United Sates
Environmental Protection
Agiticy
&EPA EPA's Composite Model
for Leachate Migration
with Transformation
Products (EPACMTP)
Technical Background
Document
-------
Office of Solid Waste (5305W)
Washington, DC 20460
EPA530-R-03-006
April 2003
www.epa.gov/osw
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EPA's Composite Model for Leachate Migration with
Transformation Products (EPACMTP)
Technical Background Document
Work Assignment Manager David Cozzie
and Technical Direction: U.S. Environmental Protection Agency
Office of Solid Waste
Washington, DC 20460
Prepared by: HydroGeoLogic, Inc.
1155 Herndon Parkway, Suite 900
Herndon, VA20170
Under Subcontract No.: RMC-B-00-021
and
Resource Management Concepts, Inc.
46970 Bradley Blvd., Suite B
Lexington Park, MD 20653
Under Contract No.: 68-W-01-004
U.S. Environmental Protection Agency
Office of Solid Waste
Washington, DC 20460
April 2003
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TABLE OF CONTENTS
Section Page
LIST OF ACRONYMS ix
LIST OF SYMBOLS xi
ACKNOWLEDGMENTS xxv
EXECUTIVE SUMMARY xxvii
1.0 INTRODUCTION 1-1
1.1 DEVELOPMENT HISTORY OF EPACMTP 1-1
1.2 WHAT IS THE EPACMTP MODEL? 1-2
1.2.1 Source-Term Module 1-5
1.2.2 Unsaturated-Zone Module 1-6
1.2.3 Saturated-Zone Module 1-7
1.2.4 Monte-Carlo Module 1-8
1.3 EPACMTP ASSUMPTIONS AND LIMITATIONS 1-9
2.0 SOURCE-TERM MODULE 2-1
2.1 PURPOSE OF THE SOURCE-TERM MODULE 2-1
2.1.1 Continuous Source 2-2
2.1.2 Finite Source 2-2
2.2 IMPLEMENTATION FOR DIFFERENT WASTE UNITS 2-4
2.2.1 Landfills 2-4
2.2 A A Assumptions for the Landfill Source Module .... 2-4
2.2.1.2 List of Parameters for the Landfill
Source Module 2-6
2.2.1.2.1 Landfill Area 2-6
2.2.1.2.2 Landfill Depth 2-6
2.2.1.2.3 Depth Below Grade 2-8
2.2.1.2.4 Waste Fraction 2-8
2.2.1.2.5 Waste Density 2-8
2.2.1.2.6 Areal Recharge and
Infiltration Rates 2-8
2.2.1.2.7 Leachate Concentration 2-9
2.2.1.2.8 Waste Concentration 2-9
2.2.1.2.9 Waste-Concentration-to-
Leachate-Concentration Ratio .... 2-10
2.2.1.2.10 Source Leaching Duration 2-10
2.2.1.2.11 Waste Volume 2-10
2.2.1.3 Mathematical Formulation of the Landfill
Source Module 2-11
2.2.1.3.1 Continuous Source Scenario 2-11
2.2.1.3.2 Pulse Source Scenario 2-11
2.2.1.3.3 Depleting Source Scenario 2-14
2.2.2 Surface Impoundments 2-17
2.2.2.1 Assumptions for the Surface Impoundment
Source-Term Module 2-17
2.2.2.2 List of Parameters for the Surface
Impoundment Source-Term Module 2-18
2.2.2.2.1 Surface Impoundment Area 2-19
2.2.2.2.2 Areal Recharge Rate 2-19
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TABLE OF CONTENTS
Section Page
2.2.2.2.3 Areal Infiltration Rate 2-20
2.2.2.2.4 Depth Below Grade 2-20
2.2.2.2.5 Operating Depth and
Ponding Depth 2-20
2.2.2.2.6 Total Thickness of Sediment 2-21
2.2.2.2.7 Distance to the Nearest Surface
Water Body 2-21
2.2.2.2.8 Leachate Concentration 2-21
2.2.2.2.9 Source Leaching Duration 2-21
2.2.2.2.10 Liner Thickness 2-22
2.2.2.2.11 Liner Hydraulic Conductivity 2-22
2.2.2.2.12 Unsaturated-zone Thickness 2-22
2.2.2.2.13 Leak Density 2-22
2.2.2.3 Mathematical Formulation of the
Surface Impoundment Source-Term Module . . 2-22
2.2.2.3.1 Surface Impoundment
Leakage (Infiltration) Rate 2-22
2.2.2.3.2 Calculation of the Surface
Impoundment Infiltration Rate .... 2-28
2.2.3 Waste Piles 2-31
2.2.3.1 Assumptions for the Waste Pile Source-
Term Module 2-31
2.2.3.2 List of Parameters for the Waste Pile Source-
Term Module 2-31
2.2.3.2.1 Waste Pile Area 2-31
2.2.3.2.2 Areal Infiltration and
Recharge Rates 2-32
2.2.3.2.3 Leachate Concentration 2-33
2.2.3.2.4 Source Leaching Duration 2-33
2.2.3.2.5 Depth Below Grade 2-33
2.2.3.3 Mathematical Formulation of the Waste Pile
Source-Term Module 2-33
2.2.4 Land Application Units 2-35
2.2.4.1 Assumptions for the Land Application Unit
Source-Term Module 2-35
2.2.4.2 List of Parameters for the Land Application
Unit Source-Term Module 2-35
2.2.4.2.1 Land Application Unit Area 2-35
2.2.4.2.2 Infiltration and Recharge Rates . . . 2-35
2.2.4.2.3 Leachate Concentration 2-36
2.2.4.2.4 Source Leaching Duration 2-37
2.2.4.3 Mathematical Formulation of the Land
Application Unit Source-Term Module 2-37
2.2.5 Limitations on Maximum Infiltration Rate 2-39
3.0 UNSATURATED-ZONE MODULE 3-1
3.1 PURPOSE OF THE UNSATURATED-ZONE MODULE 3-1
3.2 UNSATURATED-ZONE FLOWSUBMODULE 3-3
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TABLE OF CONTENTS
Section Page
3.2.1 Description of the Unsaturated-zone Flow Submodule .... 3-3
3.2.2 Assumptions Underlying the Unsaturated-zone
Flow Submodule 3-3
3.2.3 List of the Parameters for the Unsaturated-zone
Flow Submodule 3-4
3.2.3.1 Soil Characteristic Curve Parameters 3-5
3.2.3.2 Thickness of the Unsaturated Zone 3-6
3.2.3.3 Saturated Hydraulic Conductivity 3-7
3.2.4 Mathematical Formulation of the Unsaturated-zone
Flow Submodule 3-7
3.2.5 Solution Method for Flow in the Unsaturated Zone 3-7
3.3 UNSATURATED-ZONE SOLUTE TRANSPORT
SUBMODULE 3-10
3.3.1 Description of the Unsaturated-zone
Transport Submodule 3-10
3.3.2 Assumptions Underlying the Unsaturated-zone
Transport Submodule 3-10
3.3.3 List of Parameters for the Unsaturated-zone
Transport Submodule 3-12
3.3.3.1 Longitudinal Dispersivity 3-13
3.3.3.2 Percent Organic Matter 3-14
3.3.3.3 Soil Bulk Density (pbu) 3-15
3.3.3.4 Freundlich Sorption Coefficient
(Distribution Coefficient) 3-15
3.3.3.5 Freundlich Isotherm Exponent 3-15
3.3.3.6 Sorption Coefficient for Metals 3-15
3.3.3.7 Chemical and Biological
Transformation Coefficients 3-16
3.3.3.8 Molecular Diffusion Coefficient 3-17
3.3.3.9 Molecular Weight 3-17
3.3.3.10 Ground-water Temperature 3-17
3.3.3.11 Ground-water pH 3-17
3.3.4 Mathematical Formulation of the Unsaturated-zone
Transport Submodule 3-17
3.3.5 Solution Methods for Transport in the
Unsaturated Zone 3-23
3.3.5.1 Steady-state, Single Species
Analytical Solution 3-23
3.3.5.2 Transient, Decay Chain Semi-
analytical Solution 3-25
3.3.5.3 Semi-analytical Solution for Metals with Non-
linear Sorption 3-25
4.0 SATURATED ZONE (AQUIFER) MODULE 4-1
4.1 PURPOSE OF THE SATURATED-ZONE MODULE 4-1
4.2 LINKING THE UNSATURATED-ZONE AND SATURATED-
ZONE MODULES 4-1
4.3 SATURATED-ZONE FLOW SUBMODULE 4-2
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TABLE OF CONTENTS
Section Page
4.3.1 Description of the Flow Submodule 4-2
4.3.2 Assumptions Underlying the Flow Submodule 4-2
4.3.3 List of Parameters for the Flow Submodule 4-3
4.3.3.1 Particle Diameter 4-3
4.3.3.2 Porosity 4-5
4.3.3.3 Bulk Density 4-6
4.3.3.4 Saturated-zone Thickness 4-6
4.3.3.5 Hydraulic Conductivity 4-6
4.3.3.6 Anisotropy Ratio 4-7
4.3.3.7 Hydraulic Gradient 4-7
4.3.3.8 Seepage Velocity 4-8
4.3.4 Mathematical Formulation of the Saturated-Zone
Flow Submodule 4-8
4.3.5 Solution Methods for Flow in the Saturated Zone 4-8
4.3.5.1 One-dimensional Flow Solution 4-9
4.3.5.2 Two-dimensional Flow Solutions 4-12
4.3.5.3 Three-dimensional Flow Solution 4-13
4.3.6 Parameter Screening For Infeasible Ground-water
Flow Conditions 4-16
4.4 SATURATED-ZONE SOLUTE TRANSPORT SUBMODULE .... 4-20
4.4.1 Description of the Solute Transport Submodule 4-20
4.4.2 Assumptions Underlying the Saturated-zone
Transport Submodule 4-21
4.4.3 List of Parameters for the Solute Transport Submodule . . 4-21
4.4.3.1 Retardation Factor 4-23
4.4.3.2 Dispersivity 4-24
4.4.3.3 Ground-water Temperature 4-26
4.4.3.4 Ground-water pH 4-26
4.4.3.5 Fractional Organic Carbon Content 4-26
4.4.3.6 Receptor Well Location and Depth 4-26
4.4.3.6.1 Horizontal Well Location 4-27
4.4.3.6.2 Vertical Well Location 4-32
4.4.3.7 Freundlich Isotherm Coefficient 4-34
4.4.3.8 Freundlich Isotherm Exponent 4-34
4.4.3.9 Sorption Coefficient for Metals 4-34
4.4.3.10 Chemical & Biological
Transformation Coefficients 4-35
4.4.3.11 Molecular Diffusion Coefficient 4-35
4.4.3.12 Molecular Weight 4-35
4.4.4 Mathematical Formulation of the Saturated-zone
Solute Transport Submodule 4-35
4.4.4.1 Dispersion Coefficients 4-36
4.4.4.2 Retardation Factor 4-37
4.4.4.3 Coefficient Q, 4-38
4.4.4.4 Degradation Products Terms 4-39
4.4.4.5 Initial Condition 4-39
4.4.4.6 Boundary Conditions 4-40
4.4.4.7 Source Concentration 4-41
IV
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TABLE OF CONTENTS
Section Page
4.4.4.8 Treatment of Nonlinear Isotherms 4-43
4.4.5 Solution Methods for the Solute Transport Submodule . . 4-44
4.4.5.1 Aquifer Discretization and Solution
Method Selection 4-44
4.4.5.1.1 Determination of Model
Domain Dimensions 4-44
4.4.5.1.2 Discretization of Model Domain . . . 4-47
4.4.5.1.3 Solution Method Selection 4-48
4.4.5.2 Three-dimensional Transport Solutions 4-49
4.4.5.2.1 Laplace Transform
Galerkin Solution 4-49
4.4.5.2.2 Solution for Steady-state and
Nonlinear Transport 4-55
4.4.5.2.3 Analytical Solution 4-56
4.4.5.3 Two-dimensional Transport Solutions 4-59
4.4.5.3.1 Two-dimensional Cross-
sectional Transport Solution 4-59
4.4.5.3.2 Two-dimensional Areal
Transport Solution 4-62
4.4.5.3.3 Criterion for selecting Two-
dimensional Solutions 4-62
4.4.5.4 Pseudo-3D Transport Solution 4-63
4.4.6 Determining the Exposure Concentration at the
Receptor Well 4-82
4.4.6.1 Time-Averaged Concentration 4-83
4.4.6.2 Peak Concentration 4-84
4.4.6.3 Time-to-Arrival of the Peak Concentration .... 4-84
4.4.7 Determining the Contaminant Mass Flux from Ground-
water into a Surface Water Body 4-85
5.0 MONTE-CARLO MODULE 5-1
5.1 PURPOSE OF THE MONTE-CARLO MODULE 5-1
5.1.1 Treatment of Uncertainty and Variability 5-2
5.2 MONTE-CARLO MODULE OPERATION 5-3
5.3 ENSURING INTERNALLY CONSISTENT DATA SETS 5-4
5.3.1 Upper and Lower Limits 5-6
5.3.2 Screening Procedures 5-6
5.3.3 Regional Site-Based Approach 5-7
5.4 METHODOLOGY FOR GENERATING INPUT VALUES
ACCORDING TO SPECIFIED DISTRIBUTIONS 5-8
5.4.1 Constant 5-8
5.4.2 Normal Distribution 5-9
5.4.3 Lognormal Distribution 5-10
5.4.4 Exponential Distribution 5-10
5.4.5 Uniform Distribution 5-10
5.4.6 Log10 Uniform Distribution 5-11
5.4.7 Empirical Distribution 5-11
5.4.8 Johnson SB Distribution 5-13
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TABLE OF CONTENTS
Section
Page
5.4.9 Special Distributions 5-13
5.4.9.1 Gelhar Distribution for Aquifer Dispersivity .... 5-13
5.4.9.2 Vertical Well Intake Point Depth 5-14
5.4.10 Derived Parameters 5-15
5.4.11 Parameter Upper and Lower Bounds 5-15
5.5 MONTE-CARLO METHODOLOGY FOR REGIONAL
SITE-BASED, CORRELATED DISTRIBUTIONS 5-15
5.5.1 Description of Regional Site-Based Approach 5-16
5.5.2 Regional Site-Based Monte-Carlo Procedure 5-18
5.5.3 Methodology for Generating Missing Data Values 5-19
5.6 INTERPRETING A MONTE-CARLO MODELING ANALYSIS . . . 5-22
5.7 REQUIRED NUMBER OF MONTE-CARLO REALIZATIONS ...5-26
6.0 REFERENCES 6-1
APPENDIX A:
APPENDIX B.1:
APPENDIX B.2:
APPENDIX C:
APPENDIX D:
APPENDIX E:
APPENDIX F:
APPENDIX G:
EPACMTP CODE STRUCTURE
ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL
TRANSPORT OF A STRAIGHT AND BRANCHING CHAIN OF
DECAYING SOLUTES
ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL
TRANSPORT OF A SOLUTE WITH NON-LINEAR SORPTION
ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL
STEADY-STATE GROUNDWATER FLOW IN A CONSTANT
THICKNESS AQUIFER
VERIFICATION AND VALIDATION OF THE EPA'S COMPOSITE
MODEL FOR TRANSFORMATION PRODUCTS
PARAMETER SCREENING
GROUND-WATER-TO-SURFACE-WATER MASS FLUX
MINTEQA2-BASED METAL ISOTHERMS
VI
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LIST OF TABLES
Page
Table 2.1 Source-Specific Variables for Landfills 2-7
Table 2.2 Source-Specific Variables for Surface Impoundments 2-18
Table 2.3 Source-Specific Variables for Waste Piles 2-32
Table 2.4 Source-Specific Variables for Land Application Units 2-36
Table 3.1 Parameters for the Unsaturated Zone Flow Submodule 3-4
Table 3.2 Parameters for the Unsaturated Zone Transport Submodule . . 3-12
Table 4.1 Aquifer-Specific Variables for the Flow Module 4-4
Table 4.2 Ratio Between Effective and Total Porosities as a Function
of Particle Diameter (after McWorter and Sunada, 1977) 4-6
Table 4.3 Aquifer-Specific Variables for the Saturated-Zone
Transport Submodule 4-22
Table 5.1 Probability distributions and their associated codes available
for use in Monte-Carlo module of EPACMTP 5-9
Table 5.2 Example Empirical Distribution 5-12
Table 5.3 Relationship between confidence interval and number of
Monte-Carlo realizations 5-27
VII
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LIST OF FIGURES
Page
Figure 1.1 Conceptual Cross-Section View of the Subsurface System
Simulated by EPACMTP 1-3
Figure 1.2 (a) Leachate Concentration, and (b) Ground-water
Exposure Concentration 1-4
Figure 2.1 Leachate Concentration Versus Time for Pulse Source and
Depleting Source Conditions 2-3
Figure 2.2 WMU Types Modeled in EPACMTP 2-5
Figure 2.3 Schematic Cross-Section View of SI Unit 2-23
Figure 2.4 Flowchart Describing the Infiltration Screening Procedure .... 2-41
Figure 2.5 Infiltration Screening Criteria 2-42
Figure 3.1 Cross-sectional View of the Unsaturated Zone Considered
by EPACMTP 3-2
Figure 3.2 Typical Saturation Profile for a Homogenous Soil under
Steady Infiltration Conditions. The Water Table Is Located
atZu= 10m 3-11
Figure 4.1 Schematic Illustration of the Saturated Three-dimensional
Ground-water Flow System Simulated by the Model 4-3
Figure 4.2 Three-dimensional Brick Element Used in Numerical
Flow and Transport Model Showing Local Node
Numbering Convention 4-15
Figure 4.3 Flowchart Describing the Infiltration Screening Procedure .... 4-18
Figure 4.4 Infiltration Screening Criteria 4-19
Figure 4.5 Schematic View of the Two Possible Zones for Receptor
Well Location 4-29
Figure 4.6 Schematic Cross-sectional View of the Aquifer
Showing the Contributing Components of the Ground-water
Flow Field 4-33
Figure 4.7 Schematic Cross-sectional View of the Aquifer, Illustrating
the Procedure for Determining the X-Dimension of the
Model Domain 4-45
Figure 4.8 Difference (Canalytical -Cnumerical)/c0 Between Analytical and
Numerical Transport Solutions as a Function of (ratio of
regional flux to near-source flux). C0 Is the
Source Concentration 4-50
Figure 4.9 Schematic View of the Time-varying Receptor Well
Concentration (Break Through Curve) and Illustration of
the Procedure for Determining rw 4-86
Figure 4.10 Schematic Illustration of the Effect of Increasing Pulse
Duration, Tp, on the Receptor Well Break Through Curve 4-87
Figure 5.1 Flow chart of EPACMTP for a Monte-Carlo Problem 5-5
Figure 5.2 Frequency distribution of normalized receptor
well concentrations 5-25
Figure 5.3 Cumulative Distribution Function of Normalized
Receptor Well Concentration 5-25
Figure 5.4 Relative Monte-Carlo Prediction Error 5-28
VIM
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EPACMTP Technical Background Document
LIST OF ACRONYMS
1-D One-dimensional
3-D Three-dimensional
API American Petroleum Institute
CANSAZ-3D Combined Analytical-Numerical in Saturated Zone in 3 Dimensions
CDF Cumulative Distribution Function
DAF Dilution-Attenuation Factor
EPA Environmental Protection Agency
EPACML EPA's Composite Model for Landfills
EPACMS EPA's Composite Model for Surface impoundments
EPACMTP EPA's Composite Model for Leachate Migration with Transformation
Products
EPA Environmental Protection Agency
EPRI Electric Power Research Institute
FECTUZ Finite Element Contaminant Transport in the Unsaturated Zone
HBN Health-based Number
HELP Hydrologic Evaluation of Landfill Performance
HWIR Hazardous Waste Identification Rule
IWEM Industrial Waste Management Evaluation Model
LAU Land Application Unit
LF Landfill
LTG Laplace Transform Galerkin
LTD Land Treatment Unit
MCL Maximum Contaminant Level
MINTEQA2 EPA's Geochemical Equilibrium Speciation Model for Dilute Aqueous
Systems
NOAA National Oceanic and Atmospheric Administration
ORTHOMIN EPACMTP's matrix solver
IX
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EPACMTP Technical Background Document
LIST OF ACRONYMS (continued)
OSW Office of Solid Waste
OSWER Office of Solid Waste and Emergency Response
RCRA Resource Conservation and Recovery Act
RGC Reference Groundwater Concentration
SAB Science Advisory Board
SI Surface Impoundment
SPLP Synthetic Precipitation Leaching Procedure
STORE! EPA's STOrage and RETrieval database of water quality, biological,
and physical data
TC Toxicity Characteristics
TCLP Toxicity Characteristic Leaching Procedure
USEPA United States Environmental Protection Agency
VADOFT EPA's numerical unsaturated zone simulator, VADose Zone Flow and
Transport code
VMS Vertical and Horizontal Spread Model
WMU Waste Management Unit
WP Waste Pile
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EPACMTP Technical Background Document
LIST OF SYMBOLS
Symbol
A
A"
Acp
**»
Ar
av
"w
™YJ
"YLU
™YU
b
B
B'
B-
Bcp
BLU
B"
BYj
BYU
{b}
c
c(0, t)
c(zj
c
di
c,
C2
CA
cc
CCD
Definition
empirical constant (dimensionless)
log10(ALU)
parent compound Acp
area of hole in the geomembrane (m2)
anisotropy ratio = K/KZ
compressibility of the sediment (m-s2/kg)
area of WMU footprint (m2)
lower bound for YJSB
lower bound for YLU
lower bound for Yu
empirical constant (1/log(m/s))
thickness of the saturated zone (m)
estimated plume depth (m)
log10(BLU)
degradation product Bcp
upper bound for YLU
matrix of square root of V12
upper bound for YJSB
upper bound for Yu
vector containing the known transformed natural boundary
conditions, as well as contributions from decaying parents
aqueous concentration of the constituent of interest (mg/L)
aqueous concentration at zu1 = 0 (mg/L)
aqueous concentration of the constituent of interest at zu
(mg/L)
Laplace transformed concentration (y-mg/L)
initial aqueous concentration of species ; in the source
(mg/L)
constant (dimensionless)
constant (1/m)
average groundwater concentration over a specified
exposure period (mg/L)
compression index (dimensionless)
degradation product Ccp
Equation in
which the
symbol first
appears
2.14
5.6
4.37
2.24c
4.5
2.15
2.3
5.8
5.6
5.5
2.14
2.31
4.71
5.6
4.37
5.6
5.11b
5.8
5.5
4.50
3.25a
3.26
3.27
4.61
3.24
2.19
2.20
4.58
2.16
4.37
XI
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
CE
Cfact
0,
0(0, t)
c, (lu, t)
cfru, 0)
c, (~, t)
c/t)
Cj
ck
CL
ct
c,
Cm
cm
Cr
CRW
Crt/ell
CRW
cw
c\"
Cmax
L
c°
c°(t)
of
cf(t)
C/ave
r °
^k
C°L
Definition
parameter value whose cumulative probability is F3
clogging factor
aqueous concentration of species / (mg/L)
aqueous concentration of species / at zu = 0 (mg/L)
aqueous concentration of species / at time t at the bottom of
the saturated zone (mg/L)
initial aqueous concentration of species / at depth zu (mg/L)
aqueous concentration at infinity (mg/L)
concentration at node j of the finite element grid at time t
(mg/L)
Laplace-transformed concentration (y-mg/L)
aqueous concentration of species k (mg/L)
leachate concentration (mg/L)
aqueous concentration of the ^th component in the decay
chain (mg/L)
Laplace-transformed concentration of species /(y-mg/L)
aqueous concentration of parent m (mg/L)
Laplace-transformed concentration of parent m (y-mg/L)
relative concentration at receptor well (dimensionless)
instantaneous receptor well concentration
constituent concentration at receptor well (mg/L)
(instantaneous or time-averaged)
time-averaged receptor well concentration (mg/L)
constituent concentration in the waste (mg/kg)
initial aqueous concentration of species / in the unsaturated
zone (mg/L)
maximum allowable leachate concentration (mg/L)
source concentration of constituent of interest (mg/L)
source concentration of constituent of interest at time t
(mg/L)
leachate concentration of species /emanating from the
source (mg/L)
leachate concentration of species /emanating from the
source at time t (mg/L)
average concentration value during the time interval [f", t°ff\
(mg/L)
source concentration for species k (mg/L)
initial leachate concentration at the time of landfill closure
(mg/L)
Equation in
which the
