Well vertical distance m
END ARRAY
DISTRIBUTION
PARAMETERS
MEAN STD DEV
LIMITS
MIN MAX
wwwwwwwwwwwwwwwi
5
-2
-1
3
-1
-2
3
-2
-1
8
8
8
1
1
2
6
4
4
rwwwwwwwwwwww
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
256.00
45.00
0.50E+00
wwwwwwwwww
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.100E+00
0.50E-01
WWWWWWWWWW
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
O.OOE+00
WWWWWWWWW1
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0
250.
30.0
14.0
.100E-01
1631.30
90.00
1.00
EMPIRICAL DISTRIBUTIONS
** 1 ICOUNT
16 7
.000 .100 .250 .500
15.24 80.47 161.00 256.00
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
END ALL DATA
END
.750
512.10
.900
878.00
1.00
1631.10
-------
SURFACE IMPOUNDMENT INPUT DATA
WASTE VOLUME = 20,000 cu. yds.
EPACML RUNS FOR SURFACE IMPOUNDMENTS, SANDY LOAM
VERSION 3 OF EPACML MODEL
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Sandy Loam SoiI Cover
*** ISQURC
OPTION OPTAIR RUN
200 MONTE
ROUTE NT IYCHK RALPH
MONTE ISTEAD IOPEN IZCHK
5000 111001 90.0
"** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
** CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME UNITS DISTRIBUTION PARAMETERS
*** MEAN STD DEV
ป*ป***ซ*********ป****ซ****ปป*************************ป*ปป***ป******
LIMITS
MIN MAX
I*************************
1 Solid phase decay coefficient 1/yr
2 Dissolved phase decay coefficient 1/yr
3 Overall chemical decay coefficient 1/yr
4 Acid catalyzed hydrolysis rate l/M-yr
5 Neutral hydrolysis rate constant 1/yr
6 Base catalyzed hydrolysis rate l/M-yr
7 Reference temperature C
8 Normalized distribution coefficient ml/g
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone) 1/yr
END ARRAY
1
1
1
0
0
0
0
0
2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.352E+05
.221E+09
.358E+05
370.
280.
.250E+08
40.0
.331E+06
.166E+05
100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
* SOURCE SPECIFIC VARIABLES
*
***
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
******ปปป**ป*ปป****ป******ปปป***ป**ปปซ******ป*>***********ป***********ซ
*********
1 Infiltration rate
2 Area of waste disposal unit
3 Duration of pulse
4 Spread of contaminant source
5 Recharge rate
6 Source decay constant
m/yr
m*2
yr
m
m/yr
1/yr
6
6
0
-1
6
0
.700E-02 .700E-02 .OOOE+00 1.064
4060.00 2.16
.100E+31 3.00
50.0 .OOOE+00
.760E-02 .760E-02
.OOOE+00 .OOOE+00
5.95 6.86E+5
.100 .100E+31
.1006-02 .600E+05
.254E-04 .668
.OOOC+00 10.0
-------
7 Initial concentration at
8 Length scale of
9 Width scale of
END ARRAY
facility
facility
landfill
mg/l
m
m
0
-1
-1
1
11
11
EMPIRICAL DISTRIBUTIONS
* I I COUNT
1
.000 .041
.852 ' .870
.574 .800
2.20 2.30
*ซ I I COUNT
2
.001 .010
.850 .900
1124.0 1547.
13186. 14448.
*** I I COUNT
5
.000 .030
.590 .650
.000 .018
.229 .295
18
.104
.901
.900
2.40
15
.050
.950
2856.
17075.
20
.080
.700
.038
.310
.275
.943
1.10
2.60
.100
.990
4044.
21146.
.130
.755
.066
.366
.351
.965
1.20
2.80
.150
1.00
4517.
25021.
.260
.803
.071
.401
.452
.973
1.40
3.00
.250
5480.
.290
.833
.076
.475
.613
.986
1.60
3.20
.400
7216.
.400
.880
.104
.495
.698
1.000
1.80
3.70
.500
8213.
.478
.930
.142
.638
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
.100E-01 .OOOE+00 10.0
1.00 1.00 .100E+06
1.00 1.00 .100E+06
.759 .801
1.90 2.00
.600 .750
9404. 11164.