symbol first
appears
5.7b
2.23
3.14
3.22
3.23a
3.20
3.23b
4.51
4.51
4.72
2.1
4.31
4.49
3.14
4.49
5.12
4.108
5.12
4.108
2.3
3.20
5.14
3.26
4.55
3.21
3.22
4.55
4.74b
2.1
XII
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
c°t
f,
(f
?.(P)
om°
c°m
c°w
oks(t)
{c}
d
dBG
dc
DE
Dfc
D,
D,i
DLF
Dlin
DLU
DR
Dsoil
Du
Duc
Dxx
Dxv
Dxz
Dw
Dvz
Definition
source concentration of the Ath component species in the
decay chain (mg/L)
initial source concentration of the ^th species in the decay
chain (mg/L)
Laplace - transformed source concentration of species /(y-
mg/L)
Laplace transform of the source function (y-mg/L)
leachate concentration of parent m emanating from the
source (mg/L)
Laplace - transformed concentration of parent m (y-mg/L)
initial constituent concentration in the waste at the time of
landfill closure (mg/kg)
equivalent aqueous concentration of species k on the
vertical plane at the downgradient edge of the source (mg/L)
Laplace-transformed concentration vector
mean particle diameter (cm)
depth below grade of WMU (m)
distance from a point at the water table underneath the patch
source to the downgradient location xc (m)
parameter value whose cumulative probability is F4
thickness of consolidated sediment layer (m)
molecular diffusion coefficient in free water for species ;
(nf/y)
dispersion coefficient tensor (m2/y)
landfill depth (m)
liner thickness (m)
apparent dispersion coefficient (m2/y)
average penetration depth due to recharge between the
downgradient edge of the source and the observation point
(m)
thickness of unaffected native soil underneath the WMU (m)
total depth of the unsaturated zone (m)
thickness of unconsolidated sediment (m)
longitudinal dispersion coefficient (m2/y)
off-diagonal dispersion coefficient for the x-y plane (m2/y)
off-diagonal dispersion coefficient for the x-z plane (m2/y)
horizontal transverse dispersion coefficient (m2/y)
off-diagonal dispersion coefficient for the y-z plane (m2/y)
Equation in
which the
symbol first
appears
4.39b
4.40b
4.41
4.49
3.24a
4.41
2.9
4.88
4.50
4.1
2.24b
4.66a
5.7b
2.16
3.15
4.31
2.3
2.24b
3.14
4.82
2.24a
2.24b
2.17
4.32a
4.32d
4.32e
4.32b
4.32f
XIII
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
DZZ
D"dui
DSO/
D*
Ds*
or
D,s*
DAF
DAF10
e
E
e0
f
f(x*)
f(c)
F(V)
fc
F3
F4
Fc
Fh
f,
foe
ocw
f s
'oc
Definition
vertical dispersion coefficient (m2/y)
effective molecular diffusion coefficient (m2/yr)
thickness of clogged soil layer underneath the WMU (m)
diagonal matrix consisting of the square root of the
eigenvalues of V12
effective molecular diffusion coefficient for species of interest
(nf/y)
effective molecular diffusion coefficient for species k in the
saturated zone (m2/y)
effective molecular diffusion coefficient for species t (m2/y)
Dilution-Attenuation Factor (dimensionless)
10th percentile value of DAF (which corresponds to the 90th
percentile of relative concentration)
void ratio (dimensionless)
an error term arising because the Fourier coefficients are
approximations obtained from c~ rather than c/t) and
because the series is truncated after 2N terms (mg/L)
initial void ratio at no-stress condition (dimensionless)
fraction of the source that migrates downgradient in the
event that a water table crest occurs within the source area
(dimensionless)
probability density function of x*
nonlinear function representing the adsorption isotherm
(mg/kg)
a function of ifj
derivative of f(c) (dimensionless)
a cumulative probability value
a cumulative probability value
concentration ratio (dimensionless)
volume fraction of the waste in the landfill at time of closure
(nf/m3)
slope of the adsorption isotherm for species i (L/kg)
fractional organic carbon content (dimensionless)
fraction of organic carbon in the soil layer in which the waste
is mixed (dimensionless)
fractional organic carbon content of the aquifer material
(dimensionless)
Equation in
which the
symbol first
appears
4.32c
3.15
2.24a
5.11a
4.29
4.107
4.32a
5.13
5.14
2.14
4.51
2.15
4.84
5.1
3.32
3.7
3.31
5.7b
5.7b
4.89
2.3
3.16
3.10
2.26
4.30
XIV
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
9
Ga
H
H(x)
H(0,z)
H(xL, z)
H,
H2
HP
HT
Hv(-)
fi}
HBN
1
IEFF
Im
'Max
Ir
K
ki
k«
Kd
Kds
Kdw
Kfc
Klin
koc
Definition
gravitational acceleration (m/s2)
q-th coefficient (l/m)
hydraulic head (m)
hydraulic head at distance x (m)
hydraulic head at x = 0 (m)
hydraulic head at x = XL (m)
prescribed hydraulic head at the upgradient boundary (m)
prescribed hydraulic head at the downgradient boundary (m)
SI ponding depth (m)
SI operating (total) depth (m)
Heaviside step function (dimensionless)
vector of unknown nodal head values (m)
health-based number, which is a ground-water exposure
concentration corresponding to a defined risk level (mg/L)
annual infiltration rate through the source (m/y)
effective infiltration rate through the strip source area (m/y)
imaginary part of the complex Rvalues (y-mg/L)
maximum allowable infiltration rate (m/y)
effective recharge rate outside the strip source area (m/y)
or recharge rate outside the source area (m/y)
hydraulic conductivity (cm/s)
nonlinear Freundlich parameter for the unsaturated zone (mg
constituent/kg dry soil) (mg/L)"n
nonlinear Freundlich parameter for species ; in the
unsaturated zone (dimensionless)
distribution (solid-aqueous phase) coefficient in the
unsaturated zone (cm3/g)
solid-liquid distribution coefficient of the aquifer (cm3/g)
waste partition coefficient (cm3/g)
averaged saturated hydraulic conductivity of the
consolidated sediment (m/y)
saturated hydraulic conductivity of liner (m/y)
constituent-specific organic carbon partition coefficient
(cm3/g)
Equation in
which the
symbol first
appears
2.17
4.65a
4.7
4.12a
4.9a
4.9b
4.9a
4.9b
2.17
2.24c
4.55
4.15
5.14
2.6
4.9c
4.51
2.31
4.9c
4.4
4.34
3.18
3.11
4.18
2.25
2.21
2.24b
2.26
XV
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
KOC
"rw
"rw
If
rwlin
KS
K;
KSed
KU
Kw
Kx
Ky
Kz
L
#(•)
lu
L"
/'
M
m
m1
mi2
m2
Mc
mcL
MLWP
Ms
™w
MWf
Definition
normalized organic carbon distribution coefficient [cm3/g]
relative permeability of the native soil in the unsaturated
zone (dimensionless)
relative permeability of the clogged soil in the unsaturated
zone (dimensionless)
relative permeability of the liner (dimensionless)
saturated hydraulic conductivity of the native soil (m/y)
saturated hydraulic conductivity of clogged unsaturated-zone
soil (m/y)
hydraulic conductivity of consolidated sediment (m/s)
soil hydraulic conductivity at pressure ip (m/y)
waste-concentration-to-leachate-concentration ratio (L/kg)
hydraulic conductivity of the saturated zone in the
longitudinal (x) direction (m/y)
hydraulic conductivity in the saturated zone in the horizontal
transverse (y) direction (m/y)
hydraulic conductivity in the saturated zone in the vertical (z)
direction (m/y)
overall length of the model domain in the x-direction (m)
Laplace transformation operator (dimensionless)
bottom of the unsaturated zone (m)
(pxp) matrix of the eigenvectors of V12
the thickness of layer ;
number of parent species
sample mean vector of missing and observed values
sample mean vector of missing values
mean vector of Y1 conditioned by Y2
sample mean vector of observed values
total constituent mass in the landfill (mg)
annual constituent mass lost by leaching (mg/y)
total mass of constituent leached from a waste pile
contaminant mass flux (mg/m2-y) which is applied over the
rectangular source area
annual waste loading during active life (kg/y)
molecular weight of species e
Equation in
which the
symbol first
appears
3.11
2.24a
2.24a
2.24b
2.23
2.23
2.14
3.7
2.8
2.31
4.7
4.5
4.43
4.48
3.23a
5.11a
3.27
3.14
5.9
5.9
5.10a
5.9
2.3
2.6
2.27
4.62
4.37
2.4
XVI
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
N[0,1]
nc
Nn()
Ns
%OM
P
Pk
Pm
P°
[P]
Q,
Qm
4*
Q,F
Q/
Q3F
Q/
Q;
{Q}
r
Rn
R0
Definition
normally distributed value with mean of zero and standard
deviation of one
number of component species in the decay chain
(dimensionless)
n - variate normal distribution with mean vector m and
covariance matrix V
number of steps into which c°(t) is discretized
(dimensionless)
percent organic matter (dimensionless)
Laplace-transform parameter (1/y)
/<-th term of the parameter in the Laplace inversion series
(i/y)
probability that the receptor well will be located in Zone 2
(dimensionless)
a real constant for the inversion of Laplace transform (l/yr)
advective-dispersive transport matrix, including the decay
term A
coefficient to incorporate decay in the sorbed phase for
species ; (dimensionless)
coefficient to incorporate decay in the sorbed-phase of
parent m (dimensionless)
average Darcy velocity in the x direction between the
downgradient edge of the source and the point of interest
along the x direction (m/y)
background groundwater flux (m2/y)
recharge flux upgradient of the source (m2/y)
infiltration flux through the source (m2/y)
recharge flux downgradient of the source (m2/y)
ratio of the background groundwater flux to that near the
source (dimensionless)
vector of nodal boundary flux values (m3/y)
regional hydraulic gradient (m/m)
generated random number which corresponds to the
cumulative probability of Y
Equivalent source radius (m)
Equation in
which the
symbol first
appears
5.2
4.31
5.9
4.55
3.10
4.41
4.51
4.27
4.51
4.50
3.14
3.14
4.78
4.29
4.29
4.29
4.29
4.47
4.15
4.6
5.7a
2.31
XVII
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
K,
R™
R*,
^
Rs
R*
Re
[RJ
s
Se
s,
sk
[S]
t
t'
t.
t2
tA
td
'•max
*,
'•peak
Tt
jOff
jon
*• i
U
Definition
retardation factor for species i (dimensionless)
radial distance between waste management unit and well
(m)
distance between the center of the source and the nearest
downgradient boundary where the boundary location has no
perceptible effects on the heads near the source (m)
ratio between effective and total porosities
retardation factor (dimensionless)
saturated zone retardation factor of species n.
(dimensionless)
real part of the complex off) values (y-mg/L)
conductance matrix (m2/y)
sorbed concentration for constituent of interest (mg
constituent/kg dry soil)
effective saturation (dimensionless)
sorbed concentration for species ; (mg constituent/kg dry
soil)
sorbed concentration of species k (mg constituent/kg dry
soil)
Laplace-transformed mass matrix
time (y)
travel time from xu to xc (yr)
beginning of the time interval of interest (y)
end of the time interval of interest (y)
WMU active life (y)
exposure time interval of interest (y)
maximum simulation time (y)
pulse duration (y)
time value at which the receptor well concentration reaches
its peak (y)
time integration variable (y)
end of the time interval of interest (y)
beginning of the time interval of interest (y)
vector of independent and identically distributed standard
normal random variables
Equation in
which the
symbol first
appears
3.14
4.21
2.31
4.2b
4.62
4.18
4.51
4.15
3.29
3.2
3.17
4.72
4.50
2.1
4.66b
4.58
4.58
2.4
4.108
4.52
2.2
4.108
4.65a
4.55
4.55
5.11a
XVIII
-------
EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
U
U(0, 1)
U
uk
V
\v\
VH
V12
V12
V21
V22
V,
vu
vj
vx
r,
Vy
vz
X
X'
X,
X2
X3
Xc
Xcrest
Xd
X,
X,
XL
Definition
seepage (pore-water) velocity (m/y)
uniform random number varying between 0 and 1
retarded seepage velocity in layer ; (m/y)
retarded seepage velocity in layer k (m/y)
sample covariance matrix
absolute value of the Darcy velocity (m/yr)
upper left partition of V
upper right partition of V
covariance matrix of Y1 conditioned by Y2
lower left partition of V
lower right partition of V
Darcy velocity in the ^th direction (m/y)
Darcy velocity obtained from solution of the flow equation
(m/y)
Darcy velocity in the ;'-th layer (m/y)
longitudinal groundwater velocity (in the x-direction) (m/y)
average Darcy velocity in the x direction between the
downgradient edge of the source and the point of interest
along the x direction (m/y)
horizontal transverse Darcy velocity (m/y)
vertical Darcy velocity (m/y)
principal Cartesian coordinate along the regional flow
direction (m)
transformed x-coordinate (m)
x- coordinate (m)
y- coordinate (m)
z- coordinate (m)
downgradient location at which dispersion is calculated (m)
x-coordinate of the crest of the water table (m)
downgradient coordinates of the strip source area (m)
Cartesian coordinates in the i-th direction (the 1st, 2nd, and 3rd
directions correspond to the x, y, and z directions,
respectively) (m)
x-direction component of the solution for species e
length of the aquifer system, or x-coordinate at the
downgradient end of the domain (m)
Equation in
which the
symbol first
appears
3.29
4.25b
3.25a
3.27
5.9
4.32a
5.10c
5.10b
5.10c
5.10c
5.10b
4.16
3.14
3.25b
4.6
4.66b
4.32a
4.32a
4.7
4.94g
4.31
4.31
4.31
4.66
4.85
4.9c
4.31
4.92
4.9b
XIX
-------
EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
*P
Xm
*s
xt
xu
*w
X*
y. max
Arw
y-max
y
y'
y0
YI
Y2
Y12
YD
YE
YEXP
'JSB
y
YL
'LN
YLU
Jrw
Ys
YU
., max
Jrw
Definition
length of the model domain downgradient of the source (m)
distance from the downgradient boundary of the WMU to the
receptor well (m)
distance between the upgradient domain boundary and the
upgradient edge of the source (m)
average travel distance in the x direction (m)
upgradient coordinates of the strip source area (m)
length of the WMU in the x-direction (parallel to groundwater
flow) (m)
random variable
distance from the downgradient boundary of the WMU to the
receptor well (m)
maximum allowable distance between the upgradient
domain boundary and the upgradient edge of the source (m)
principal Cartesian coordinate normal to the flow direction, or
distance from the plume centerline (m)
transformed y-coordinate (m)
source half-width (yD/2) (m)
vector of missing values
vector of observed values
prediction of the missing vector Y.,
source width along the y-axis (m)
random variable with empirical distribution
exponentially distributed random variable
random variable with Johnson SB distribution
y-direction component of the solution for species e
length of the model domain in the y-direction (see Figure 4.1)
lognormally distributed random variable
Iog10 uniform random variable
Cartesian coordinate of the receptor well in the y-direction
(m)
equivalent source width in the direction normal to the
regional flow direction on the vertical plane at the
downgradient edge of the waste (m)
uniform random variable
farthest horizontal distance between the receptor well and
the plume centerline (m)
Equation in
which the
symbol first
appears
4.43
4.20
4.42a
4.19
4.9c
4.20
5.1
4.43
4.42a
4.7
4.94g
4.62
5.10a
5.10a
5.11a
4.10
5.7b
5.4
5.8
4.92
4.10
5.3
5.6
4.22
4.81
5.5
4.45a
XX
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
., New
yplume
Z
z
zs
ZSed
zu
Z'
?'l
z'2
z;
z*
*• ni
Z*'
*• ni
^ rwmax
zu'
., New
ZS
Definition
ys adjusted to account for 2"*™ (m)
transverse extent of the plume (m)
principal Cartesian coordinate in the vertical direction (m)
z-direction component of the solution for species e
equivalent source depth in the vertical direction on the
vertical plane at the downgradient edge of the waste
management unit (m)
vertically downward distance from the top of the
consolidated sediment (m)
depth coordinate measured from the bottom of the base of a
waste management unit (m)
transformed z-coordinate (m)
transformed well depth in image 1 (m)
transformed well depth in image 2 (m)
a component of Zt
z-coordinate of the receptor well positive downward from the
water table(m)
transformed well depth (m)
maximum allowable z-coordinate of the receptor well (m)
local depth coordinate measured from the tip of layer ; (m)
zs adjusted to account for the presence of recharge depth DR
(m)
Equation in
which the
symbol first
appears
4.91
4.45a
4.7
4.92
4.82
2.16
3.4
4.94g
4.105
4.105
4.102
4.29
4.106
4.29
3.25a
4.90
GREEK SYMBOLS
a
aL
VLU
OfRef
aT
av
ofLJ
P
y
van Genuchten soil-specific shape parameter (1/m)
longitudinal dispersivity of the aquifer (m)
longitudinal dispersivity in the unsaturated zone [m]
reference longitudinal dispersivity, as determined from the
probabilistic distribution (m)
horizontal transverse dispersivity (m)
vertical transverse dispersivity (m)
longitudinal dispersivity for the i-th layer (m)
van Genuchten soil-specific shape parameter
(dimensionless)
van Genuchten soil-specific shape parameter
(dimensionless)
3.1
4.19
3.9
4.19
4.28
4.29
3.25a
3.1
3.1
XXI
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
Y,
Ym
6(>)
5aa
As
&u
{
Hi
rf
9
er
0m
0s
0*
0!
A,
A2
^bu
^cu
A,
Am
*u
X
As
V
V
Definition
first-order decay rate for species i (1/y)
first order decay rate for parent m (1/y)
Dirac Delta function
empirical adjustment factor (dimensionless)
magnitude of nodal spacing (m)
grid size in the zu direction (m)
distance along a principal Cartesian coordinate direction (m)
non-linear Freundlich exponent for species ; for the
unsaturated zone (dimensionless)
Freundlich exponent for the saturated zone (dimensionless)
soil water content (dimensionless)
residual soil water content (dimensionless)
angle measured counter-clockwise from the plume centerline
(degrees)
saturated soil water content (dimensionless)
water content of the waste (dimensionless)
water content of the ;'-th layer (dimensionless)
hydrolysis constant for dissolved phase (1/y)
hydrolysis constant forsorbed phase (1/y)
transformation coefficient due to biological transformation
(1/y)
transformation coefficient due to chemical transformation
(1/y)
first-order decay constant for species ; (1/y)
first-order decay constant of parent m (1/y)
overall decay coefficient (first-order transformation) (1/y)
first order decay constant for layer ; (1/y)
first-order decay constant (l/y)
first-order decay coefficient for species /in the saturated
zone (1/y)
first-order decay coefficient for parent m in the saturated
zone (1/y)
Equation in
which the
symbol first
appears
3.24a
3.24a
4.62
4.71
4.46
3.7
4.16
3.18
4.34
3.1
3.1
4.21
3.1
2.25
3.25b
3.13
3.13
3.12
3.12
3.14
3.14
3.12
3.25a
4.62
4.31
4.31
XXII
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EPACMTP Technical Background Document
LIST OF SYMBOLS (continued)
Symbol
fJ
PN
S/m
P
pb
Pbu
Pbw
Phw
Pleak
PS
Psed
ON
°«
e
eu
0Sed
V
V,
^
Vzu
*
(l)
Definition
dynamic viscosity of water (N-s/m2)
mean of normal distribution
stochiometric fraction of parent m that degrades into
daughter ; (dimensionless)
density of water (kg/m3)
bulk density of the aquifer (g/cm3)
soil bulk density of the unsaturated zone (g/cm3)
dry bulk density of the waste (g/cm3)
waste density (g/cm3)
leak density (number of pinholes/m2)
bulk density of the solid phase (g/cm3)
sediment grain density (kg/m3)
standard deviation of normal distribution
vertical effective stress in the consolidated sediment layer
(kg/m-s2)
total porosity (dimensionless)
effective porosity of the saturated zone (dimensionless)
effective porosity of the unsaturated zone (dimensionless)
consolidated sediment porosity (dimensionless)
soil pressure head (m)
pressure head at the water table located at distance n. from
the bottom of a waste management unit (m)
q-th constant (1/m)
pressure head at zu (m)
effective pressure head between z and zu - A zu (m)
weighting factor, 0 < w < 1 (dimensionless)
Equation in
which the
symbol first
appears
4.4
5.1
3.14
2.17
3.13
3.16
2.25
2.3
2.24c
4.72
2.17
5.1
2.15
4.1
4.2b
3.15
2.14
3.1
3.5
4.65a
3.7
3.7
3.8
XXIII
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EPACMTP Technical Background Document
ACKNOWLEDGMENTS
A number of individuals have been involved with this work. Ms. Ann Johnson and
Mr. David Cozzie of the U.S. EPA, Office of Solid Waste (EPA/OSW) provided
overall project coordination and review and guidance throughout this work. The
report was prepared by the staffs of Resource Management Concepts, Inc. (RMC)
and HydroGeoLogic, Inc. (HGL) under EPA Contract Number 68-W-01-004.
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EPACMTP Technical Background Document
EXECUTIVE SUMMARY
EPACMTP version 2.0 is a subsurface fate and transport model used by the U.S.
Environmental Protection Agency (EPA) to simulate the impact of the release of
constituents present in waste that is managed in land disposal units. Figure ES.1
shows a conceptual, cross-sectional view of the aquifer system modeled by
EPACMTP.
EPACMTP simulates fate and transport in both the unsaturated zone and the
saturated zone (ground water) using the advective-dispersive equation with terms to
account for equilibrium sorption and first-order transformation. The source of
constituents is a waste management unit (WMU) located at the ground surface
overlying an unconfined aquifer. The base of the WMU can be below the actual
ground surface. Waste constituents leach from the base of the WMU into the
underlying soil. They migrate vertically downward until they reach the water table.
As the leachate enters the ground water, it will mix with ambient ground water (which
is assumed to be free of pollutants) and a ground-water plume, which extends in the
direction of downgradient ground-water flow, will develop. EPACMTP accounts for
the spreading of the plume in all three dimensions.
Leachate generation is driven by the infiltration of precipitation that has percolated
through the waste unit, from the base of the WMU into the soil. Different liner
designs control the rate of infiltration that can occur. EPACMTP models flow in both
the unsaturated and saturated zones as steady-state processes, that is, representing
long-term average conditions.
LEACHATE CONCENTRATION
_ WASTE MANAGEMENT UNIT
JNSATURATED
ZONE
SATURATED
ZONE LEACHATE PLUM
Figure ES.1 Conceptual Cross-Section View of the Subsurface System
Simulated by EPACMTP.
XXVII
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EPACMTP Technical Background Document
In addition to dilution of the constituent concentration caused by the mixing of the
leachate with ground water, EPACMTP accounts for attenuation due to sorption of
waste constituents in the leachate onto soil and aquifer solids, and for bio-chemical
transformation (degradation) processes in the unsaturated and saturated zone.
For organic constituents, EPACMTP models sorption between the constituents and
the organic matter in the soil or aquifer, based on constituent-specific organic carbon
partition coefficients, and a site-specific organic carbon fraction in the soil and
aquifer. In the case of metals, EPACMTP accounts for more complex geochemical
reactions by using effective sorption isotherms for a range of aquifer geochemical
conditions, generated using EPA's geochemical equilibrium speciation model for
dilute aqueous systems (MINTEQA2).
Four types of WMUs with the following key characteristics are simulated by
EPACMTP:
• Landfill (LF). EPACMTP considers LFs closed with an
earthen cover. The release of waste constituents into the soil
and ground water underneath the LF is caused by dissolution
and leaching of the constituents due to precipitation that
percolates through the LF.
• Surface Impoundment (SI). In EPACMTP, Sis are ground
level or below-ground level, flow-through units. Release of
leachate is driven by the ponding of water in the impoundment,
which creates a hydraulic head gradient with the ground water
underneath the unit.
• Waste Pile (WP). WPs are typically used as temporary
storage units for solid wastes. Due to their temporary nature,
EPACMTP does not consider them to be covered.
• Land Application Unit (LAU). LAUs are areas of land which
receive regular applications of waste that can be either tilled or
sprayed directly onto the soil and subsequently mixed with the
soil. EPACMTP simulated the leaching of wastes after tilling
with soil. Losses due to volatilization during or after waste
application are not accounted for by EPACMTP.
The output from EPACMTP is the predicted maximum ground-water exposure
concentration, measured at a well located down-gradient from a WMU.
EPACMTP uses a regional site-based Monte-Carlo simulation approach to determine
the probability distribution of predicted ground-water concentrations, as a function of
the variability of modeling input parameters. The Monte-Carlo technique is based on
the repeated random sampling of input parameters from their respective frequency
distribution, executing the EPACMTP fate and transport model for each realization of
input parameter values. The regional site-based approach is incorporated into the
EPACMTP model to reduce the likelihood that a physically infeasible set of
XXVIII
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EPACMTP Technical Background Document
environmental data will be generated. The results of EPACMTP Monte-Carlo
simulations are used to generate probability distributions of constituent
concentrations at receptor wells and associated ground-water dilution and
attenuation factors (DAFs).
EPACMTP has been peer-reviewed, verified, and enhanced extensively during the
past decade. It has also been validated using actual site data from four different
sites.
EPACMTP has been applied to support the development of regulations for
management and disposal of hazardous wastes. Examples of regulations based on
EPACMTP analysis include: Toxicity Characteristic (TC) Rule, Hazardous Waste
Identification Rule (HWIR), and Petroleum Refining Process Wastes Listing
Determination.
XXIX
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Introduction Section 1.0
1.0 INTRODUCTION
This document provides technical background for EPA's Composite Model for
Leachate Migration with Transformation Products (EPACMTP). EPACMTP is a
subsurface fate and transport model used by EPA to simulate the impact of the
release of constituents present in waste that is managed in land disposal units. This
document describes the science and assumptions underlying the EPACMTP. EPA
has also developed a complementary document, the EPACMTP Parameters/Data
Background Document (U.S. EPA, 2003), which describes the EPACMTP input
parameters, data sources and default parameter values and distributions which EPA
has assembled for its use of EPACMTP as a ground-water assessment tool.
This document is organized as follows. The remainder of this section introduces the
main components and features of EPACMTP, and also presents the primary
assumptions and limitations of the model. The purpose of this section is to provide
the user with an overall understanding of the model and its capabilities. Subsequent
sections of this document describe the components, or modules, of EPACMTP in
detail:
• Section 2 describes the source-term module;
• Section 3 describes the unsaturated-zone module;
• Section 4 describes the saturated-zone module; and
• Section 5 describes the Monte-Carlo module.
Several appendices provide detailed mathematical formulations, and testing and
verification of the unsaturated zone and saturated zone flow and transport solutions
incorporated into EPACMTP.
1.1 DEVELOPMENT HISTORY OF EPACMTP
The U.S. Environmental Protection Agency (EPA), Office of Solid Waste (OSW) has
been using and improving mathematical models since the early 1980s when the
Vertical ^Horizontal Spread (VMS) model (Domenico and Palciauskas, 1982) was
used. In the late 1980s, the model was replaced by the EPA's Composite Model for
Landfills [EPACML] (U.S. EPA, 1990). EPACML simulates the movement of
contaminants leaching from a landfill through the unsaturated and saturated zones.
The composite model consists of a steady-state, one-dimensional numerical module
that simulates flow and transport in the unsaturated zone. The contaminant flux at
the water table is 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 ground-water plume.
EPACML accounts for first-order decay and linear equilibrium sorption of chemicals,
but disregards the formation and transport of transformation products (also known as
degradation products). The analytical ground-water transport solution technique
employed in EPACML further imposes certain restrictive assumptions; specifically,
the solution can handle only uniform, unidirectional ground-water flow and thereby
1-1
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Introduction Section 1.0
ignores the effects of ground-water mounding on contaminant migration and ground-
water flow. To address the limitations of EPACML, the modeling approach has been
enhanced and implemented in EPACMTP. The EPACMTP modeling approach
incorporates greater flexibility and versatility in the simulation capability; i.e., the
model explicitly can take into consideration:
a) chain transformation reactions and transport of degradation products,
b) effects of water-table mounding on ground-water flow and contaminant
migration,
c) finite source, as well as continuous source, scenarios, and
d) metals transport by linking EPACMTP with outputs from the MINTEQA2
metals speciation model (U.S. EPA, 1999).
EPACMTP contains an unsaturated-zone module called Finite Element Contaminant
Transport in the LJrisaturated zone (FECTUZ) (U.S. EPA, 1989), a saturated-zone
module called Combined Analytical-Numerical SAturated Zone in 3-Dimensions
(CANSAZ-3D) (Sudicky et al., 1990) and a Monte-Carlo module for nationwide
uncertainty analysis. The FECTUZ model and the CANSAZ model were reviewed by
the Science Advisory Board (SAB) in 1988, and 1990 (SAB, 1988; 1990),
respectively. In March 1994, the SAB provided a consultation on an earlier verison
of EPACMTP. Based on recommendations for the SAB, EPACMTP was further
enhanced and improved. The code received a favorable review by the SAB in 1995
for its intended use in RCRA/Superfund regulations (SAB, 1995).
EPACMTP and its predecessors (EPACML, CANSAZ-3D, and FECTUZ) have been
peer-reviewed, verified and enhanced extensively during the past decade at each of
the developmental stages. The model has been verified, in numerous cases, by
comparing the simulation results against both analytical and numerical solutions.
Additionally, EPACMTP and its predecessors have been validated using actual site
data from four different sites. Details of verification and validation history and results
are presented in Appendix D of this document.
EPACMTP has been applied to support the development of regulations for
management and disposal of hazardous wastes. Examples of regulations based on
EPACMTP analysis include: Toxicity Characteristic (TC) Rule, and Petroleum
Refining Process Wastes Listing Determination. The Agency has implemented a
version control procedure over the development of EPACMTP to ensure repeatability
of simulation results. The current version of EPACMTP is 2.0.
1.2 WHAT IS THE EPACMTP MODEL?
Figure 1.1 depicts a cross-sectional view of the subsurface system simulated by
EPACMTP. EPACMTP treats the subsurface aquifer system as a composite
domain, consisting of an unsaturated (vadose) zone and an underlying saturated
zone. The demarcation between the two zones is the water table. EPACMTP
simulates one-dimensional, vertically downward flow and transport of constituents in
the unsaturated zone beneath a waste disposal unit as well as ground-water flow
and three-dimensional constituent transport in the underlying saturated zone. The
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Introduction
Section 1.0
unsaturated-zone and saturated-zone modules are computationally linked through
continuity of flow and constituent concentration across the water table directly
underneath the waste management unit (WMU). The model accounts for the
following processes affecting constituent fate and transport as the constituent
migrates from the bottom of a WMU through the unsaturated and saturated zones:
advection, hydrodynamic dispersion and molecular diffusion, linear or nonlinear
equilibrium sorption, first-order decay and zero-order production reactions (to
account for transformation breakdown products), and dilution due to recharge in the
saturated zone.
L£ACHATE CONCENTRATION
WASTE MANAGEMENT UNIT
Figure 1.1 Conceptual Cross-Section View of the Subsurface System
Simulated by EPACMTP.
The primary input to the model is the rate and the concentration of constituent
release (leaching) from a WMU. The output from EPACMTP is a prediction of the
constituent concentration arriving at a downgradient well. This can be either a
steady-state concentration value, corresponding to a continuous-source scenario, or
a time-dependent concentration, corresponding to a finite-source scenario. In the
latter case, the model can calculate the peak concentration arriving at the well or a
time-averaged concentration corresponding to a specified exposure duration (for
example a 30-year average exposure time).
The relationship between the constituent concentration leaching from a WMU and
the resulting ground-water exposure at a well located down-gradient from the WMU
is depicted in Figure 1.2. This figure shows the time history of the leachate
concentration emanating from a landfill-type WMU, and the corresponding time
history (also called a breakthrough curve) of the concentration in ground water at a
well, located downgradient from the WMU. The figure shows how the leachate
concentration emanating from the landfill unit gradually diminishes over time as a
result of depletion of the waste mass in the WMU. The constituent does not arrive at
the well until some time after the leaching begins. The ground-water concentration
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Introduction
Section 1.0
u>
o
I
I
o
o
&
CO
o
(0
Initial Leachate Concentration
Time >
(a) Leachate Concentration Versus Time
O)
E
o
•?
(0
0)
o
c
o
o
1
Peak
Concentration
.Time-averaged well concentration, C,
Time
Exposure
Averaging Period
(b) Groundwater Well Concentration Versus Time
Figure 1.2 (a) Leachate Concentration, and
(b) Ground-water Exposure Concentration.
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Introduction
Section 1.0
will reach a peak value at the
well, and will eventually begin to
diminish again because the
leaching from the waste unit
occurs only over a finite period of
time. The maximum constituent
concentration at the well will
generally be lower than the
original leachate concentration
as a result of various dilution and
attenuation processes which
occur during its transport through
the unsaturated and saturated
zones. For risk assessment
purposes, the concentration
measure of interest is the
magnitude of the ground-water
concentration, averaged over
some defined exposure period.
EPACMTP has the capability to
calculate the maximum average
ground-water concentration, as
depicted by the horizontal
dashed line in Figure 1.2. Cw in
this figure represents the time-
averaged well concentration that
is used in risk evaluations.
1.2.1 Source-Term Module
In an EPACMTP ground-water flow and transport analysis, the source term
describes the rate of leaching and the constituent concentration in the leachate as a
function of time. The leachate concentration used in the model directly represents
the concentration of the leachate released from the base of the WMU as a boundary
condition for the fate and transport model.
The source term as conceptualized and modeled in EPACMTP contains a number of
simplifications. The model does not attempt to account explicitly for the multitude of
physical and biochemical processes inside the WMU that may control the release of
waste constituents to the subsurface. Instead, the net result of these processes are
used as inputs to the model. For instance, EPA uses the Hydrologic Evaluation of
Landfill Performance (HELP) model (Schroeder et al., 1994a and 1994b) to
determine infiltration rates for unlined, single lined, and composite-lined units
externally to EPACMTP. The HELP-calculated infiltration rates are used as inputs to
EPACMTP. Likewise, the model does not explicitly account for the complex
physical, biological, and geochemical processes in the WMU that determines the
resultant leachate concentration used as an input to EPACMTP. These processes
EPACMTP consists of four major
components:
• A source-term module that simulates the
rate and concentration of leachate exiting
from beneath a WMU and entering the
unsaturated zone;
• An unsaturated-zone module which
simulates one-dimensional vertical flow of
water and dissolved constituent transport
in the unsaturated zone;
• A saturated-zone module which simulates
ground-water flow and dissolved
constituent transport in the saturated
zone.
• A Monte-Carlo module for randomly
selecting input parameter values to
account for variations in the model input,
and determining the probability
distributions of predicted ground-water
concentrations.
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Introduction Section 1.0
are typically estimated outside the EPACMTP model using geochemical modeling
software, equilibrium partitioning models, or analytical procedures such as the
Toxicity Characteristic Leaching Procedure (TCLP) or the Synthetic Precipitation
Leaching Procedure (SPLP) test. Given the broad range of EPACMTP model
applications, making these source-specific calculations outside the model maintains
flexibility, and computational efficiency, as well as allows the EPACMTP analyses to
be tailored to the requirements of a specific application.
The constituent source term for the EPACMTP fate and transport model is defined in
terms of four primary parameters:
1) Area of the waste unit,
2) Leachate flux rate emanating from the waste unit (infiltration rate),
3) Constituent-specific leachate concentration, and
4) Leaching duration.
Leachate flux rate and leaching duration depend on both the design and operational
characteristics of the WMU and the waste stream characteristics (waste quantities
and waste constituent concentrations).
EPACMTP represents the leaching process in one of two ways: 1) The WMU is
modeled as a depleting source; or 2) The WMU is modeled as a pulse source. In the
depleting-source scenario, the WMU is considered permanent and leaching
continues until all waste that is originally present has been depleted. In the pulse-
source scenario, leaching occurs at a constant leachate concentration for a fixed
period of time, after which leaching stops1. EPACMTP uses the pulse source
scenario to model temporary WMUs; usually the leaching period represents the
operational life of the unit. Under clean closure conditions, the leaching stops when
the unit is closed.
1.2.2 Unsaturated-Zone Module
The unsaturated-zone module of EPACMTP simulates vertical water flow and solute
transport through the unsaturated zone between the base of the WMU and the water
table of an unconfined aquifer. Constituents migrate downward from the disposal
unit through the unsaturated zone to the water table. The general simulation
scenario for which the module was designed is depicted schematically in Figure 1.1.
This figure shows a vertical cross-section through the unsaturated zone underlying a
WMU.
EPACMTP models flow in the unsaturated zone as a one-dimensional, vertically
downward process. EPACMTP assumes the flow rate is steady-state, that is, it does
not change with time. The flow rate is determined by the long-term average
infiltration rate from the WMU.
1 If the leaching period is set to a very large value, EPACMTP will simulate continuous
source conditions.
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Introduction Section 1.0
Constituent transport in the unsaturated zone is assumed to occur by advection and
dispersion2. Advection refers to transport along with ground-water flow.
Hydrodynamic dispersion is caused by local variations in ground-water flow and acts
as a mixing mechanism, which causes the constituent plume to spread, but also be
diluted.
The unsaturated zone is assumed to be initially constituent-free and constituents
migrate vertically downward from the WMU. EPACMTP can simulate both steady-
state and transient contaminant transport in the unsaturated zone with single-species
or multiple-species chain decay reactions. Steady-state refers to situations in which
the release of constituents from a WMU occurs at a constant rate for a very long
period of time, so that eventually constituent concentrations in the subsurface reach
a constant level. In a transient (or time-dependent) analysis, the constituent
concentration in the subsurface may not reach steady-state and therefore, the
constituent fate and transport processes are simulated as a function of time.
1.2.3 Saturated-Zone Module
The saturated-zone module of EPACMTP is designed to simulate flow and transport
in an idealized aquifer with uniform saturated thickness (see Figure 1.1). The
module simulates regional flow in a horizontal direction with recharge and infiltration
from the overlying unsaturated zone and WMU. The lower boundary of the aquifer is
assumed to be impermeable. The aquifer is assumed to be initially constituent-free,
and constituents enter the saturated zone only from the overlying unsaturated zone
directly underneath the waste disposal facility.
EPACMTP assumes that flow in the saturated zone is steady-state. In other words,
EPACMTP models long-term average flow conditions. EPACMTP accounts for
different recharge rates beneath and outside the source area. Ground-water
mounding beneath the source is represented in the flow system by increased head
values at the top of the aquifer. It is important to realize that while EPACMTP
calculates the degree of ground-water mounding that may occur underneath a WMU
due to high infiltration rates, and will restrict the allowable infiltration rate to prevent
physically unrealistic input parameter combinations, the actual saturated-zone flow
and transport modules in EPACMTP are based on the assumption of a constant
saturated thickness. That is, the water table position is assumed to be fixed, and the
only direct effect of ground-water mounding is to increase simulated ground-water
velocities.
EPACMTP simulates the transport of dissolved constituents in the saturated zone
using the advection-dispersion equation. Advection refers to transport along with
ground-water flow. Dispersion encompasses the effects of both hydrodynamic
dispersion and molecular diffusion. Both act as mixing mechanisms which cause a
2 In the case of metals which are subject to nonlinear sorption, EPACMTP uses a
method-of-characteristics solution method that does not include dispersion. In these case,
transport is dominated by the nonlinear sorption behavior and dispersion effects are considered
minor.
1-7
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Introduction Section 1.0
constituent plume to spread, but also be diluted. Hydrodynamic dispersion is caused
by local variations in ground-water flow and is usually a significant plume-spreading
mechanism in the saturated zone. Molecular diffusion on the other hand is usually a
very minor mechanism, except when ground-water flow rates are very low. The
saturated-zone transport simulation also accounts for first-order transformation
reactions in both the aqueous and sorbed phases, and retardation due to linear
equilibrium sorption of constituents onto aquifer particles.
1.2.4 Monte-Carlo Module
The final component of EPACMTP is a Monte-Carlo module which allows the model
to perform probabilistic analyses of constituent fate and transport in the subsurface.
Monte-Carlo simulation is a statistical technique by which a quantity is calculated
repeatedly, using randomly selected model input parameter values for each
calculation. The results approximate the full range of possible outcomes, and the
likelihood of each. In particular, EPA uses Monte-Carlo simulation to determine the
likelihood, or probability, that the concentration of a constituent at the receptor well,
and hence exposure and risk, will be either above or below a certain value.
EPACMTP requires values for the various source-specific, chemical-specific,
unsaturated-zone-specific and saturated-zone-specific model parameters to
determine well concentrations. For many assessments it is not appropriate to assign
single values to all of these parameters. Rather, the values are represented as a
probability distribution, reflecting both the range of variation that may be encountered
at different waste sites, as well as the uncertainty about site-specific conditions.
Thus, the fate and transport simulation modules in EPACMTP are linked to a Monte-
Carlo module to allow quantitative estimation of the probability that the receptor well
concentration will be below a threshold value, due to variability and uncertainty in the
model input parameters.
Variability describes parameters whose values are not constant, but which we can
measure and characterize with relative precision in terms of a frequency distribution.
Uncertainty pertains to parameters whose values or distributions we know only
approximately. An example of variability is a distribution of body weights of the
human population across the nation. Body weight data are abundant and
measurement errors are considered insignificant. The distribution of body weights
based on a large volume of data may be regarded as variable but not uncertain. A
distribution of hydraulic conductivity values for a heterogenous aquifer may be
regarded as variable and uncertain. Variability is due to the fact that hydraulic
conductivity values are spatially varied. Uncertainty of the distribution may be
attributed to, at least, measurement and analysis errors, and sampling errors. In
practice, we normally use probability distributions to describe variability which may
also be associated with uncertainty. In the EPACMTP Monte-Carlo module,
parameter distributions include both variability and uncertainty of parameter data.
The combined entities are not separated nor distinguished by the module.
The Monte-Carlo module requires that for each input parameter, except constant
parameters, a probability distribution be provided. The method involves the repeated
1-8
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Introduction Section 1.0
generation of pseudo-random values of the input variables (drawn from the known
distribution and within the range of any imposed bounds). The EPACMTP model is
executed for each set of randomly generated model parameters and the
corresponding ground-water well exposure concentration is computed and stored.
Each simulation of a site by the model based on a set of input parameter values is
termed a realization. The simulation process is repeated by generating additional
realizations.