.498
.980
.147
.729
.540
1.064
.211
1.064
CONTROL PARAMETERS
*** NP NMAT
7 1
KPROP IMSGN
1 1
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
* COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
*** SATURATED MATERIAL VARIABLES
2.00
* VARIABLE NAME UNITS
*
*************************************************
1 Saturated hydraulic conductivity cm/hr
2 Unsaturated zone porosity
3 Air entry pressure head m
DISTRIBUTION
7
0
0
PARAMETERS
MEAN STD DEV
2.296
.410
.OOOE+00
24.65
.200E-01
.OOOE+00
LIMITS
MIN MAX
********
.OOOE+00 30.0
.200 .700
.OOOE+00 1.00
30
-------
4 Depth of the unsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
** I ICOUNT
4 20
.000 . .050 .100 .200
.600 .650 .700 .750
.100E-01 ..910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END .
SOIL MOISTURE PARAMETERS
*** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
* FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
VARIABLE NAME
**
*
*ป******ปปซ*ป**ป*ป
UNITS
.DISTRIBUTION PARAMETERS
LIMITS
MEAN STD DEV MIN MAX
*ป*********ป************ป*******
1 Residual water content
2 Brook and Corey exponent,EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
A************************************
7 .065 .074 .OOOE+00 .11
0 .500 .100 .OOOE+00 1.00
1/cm 7 .070 .171 .OOOE+00 .250
2 1.891 .155 1.35 3.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
NLAY
1
*** WTFUN
1.200
NTSTPS
20
IADU
1
I SOL
1
N
18
NTEL
3
NGPTS
104
NIT
2
I BOUND
1
ITSGEN
1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
*** UNSATURATED TRANSPOR VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
********ป****
MEAN STD OEV MIN MAX
ป***************************************************************ป********ป
1 Thickness of layer m
2 Longitudinal dispersivity of layer m
3 Percent organic matter
0
0
7
6.10
.400
.25
1.00
.400E-01
7.538
.OOOE+00 500.
.OOOE+00 10.0
.OOOE+00 11.0
3/
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
9/CC
1/yr
1.6
.OOOE+QO
.200E-01
.2006-01
.795
.OOOE+00
2.12
5.00
END LAYER 1
END UNSATURATEO TRANSPORT PARAMETERS
END TRANSPORT MODEL .
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** AQUIFER SPECIFIC VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
LIMITS
**ป*ซ*ซ***ซ*ป*ปปป********ป****ซป
1 Particle diameter cm
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Grounduater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
14 pH
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center degree
18 Well vertical distance m
END ARRAY
rwwwwi
5
2
1
3
1
2
3
2
1
8
8
8
1
1
2
6
4
4
rwwwwwwwwwwww
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
256.00
45.00
0.50E+00
wwwwwwwwww
.630E-04
.OOOE+00
.OOOE+00
78.6
.600
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
.1'OOE+OO
0.50E-01
wwwwwwwwww
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
15.2
.OOOE+00
O.OOE+00
WWWWWWWWW1
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0
250.
30.0
14.0
.100E-01
1631.30
90.00
1.00
EMPIRICAL DISTRIBUTIONS
I
I COUNT
16
.000
15.24
END ARRAY
7
.100
80.47
.250
161.00
.500
256.00
.750
512.10
.900
878.00
1.00
1631.10
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
END ALL DATA
-------
SURFACE IMPOUNDMENT INPUT DATA
WASTE VOLUME = 20,000 cu. yds.
EPACML RUNS FOR SURFACE IMPOUNDMENTS, SILTLOAM
VERSION 3 OF EPACML MODEL
GENERAL DATA
** CHEMICAL NAME FORMAT(80A1)
Silty Loam Soil Cover
** ISOURC
***OPTIO*T OPTAIR RUN
200 MONTE
ROUTE NT
MONTE I STEAD
5000 1 1 1
IYCHK PALPH
IOPEN IZCHK
0 0 1 90.0
*** XST
END GENERAL
CHEMICAL SPECIFIC VARIABLE DATA
ARRAY VALUES
* CHEMICAL SPECIFIC VARIABLES
VARIABLE NAME
1 Solid phase decay coefficient
2 Dissolved phase decay coefficient
3 Overall chemical decay coefficient
4 Acid catalyzed hydrolysis rate
5 Neutral hydrolysis rate constant
6 Base catalyzed hydrolysis rate
7 Reference temperature
8 Normalized distribution coefficient
9 Distribution coefficient
10 Biodegradation coefficient (sat. zone)
END ARRAY
UNITS
1/yr .