At the conclusion of the Monte-Carlo simulation, the realizations are statistically
analyzed to yield a cumulative distribution function (CDF), a probability distribution of
the ground-water well exposure concentration. The construction of the CDF simply
involves sorting the ground-water well concentration values calculated in each of the
individual Monte-Carlo realizations from low to high. The well concentration values
simulated in the EPACMTP Monte-Carlo process range from very low values to
values that approach the original leachate concentration. By examining how many of
the total number of Monte-Carlo realizations resulted in a high value of the predicted
ground-water concentration, it is possible to assign a probability to these high-end
events, or conversely determine what is the expected ground-water concentration
level corresponding to a specific probability of occurrence.
1.3 EPACMTP ASSUMPTIONS AND LIMITATIONS
EPA designed EPACMTP to be used for regulatory assessments in a probabilistic
framework. The simulation algorithms that are incorporated into the model are
intended to meet the following requirements:
• Account for the primary physical and chemical processes that affect
constituent fate and transport in the unsaturated and saturated zones;
• Be useable with relatively little site input data; and
• Be computationally efficient for Monte-Carlo analyses.
This section discusses the primary assumptions and limitations of EPACMTP that
EPA made in developing the model to balance the competing requirements.
EPACMTP may not be suitable for all sites, and the user should understand the
capabilities and limitations of the model to ensure it is used appropriately.
Source-Term Module
The EPACMTP source-term module provides a relatively simple representation of
different types of WMUs. EPACMTP does not simulate the fate and transport of
chemical constituents within a WMU. WMUs are represented in terms of a source
area, and a defined rate and duration of leaching. EPACMTP only accounts for the
release of leachate through the base of the WMU, and assumes that the only
mechanism of constituent release is through dissolution of waste constituents in the
water that percolates through the WMU. In the case of surface impoundments
EPACMTP assumes that the leachate concentration is the same as the constituent
1-9
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Introduction Section 1.0
concentration in the waste water in the surface impoundment. EPACMTP does not
account for the presence of non-aqueous free-phase liquids, such as an oily phase
that might provide an additional release mechanism into the subsurface. EPACMTP
does not account for releases from the WMU via other environmental pathways,
such as volatilization or surface run-off. EPACMTP assumes that the rate of
infiltration through the WMU is constant, representing long-term average conditions.
EPACMTP does not account for fluctuations in rainfall rate, or degradation of liner
systems that may cause the rate of infiltration and release of leachate to vary over
time.
Unsaturated-Zone and Saturated-Zone Modules
EPACMTP simulates the unsaturated zone and saturated zone as separate domains
that are connected at the water table. Both the unsaturated zone and the saturated
zone are assumed to be uniform porous media. The thickness of the saturated zone
is uniform in space and constant in time. EPACMTP does not account for the
presence of macro-pores, fractures, solution features, faults or other heterogeneities
in the soil or aquifer that may provide pathways for rapid or retarded movement of
constituents. EPACMTP may not be appropriate for sites overlying fractured or very
heterogeneous aquifers.
EPACMTP is designed for relatively simple ground-water flow systems in which flow
is predominantly horizontal along the regional gradient direction. Flow in the
saturated zone is assumed to be driven by long-term average infiltration and
recharge; EPACMTP treats flow in the unsaturated zone as steady-state and does
not account for fluctuations in the infiltration or recharge rate. The rate of ambient
recharge outside of the WMU is assumed to be uniform and constant over time.
With this assumption, EPACMTP is appropriate for the simulation of long-term flow
and transport at sites where the general flow direction does not change over time,
and where the long-term average saturated thickness is relatively constant.
EPACMTP does not account for the presence of major ground-water sources or
sinks such as surface water bodies or large municipal pumping or injection wells.
Therefore, use of EPACMTP may not be appropriate at sites with these or any other
features which significantly modify regional flow fields, or at sites where the recharge
varies locally.
EPACMTP models ground-water flow based on the assumption that the contribution
of recharge and infiltration from the unsaturated zone are small relative to the
regional ground-water flow, and that the rise of water table elevation due to
infiltration and recharge is small compared with the initial saturated thickness. The
implication is that the saturated zone can be modeled as having a thickness
unaffected by infiltration and recharge and constant in time, with mounding
underneath the WMU represented by an increased head distribution along the water
table. The foregoing assumption allows EPACMTP to approximate an unconfined
aquifer by an equivalent confined aquifer with constant and uniform thickness. The
major benefit of this approximation is that the flow equation becomes linear and the
computational effort for its solution is significantly less (by a factor of 10 or 20) than
that for the truly unconfined scenario. With this approximation, the general flow
1-10
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Introduction Section 1.0
characteristics are preserved in terms of general flow direction and velocity
distribution. However, as stated earlier, with the confined approximation, EPACMTP
does not account for the actual physical increase in saturated thickness, thereby
tending to overestimate ground-water velocities at downgradient locations. The
overestimation of velocity usually results in conservative estimates of constituents'
arrival times and peak concentrations. The assumption of constant and uniform
saturated-zone thickness means that EPACMTP may not be suitable at sites with a
highly variable thickness of the water-bearing zone. Similar to the source module,
the unsaturated-zone and saturated-zone modules do not account for free-phase
flow conditions of an oily, non-aqueous phase liquid, and vapor-phase transport of
volatile organic chemicals.
The unsaturated-zone and saturated-zone modules of EPACMTP account for
constituent fate and transport by advection, hydrodynamic dispersion, molecular
diffusion, sorption and first-order transformation. However, EPACMTP does not
account for matrix-diffusion processes, which may occur when the aquifer formation
comprises zones with large contrasts in permeability. In these situations, transport
occurs primarily in the more permeable zones, but constituents can move into and
out of the low permeability zones by diffusion. Lateral diffusion is assumed very
small, compared with advection and hydrodynamic dispersion.
Leachate constituents can be subject to complex biological and geochemical
interactions in soil and ground water. EPACMTP treats these interactions as
equilibrium sorption and first-order degradation processes. In the case of sorption
processes, the equilibrium assumption means that the sorption process occurs
instantaneously, or at least very quickly relative to the time-scale of constituent
transport. Although sorption, or the attachment of leachate constituents to solid soil
or aquifer particles may result from multiple chemical processes, EPACMTP lumps
these processes together into an effective soil-water partition coefficient.
For organic constituents, EPACMTP assumes that the partition coefficient is
constant, and equal to the product of the mass fraction of organic carbon in the soil
or aquifer, and a constituent-specific organic carbon partition coefficient. This
relationship should be used when the mass fraction of organic carbon is greater than
0.001, otherwise sorption of the organic constituents on non-organic solids can
become significant. A majority of soils and aquifer materials across the U. S. have a
mass fraction of organic carbon larger than 0.001 (Carsel et al., 1988). In addition,
the partition coefficient of a constituent remains relatively constant when the
aqueous concentration of the constituent remains below one half of its solubility limit
(deMarsily, 1986).
For metals, EPACMTP allows the partition coefficient to vary as a function of a
number of primary geochemical parameters, including pH, leachate organic matter,
soil organic matter, and the fraction of iron-oxide in the soil or aquifer (see Section
3.3.3.2 in The EPACMTP Parameters/Data Background Document (U.S. EPA,
2003). EPACMTP uses a set of effective sorption isotherms which were developed
by EPA by running the MINTEQA2 geochemical speciation model for each metal and
combination of geochemical parameters. In modeling metals transport in the
unsaturated zone, EPACMTP uses the complete, nonlinear sorption isotherms. In
1-11
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Introduction Section 1.0
modeling metals transport in the saturated zone, EPACMTP uses linearized
MINTEQA2 isotherms, based on the assumption that after dilution of the leachate
plume in ground water, concentration values of metals will typically be in a range
where the isotherm is approximately linear. This assumption may not be valid when
metals concentrations in the leachate are high. Although EPACMTP is able to
account for the effect of the geochemical environment at a site on the mobility of
metals, the model assumes that the geochemical environment at a site is constant
and not affected by the presence of the leachate plume. In reality, the presence of a
leachate plume may alter the ambient geochemical environment locally.
EPACMTP does not account for colloidal transport or other forms of facilitated
transport. For metals and other constituents that tend to strongly sorb to soil
particles, and which EPACMTP will simulate as relatively immobile, movement as
colloidal particles can be a significant transport mechanism. It is possible to
approximate the effect of these transport processes by using a lower value of the
partition coefficient as a user-input.
EPACMTP accounts for biological and chemical transformation processes as first-
order degradation reactions. That is, it assumes that the transformation process can
be described in terms of a constituent-specific half-life. EPACMTP allows the
degradation rate to have different values in the unsaturated zone and the saturated
zone, but the model assumes that the value is uniform throughout each zone for
each constituent. EPA's ground-water modeling database includes constituent-
specific hydrolysis rate coefficients for constituents that are subject to hydrolysis
transformation reactions; for these constituents, EPACMTP simulates transformation
reactions subject to site-specific values of pH and soil and ground-water
temperature, but other types of transformation processes are not explicitly simulated
in EPACMTP.
For many organic constituents, biodegradation can be an important fate mechanism,
but EPACMTP has only limited ability to account for this process. The user must
provide an appropriate value for the effective first-order degradation rate. In an
actual leachate plume, biodegradation rates may be different in different regions in
the plume; for instance in portions of the plume that are anaerobic some constituents
may biodegrade more readily, while other constituents will biodegrade only in the
aerobic fringe of the plume. EPACMTP does not account for these processes that
may cause a constituent's rate of transformation to vary in space and time.
Monte-Carlo Module
The Monte-Carlo module of EPACMTP allows you to take into account the effects of
parameter distributions on predicted ground-water concentrations. The validity of the
resulting probability distribution of outcomes is based on assumptions that the
models of the flow and transport processes can accurately capture the salient flow
and transport characteristics in the field and that the distributions of parameters are
accurate. The resulting probability distribution is also subject to uncertainties
associated with sampling errors (due to the fact that a small sample is used to
1-12
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Introduction Section 1.0
represent the whole data population), model errors (because the flow and transport
models are approximations of the actual flow and transport processes),
measurement errors of parameters, and possible misspecification of parameter
distributions. Because the Monte-Carlo module in EPACMTP Version 2 is based on
a single-stage Monte-Carlo methodology, the confidence interval of a given
percentile of the resulting probability distributions cannot be ascertained.
In addition, EPACMTP can account only for intersite variability of flow and transport
properties. Intrasite variability of properties (heterogeneity within the site) is not
included as part of the analysis. As a result, EPACMTP does not account for
uncertainty arising from treating each site as a homogeneous site with uniform flow
and transport properties.
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Source-Term Module Section 2.0
2.0 SOURCE-TERM MODULE
The source-term module simulates the rate of water leakage from a waste
management unit (WMU) into the underlying unsaturated (or vadose) zone, and the
concentration(s) of dissolved constituent(s) in the leachate. In EPACMTP, the rate
of water leakage is called the infiltration rate, and the concentration of a constituent
in the infiltrating water is called the leachate concentration.
The EPACMTP source-term module can simulate various types of WMUs. The
module is not designed to model the multitude of physical and bio-chemical
processes that result in leachate generation inside a WMU in detail. Rather, this
module is designed to capture significant and salient physical and biochemical
processes within a WMU. However, if processes not included in the current source-
term module are required, the simulation of the source-term processes should be
carried out externally to EPACMTP. The EPACMTP source-term module can
accommodate output from external process models to represent relevant processes
in more detail. An example of such an external model is the HELP model (Hydraulic
Evaluation of Landfill Performance; Schroeder et al., 1994a and 1994b) which
predicts infiltration through landfill units as a function of unit design and climate
characteristics.
This section is organized as follows:
• Section 2.1 discusses the purpose of the source-term module and
describes the difference between a continuous and finite source;
• Section 2.2 discusses how the source-term module is implemented for
four different types of WMUs - landfills, surface impoundments, land
application units, and waste piles.
2.1 PURPOSE OF THE SOURCE-TERM MODULE
The release of contaminants into the subsurface constitutes the source term for the
ground-water fate and transport model. In an EPACMTP modeling analysis, the
source term can be characterized as either a continuous source or a finite source. A
continuous source simply means that leachate is generated at a constant rate and
with constant leachate concentration, without a cut-off time. A continuous source
scenario conceptually represents an inexhaustible supply of leachate. The
continuous source is the simplest and the most protective, but may not be realistic in
many cases. For this reason, the finite source option is available. In the finite
source scenario, release of leachate occurs over only a finite period of time, as
controlled by the operational life of a WMU or the gradual depletion of the waste
constituent mass in the WMU.
EPACMTP defines the source term for the subsurface fate and transport model in
terms of four primary parameters:
(1) Area of the waste unit,
(2) Leachate flux rate emanating from the waste unit (infiltration rate),
2-1
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Source-Term Module Section 2.0
(3) Constituent-specific leachate concentration, and
(4) Duration of the constituent leaching.
The infiltration rate and leaching duration are a function of both the design and
operational characteristics of the waste management unit and the waste stream
characteristics (waste quantities and waste constituent concentrations). EPACMTP
assumes that the leachate concentration is a characteristic of a particular waste and
constituent. The source-term module does not account for constituent losses from
the WMU via processes other than leaching. Such other loss mechanisms can
include volatilization, surface run-off, and bio-chemical transformation reactions. Not
accounting for these processes means that the modeled leaching will generally
maximize leaching concentrations.
2.1.1 Continuous Source
In the continuous source scenario, the constituent concentration in the leachate
remains constant over time. Under these conditions, the ground-water concentration
at the modeled receptor well location will also eventually reach a constant value. We
refer to this well concentration as the steady-state concentration level. The steady-
state concentration value is the theoretical maximum ground-water well
concentration that can be achieved for a given value of the leachate concentration.
While true steady-state conditions are unlikely to be achieved at actual waste sites, a
WMU which releases leachate at a more or less constant rate and concentration
over a long period of time, may cause the ground-water well concentrations to
approach or reach this steady-state level. For a given waste management scenario,
EPACMTP can calculate the steady-state ground-water well concentration much
more quickly than it can calculate the ground-water concentration values for finite
source conditions.
The continuous source scenario in EPACMTP is therefore useful for screening
purposes and to ensure a protective analysis. If the ground-water concentrations
predicted by EPACMTP under continuous source (steady-state) conditions remain
below appropriate regulatory or health-based levels, the user has assurance that
these levels will not be exceeded under more realistic finite source conditions. A
continuous source analysis may also be appropriate when it is desirable to ensure a
protective evaluation of potential ground-water exposures.
2.1.2 Finite Source
In EPACMTP, the finite source scenario refers to the situation in which a
constituent's leachate concentration is a function of time. Specifically, under finite-
source conditions the constituent is present in the leachate for a finite period of time.
EPACMTP version 2.0 can model two basic types of finite source conditions. The
first is a pulse source in which the leachate concentration is constant over a
prescribed period of time (tp) and then goes to zero. The second scenario is in which
the leachate concentration diminishes gradually to reflect depletion of the
contaminant mass in the waste unit. The two scenarios are depicted graphically in
Figure 2.1.
2-2
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Source-Term Module
Section 2.0
o
^p
CO
o
o
0)
13
o
CO
4)
Initial Leachate Concentration
- Pulse Source
Depleting Source
Time +
Figure 2.1 Leachate Concentration Versus Time for Pulse
Source and Depleting Source Conditions.
The pulse source scenario is most appropriate for WMUs which operate for a
prescribed period of time, followed by clean closure. Examples include waste piles,
surface impoundments and land application units where the leaching occurs during
the active life of the unit. During this period, continual addition of "fresh" waste will
serve to keep the leachate concentration at a more or less constant value. If the
user specifies a very long value for the pulse duration, tp, then the pulse source
scenario becomes equivalent to a continuous source.
The depleting source scenario is most appropriate for a landfill waste management
scenario, where the waste accumulates during the active life of the unit, but leaching
may continue for a long period of time after the unit is closed.
The finite source module in EPACMTP version 2.0 has the following restrictions:
• The module does not account for situations in which the leachate
concentration increases with time; it can only handle scenarios with a
constant concentration pulse or scenarios with a depleting source.
• The depleting source option for landfills cannot be used to model
metals that have non-linear sorption isotherms; for these constituents,
the pulse source must be used. In other words, the depleting source
option for landfills can only be used for organic constituents. To
model a metal constituent, the depletion of the source is approximated
or linearized using a linear sorption isotherm, or a single value of Kw
(waste-concentration-to-leachate-concentration ratio).
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Source-Term Module Section 2.0
2.2 IMPLEMENTATION FOR DIFFERENT WASTE UNITS
EPACMTP can perform Monte-Carlo or deterministic analyses for four different types
of waste management units:
• Landfills,
• Surface impoundments,
• Waste piles, and
• Land application units.
Figure 2.2 shows a schematic, cross-sectional view of the four types of waste units.
In EPACMTP, each type of waste management unit is described by a relatively small
number of parameters. The differences between waste units are generally
represented by different values or frequency distributions of these source-specific
parameters. Source-specific parameters that are used by EPACMTP include:
• Dimensions of the waste unit, i.e., area and depth, as well as depth of
the base of the unit below grade;
• Amount of waste in the WMU, as given by an average annual waste
addition rate and number of years of operation, or fraction of the WMU
that is dedicated to a particular waste;
• Infiltration (or leakage rate) of water through the unit;
• Type of source condition (continuous, or finite source)
• If finite source, constituent concentration in the leachate when
leaching begins, and either duration of the leachate pulse, or amount
of waste in the unit when leaching begins, density of the waste, and
concentration of the chemical constituent in the waste.
The four types of waste management units and the source-specific input parameters
used to conceptualize and model each type of unit are discussed in the following
sections.
2.2.1 Landfills
2.2.1.1 Assumptions for the Landfill Source Module
The landfill is modeled as a permanent waste management unit, with a rectangular
footprint and a uniform depth. In EPACMTP version 2.0, only square footprints are
allowed. The landfill is filled with waste during the unit's operational life. Upon
closure of the landfill, the waste is left in place, and a final soil cover is installed. The
starting point for the EPACMTP simulation is at the time when the landfill is closed,
i.e., the unit is at its maximum capacity. EPACMTP does not implicitly simulate any
loss process that may occur during the unit's active life, e.g., due to leaching,
volatilization, runoff on erosion, or biochemical degradation. If these losses are
considered to be significant they can be taken into account by subtracting the
2-4
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Source-Term Module
Section 2.0
Cover
unsaturated zone
V
saturated zone
(A) LANDFILL
unsaturated zone
V
saturated zone
(B) IMPOUNDMENT
unsaturated zone
V
saturated zone
(C) WASTE PILE
-r
unsaturated zone
V
saturated zone
(D) LAND APPLICATION UNIT
Figure 2.2 WMU Types Modeled in EPACMTP.
2-5
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Source-Term Module Section 2.0
cumulative amount of contaminant mass loss that occurred during the unit's active
life, from the amount of contaminant mass that is present at the time of landfill
closure.
Leaching of contaminant(s) from the landfill into the subsurface is the result of
dissolution as partitioning of constituent(s) from the waste into water that percolates
(infiltrates) downward through the landfill unit. EPACMTP assumes that this process
is driven by natural precipitation. Because of the long term nature of the ground-
water pathway analysis, EPACMTP assumes a steady-state infiltration rate which is
equal to the long-term average annual rate. The value of the infiltration rate is a
user-input. However, EPACMTP provides a database of nationwide infiltration rates
generated with the HELP model (Hydrologic Evaluation of Landfill Performance),
using climatic date from climate stations throughout the United States (see the
EPACMTP Parameters/Data Background Document, U.S. EPA, 2003). The HELP-
generated infiltration rates are based on an assumption that each landfill is covered
by 2 feet of soil, and does not have a liner or leachate collection system.
2.2.1.2 List of Parameters for the Landfill Source Module
The source-specific input parameters for the landfill scenario include parameters to
determine the amount of waste disposed in the landfill, the infiltration and recharge
rates, the initial waste and leachate concentrations, and the source leaching
duration. Together these parameters are used to determine how much contaminant
mass enters the subsurface and over what time period. The source-specific
parameters for the landfill scenario are presented in Table 2.1 and are described in
the following sections.
EPACMTP allows the user to specify the amount of waste that is placed in the landfill
in two different ways. The first is to specify the duration of the unit's active life and
the average annual quantity of waste. The second is to provide the dimensions
(area and depth) of the landfill and the fraction of the landfill volume that is occupied
by the waste of concern. EPACMTP then calculates the actual amount of waste. In
the former case, EPACMTP will check that the cumulative waste amount, as
determined by multiplying the number of years of operation by the average annual
waste quantity, does not exceed the capacity of the landfill.
2.2.1.2.1 Landfill Area
The landfill area is defined as the square footprint of the landfill. The length and
width of the landfill are each calculated as the square root of the area. The landfill
area is used to determine the area over which the infiltration rate is applied and is
one of several parameters used to calculate the contaminant mass within the landfill
for the landfill depleting source option.
2.2.1.2.2 Landfill Depth
The landfill depth is defined as the average depth of the landfill, from top to bottom;
the thickness of the cover soil is assumed to be insignificant. The landfill depth is
measured from the top to the base of the unit, irrespective of where the ground
2-6
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Source-Term Module
Section 2.0
Table 2.1 Source-Specific Variables for Landfills
Parameter
Waste Site Area: the footprint of the
square landfill (Section 2.2.1.2.1)
Landfill Depth: the average depth of the
landfill, from top to bottom (Section
2.2.1.2.2)
Depth Below Grade: the depth of the
bottom of the landfill below the
surrounding ground surface (Section
2.2.1.2.3)
Waste Fraction: the fraction of the
landfill volume that is occupied by the
waste of concern when the landfill is
closed (Section 2.2.1.2.4)
Waste Density: the average bulk density
of the waste of concern (Section
2.2.1.2.5)
Areal Recharge Rate: water percolating
through the soil to the aquifer outside of
the footprint of the WMU (Section
2.2.1.2.6)
Areal Infiltration Rate: water percolating
through a WMU to the underlying soil
(Section 2.2.1. 2.6)
Leachate Concentration: the
concentration of a constituent in the
leachate emanating from the base of the
waste management unit (Section
2.2.1.2.7)
Waste Concentration: the total
concentration of constituent in the waste
which may eventually leach out (Section
2.2.1.2.8)
Waste-Concentration-to-Leachate
Concentration Ratio: the ratio of the
waste concentration (Cw) to the leachate
concentration (CL) (Section 2.2.1.2.9)
Source Leaching Duration: the duration
of the leachate release period (Section
2.2.1.2.10)
Symbol
A
"w
DLF
dBG
Fh
Phw
IR
1
CL
cw
Kw
tp
Units
m2
m
m
unitless
g/cm3
m3/m2/y
or m/y
m3/m2/y
or m/y
mg/L
mg/kg
L/kg
y
Section in EPACMTP
Parameters/Data
Background Document
2.3.1
2.3.2
2.3.3
2.3.4
3.2.1
4.4
4.3.1
3.2.3
3.2.2
3.2.2 and 3.2.3
2.3.6
Note: Aw and DLF are used to calculate landfill capacity. However, if the landfill is not used to its
capacity, other methods of calculating waste volume must be employed. See Section 2.2.1.3.2.