1/yr
1/yr
l/M-yr
1/yr
l/M-yr
C
ml/g
1/yr
DISTRIBUTION PARAMETERS
MEAN STD DEV
*******************************
-1
-1
-1
0
0
0
0
0
-2
0
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
25.0
.OOOE+00
.219
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
.OOOE+00
LIMITS
MIN MAX
*ป**ซ************
.OOOE+00 .352E+05
.OOOE+00 .221E+09
.OOOE+00 .358E+05
.OOOE+00 .000
.OOOE+00 .000
.OOOE+00 .OOOE+00
.OOOE+00 40.0
.OOOE+00 .331E+06
.OOOE+00 .166E+05
.OOOE+00 100.
END CHEMICAL SPECIFIC VARIABLE DATA
SOURCE SPECIFIC VARIABLE DATA
ARRAY VALUES
*** SOURCE SPECIFIC VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS LIMITS
MEAN STD DEV MIN MAX
*ป*ปป*****ป**ป****ป****ปปปซป
1 Infiltration rate m/yr
2 Area of waste disposal unit m"2
3 Duration of pulse yr
4 Spread of contaminant source m
5 Recharge rate m/yr
6 Source decay constant 1/yr
**<
6
6
0
-1
6
0
>***********
.100E-01
4060.00
.100E+31
50.0
.760E-02
.OOOE+00
****
.700E-02
2.16
3.00
.OOOE+00
.760E-02
.OOOE+00
**********ซ***ป
.000 .787
5.95 6.86E+5
.100 .100E+31
.100E-02 .6006+05
.254E-04 .668
.OOOE+00 10.0
33
-------
7 Initial concentration at
8 Length scale of facility
9 Width scale of facility
END ARRAY
EMPIRICAL DISTRIBUTIONS
** I I COUNT
1 20
.000 , .002 .008
.816 .872 .914
4.80E-7 .200 .400
2.00 2.20 2.40
** I t I COUNT
2 15
.001 .010 .050
.850 .900 .950
1124.0 1547. 2856.
13186. 14448. 17075.
* I I COUNT
5 20
.000 .260 .310
.801 .851 .865
.000 .001 .003
.127 .147 .175
landfill
.020
.957
.600
2.60
.100
.990
4044.
21146.
.498
.871
.005
.185
mg/l
m
m
.070
.973
.800
2.80
.150
1.00
4517.
25021.
.548
.901
.010
.216
.235
.979
1.000
3.00
.250
5480.
.624
.905
.053
.231
0
-1
-1
.384
.991
1.20
3.20
.400
7216.
.674
.914
.089
.251
1.00
100.
100.
.503
.996
1.40
3.40
.500
8213.
.726
.964
.102
.267
.
1
1
.643
.998
1.60
3.60
.600
9404.
.746
.980
.109
.274
100E-01 .1
.00 1
.00 1
.732
1.000
1.80
3.80
.750
11164.
.771
1.000
.124
.787
.OOOE+00 10.0
.100E+06
.100E+06
END EMPIRICAL DISTRIBUTIONS
END SOURCE SPECIFIC VARIABLE DATA
VFL UNSATURATED FLOW MODEL PARAMETERS
CONTROL PARAMETERS
*** NP NMAT KPROP IMSGN
7111
END CONTROL PARAMETERS
SPATIAL DISCRETIZATION PARAMETERS
** COMPUTER GENERATED COORDINATE DATA
*** XSTART XO DX XFAC DXMAX
.OOOE+00 6.10 .500 1.50
END SPATIAL DISCRETIZATION PARAMETERS
SATURATED MATERIAL PROPERTY PARAMETERS
ARRAY VALUES
*** SATURATED MATERIAL VARIABLES
2.00
VARIABLE NAME
**
********
1 Saturated hydraulic conductivity
2 Unsaturated zone porosity
3 Air entry pressure head
UNITS
cm/hr
DISTRIBUTION PARAMETERS
LIMITS
MIN
MAX
i****i
2
0
0
>**********
.343
.450
.OOOE+00
.989
0.0
.OOOE+00
.OOOE+00
.200
.OOOC+00
15.0
.700
1.00
-------
4 Depth of the unsaturated zone
END ARRAY
6.10
1.00
.610
366.