2-7
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Source-Term Module Section 2.0
surface is. The landfill depth is one of several parameters used to calculate the
contaminant mass within the landfill for the landfill depleting source option.
2.2.12.3 Depth Below Grade
The depth below grade is defined as the depth of the bottom of the landfill below the
surrounding ground surface. If a non-zero value is entered for this input, then the
thickness of the unsaturated zone beneath the landfill is adjusted accordingly.
2.2.12.4 Waste Fraction
The waste fraction is defined as the volume fraction of the landfill that is occupied by
the waste of concern when the landfill is closed. This value can range from a very
small value to 1.0; the value of 1.0 is the most conservative value and means that
the entire landfill is filled with leachate forming waste. In most applications of
EPACMTP, the analysis is performed for specific waste. The situation of a waste
fraction equal to 1.0, is therefore equivalent to a monofill scenario. The waste
fraction is one of several parameters used to calculate the contaminant mass within
the landfill; the contaminant mass is an important input for the landfill depleting
source option.
2.2.12.5 Waste Density
The waste density is defined as the average bulk density of the waste, i.e., mass of
waste per unit volume (kg/L or g/cm3) containing the constituent(s) of concern and
should be measured on the waste as disposed, as opposed to a dry bulk density.
The waste density is used to convert the waste volume to an equivalent mass of
waste or vice-versa.
2.2.12.6 Areal Recharge and Infiltration Rates
The EPACMTP model requires input of the net areal rate of vertical downward
percolation of water and leachate through the unsaturated zone to the water table.
Infiltration is defined as water percolating through a WMU to the underlying soil,
while recharge is water percolating through the soil to the aquifer outside of the
footprint of the WMU. The model allows the infiltration rate to be different from the
regional recharge rate. The landfill infiltration rate can be different from the recharge
rate for a variety of reasons, including the engineering design of the landfill (for
instance, a soil tighter than the local soil being used for the final cover), topography,
land use, and vegetation. The recharge rate is determined by regional climatic
conditions, such as precipitation, evapotranspiration, and surface run-off, and
regional soil type.
Infiltration and recharge rates for selected soil types at cities around the country
have been estimated using the HELP water-balance model and are incorporated into
a database included in one of the EPACMTP input files. Further details about how
these rates were determined and other options for determining recharge and
infiltration rates outside of the EPACMTP model can be found in Section 4.0 of the
EPACMTP Parameters/Data Background Document (U.S. EPA, 2003).
2-8
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Source-Term Module Section 2.0
2.2.1.2.7 Leachate Concentration
The leachate concentration (CL mg/L) used in the model represents the
concentration of the leachate emanating from the base of the waste management
unit. This parameter provides the boundary condition for the EPACMTP simulation
of constituent fate and transport through the unsaturated and saturated zones.
Consistent with the continuous and finite source options of EPACMTP, the model will
treat the leachate concentration as either a constant value, or as a parameter that
can change with time.
In the finite source option, the simplest and generally most protective case is to
assign the leachate concentration a constant value until all of the initially present
contaminant mass has leached out of the disposal unit. After this time, the leachate
concentration is zero. This case is referred to as the pulse source scenario. The
boundary condition for the fate and transport model then becomes a constant
concentration pulse, with defined duration. Alternatively, EPACMTP can simulate
conditions in which the value of the leachate concentration diminishes gradually over
time. In other words, as the waste in the landfill is depleted, the value of the
leachate concentration also goes down. When using this depleting source option,
the user specifies the initial leaching concentration, and the model automatically
adjusts this rate over time as explained below in Section 2.2.1.3.3. As stated in
Section 2.1.2, for constituents with non-linear isotherms, the depleting source
scenario is applicable only when the isotherms are linearized by making the
distribution coefficient (Kd) constant.
2.2.1.2.8 Waste Concentration
The waste concentration (Cw, mg/kg), represents the total mass fraction of
constituent in the waste which may eventually leach out. Therefore, in the context of
the finite source methodology, Cw is the total leachable waste concentration. From a
practical perspective it is important to know how this property will be measured for
actual waste samples. There are established procedures to measure the leachate
concentration CL, but these methods may not measure the "leachable" waste
concentration very precisely. Thus, Cw may be interpreted to represent the total
waste concentration and measured accordingly. This approach will be protective
because the measured total waste concentration should always be at least as high
as the potentially more difficult to quantify "leachable" waste concentration.
The waste concentration used by EPACMTP reflects the average concentration of
the constituent(s) of concern in the waste in the landfill at the time of closure.
Contaminant losses that may occur during the WMU's active life are not explicitly
modeled in EPACMTP. If such loses are significant, it may be appropriate to adjust
the waste concentration value that is entered into EPACMTP, to represent the
constituent concentration that remains, and is available for leaching. Ignoring these
other loss pathways will be protective for the ground-water pathway analysis.
2-9
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Source-Term Module Section 2.0
2.2.1.2.9 Waste-Concentration-to-Leachate-Concentration Ratio
For the landfill waste management scenario in which leaching continues until the
source is depleted (depleting source option), the duration of the leaching period is
dependent on both the waste concentration (CJ and the leachate concentration (CL).
The EPACMTP model uses these concentrations in terms of the ratio of waste
concentration to leachate concentration, or CJCL.
The waste-to-leachate ratio can be thought of as a type of partition coefficient or as a
measure of the relative leachability of waste constituents. In general, a relatively
high value of this parameter means that the waste leaches slowly from the unit,
resulting in a source with a long duration. Conversely, a relatively low value means
that the waste can be rapidly leached to the subsurface.
In applications that involve back-calculating threshold waste and/or leachate
concentrations that satisfy regulatory or risk-based ground-water thresholds, it is
convenient for the user to provide the EPACMTP input in terms of a ratio of waste-to-
leachate concentrations rather than as individual waste concentration and leachate
concentration values.
2.2.1.2.10 Source Leaching Duration
In finite source analyses with a pulse-type source, the user must specify the duration
of the leaching period (tp) in years. If leaching is modeled with the depleting source
option, EPACMTP will internally calculate the leachate concentration as a function of
time, as well as the leaching period.
2.2.1.2.11 Waste Volume
The waste volume is defined as the volume of the waste of interest (at landfill
closure) contributed to the landfill. EPACMTP uses the waste volume to calculate
the contaminant mass within the landfill for the landfill depleting source option (see
Section 2.2.1.3.3).
For waste-stream-specific applications of EPACMTP, the total waste volume to be
input to EPACMTP can be calculated by multiplying the annual waste volume by the
number of years of landfill operation. If the annual waste amount is given as a mass
value (e.g., tons/year), it should be divided by the waste density in order to yield the
value as a volume (m3). The user should ensure that the modeled waste volume
does not exceed the total landfill capacity.
For nationwide risk assessments, a distribution of values can be used for the waste
volume by entering the waste volume as a fraction of the entire landfill volume (see
Section 2.2.1.2.4). If the landfill volume and the waste volume are treated as
random parameters, specifying the waste volume in terms of a waste fraction
ensures that the modeled waste volume can never exceed the modeled landfill
capacity.
2-10
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Source-Term Module Section 2.0
2.2.1.3 Mathematical Formulation of the Landfill Source Module
The mathematical formulation of the landfill source module is presented below.
2.2.1.3.1 Continuous Source Scenario
In the continuous (infinite) source scenario, the leachate concentration is simply set
to a constant value with no time cut-off. The continuous source scenario represents
the most protective leaching assumption, namely that there is an infinite supply of
waste in the landfill. In this case, the leachate concentration at any time t is given by
CL(f)=C° (2.1)
where
CL = leachate concentration (mg/L)
t = time since leaching began at landfill closure (y)
C° = initial leachate concentration at the time of landfill closure
(mg/L)
2.2.13.2 Pulse Source Scenario
In the pulse source scenario the leachate concentration is constant over a prescribed
period, tp, and then goes to zero:
CL = C° t < t, (2.2)
CL = 0 t>t
p
where
C, = leachate concentration (mg/L)
CL = initial leachate concentration at the time of landfill closure
(mg/L)
t = time since leaching began at landfill closure (y)
tp = pulse duration (y)
Although it is possible to set tp to any value, the duration of the leachate pulse is
usually derived from mass balance principles. The total mass of constituent which is
present in the landfill at the time that leaching is assumed to start (i.e., at the time of
landfill closure) is given by
Mc = CW*AW* DLF x Fh x phw x 1000 (2.3)
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Source-Term Module Section 2.0
where
Mc = total constituent mass in the landfill (mg)
Cw = constituent concentration in the waste (mg/kg)
Aw = area of the landfill footprint (m2)
DLF = landfill depth (m)
Fh = volume fraction of the waste in the landfill at time of closure
(m3/m3)
-*hw
phw = waste density (g/cm3)
1000 = conversion factor used to convert volume from m3 to liters
Equation (2.3) states that the total constituent mass is equal to the waste
concentration times the volume of the landfill dedicated to the waste (Aw • DLF • Fh)
multiplied by the density of the waste (£>hw). The latter converts the waste volume to
waste mass.
In many practical situations, the waste loading into the landfill may be specified in
terms of an annual waste amount and duration at the landfill active life, or:
mw x tA (2.4)
where
Mc = total constituent mass in the landfill (mg)
Cw = constituent concentration in the waste (mg/kg)
mw = annual waste loading during active life (kg/y)
tA = WMU active life (y)
If the landfill is characterized in terms of annual waste loading, the parameters in
Equation (2.3) which are needed in EPACMTP can be easily calculated by simply
combining the two equations to yield:
(2.5)
(Aw* DLFx p/wx1000)
where
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
mw = annual waste loading during active life (kg/y)
tA WMU active life (y)
Aw = area of the landfill footprint (m2)
DLF = landfill depth (m)
2-12
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Source-Term Module Section 2.0
phw = waste density (g/cm3)
1000 = conversion factor used to convert volume from m3 to liters
When the waste density is unknown, a default value of phw =1.0 can be used. In that
case the calculated waste fraction, Fh, may be different from the actual waste fraction
in the landfill, but mathematically, the model will still simulate the correct waste
amount in the landfill.
During the period the landfill is generating leachate, the annual mass of constituent
which is lost by leaching is equal to:
= CL (f) x X\w x / x 1000 (2.6)
where
mcL = annual constituent mass lost by leaching (mg/y)
CL = leachate concentration (mg/L)
t = time since leaching began at landfill closure (y)
Aw = area of the landfill (m2)
/ = annual areal infiltration rate (m/y)
1000 = conversion factor used to convert volume from liters to m3
From basic mass balance considerations, leaching from the landfill will stop when all
of the constituent mass Mc has leached from the landfill. For the constant
concentration pulse source condition, the pulse duration, tp, is then simply given by
mcL x tp = Mc (2.7a)
or
MO
(2.7b)
x 1000
CL x Aw* /x 1000 ( '
2-13
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Source-Term Module Section 2.0
Cw x DLF x Fh
CL
/o 7^
(2-7d)
where
mcL = annual constituent mass lost by leaching (mg/y)
tp = pulse duration (y)
Mc = total constituent mass in the landfill (mg)
Cw = constituent concentration in the waste (mg/kg)
Aw = area of the landfill footprint (m2)
DLF = landfill depth (m)
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
phw = waste density (g/cm3)
1000 = conversion factor used to convert volume from m3 to liters
CL = leachate concentration (mg/L)
/ = annual areal infiltration rate (m/y)
1000 = conversion factor used to convert volume from liters to m3
2.2.1.3.3 Depleting Source Scenario
In the pulse source scenario described above, the leachate concentration is constant
until all of the constituent mass which is present in the waste has leached out. This
approximation may be valid when the leachate concentration is controlled by
solubility of the constituent(s) of concern. More generally, however, it is expected
that the leachate concentration emanating from a landfill will gradually diminish with
time, as the amount of constituent that remains in the WMU gets depleted.
The EPACMTP depleting source option assumes that the leachate concentration at
any time (t) since the beginning of the leaching process, i.e., CL(t), is a linear function
of the remaining constituent concentration in the waste, Cw(t), or:
where
CL(f) = KwCw(t) (2.8)
CL = leachate concentration (mg/L)
t = time since leaching began at landfill closure (y)
Kw = waste-concentration-to-leachate-concentration ratio (L/kg)
Cw = constituent concentration in the waste (mg/kg)
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Source-Term Module Section 2.0
The waste-concentration-to-leachate concentration ratio, Kw in this equation can be
thought of as a partition coefficient between the concentrations in the waste itself
and the concentration dissolved in the leachate. In general, Kw may depend on both
the chemical composition of the waste and leachate, as well as the physical waste
form.
The general mass balance for the WMU source term is that the difference between
the initial constituent mass in the WMU and the mass remaining at time t is equal to
the amount that has leached out up to that time, which can be written as:
t
Aw x DLF x Fhx phwx(C°w - Cw(f)) =AwxI J CL(t)dt (2.9)
where
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
-i3\
Aw = area of the landfill footprint (rrr)
DLF = landfill depth (m)
volume fraction <
(dimensionless)
phw = waste density (g/cm3)
C° = initial constituent concentration in the waste at the time of
landfill closure (mg/L)
Cw = constituent concentration in the waste (mg/kg)
t = time since leaching began at landfill closure (y)
/ = annual areal infiltration rate (m/y)
CL = leachate concentration (mg/kg)
The left-hand side of the equation represents the difference in the mass of
constituent in the landfill, from the initial amount (represented by C^) to the amount
remaining at time t (represented by Cw(t)) The right-hand side represents the
cumulative amount of mass lost via leaching. Equation (2.9) can alternatively be
written as
riC*
Awx DLF xFhxphw- = AwxlxCL(t) (2.10)
where
Aw = area of the landfill footprint (m2)
DLF = landfill depth (m)
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
phw = waste density (g/cm3)
Cw = constituent concentration in the waste (mg/kg)
t = time since leaching began at landfill closure (y)
2-15
-------
Source-Term Module Section 2.0
I = annual areal infiltration rate (m/y)
CL = leachate concentration (mg/L)
Using Equation (2.8) in Equation (2.10) and rearranging the resulting equation yields
dCL -I
dt
(2.11)
where
CL = leachate concentration (mg/L)
t = time since leaching began at landfill closure (y)
/ = annual areal infiltration rate (m/y)
DLF = landfill depth (m)
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
phw = waste density (g/cm3)
Kw = waste-concentration-to-leachate-concentration ratio (L/kg)
Integration of Equation (2.11) gives
CL(0=C°exp](n >c;'n >|f)f| (2.12)
where
CL = leachate concentration (mg/L)
t = time since leaching began at landfill closure (y)
C° = initial leachate concentration at the time of landfill closure
(mg/L)
exp(') = exponential operator
/ = annual areal infiltration rate (m/y)
DLF = landfill depth (m)
Fh = volume fraction of the waste in the landfill at time of closure
(dimensionless)
phw = waste density (g/cm3)
Kw = waste-concentration-to-leachate-concentration ratio (L/kg)
The depleting landfill source option of EPACMTP uses both the waste concentration,
Cw, and the leachate concentration CL. In EPACMTP version 2.0, the user must
provide as inputs, the initial leachate concentration of the waste stream entering the
landfill, and the waste-to-leachate concentration ratio, Kw. The latter input parameter
can be calculated by the user from waste characterization data as
2-16
-------
Source-Term Module Section 2.0
(2.13)
where
K = waste-to-leachate-concentration ratio (L/kg)
Cw = waste concentration of the waste stream entering the landfill
(mg/kg)
C" = initial leachate concentration at the time of landfill closure
(mg/L)
The superscript 0 is used to denote that these concentrations reflect the initial waste
characteristic, prior to any depletion.
2.2.2 Surface Impoundments
2.2.2.1 Assumptions for the Surface Impoundment Source-Term Module
The surface impoundment is modeled as a temporary waste management unit with a
prescribed operational life. Clean closure is assumed, that is, at the end of the unit's
operational life, the model assumes there is no further release of waste constituents
to the ground water.
Following the unit's closure; however, it is further assumed that the contaminated
liquid and sediment compartments are replaced by contaminant-free liquid and
sediment compartments with identical configurations and properties. The remaining
contaminants in the unsaturated zone are allowed to continue to migrate towards the
water table with the same infiltration rate. This assumption allows the infiltration
through the surface impoundment unit to be treated as a single steady-steady flow
regime throughout the simulation period. A decrease of infiltration rate due to the
closure of the surface impoundment unit requires that the flow be treated as a
transient flow regime, otherwise the mass of contaminants within the unsaturated
zone cannot be conserved. Because of the non-linearity of the flow equation, a great
deal of computational effort is required per Monte-Carlo realization, thereby making
the transient solution for the infiltration rate after the unit's closure computationally
impractical. In addition, by maintaining the same infiltration rate, the flow and
transport in the unsaturated and saturated zones are considered conservative
because the ground-water velocity at any downgradient location does not decrease
with time, thus causing the contaminant to reach receptor wells sooner. In the case
of degradable contaminants, their concentrations tend to be larger at receptor wells
due to less degradational time available.
The surface impoundment is modeled as a unit with a square foot print, with a
constant ponding depth during its operational life (see Figure 2.2B). By default,
EPACMTP assumes an unlined impoundment. The model assumes that while the
impoundment is in operation, a consolidated layer of sediment accumulates at the
2-17
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Source-Term Module
Section 2.0
bottom of the impoundment; the leakage (infiltration) rate through the impoundment
is a function of the ponding depth in the impoundment, and the thickness and
effective permeability of the consolidated sediment layer at the bottom of the
impoundment.
The rate of leakage is constrained to ensure there is not a physically unrealistic high
rate of leakage which would cause ground-water mounding beneath the unit to rise
above the ground surface. Underlying the assumption of a constant ponding depth,
EPACMTP assumes that the waste water in the impoundment is continually being
replenished while the impoundment is in operation. It is also assumed that the
sediment is always in equilibrium with the waste water since the onset of the unit's
operation so that the presence of sediment does not alter the concentration of
leachate. Accordingly, EPACMTP also assumes that the leachate concentration is
constant during the impoundment operational life, and typically it is equal to the
concentration in the waste water entering the impoundment.
2.2.2.2 List of Parameters for the Surface Impoundment Source-Term Module
The source-specific input parameters for the surface impoundment scenario include
parameters to determine the unit dimensions; ponding depth; infiltration rate; the
ambient recharge rate; the leachate concentration; and the leachate concentration
and leaching duration. Together these parameters are used to determine how much
contaminant mass enters the subsurface and over what time period.
The source-specific parameters for the surface impoundment scenario are presented
in Table 2.2 and are described in the following sections.
Table 2.2 Source-Specific Variables for Surface Impoundments
Parameter
Surface Impoundment Area: the footprint of the
impoundment (Section 2.2.2.2.1)
Areal Recharge Rate: water percolating through the
soil to the aquifer outside of the footprint of the waste
management unit (Section 2.2.2.2.2)
Areal Infiltration Rate: water percolating through a
WMU to the underlying soil (Section 2.2.2.2.3)
Depth Below Grade: the depth of the bottom of the
impoundment below the surrounding ground surface.
(Section 2.2.2.2.4)
Operating Depth: total average depth of the
impoundment, including both water and sediment
(Section 2.2.2.2.5)
Ponding Depth: the average total depth of waste water
in the impoundment above the consolidated sediment
(Section 2.2.2.2.5)
Symbol
A
"w
lr
1
dBG
HT
HP
Units
m2
m3/m2/y or
m/y
m3/m2/y or
m/y
m
m
m
Section in
EPACMTP
Parameters/Data
Background
Document
2.4.1
4.4
4.3.4
2.4.6
2.4.2
2.4.2
2-18
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Source-Term Module
Section 2.0
Table 2.2 Source-Specific Variables for Surface Impoundments (continued)
Parameter
Total Sediment Thickness: thickness of sediment,
including both the consolidated and non-consolidated
sediments (Section 2.2.2.2.6)
Consolidated Sediment Thickness: Thickness of
consolidated sediment at base of impoundment (Section
2.2.2.2.6)
Unconsolidated Sediment Thickness: Thickness of
loose sediment layer at base of impoundment (Section
2.2.2.2.6)
Distance to Surface Water Body: provides a boundary
condition in screening the calculated surface
impoundment infiltration rate against physically
unrealistic values (Section 2.2.2.2.7)
Leachate Concentration: the concentration of a
constituent in the leachate emanating from the base of
the impoundment (Section 2.2.2.2.8)
Source Leaching Duration: the duration of the
leachate release period (Section 2.2.2.2.9)
Liner Thickness: the thickness of a single liner
underlying the SI unit (Section 2.2.2.2.10)
Liner Hydraulic Conductivity: The saturated hydraulic
conductivity of a single liner underlying the SI unit
(Section 2.2.2.2.11)
Unsaturated-zone Thickness: The total thickness of
the unsaturated zone at the SI site (Section 2.2.2.2.12)
Leak Density: number of holes per unit area (Section
2.2.2.2.13)
Symbol
Ds
Dfc
Duc
R»
CL
(P
Dlin
K/in
Du
Pleak
Units
m
m
m
m
mg/L
y
m
m/y
m
holes/m2
Section in
EPACMTP
Parameters/Data
Background
Document
2.4.3
2.4.3
2.4.3
2.4.8
3.2.3
2.4.9
2.4.4
2.4.5
5.2.1
2.4.7
2.2.2.2.1 Surface Impoundment Area
The surface impoundment area is defined as the footprint of the impoundment. In
EPACMTP, the impoundment is assumed to be square. The impoundment area is
used to determine the area over which the infiltration rate is applied.
2.2.2.2.2 Areal Recharge Rate
Recharge is water percolating through the soil to the aquifer from outside of the
footprint of the WMU. The recharge rate is determined by the regional climatic
conditions and regional soil type. Recharge is specified as areal rates, with the units
of cubic meters of fluid (water or leachate) per square meter per year (m3/m2/y).
Thus, the units for recharge simplify to meters per year (m/y).
For surface impoundments, recharge rates for selected soil types at cities around the
country have been estimated using the HELP water-balance model and are
2-19
-------
Source-Term Module Section 2.0
incorporated into a database included in one of the EPACMTP input files. Further
details about how these rates were determined and other options for determining
recharge rates outside of the EPACMTP model can be found in Section 4.0 of the
EPACMTP Parameters/Data Background Document (U.S. EPA, 2003).
2.2.2.2.3 Areal Infiltration Rate
For the surface impoundment scenario, the leachate flux (infiltration) rate is typically
computed internally by EPACMTP, as a function of the ponding depth in the
impoundment and other characteristics. In essence, the leachate flux rate is
calculated by applying Darcy's law as a function of:
• Impoundment depth,
• Thickness of an engineered liner or sediment layer at the base of the
impoundment, and
• Hydraulic conductivity of this liner or sediment layer and the
underlying soil material.
The algorithm is more fully described below in Section 2.2.2.3. However, you can
also determine the infiltration rate outside the EPACMTP model (for example, by
using the HELP model or variably unsaturated flow simulation models) and provide it
as an input value or a distribution of values in the input file.
The surface impoundment source-term module in the EPACMTP model cannot
accommodate a time-varying infiltration rate; the infiltration rate that is derived or
specified in the input file is applied over the area of the impoundment for the entire
modeling period even after the unit has been closed. The contaminant mass,
however, only enters the subsurface during the period of the leaching duration.
Consistent with the assumption of clean closure in Section 2.2.2.1, it is assumed that
all the contaminants within the source (contaminants in the liquid and sediment
compartments) are removed at the end of the operational period. However, the
remaining contaminants in the unsaturated zone are allowed to continue to migrate
toward the water table.
2.2.2.2.4 Depth Below Grade
The depth below grade is defined as the depth of the bottom of the impoundment
below the surrounding ground surface. If a non-zero value is entered for this input,
then the thickness of the unsaturated zone beneath the impoundment is adjusted
accordingly.
2.2.2.2.5 Operating Depth and Ponding Depth
The operating depth is defined as the average total depth of waste water in the
impoundment, measured from the base of the impoundment, that is, it is not just the
depth of free standing water above any sediment layer that may have accumulated in
the impoundment. The operating depth includes the sediment layer. Seasonal
2-20
-------
Source-Term Module Section 2.0
differences and differences due to non-uniform bottom elevation should be averaged
out into a long-term average value or distribution of values. The ponding depth is
defined as the average depth of water above the consolidated sediment, including
the depth of unconsolidated sediment.
2.2.2.2.6 Total Thickness of Sediment
By default, EPACMTP models unlined, surface impoundments with a layer of
"sludge" or sediment above the base of the unit. The sediment layer is divided into
two sublayers: the upper sublayer with loose sediment, and the lower sublayer with
sediment consolidated by the weight of overlying waste water and the loose
sediment. The consolidated sediment has relatively low hydraulic conductivity and
acts to impede flow. The calculated infiltration rate is inversely related to the
thickness of the consolidated sediment sublayer. Smaller consolidated sediment
thickness will result in a higher infiltration rate, and greater rate of constituent loss
from the impoundment. If the impoundment is periodically dredged, using the
minimum consolidated sediment thickness is recommended.
2.2.2.2.7 Distance to the Nearest Surface Water Body
In the case of deep unlined impoundments, EPACMTP may calculate very high
surface impoundment infiltration rates. EPACMTP checks against the occurrence of
excessively high rates by calculating the estimated height of ground-water mounding
underneath the WMU, and if necessary reduces the infiltration rate to ensure the
predicted water table does not rise above the ground surface. This screening
procedure requires as input the distance to the nearest point at which the water table
elevation is kept at a fixed value. Operationally, this is taken to be the distance to
the nearest surface water body.
2.2.2.2.8 Leachate Concentration
The fate and transport model requires stipulation of the leachate concentration as a
function of time, CL(t). The leachate concentration, CL(t), used in the model directly
represents the concentration of the leachate emanating from the base of the waste
management unit, as a boundary condition for the fate and transport model. For the
surface impoundment scenario, the EPACMTP model accounts for this boundary
condition as a constant concentration pulse condition. The boundary condition for
the fate and transport model then becomes a constant concentration pulse, with a
defined duration. When there are no contaminant losses in the impoundment, the
leachate concentration value can be assumed equal to the incoming waste water
concentration. EPACMTP version 2.0 does not account for losses (e.g.,
volatilization, biochemical degradation) in surface impoundments.
2.2.2.2.9 Source Leaching Duration
The duration of the leaching period may be assigned a constant value or an
appropriate frequency distribution in EPACMTP. For surface impoundments, the
addition and removal of waste during the operational life period are more or less
balanced, without significant net accumulation of waste. In the finite source
2-21
-------
Source-Term Module Section 2.0
implementation for surface impoundments, the duration of the leaching period is, for
practical purposes, assumed to be the same as the operational life of the surface
impoundment.
2.2.2.2.10 Liner Thickness
In the event that the SI is underlain by a single liner, the thickness of the liner must
be provided. The liner thickness is defined as the average thickness of the single
liner by which the SI unit is underlain. Examples of single liner include compacted
clay liners, and synthetic clay liners. This parameter is required for the calculation of
infiltration rate.
2.2.2.2.11 Liner Hydraulic Conductivity
The liner hydraulic conductivity is defined as the average hydraulic conductivity of
the liner mentioned in Section 2.2.2.2.10. Hydraulic conductivity is the volume of
fluid that is allowed to traverse a liner of unit thickness and unit hydraulic head
difference in a given unit time over a unit area.
2.2.2.2.12 Unsaturated-zone Thickness
The unsaturated-zone thickness is defined as the average height of natural soil
surface above the local water table elevation.
2.2.2.2.13 Leak Density
EPACMTP can also account for infiltration through composite liners. The infiltration
is assumed to result from defects (pin holes) in the geomembrane. The pin holes
are assumed to have a circular shapes and to be uniform in size. The leak density is
defined as the average number of circular pin holes per square meter.
2.2.2.3 Mathematical Formulation of the Surface Impoundment Source-Term
Module
2.2.2.3.1 Surface Impoundment Leakage (Infiltration) Rate
Figure 2.3 illustrates a compartmentalized surface impoundment with stratified
sediment. Shown in the figure are: the liquid compartment, the sediment
compartment (with loose and consolidated sediments), and the unsaturated zone
(with clogged and unaffected native materials). The model assumes that all
sediment layer thicknesses remain unchanged throughout the life of the unit.
EPACMTP calculates infiltration through the accumulated sediment at the bottom of
an impoundment, accounting for clogging of the native soil materials underlying the
impoundment and mounding due to infiltration. No leachate collection system is
assumed to exist beneath the unit.
2-22
-------
Source-Term Module
Section 2.0
I Compartment
Ground
Surface
Elevation
I Compartment
Consolidated Sediment
Cloqqed Soil
Ground'«
Surface
Elevation
Unaffected Native Material
,r Infiltration
V Water
•= Table
Figure 2.3 Schematic Cross-Section View of SI Unit.
The modeled infiltration is governed by the following:
• Effective hydraulic conductivity of consolidated sediment layer.
As sediment accumulates at the base of the impoundment, the weight
of the liquid and upper sediments tends to compress (or consolidate)
the lower sediments. The consolidation process reduces the
hydraulic conductivity of the sediment layer, and the layer of
consolidated sediment will act as a restricting layer for flow out of the
impoundment. This consolidated sediment acts as a filter cake, and
its hydraulic conductivity may be much lower than the
nonconsolidated sediment. The layer of loose, unconsolidated
sediment which is part of the conceptual model for SI units, and which
overlies the consolidated sediment layer, is not explicitly considered in
the SI flow module. Instead, EPACMTP assumes that the
permeability of this loose material is so large that it does not restrict
the flow rate.
• Effective hydraulic conductivity of clogged native material. As
liquids infiltrate soils underlying the impoundment, suspended
particulate matter accumulates in the soil pore spaces, reducing
hydraulic conductivity and lowering infiltration rates.
• Limitations on maximum infiltration rate from mounding. If the
calculated infiltration rate exceeds the rate at which the saturated
zone can transport the ground water, the ground-water level will rise
2-23
-------
Source-Term Module Section 2.0
into the unsaturated zone and the assumption of zero pressure head
at the base of the unsaturated zone is violated. This ground-water
"mounding" will reduce the effective infiltration rate so that the
maximum infiltration rate is estimated as the rate that does not cause
the ground-water mound to rise to the bottom elevation of the SI unit.
The following sections describe the algorithms used in this model to calculate the
infiltration rate through the consolidated sediment at the bottom of the impoundment.
A detailed discussion of the maximum allowable infiltration rate based on the ground-
water mounding condition is presented in Section 2.2.5.
Effective Hydraulic Conductivity of Consolidated Sediment Layer. EPACMTP
estimates the effective hydraulic conductivity of the consolidated sediment layer
using principles of soil mechanics. From a number of tests on soil samples as
reported by Lambe and Whitman (1969), the following empirical relationship between
the hydraulic conductivity and void ratio of a layer of consolidated granular material
was derived:
where
hydraulic conductivity of the consolidated sediment (m/s)
void ratio (dimensionless)
**" .with
$sed = porosity of the consolidated sediment (dimensionless)
A = empirical constant (119) (dimensionless)
b = empirical constant (0.206 1/log (m/s))
The values of the empirical constants A and b are 119 and 0.206, respectively. The
void ratio, e, is a function of the initial void ratio of the sediment (before
consolidation) and the stress that results from the combined weight of the waste
water in the impoundment and the overlying loose sediment deposits, or:
e = e0 -a^Acv (2.15)
where
e = void ratio (dimensionless)
e0 = initial void ratio at no-stress condition (dimensionless)
av = compressibility of the sediment (m-s2/kg)
ovf = vertical effective stress in the consolidated sediment layer
(kg/m-s2)
2-24
-------
Source-Term Module
Section 2.0
The compressibility, av, is given by:
0.435C
av =
(2.16)
where
a
vf
sed
D
compressibility of the sediment (m-s2/kg)
compression index (0.55) (dimensionless)
vertical effective stress in the consolidated sediment layer
(kg/m-s2)
vertically downward distance from the top of the consolidated
sediment (m)
thickness of consolidated sediment layer (m)
The value assigned to the compression index, Cc, is 0.55; this value is an average of
values presented in Lambe and Whitman (1969). The vertical effective stress in the
sediment layer, ovf, is a function of the depth of water in the SI unit, and the thickness
and density of the sediment layer, and is given by:
- Duo~
uc
sedpgzsecr [(Hp- Dfc)pg-
p- Dfc)pg]
fc
where
ovf
Hp
Duc
Dfc
p
g
-------
Source-Term Module Section 2.0
Ksed = (C,
where
K^ = hydraulic conductivity of the consolidated sediment (m/s)
C1 = constant defined in Equation (2.19) (dimensionless)
C2 = constant defined in Equation (2.20) (1/m)
zsed = vertically downward distance from the top of the consolidated
sediment (m)
b = empirical constant (= 0.206) (1/log (m/s))
The constants C1 and C2 are given by:
= eo - K*«A« - DfJf>9 + (1 - *sed)Docpsedg] (2.19)
r *
- - -f [(1 - *sed)PsedS' + 9 + — (Hp - Dfc)pg] (2.20)
where
C1 = constant defined by Equation (2.19) (dimensionless)
e0 = initial void ratio at no-stress condition (dimensionless)
av = compressibility of the sediment (m-s2/kg)
A = empirical constant (119) (dimensionless)
-------
Source-Term Module Section 2.0
where
Kfc = averaged saturated hydraulic conductivity of the consolidated
sediment (m/y)
Dfc = thickness of consolidated sediment layer (m)
C1 = constant defined in Equation (2.19) (dimensionless)
C2 = constant defined in Equation (2.20) (1/m)
zsed = vertically downward distance from the top of the consolidated
sediment (m)
b = empirical constant (0.206 1/log (m/s))
EPACMTP determines the final value of the hydraulic conductivity of the
consolidated sediment layer by integrating Equation (2.21), which results in:
1-1 1-1
-1
(C,+ C2Dfc)
1 2 fc ' " (2.22)
where
Kfc = averaged saturated hydraulic conductivity of the consolidated
sediment (m/y)
C1 = constant defined in Equation (2.19) (dimensionless)
C2 = constant defined in Equation (2.20) (1/m)
Dfc = thickness of consolidated sediment layer (m)
b = empirical constant (0.206 1/log (m/s))
EPACMTP requires values for the thickness of the consolidated and unconsolidated
sediment that has accumulated at the base of an impoundment unit. The actual
range of values in unlined impoundments across the United States is not well
characterized. In developing the EPACMTP SI module, EPA therefore assigned the
following values: the total sediment thickness is set to 20 centimeters (0.2 meters),
and it is assumed that the upper half (0.1 meters) consists of unconsolidated
material, while the lower half (0.1 meters) consists of consolidated deposits. In other
words: Duc = Dfc =0.1 meters. The void ratio of the sediment before consolidation is
assigned a value of e0 = 2.7, which corresponds to an initial porosity of 0.73. This
value represents the mean initial void ratio of data presented by Lambe and
Whitman (1969) and Bear (1972).
The hydraulic conductivity calculated in Equation (2.22) has units of m/s. EPACMTP
converts this value to m/y by multiplying by 31,536,000.
In EPACMTP, the unconsolidated or loose sediment is not included as part of the
calculation of infiltration. It is assumed that the loose material is so conductive that
the hydraulic gradient across the material is negligible. As a result, it does not exert
significant resistance to the flow.
2-27
-------
Source-Term Module Section 2.0
Effective Hydraulic Conductivity of Clogged Native Soil
EPACMTP determines the reduction in hydraulic conductivity of the upper part of the
soil by assigning a 'clogging' factor. The value of saturated hydraulic conductivity of
the clogged zone is lower than that of the native soil at the site according to, or
where
K* = saturated hydraulic conductivity of the clogged unsaturated-
zone soil (m/y)
Cfact = clogging factor (=0.1) (dimensionless)
Ks = saturated hydraulic conductivity of the native unsaturated-zone
soil (m/y)
The assigned value of the clogging factor of 0.1 is based upon technical judgment.
The depth of the clogged layer is set to a value of 0.5 meters in EPACMTP.
2.2.2.3.2 Calculation of the Surface Impoundment Infiltration Rate
EPACMTP uses the unsaturated-zone flow module to calculate the infiltration rate
out of the bottom of the impoundment. This module, which is described in detail in
Section 3 of this document, is designed to simulate steady-state downward flow
through the unsaturated zone consisting of one or more soil layers. Steady-state
means that the rate of flow does not change with time.
In the case of flow out of a surface impoundment, the module simulates flow through
a three-layer system, consisting of:
• Consolidated sediment layer;
• Clogged soil layer; and
• Native unsaturated-zone soil.
The native unsaturated-zone soil extends downward to the water table. The steady-
state infiltration rate out of the surface impoundment is driven by the head gradient
between the water ponded in the impoundment and the head at the water table. The
pressure head at the top of the consolidated sediment layer is equal to the water
depth in the impoundment plus the thickness of the unconsolidated sediment.
The pressure head at the water table is zero by definition. The rate of infiltration is
then given by:
/= (Up + Dfc + D~ + Dso//)
Dfc . D;OJI _ Dso/, (2.24a)
2-28
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Source-Term Module Section 2.0
where
/ = areal infiltration rate (m/y)
Hp = ponding depth of waste water in the SI unit (m)
Dfc = thickness of consolidated sediment layer (m)
DSOH = thickness of clogged soil layer ( = 0.5 m)
DSOH = thickness of remaining unaffected native soil underneath the
WMU from below the clogged soil layer to the water table (m)
Kfc = saturated hydraulic conductivity of the consolidated sediment
(m/y)
K* = saturated hydraulic conductivity of clogged soil ( = 0.1 Kg)
(m/y)
k^ = relative permeability of the clogged soil (dimensionless)
Ks = saturated hydraulic conductivity of native soil (m/y)
km = relative permeability of the native soil (dimensionless)
The relative permeability of each soil layer is a dimensionless factor that represents
the reduction in the hydraulic conductivity of the layer once it becomes unsaturated.
Under these conditions, the actual hydraulic conductivity of the layer is less than its
saturated value. EPACMTP assumes that the consolidated sediment layer is always
fully saturated, hence its relative permeability is always 1.0 and this term is omitted
from Equation (2.24a). In general, if a more permeable layer lies underneath a less
permeable layer, the higher permeability layer may become partially unsaturated.
For instance, the upper part of the unaffected soil underneath an impoundment unit
may become unsaturated because of the reduced permeability of the clogged layer
above it. Moving downward through the soil, the soil will become fully saturated
again at the watertable and the capillary fringe just above the water table. The
relative permeabilities in Equation (2.24a) represent effective, average, values for
each soil layer. EPACMTP assumes that the relative permeability - pressure head
relation for the clogged soil is the same as for the unaffected soil. The latter is
determined by the values of the soil characteristic parameters that are provided as
EPACMTP inputs (see Section 3.0).
EPACMTP solves Equation (2.24a) in an iterative manner. The equation cannot be
solved directly because the infiltration rate, /, and the relative permeabilities, km, in
the soil layers are mutually dependent. The calculation begins with an estimate of
infiltration rate based upon a combination of bounding conditions in which (a) all
layers are saturated, and (b) the clogged native material is the primary flow
restriction. Using the initial estimate of /, EPACMTP calculates the vertical pressure
head distribution throughout the sediment-soil system, and adjusts the value for / as
necessary, until the calculated pressure head at the water table is equal to zero,
within a convergence tolerance of 0.001 meters.
In the event that the SI unit is underlain by a single liner, the rate of infiltration is then
given by:
2-29
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Source-Term Module Section 2.0
I =
D,,n ^ (Du~dBG) (2.24b)
+ +
"im *rwlin
where
/ = areal infiltration rate (m/y)
Hp = ponding depth of waste water in the SI unit (m)
Dfc = thickness of consolidated sediment layer (m)
Dlin = thickness of clogged soil layer ( = 0.5 m)
Du = thickness of initially unaffected native soil underneath the
WMU from below the base of the SI to the water table (m)
dBG = depth below grade of the SI unit (m)
Kfc = saturated hydraulic conductivity of the consolidated sediment
(m/y)
Klin = saturated hydraulic conductivity of the liner (m/y)
kmlin = relative permeability of the liner (dimensionless)
Ks = saturated hydraulic conductivity of native soil (m/y)
km = relative permeability of the native soil (dimensionless)
In the event that the SI unit is underlain by a composite liner (a geomembrane
underlain by a low permeability liner such as either a compacted clay liner or a
geosynthetic clay liner), the following modified equation of Bonaparte et al. (1989) is
used to calculate the infiltration rate:
/ = 0.21 a*1 H°T'9 K,°,74 (31,536,000) p/eak (2.24c)
where
/ = areal infiltration rate (m/y)
0.21 = empirical constant (ml16/s026)
aah = average area of a hole in the geomembrane = 6 x 10~6
m2
HT = head of liquid on top of geomembrane (m)
Kljn = hydraulic conductivity of the low-permeability liner (e.g.,
compacted clay) underlying the geomembrane = 1 x 10~9
m/s
31,536,000 = conversion factor, from year to seconds
pleak = leak density (holes/m2)
This equation is applicable to cases where there is good contact between the
geomembrane and the underlying compacted clay liner.
2-30
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Source-Term Module Section 2.0
In EPACMTP, a uniform leak size of 6 millimeters squared (mm2) is assumed. This
leak size is the middle of a range of hole sizes reported by Rollin et al. (1999), who
found that 25 percent of holes were less than 2 mm2, 50 percent of holes were 2 to
10 mm2, and 25 percent of holes were greater than 10 mm2. Equation (2.24c) also
assumes that the hydraulic conductivity of the underlying compacted clay liner is
always 1 x 10~7 cm/s (or 1 x 10~9 m/s).
2.2.3 Waste Piles
2.2.3.1 Assumptions for the Waste Pile Source-Term Module
The waste pile management scenario is conceptually similar to that of the landfill, but
differs in a number of key aspects. In contrast to landfills which represent a long-
term waste management scenario, waste piles represent a more temporary
management scenario. During the operational life of the waste pile, it may be
regarded as an uncovered landfill. Typically at the end of the active life of a waste
pile, the waste material is either removed for land filling, or the waste pile is covered
and left in place. If the waste is removed, there is no longer a source of potential
contamination. If a waste pile is covered and left in place, it then becomes
equivalent to a landfill. In this case, it should be treated as a landfill in EPACMTP.
However, the treatment of a covered waste pile as a landfill is valid only when the
operational period is very short compared with the total leaching period.
2.2.3.2 List of Parameters for the Waste Pile Source-Term Module
The source-specific input parameters for the waste pile scenario include the area of
the waste pile, the infiltration rate; the ambient recharge rate, the leachate
concentration, and the source leaching duration. Together these parameters are
used to determine how much contaminant mass enters the subsurface and the time
period over which this occurs.
The source-specific parameters for the waste pile scenario are presented in Table
2.3 and are described in the following sections.
2.2.3.2.1 Waste Pile Area
The waste pile area is defined as the footprint of the unit. In EPACMTP, the waste
pile is assumed to be square. The length and width of the waste pile are each
calculated as the square root of the area. The waste pile area is used to determine
the area over which the infiltration rate is applied.
2-31
-------
Source-Term Module
Section 2.0
Table 2.3 Source-Specific Variables for Waste Piles
Parameter
Waste Pile Area: the square footprint of the waste
pile (Section 2.2. 3. 2.1)
Areal Recharge Rate: water percolating through
the soil to the aquifer outside of the footprint of the
waste pile (Section 2.2.3.2.2)
Areal Infiltration Rate: water percolating through
the waste pile to the underlying soil (Section
2.2.3.2.2)
Leachate Concentration: the concentration of the
leachate emanating from the base of the waste pile
(Section 2.2.3.2.3)
Source Leaching Duration: the duration of the
leachate release period (Section 2.2.3.2.4)
Depth Below Grade: the depth of the bottom of
the waste pile below the surrounding ground
surface (Section 2.2.3.2.5)
Symbol
A
"w
Ir
1
CL
tp
dBG
Units
m2
m3/m2/y
or m/y
m3/m2/y
or m/y
mg/L
y
m
Section in
EPACMTP
Parameters/Data
Background
Document
2.5.1
4.4
4.3.2
3.2.3
2.5.2
2.5.3
2.2.3.2.2 Areal Infiltration and Recharge Rates
The EPACMTP model requires input of the net areal rate of vertical downward
percolation of water and leachate through the unsaturated zone to the water table.