EMPIRICAL DISTRIBUTIONS
** I I COUNT
4 20
.000 .050 .100 .200
.600 .650 .700 .750
.100E-01 ..910 1.22 1.83
12.2 15.2 16.8 21.3
END EMPIRICAL DISTRIBUTIONS
END MATERIAL 1
END
SOIL MOISTURE PARAMETERS
** FUNCTIONAL COEFFICIENTS
ARRAY VALUES
*** FUNCTIONAL COEFFICIE VARIABLES
.250
.800
.300
.850
.350
.900
.400
.950
.450
.980
2.74
30.5
3.05
34.8
3.66
61.0
4.75
107.
6.09
183.
.500
1.000
6.10
366.
*ป* VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
*** MEAN STD DEV MIN MAX
*******************************************************************************************************************
1 Residual water content
2 Brook and Corey exponent, EN
3 ALFA coefficient
4 Van Genuchten exponent, ENN
END ARRAY
1/cm
.068
.500
.019
1.409
.071
.100
.012
1.629
.OOOE+00 .11
.OOOE+00 1.00,
.OOOE+00 .150
1.00 2.00
END MATERIAL 1
END
END UNSATURATED FLOW
VTP UNSATURATED TRANSPORT MODEL
CONTROL PARAMETERS
** NLAY NTSTPS IADU
1 20 1
* WTFUN
1.200
I SOL
1
N
18
NTEL NGPTS
3 104
NIT I BOUND ITSGEN
2 1 1
END CONTROL PARAMETERS
TRANSPORT PARAMETER
ARRAY VALUES
* UNSATURATED TRANSPOR VARIABLES
VARIABLE NAME UNITS DISTRIBUTION PARAMETERS LIMITS
* MEAN STD DEV MIN MAX
A***********************************************************************************************************************
1 Thickness of layer m
2 Longitudinal dispersivity of layer m
3 Percent organic matter
6.10
.400
.039
1.00
.400E-01
7.74
.OOOE+00 500.
.OOOE+00 10.0
.OOOE+00 11.0
36-
-------
4 Bulk density of soil for layer
5 Biological decay coefficient
END ARRAY
g/cc
1/yr
1.65
.OOOE+00
.200E-01
.200E-01
.795
.OOOE+00
2.12
5.00
END LAYER 1
END UNSATURATED TRANSPORT PARAMETERS
END TRANSPORT MODEL
AQUIFER SPECIFIC VARIABLE DATA
ARRAY VALUES
*** .AQUIFER SPECIFIC VARIABLES
VARIABLE NAME
UNITS
DISTRIBUTION PARAMETERS
*****ปป***ป**************ป
1 Particle diameter
2 Aquifer porosity
3 Bulk density g/cc
4 Aquifer thickness m
5 Source thickness (mixing zone depth) m
6 Conductivity (hydraulic) m/yr
7 Gradient (hydraulic)
8 Groundwater seepage velocity m/yr
9 Retardation coefficient
10 Longitudinal dispersivity m
11 Transverse dispersivity m
12 Vertical dispersivity m
13 Temperature of aquifer C
14 pN
15 Organic carbon content (fraction)
16 Well distance from site m
17 Angle off center degree
18 Well vertical distance m
END ARRAY
LIMITS
MEAN STD DEV MIN MAX
**********ป*******ป***ป*****ซ************ป*******************
cm
5
-2
-1
3
-1
-2
3
-2
-1
8
8
8
1
1
2
6
4
4
.630E-03
.OOOE+00
1.64
78.6
6.00
.758E+05
.309E-01
300.
1.00
15.2
8.00
160.
14.4
6.20
.315E-02
256.00
45.00
0.50E+00
.630E-04
.OOOE+00
.OOOE+00
78.6
6.00
.758E+04
.310E-01
.OOOE+00
.100
.700
.OOOE+00
.950E-01
5.29
1.28
.300E-03
.OOOE+00
. 1 OOE+00
0.50E-01
.400E-03
.300
1.16
3.00
2.00
31.6
.100E-04
.100E-01
1.00
.100
.100
.380
5.00
.300
.100E-02
*&.2
.OOOE+00
0. OOE+00
.100
.560
1.80
560.
10.0
.151E+06
.100
.925E+04
.352E+06
324.
41.0 "
250.
30.0
14.0
.100E-01
1631.30
90.00
1.00
EMPIRICAL DISTRIBUTIONS
** I I COUNT
16 7
.000 .100 .250 .500
15.24 80.47 161.00 256.00
END EMPIRICAL DISTRIBUTIONS
END AQUIFER SPECIFIC VARIABLE DATA
END ALL DATA
.750
512.10
.900
878.00
1.00
1631.10
------- |