Infiltration is defined as water percolating through a WMU to the underlying soil,
while recharge is water percolating through the soil to the aquifer outside of the
footprint of the WMU. The model allows the infiltration rate to be different from the
ambient regional recharge rate. The waste pile infiltration rate can be different from
the ambient recharge rate for a variety of reasons, including the engineering design
of the waste pile (for instance, waste with a conductivity much lower than that of the
regional soil type), topography, land use, and vegetation. The recharge rate is
determined by the regional climatic conditions, such as precipitation,
evapotranspiration, surface run-off, and regional soil type.
Both infiltration and recharge are specified as areal rates, with the units of cubic
meters of fluid (water or leachate) per square meter per year (m3/m2/y or m/y).
Infiltration and recharge rates for selected soil types at cities around the country
have been estimated using the HELP water-balance model and are incorporated into
a database included in one of the EPACMTP input files. Further details about how
these rates were determined and other options for determining recharge and
infiltration rates outside of the EPACMTP model can be found in Section 4.0 of the
EPACMTP Parameters/Data Background Document (U.S. EPA, 2003).
2-32
-------
Source-Term Module Section 2.0
2.2.3.2.3 Leachate Concentration
The leachate concentration (CL, mg/L) is the concentration of dissolved constituent in
the leachate that enters the subsurface from the base of the WMU. For the waste
pile scenario, the EPACMTP model assumes a constant concentration pulse
condition. This parameter is a user-input parameter. Alternatively, EPACMTP can
estimate it from the waste concentration using Equation (2.25).
2.2.3.2.4 Source Leaching Duration
Waste piles are a temporary management scenario in which the addition and
removal of waste during the operational life period are more or less balanced,
without significant net accumulation of waste. Typically at the end of the active life of
a waste pile, the waste material is either removed for land filling, or the waste pile is
covered and left in place. If the waste is removed, there is no longer a source of
potential contamination. Consequently, the finite source implementation that is most
appropriate for waste piles is the pulse (or non-depleting) source scenario. The
boundary condition for the fate and transport model then becomes a constant
concentration pulse, with a defined duration that is equal to the operational life of the
waste pile. When conducting a Monte-Carlo modeling simulation of a waste pile in
EPACMTP using a pulse source, the duration of the leaching period may be
assigned a constant value or an appropriate frequency distribution, based on the
available data. Alternatively, if a waste pile is covered and left in place, it then
becomes equivalent to a landfill and should be simulated as a landfill (that is, using
the depleting source option of the finite source scenario). However, this approach is
valid only when the operational life of the waste pile is much shorter than the
subsequent leaching period.
2.2.3.2.5 Depth Below Grade
The depth below grade is defined as the depth of the bottom of the waste pile below
the surrounding ground surface. If a non-zero value is entered for this input, then the
thickness of the unsaturated zone beneath the impoundment is adjusted accordingly.
2.2.3.3 Mathematical Formulation of the Waste Pile Source-Term Module
The waste pile source module assumes a constant leachate concentration applied
uniformly over the area of the waste pile unit for a period of time equal to the unit's
operating life. EPACMTP requires the user to specify the duration of the leachate
pulse, and the leachate concentration of constituents of concern. If available, the
leachate concentration value can be set equal to measured concentration values
from appropriate leaching tests such as the TCLP or SPLP tests.
Alternatively, the leachate concentration emanating from the waste pile can be
estimated from the total waste concentrations as:
2-33
-------
Source-Term Module Section 2.0
c =
L 9W (2.25)
Kw
~
f>hw
where
CL = leachate concentration (mg/L)
Cw = total waste concentration (mg/kg)
Kw = waste partition coefficient (cm3/g)
0W = volumetric water content of the waste (dimensionless)
phw = waste density (g/cm3)
For organic constituents, the partition coefficient, Kw, in the above equation can be
determined from the constituent-specific organic carbon partition coefficient and the
fraction organic carbon in the waste.
Kw = foow X koc (2.26)
where
Kw = waste partition coefficient (cm3/g)
/^ = fraction organic carbon in the waste (g/g)
koc = constituent-specific organic carbon partition coefficient (cm3/g)
Under conditions of a constant leachate concentration and defined leaching period,
tp, the total mass lost from the waste pile by leaching is
MLWP = *p x ' x Aw x CL x 100° (2.27)
where
MLWP = total mass of constituent leached from a waste pile (mg)
tp = duration of leaching period (y)
/ = areal infiltration rate (m/y)
Aw = area of the waste pile footprint (m2)
CL = leachate concentration (mg/L)
1000 = conversion factor used to convert volume from m3 to liters
2-34
-------
Source-Term Module Section 2.0
2.2.4 Land Application Units
2.2.4.1 Assumptions for the Land Application Unit Source-Term Module
EPACMTP models land application units (LAUs) as temporary management units in
which waste is spread on the soil on a periodic basis. EPACMTP assumes the LAU
has no liner or leachate collection system, and that the rate of leachate generation
from the unit is driven primarily by ambient climate conditions. EPACMTP assumes
the water contained in the land applied waste is insignificant relative to the ambient
regional recharge rate.
The annual waste amount applied to land application units is typically constrained by
the capacity of the site to absorb waste (e.g., remove through biodegradation and/or
plant uptake) without significant accumulation of potentially hazardous constituents.
While there may be significant leaching to ground water occurring during the
operational life of a land application unit, the leaching will diminish quickly after
waste application ceases.
2.2.4.2 List of Parameters for the Land Application Unit Source-Term Module
The source-specific input parameters for the land application unit (LAU) scenario
include the WMU area, infiltration rate; the ambient recharge rate, the leachate
concentration, and the source leaching duration. Together these parameters are
used to determine how much contaminant mass enters the subsurface and over
what time period.
The source-specific parameters for the LAU scenario are presented in Table 2.4 and
are described in the following sections.
2.2.4.2.1 Land Application Unit Area
The land application unit (LAU) area is defined as the footprint of the unit. In
EPACMTP, the LAU is modeled as being square, i.e., equal length and width. Thus,
the length and width of the LAU are each calculated as the square root of the area.
The LAU area is used to determine the area over which the infiltration rate is applied.
2.2.4.2.2 Infiltration and Recharge Rates
The EPACMTP model requires input of the net areal rate of vertical downward
percolation of water and leachate through the unsaturated zone to the water table.
Infiltration is defined as water percolating through a WMU to the underlying soil,
while recharge is water percolating through the soil to the aquifer outside of the
footprint of the WMU. The model allows the infiltration rate to be different from the
ambient regional recharge rate. The LAU infiltration rate can be different from the
ambient recharge rate for a variety of reasons, including the engineering design of
the LAU (for instance, a high water content in the land applied sludge), topography,
land use, and vegetation. The recharge rate is determined by the regional climatic
2-35
-------
Source-Term Module
Section 2.0
Table 2.4 Source-Specific Variables for Land Application Units
Parameter
Waste Site Area: the footprint of the LAD
(Section 2.2.4.2.1)
Areal Recharge Rate: water percolating
through the soil to the aquifer outside of the
footprint of the LAU (Section 2.2.4.2.2)
Areal Infiltration Rate: water percolating
through the LAU to the underlying soil
(Section 2.2.4.2.2)
Leachate Concentration: the concentration
of a constituent in the leachate emanating
from the base of the LAU (Section 2.2.4.2.3)
Source Leaching Duration: the duration of
the leachate release period (Section
2.2.4.2.4)
Symbol
"w
Ir
1
CL
tp
Units
m2
m3/m2/y or
m/y
m3/m2/y or
m/y
mg/L
y
Section in
EPACMTP
Parameters/Data
Background
Document
2.6.1
4.4
4.3.3
3.2.3
2.6.2
conditions, such as precipitation, evapotranspiration, and surface run-off, and
regional soil type.
Both infiltration and recharge are specified as areal rates, with the units of cubic
meters of fluid (water or leachate) per square meter per year (m3/m2/y or m/y).
Default infiltration and recharge rates for selected soil types at 102 climate stations
around the country have been estimated using the HELP water-balance model and
are incorporated into a database included in the EPACMTP input files. The default
infiltration rate is based on an assumption that 6 inches of waste sludge with 80
percent water is applied on a yearly basis. Further details about how these rates
were determined and other options for determining recharge and infiltration rates
outside of the EPACMTP model can be found in Section 4.0 of the EPACMTP
Parameters/Data Background Document (U.S. EPA, 2003).
2.2.4.2.3 Leachate Concentration
The fate and transport model requires stipulation of the leachate concentration as a
function of time, CL(t). The leachate concentration CL(t) used in the model directly
represents the concentration of the leachate emanating from the base of the waste
management unit, as a boundary condition for the fate and transport model. For the
LAU scenario, the EPACMTP model accounts for this time variation as a constant
concentration pulse condition, but it does not attempt to account explicitly for the
multitude of physical and biochemical processes inside the waste unit that may
control the release of waste constituents. Given the difficulty of accurately predicting
2-36
-------
Source-Term Module Section 2.0
leachate concentration over time as a function of both chemical and waste properties
and the intended use of EPACMTP for generic application to a wide range of site
conditions and chemical constituents, the parameterization of the source term, and
the leachate concentration in particular, is simplified. However, other models can be
used to simulate processes not included in EPACMTP (such as biodegradation of
organic constituents within the LAU), but considered significant in some land
application scenarios. The results of these models can be used as input to the
EPACMTP model.
2.2.4.2.4 Source Leaching Duration
The finite source option that is most appropriate for the LAU scenario is the pulse (or
non-depleting) source scenario. The boundary condition for the fate and transport
model then becomes a constant concentration pulse, with a defined duration. For
land application units, the addition and removal of waste (via leaching,
biodegradation, etc.) during the operational life usually are more or less balanced,
without significant net accumulation of waste. Once waste application ceases at the
end of the operational life of the LAU, the leachable waste is expected to be rapidly
depleted. Consequently, in the finite source implementation for LAUs, the duration
of the leaching period will, in most cases be the same as the operational life of the
LAU. The duration of the leaching period may be assigned a constant value or an
appropriate frequency distribution.
2.2.4.3 Mathematical Formulation of the Land Application Unit Source-Term
Module
By default, the LAU source-term module assumes a constant leachate concentration
applied uniformly over the area of the LAU waste unit for a period of time equal to
the unit's operating life. EPACMTP requires the user to specify the duration of the
leachate pulse, and the leachate concentration of contaminants of concern. The
duration of the leachate pulse is equal to or shorter than the unit's operating life.
If not given by a measured value such as the TCLP or SPLP leaching test, the
leachate concentration in LAU applied wastes can be estimated from the total waste
concentration as:
CL = ^
(Kw +
where
CL = leachate concentration (mg/L)
Cw = total waste concentration (mg/kg)
Kw = waste partition coefficient (cm3/g)
0W = water content of the waste (dimensionless)
phw = density of the waste (g/cm3)
2-37
-------
Source-Term Module Section 2.0
For organic constituents, the partition coefficient Kw in the above equation can be
determined from the constituent specific organic carbon partition coefficients and the
fraction organic carbon in the LAU waste-soil mixing layer:
Kw = focw x koo (2.29)
where
Kw = waste partition coefficient (cm3/g)
faw = fraction of organic carbon in the soil layer in which the waste is
mixed (dimensionless)
koc = constituent-specific organic carbon partition coefficient (cm3/g)
A key purpose of many LAU waste management units is to promote degradation of
waste constituents by spreading and mixing them with soil, so that most of the
constituent mass is consumed between waste application intervals. EPACMTP does
not explicitly simulate the resulting variations in leachate concentration, but rather
approximates the source as a constant concentration pulse, with duration equal to
the WMU's operational life. This approximation may not be protective for
constituents (such as metals) which tend to accumulate in the LAU treatment zone,
because the residual constituent mass which remains after the end of the units'
operational life may continue to act as a source of leachate. In these situations, the
effective leachate pulse duration can be determined from mass-balance analysis as:
*A x mw x cw (2.30)
p~ CL x / x Aw x 1000
where
tp = duration of leaching period (y)
tA = WMU active life (y)
mw = annual waste mass loading during active life (kg/y)
Cw = constituent concentration in waste (mg/kg)
CL = leachate concentration (mg/L)
/ = infiltration rate (m/y)
Aw = area of WMU footprint (m2)
1000 = conversion factor used to convert volume from m3 to liters
In Equation (2.30), the leachate concentration, CL, as well as all other variables in
the equation are assumed to be unchanged throughout the leaching period. The use
of the total applied waste mass in Equation (2.30) assumes no losses other than
through leaching which may conservatively overestimate the magnitude of potential
exposure of the ground-water pathway.
2-38
-------
Source-Term Module Section 2.0
2.2.5 Limitations on Maximum Infiltration Rate
The EPACMTP source-term module incorporates several checks to ensure that
WMU infiltration rate does not result in an unrealistic degree of ground-water
mounding. This screening procedure is especially important when EPACMTP is
used in Monte-Carlo mode (see Section 5), to provide a safeguard that parameter
values drawn randomly from their individual probability distributions, do not result in
physically infeasible situations. One such situation can occur when the infiltration
rate from the WMU unit is high, and the aquifer underlying the site has a low
transmissivity. This could result in an excessive degree of simulated ground-water
mounding. Specifically, the EPACMTP source module checks the following
conditions:
• Infiltration and recharge so high they cause the water table to rise
above the ground surface;
• The top of the water level in an SI unit below the water table, causing
flow into the SI; and
• Infiltration rate from an SI exceeds the saturated hydraulic
conductivity of the soil underneath.
The logic diagram for the infiltration screening procedure is presented in Figure 2.4;
Figure 2.5 provides a graphical illustration of the screening criteria. The numbered
criteria checks in Figure 2.4 correspond to the numbered diagrams in Figure 2.5.
High infiltration rates are most likely with surface impoundments. Therefore, the
screening procedure is the most involved for surface impoundment WMUs.
Figure 2.4(a) depicts the screening procedures for landfills, waste piles, and land
application units. For these units, after the WMU infiltration rate, as well as regional
recharge rate and values for the primary hydrogeologic parameters (depth to water
table, aquifer saturated thickness, aquifer hydraulic conductivity, and regional
gradient), have been assigned, either as user input values, or generated by the
EPACMTP Monte-Carlo module, EPACMTP calculates the estimated water table
mounding that would result from the selected combination of parameter values. The
combination of parameters is accepted if the calculated maximum water table
elevation (the ground-water 'mound') remains below the ground surface elevation at
the site. If the criterion is not satisfied, the selected parameters for the realization
are rejected. If the model is used in Monte-Carlo mode, a new set of parameter
values is generated, otherwise EPACMTP generates an error message.
For surface impoundments, there are two additional screening steps, as depicted in
Figure 2.4(b). EPACMTP first determines whether the base of the impoundment is in
direct hydraulic contact with the water table. If the base of the surface impoundment
is below the water table, the surface impoundment unit is said to be hydraulically
connected to the water table (see Figure 2.5, Criterion 1). The realization is rejected
and a new set of hydrogeologic parameters is regenerated if the hydraulically
connected surface impoundment is an inseeping type (see Figure 2.5, Criterion
1(b)). As long as the elevation of the waste water surface in the impoundment is
2-39
-------
Source-Term Module Section 2.0
above the water table, and the surface impoundment is an outseeping source (see
Figure 2.5, Criterion 1 (a)), the first criterion is passed.
If the base of the unit is located above the water table, the unit is said to be
hydraulically separated from the water table (see Figure 2.5, Criterion 2). However,
in this case, it is necessary to ensure that the calculated infiltration rate does not
exceed the maximum feasible infiltration rate. The maximum feasible infiltration rate
is the maximum infiltration that allows the water table to be hydraulically separated
from the surface impoundment. In other words, it is the rate that does not allow the
crest of the local ground-water mound to be higher than the base of the surface
impoundment. This limitation allows EPACMTP to determine a conservative
infiltration rate that is based on the free-drainage condition at the base of the surface
impoundment. If the water table is allowed to be in hydraulic contact with the base of
the surface impoundment, the hydraulic gradient across the bottom of the surface
will decrease thereby causing the infiltration rate to decrease accordingly.
EPACMTP calculates the maximum allowable infiltration rate as:
2KXB(DU- dBG)
Max ^ r->
where
/Max = maximum allowable infiltration rate (m/y)
Kx = longitudinal hydraulic conductivity of the saturated zone (m/y)
6 = thickness of the saturated zone (m)
Du = thickness of the unsaturated zone (m)
dBG = depth below grade of the surface impoundment (m)
R0 = equivalent source radius (m)
/?„ = distance between the center of the source and the nearest
downgradient boundary where the boundary location has no
perceptible effects on the heads near the source (m).
Equation (2.31) is based on the Thiem equation for steady-state water level rise in a
uniform aquifer with constant infiltration within the equivalent source area (radius =
R0) (see, for instance, Todd, 1959). The equivalent source radius, R0, is based on a
circular infiltration source. For a rectangular WMU with area A (m2), EPACMTP
calculates the equivalent source radius as:
RO = .— (2-32)
A TT
2-40
-------
Source-Term Module
Section 2.0
Lan
Wast
Land Appli
1
Pi
f Corrt
Hydroge
Paran
Reject s' Ch(
N. Crite
^**^ %,
i
Screening F
dfill
3 Pile
cation Unit
ck
lated
'©logical
leters
3Ck ^v C
>rion ^ -
\/^
' Accept
Perform
Unsaturated
Zone
Simulation
i
Perform
Saturated
Zone
Simulation
i •
Next
Realization
low Chart
Surface
Impoundment
Pick
Cotielaled *
Hydrogeological ^
Parameters
5 Y Hydraulically
5 xXConnected
n s' ^\
1 / Check \vlnseepinq
>, \ Gmerion / Reject
1 \i^r
5 yuutseeping
5 y Accept
>• Perform
Unsaturated
Zone
"
Compute
Maximum
Feasible
Infiltration (lmax)
^/CheckX^ i > |max
\^ uriterion ^
\^ 2 //
jT^ i 1 - 'max
sS Check \^ Reject
\. Uriterion ^
^xSx^
y Accept
Perform
Saturated
Zone
Simulation
Next
Realization
Figure 2.4 Flowchart Describing the Infiltration Screening Procedure.
2-41
-------
Source-Term Module Section 2.0
i) Surface impoundment initially hydraulically connected with the saturated zone,
/ V s /\ Ground surface
\ SI /
•='• \ / \ / = ? Accepted
jg^ ~/ K~ The unsaturated zone is bypassed
1.b Inseepina SI Unit
ci / \ Ground surface i
Si / y V Rejected
Water ™
Table V-
2 Surface impoundment initially hydraulically separated from the saturated zone.
Si
Groundwater mound
due to infiltration
\max = maximum feasible infiltration rate
Initial Water Table
(3) Feasible criterion for all WMU types.
Recharge
^
\ SI / ~~~~-~-_ v/ New Water Table
Initial Water Table
Figure 2.5 Infiltration Screening Criteria.
2-42
-------
Source-Term Module Section 2.0
where
R0 = equivalent source radius (m)
Aw = areaofWMU footprint (m2)
The distance to the nearest downgradient boundary location, Rx, is normally the
nearest surface water body located along one of the streamlines traversing WMU.
The implied assumption is that the water level in this surface water body is in
hydraulic equilibrium with the ground-water level, and the surface water body is not
affected by the infiltration of water from the WMU.
For surface impoundments, Criterion 2 is used to cap the infiltration rate at lmax.
Once Criteria 1 and 2 are passed, the combination of infiltration rate, recharge rate,
and primary hydrogeologic parameters is used to estimate water table mounding
elevation. As for LFs, LAUs, and WPs, Criterion 3 is passed if the calculated
maximum ground-water elevation is below the ground surface elevation at the site.
2-43
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-------
Unsaturated Zone Module Section 3.0
3.0 UNSATURATED-ZONE MODULE
3.1 PURPOSE OF THE UNSATURATED-ZONE MODULE
The unsaturated-zone module simulates vertical water flow and solute transport
through the unsaturated zone above an unconfined aquifer. Since one of the
primary intended uses of the module is for Monte-Carlo uncertainty analysis, the flow
and transport routines in this module are designed for optimal computational
efficiency.
The unsaturated zone is based on the Finite-Element Contaminant Transport in the
Unsaturated Zone (FECTUZ) code (U.S. EPA, 1989). The FECTUZ code is
designed to simulate vertically downward steady-flow and contaminant transport
through the unsaturated zone above an unconfined aquifer. FECTUZ is based on
the EPA's numerical unsaturated-zone simulator, VADOse zone Flow and Transport
code (VADOFT) (Huyakorn and Buckley, 1987), but with extensions and
enhancements to optimize the computational efficiency for Monte-Carlo analyses
(McGrath and Irving, 1973) and to handle multi-species decay chains. The FECTUZ
code was reviewed by the EPA's Science Advisory Board in 1988 (SAB, 1988).
The module consists of a number of solution schemes which solve the flow and
transport equations governing fate and transport of contaminants in the unsaturated
zone. The general simulation scenario for which the module was designed is
depicted schematically in Figure 3.1. This figure shows a vertical cross-section
through the unsaturated zone underlying a waste management unit (WMU; e.g.,
landfill, surface impoundment, waste pile, or land application unit). Contaminants
migrate downward from the WMU, through the unsaturated zone to an unconfined
aquifer with a water table present at some depth. The module simulates the
unsaturated zone in between the base of the WMU and the water table. Inputs are
the rate of water and contaminant leakage from the WMU, as well as soil and
contaminant properties. The primary output is the contaminant concentration
entering the saturated zone at the water table, either as a function of time (transient
simulation) or at steady-state. The transient or steady-state contaminant
concentration at the water table provides the source term for the saturated-zone
module.
The assumptions used in deriving the flow and transport solutions are detailed in
Sections 3.2.2 and 3.3.2, but the most important assumptions are summarized
below.
• Flow and transport are one-dimensional, in the downward vertical
direction.
• Flow and transport are driven by seepage from a WMU, which is
assumed to occur at a constant rate.
3-1
-------
Unsaturated Zone Module
Section 3.0
Waste Managementl Unit
Leachate
Infiltration
Leachate from WMU
Enters Water Table Here
_Soil Surface
Unsaturated Zone
_Water Table
Figure 3.1 Cross-sectional View of the Unsaturated Zone Considered by EPACMTP.
3-2
-------
Unsaturated Zone Module Section 3.0
• Flow is always at steady state, while either transient or steady-state
solute transport simulations can be performed.
• The unsaturated zone comprises a soil with a single uniform layer.
3.2 UNSATURATED-ZONE FLOW SUBMODULE
3.2.1 Description of the Unsaturated-zone Flow Submodule
A schematic view of the one-dimensional system simulated by the unsaturated-zone
module is provided in Figure 3.1. In order to simulate flow in the unsaturated zone
between the base of the waste management facility and water table, the following
data are required:
• Thickness of the unsaturated zone (depth to water table from base of
WMU).
• Soil hydraulic parameters. If these parameters are not available, but
the soil type is known, the parameter values from the database of
Carsel and Parrish (1988) are suggested. Parametric distributions
based on these databases are incorporated into the EPACMTP
model; however, site-specific values can be used, if available.
• The water flow rate (infiltration rate) through the WMU. The user can
assign infiltration rates for landfills, waste piles, and land application
units from the long term net percolation rate (precipitation minus
runoff minus evapotranspiration). However, infiltration rates for
selected soil types at cities around the country estimated using the
HELP water-balance model are incorporated into the nationwide
databases for these WMUs that are distributed with EPACMTP (see
Sections 2.2.1.2.6, 2.2.2.3.2, 2.2.3.2.2, and 2.2.4.2.2). For surface
impoundments, the code is capable of estimating the infiltration rate
from the characteristics of the impoundment and the soil column, Du,
as shown in Figure 3.1 (see also Section 2.2.2.3.1).
3.2.2 Assumptions Underlying the Unsaturated-zone Flow Submodule
The most important assumptions and limitations incorporated in the unsaturated-
zone flow model are described below:
• Flow of the fluid phase is one-dimensional, isothermal and governed
by Darcy's law.
• The air phase is assumed to be immobile, and no volatilization
occurs.
• The fluid considered is slightly compressible and homogeneous.
• Flow of water is always steady.
3-3
-------
Unsaturated Zone Module
Section 3.0
• Effects of hysteresis in soil constitutive relations (relations between
water content and pressure head, and between water content and
relative permeability) are negligible.
• The soil is an incompressible porous medium which does not contain
fractures or macro pores. The module in EPACMTP assumes only
one layer in the unsaturated zone for LFs, LAUs, and WPs. For
surface impoundment units, a layer of consolidated sediment at the
base of the impoundment on top of the unsaturated zone may be
modeled. Underneath the consolidated sediment layer, a layer of the
unsaturated-zone soil with decreased hydraulic conductivity due to
clogging by the invading suspended solids may also be modeled.
• Flow of water is not affected by the presence of dissolved chemicals.
3.2.3 List of the Parameters for the Unsaturated-zone Flow Submodule
The unsaturated-zone-specific input parameters for the ground-water flow module
include parameters to characterize the flow regime in the unsaturated zone in the
vicinity of the waste management unit. These unsaturated-zone flow parameters,
together with the transport parameters described in Section 3.3.3, are used to
determine the advective-dispersive transport (in the vertical direction) of dissolved
contaminants through the soil to the water table. These unsaturated-zone-specific
parameters for the ground-water flow module are presented below in Table 3.1.
Table 3.1 Parameters for the Unsaturated-zone Flow Submodule
Parameter
Saturated hydraulic conductivity: a
measure of the soil's ability to transmit water
under fully saturated conditions (Section
3.2.3.3)
Residual water content: the water content
at which no additional water will flow (Section
3.2.3.1)
Saturated water content: the fraction of the
total volume of the soil that is occupied by
water contained in the soil (Section 3.2.3.1)
van Genuchten parameter (a): soil-specific
shape parameter that is obtained from an
empirical relationship between pressure head
and volumetric water content (Section 3.2.3.1)
Symbol
Ks
9r
0s
a
Units
cm/hr in
input file;
m/y in
output file
unitless
unitless
1/cm in
input file;
1/m in
output file
Section in
EPACMTP
Parameters/
Data
Background
Document
5.2.3.1
5.2.3.4
5.2.3.5
5.2.3.2
3-4
-------
Unsaturated Zone Module
Section 3.0
Table 3.1 Parameters for the Unsaturated-zone Flow Submodule (continued)
Parameter
van Genuchten parameter (/3): soil-specific
shape parameter that is obtained from an
empirical relationship between pressure head
and volumetric water content (Section 3.2.3.1)
Unsaturated-zone thickness: regional
average depth to the water table (Section
3.2.3.2)
Svmbol
P
Du
Units
unitless
m
Section in
EPACMTP
Parameters/
Data
Background
Document
5.2.3.3
5.2.1
3.2.3.1 Soil Characteristic Curve Parameters
In unsaturated flow, the pore water is under a negative pressure head caused by
capillary pressure within the pore space. The relationship between pressure head
and water content for a particular soil is known as a soil-water characteristic curve,
the other characteristic curve needed to solve unsaturated-zone flow is the
relationship between hydraulic conductivity and water saturation.
The van Genuchten (1980) model is used for modeling soil-water content as a
function of pressure head.
According to the van Genuchten model, the water content-pressure head relation is
given by
6 = Br+ (9S- 6r)[1
e = 6
0
o
(3.1)
or
= [1
= 1
< 0
> 0
(3.2)
where
6
er
0S
a
soil water moisture content (dimensionless)
residual soil water content (dimensionless)
saturated soil water content (dimensionless)
van Genuchten soil-specific shape parameter (1/m)
3-5
-------
Unsaturated Zone Module Section 3. 0
ifj = soil pressure head (m)
JB = van Genuchten soil-specific shape parameter (dimensionless)
/ = a p-dependent soil-specific shape parameter = 1-1/p
(dimensionless)
Se = effective saturation (dimensionless)
Parameters /?and /in Equation (3.1) are related through j/= 1-1//?, and in practice
only the parameters a and flare specified.
At atmospheric pressure head (yj= 0), the soil is saturated, with the water content
equal to <9S. The saturated water content (<9S) represents the maximum fraction of the
total volume of soil that is occupied by the water contained in the soil. The soil will
remain saturated as the pressure head is gradually decreased. Eventually, the
pressure head will become sufficiently negative to where water can drain from the
soil. This pressure head is known as the bubbling pressure. The moisture content
will continue to decline as the pressure head is lowered, until it reaches some
irreducible residual water content (<9r). Should the pressure head be further reduced,
the soil would not lose any additional moisture.
The unsaturated hydraulic conductivity is indirectly determined using the relative
permeability which, for water, is defined as the ratio of unsaturated soil hydraulic
conductivity over saturated hydraulic conductivity of the same soil. The relative
permeability as a function of the effective saturation is given by the Mualem-van
Genuchten model (van Genuchten, 1980):
klw=
where
km = relative permeability (dimensionless)
Se = effective saturation (dimensionless)
a = van Genuchten soil-specific shape parameter (1/m)
/? = van Genuchten soil-specific shape parameter (dimensionless)
/ = a P-dependent soil-specific shape parameter = 1-1/p
(dimensionless)
Relative permeabilities depend on the characteristics of the soil, the wettability
characteristics, and the surface tension of the wetting fluid (in this case, water).
3.2.3.2 Thickness of the Unsaturated Zone
The unsaturated-zone thickness, or depth to the water table, for each waste site can
be specified as a single value or distribution of values or it can be obtained from the
regional hydrogeologic data base. In the latter case, based on a site's geographic
location, the corresponding hydrogeologic region is selected. In a Monte-Carlo
simulation, the unsaturated-zone thickness is selected randomly from data available
for that hydrogeologic region.
3-6
-------
Unsaturated Zone Module Section 3.0
3.2.3.3 Saturated Hydraulic Conductivity
The hydraulic conductivity of the soil is a measure of the soil's ability to transmit
water under fully saturated conditions. It is used as an input to the unsaturated zone
flow module and is used to calculate the moisture content in the soil under a given
rate of leachate infiltration from the WMU. Details relating to the available data for
this parameter are presented in U.S. EPA (2003).
3.2.4 Mathematical Formulation of the Unsaturated-zone Flow Submodule
The steady-state flow module of EPACMTP simulates steady downward flow to a
water table. The governing equation is given by Darcy's law below (Bear, 1972):
\dZu )
where
/ = infiltration rate (m/y)
Ks = saturated hydraulic conductivity (m/y)
km = relative permeability (dimensionless)
ifj = soil pressure head (m)
zu = depth coordinate which is taken positive downward from the
base of a WMU (m)
The boundary condition at the water table is
% = 0 (3.5)
where
yj, = pressure head at the water table located at distance tt from the
bottom of a waste management unit (m)
Solution of Equation (3.4) requires stipulation of the relationships between relative
permeability and water content and between water content and pressure head. The
permeability-water content relation km(6) is assumed to follow the Mualem-van
Genuchten model described above.
3.2.5 Solution Method for Flow in the Unsaturated Zone
As a first step in the solution of Equation (3.4), the soil constitutive relations in
Equations (3.1, 3.2, and 3.3) are combined, leading to the following expression for
the km(w) relation
3-7
-------
Unsaturated Zone Module
Section 3.0
Krw ~
1
(-atU)|B]"Y}
"Y2
ip > 0
0
(3.6)
where
' Vw
a
V
P
Y
relative permeability (dimensionless)
van Genuchten soil-specific shape parameters (1/m)
the soil pressure head (m)
van Genuchten soil-specific shape parameter (dimensionless)
a p-dependent soil-specific shape parameter = 1 - 1/p
(dimensionless)
Next, Equation (3.6) is substituted into Equation (3.4) and the derivative replaced by
a backward finite-difference approximation (Huyakorn and Pinder, 1983). This
results, after some rearranging, in
where
K.,
K,
a
P
Y
(3.7)
-1 = 0 ijj<0
function F of ip
soil hydraulic conductivity of pressure ip (m/y)
^s ' Km
saturated hydraulic conductivity (m/y)
relative permeability (dimensionless)
infiltration rate (m/y)
depth coordinate which is taken positive downward from the
base of a WMU (m)
soil pressure head (m) at zu
grid size along the zu direction (m)
effective pressure head for the soil layer between z and zu -
kzu (m)
van Genuchten soil-specific shape parameter (1/m)
van Genuchten soil-specific shape parameter (dimensionless)
1-1/P (dimensionless)
3-8
-------
Unsaturated Zone Module Section 3.0
The parameter (jjcan be written as a weighted average of yjz and yz - Azu.
Y = ^ZU-LZU+ (1 - w)MJZH (3.8)
where
(jj = effective pressure head for the soil layer between z and zu -
bj.u (m)
a) = weighting factor, 0 < w < 1 (dimensionless)
yj = soil pressure head (m)
yjz = soil pressure head (m) at zu
kzu = grid size in the zu direction (m)
Analysis of a number of example problems showed that optimal results, in terms of
accuracy and rate of convergence, are achieved when co, which corresponds to an
upstream-weighted approximation, is set to 1.0.
Using Equations (3.7 and 3.8) together with the lower boundary condition (Equation
(3.5)), allows i(j7 A7 to be solved. This value for i(j7 _A7 is then used in the place of
£u **£u u u
if/z in Equations (3.7 and 3.8) 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 can be computed. A combined
Newton-Raphson and bi-section method is used to solve the nonlinear root-finding
problem (Equation (3.7)).
After the pressure head distribution in the unsaturated zone has been found, the
corresponding water content distribution 9(zl), is computed using Equation (3.1). In
principle, the saturation distribution can be found without first solving for yj(zj by
substituting Equation (3.3) rather than Equation (3.6) into Equation (3.8). The
disadvantage of this approach is that it becomes more difficult to accommodate
layered soils. Whereas the ^-profile is continuous in the unsaturated zone, the
(9-profile is discontinuous at the interface of soil layers with contrasting hydraulic
properties. A Abased solution also cannot handle saturated or partially saturated
conditions.
Unsaturated-zone Discretization. Solution of the steady-state flow equation
requires discretization of the unsaturated zone into a number of one-dimensional
segments of finite thickness. These segments are similar to elements in the finite
element method. Optimized for computational efficiency, the unsaturated-zone
module will perform the discretization automatically in a manner which ensures a fine
discretization in regions where the water content changes rapidly with depth and a
coarser discretization in regions with constant water content. A typical steady-state
saturation profile for a homogeneous soil is shown in Figure 3.2. This figure shows
that the saturation is essentially constant throughout much of the unsaturated zone,
and varies significantly only in a relatively narrow zone above the water table. To
accurately but efficiently represent this saturation profile, a fine discretization is
required only close to the water table (or close to layer interfaces for layered soils).
Previous verification work of the unsaturated-zone module (U.S. EPA, 1996b)
3-9
-------
Unsaturated Zone Module Section 3.0
suggests that for single-layer soils, an accurate discretization requires no more than
5 to 6 points. The discretization algorithm used in the semi-analytical flow module is
based on this principle.
3.3 UNSATURATED-ZONE SOLUTE TRANSPORT SUBMODULE
3.3.1 Description of the Unsaturated-zone Transport Submodule
A schematic view of the one-dimensional system simulated by the unsaturated-zone
module is provided in Figure 3.1. In order to simulate contaminant transport in the
unsaturated zone between the base of the WMU and water table, the following data
are required:
• Soil transport parameters. If not available, the dispersivity can be
estimated from the unsaturated-zone thickness, and, for organics, the
retardation and decay coefficients can be estimated from the soil bulk
density, fraction of organic matter and chemical-specific properties.
• The leachate concentration emanating from the base of the waste
site. If a finite source is being simulated, the duration of the pulse
must be specified (or internally derived in the case of landfills).
• The number of component species and decay reaction stoichiometry,
in the case of chain decay reactions.
• Organic carbon partition coefficient (k^) for organic chemicals and the
effective distribution coefficient (Kd), as a function of concentration, in
the case of metals with nonlinear sorption.
The transport submodule can simulate the effects of both linear and nonlinear
sorption reactions, as well as first-order decay reactions. When decay reactions
involve the formation of hazardous degradation products, it has the capability to
perform a multi-species transport simulation of a decay chain consisting of up to
seven members. Decay reaction paths can be represented by either straight or
branched decay chains.
3.3.2 Assumptions Underlying the Unsaturated-zone Transport Submodule
The most important assumptions and limitations incorporated in the unsaturated-
zone transport model are described below:
• Only the transport of chemicals in the aqueous phase is considered.
• Advection and dispersion are one-dimensional.
• Fluid properties are independent of concentrations of contaminants.
3-10
-------
Unsaturated Zone Module
Section 3.0
0
2 -
4-
ffi
Q
6 -
8
10
0.20
0.4 0.6
SATURATION
0.8
1.0
Figure 3.2 Typical Saturation Profile for a Homogeneous Soil under Steady
Infiltration Conditions. The Water Table Is Located at Z,, = 10 m.
3-11
-------
Unsaturated Zone Module
Section 3.0
• Diffusive/dispersive transport in the porous medium system is
governed by Pick's law. The hydrodynamic dispersion coefficient is
defined as the sum of the coefficients of mechanical dispersion and
molecular diffusion.
• Sorption reactions can be described by a linear or non-linear
Freundlich equilibrium isotherm.
• The effects of biological and chemical decay can be described by
first-order degradation and zero-order production reactions.
• The soil can be modeled as a layered uniform porous medium.
3.3.3 List of Parameters for the Unsaturated-zone Transport Submodule
The unsaturated-zone-specific input parameters for the transport module include
parameters to characterize ground-water transport in the unsaturated zone in the
vicinity of the waste management unit. These unsaturated-zone transport
parameters, together with the ground-water flow parameters described in Section
3.2.3, are used to determine the advective-dispersive transport (in the vertical
direction) of dissolved contaminants through the soil to the water table. These
unsaturated-zone-specific parameters for the ground-water transport module are
presented below and summarized in Table 3.2.
The ground-water temperature and pH for the unsaturated zone are not inputs to the
EPACMTP model. The model assumes that these values are the same as those
input or generated for the saturated zone. The assumed temperature and pH for the
unsaturated zone are used to calculate the overall hydrolysis rate for organics from
the temperature- and pH-dependent hydrolysis rate constants.
Table 3.2 Parameters for the Unsaturated-zone Transport Submodule
Parameter
Longitudinal dispersivity: The characteristic
length of longitudinal dispersion (Section
3.3.3.1)
Percent organic matter: The percent
organic matter in the soil (Section 3.3.3.2)
Soil bulk density: The ratio of the mass of
the solid soil to its total volume (Section
3.3.3.3)
Freundlich Sorption Coefficient: A constant
used with the aqueous concentration to
determine the adsorption isotherm according
to the Freundlich model (Section 3.3.3.4)
Svmbol
<*Lu
%OM
Pbu
Kd
Units
m
unitless
g/cm3
cm3/g
Section in
EPACMTP
Parameters/Data
Background
Document
5.2.4
5.2.3.7
5.2.3.6
5.2.5.1
3-12
-------
Unsaturated Zone Module
Section 3.0
Table 3.2 Parameters for the Unsaturated-zone Transport Submodule
(continued)
Parameter
Freundlich Isotherm Exponent: the
exponent to which the aqueous concentration
is raised in the determination of the adsorption
isotherm according to the Freundlich model;
when the adsorption isotherm is linear, this
exponent is one (Section 3.3.3.5)
Metals Sorption Coefficient: The non-linear,
non-Freundlich type sorption isotherm for
metals (Section 3.3.3.6)
Chemical transformation coefficient:
EPACMTP accounts for biochemical
transformation processes using a lumped first-
order decay coefficient (Section 3.3.3.7)
Biological transformation coefficient:
EPACMTP accounts for biological
transformation processes using a lumped first-
order decay coefficient (Section 3.3.3.7)
Molecular diffusion coefficient: EPACMTP
accounts for chemical-specific molecular
diffusion (Section 3.3.3.8)
Molecular Weight: EPACMTP accounts for
concentrations of degradation products using
stoichiometry (Section 3.3.3.9)
Ground-water Temperature: average
temperature of the unsaturated zone, used to
derive hydrolysis rates for degrading organic
constituents (Section 3.3.3.10)
Ground-water pH: average regional ground-
water pH, assuming that pH is not influenced
by the addition of leachate from the WMU or
changes in temperature, used to derive
hydrolysis rates for degrading organic
constituents and can be used to calculate
sorption of metals (Section 3.3.3.11)
Symbol
n
Kd
ACU
A>u
D,
MW
T
pH
Units
unitless
cm3/g
1/y
1/y
m2/y
g
°C
std.
units
Section in
EPACMTP
Parameters/Data
Background
Document
5.2.5.2
3.3.3 and 5.2.5.1
5.2.6
5.2.7
3.3.1.1
3.3.1.3
5.2.8
5.2.9
3.3.3.1 Longitudinal Dispersivity
Dispersion is caused by contaminants encountering heterogeneities in the soil,
resulting in differing travel distances. These differing travel distances in turn cause
some of the contaminants to arrive sooner and some to arrive later at the water table
3-13
-------
Unsaturated Zone Module Section 3. 0
than would occur by advection alone. Dispersion along the flow direction is
characterized by a characteristic length called longitudinal dispersivity.
The longitudinal dispersivity of the soil (measured in the direction of flow, that is,
vertically downward) can be input as a distribution or it may be derived by
EPACMTP. If derived, it is computed as a linear function of the total depth of the
unsaturated zone using
aLo = 0.02+ 0.022 Du (3.9)
where
ocLu = longitudinal dispersivity for the unsaturated zone (m)
Du = total depth of the unsaturated zone (m)
Equation (3.9) is based on a regression analysis of data presented by Gelhar et al.
(1985).
3.3.3.2 Percent Organic Matter
EPACMTP uses the average percent organic matter in the soil to determine the
retardation of organic constituents. The percent organic matter is converted
internally by EPACMTP to fractional organic carbon content through the following
equation (Enfield et al., 1982):
where
/oc = fractional organic carbon content (dimensionless)
%OM = percent organic matter (dimensionless)
Once the fractional organic carbon content is obtained, the linear distribution
coefficient can be found using:
Kd =" koofoo (3.11)
where
Kd = distribution coefficient (cm3/g)
k^ = normalized organic carbon partition coefficient (cm3/g)
/oc = fractional organic carbon content (dimensionless)
3-14
-------
Unsaturated Zone Module Section 3.0
Equation (3.11) is based on the assumption that hydrophobia binding dominates the
sorption process (Karickhoff, 1985).
3.3.3.3 Soil Bulk Density (pbu)
The dry soil bulk density (mass of soil per unit volume) is used to calculate the
retardation coefficient of organic constituent and convert soil mass to volume.
3.3.3.4 Freundlich Sorption Coefficient (Distribution Coefficient)
For organic constituents, EPACMTP version 2.0 only allows using a linear Freundlich
isotherm to describe the constituent's sorption behavior. In this case, the leading
Freundlich coefficient is known as the solid-liquid phase distribution coefficient (Kd).
The distribution coefficient may be specified directly or as a derived parameter. In
the latter case, it is computed through Equation (3.11) from the fraction organic
carbon (f^) and the organic carbon partition coefficient (k^). Additionally, if Kd is
derived, f^ is internally calculated from the percent organic matter specified in the
unsaturated-zone-specific input group according to Equation (3.10), and the k^ is
specified in the chemical-specific input group.
For metals that are modeled using MINTEQA2-derived isotherms or pH-dependent
empirical isotherms, the Kd data is either read in from an auxiliary input file or
internally calculated based on the ground-water pH. In both cases, the Freundlich
isotherm coefficient is not used; see Section 3.3.3.6 below. Alternatively, metals can
be modeled using an empirical distribution of distribution coefficients (e.g., based on
reported Rvalues in the scientific literature).
3.3.3.5 Freundlich Isotherm Exponent
For organic constituents, EPACMTP version 2.0 only allows using a linear Freundlich
isotherm to describe the constituent's sorption behavior. That is, the Freundlich
isotherm exponent (77) must be set equal to 1.0. If this parameter is omitted from the
input data file, it is assigned a default value of 1.0, which is equivalent to specifying a
linear sorption isotherm.
For metals that are modeled using MINTEQA2-derived isotherms or pH-dependent
empirical isotherms, the Kd data is either read in from an auxiliary input file or
internally calculated based on the ground-water pH. In both cases, the Freundlich
isotherm exponent is not used; see Section 3.3.3.6 below.. Alternatively, metals can
be modeled using an empirical distribution of distribution coefficients (e.g., based on
reported Rvalues in the scientific literature); in this case, the Freundlich isotherm
exponent should be set to its default value of 1.0.
3.3.3.6 Sorption Coefficient for Metals
In the subsurface, metal constituents may undergo reactions with ligands in the pore
water and with surface sites on the soil or aquifer matrix material. Reactions in
which the metal is bound to the solid matrix are referred to as sorption reactions. In
EPACMTP, users can specify a metal sorption coefficient (Kd) as:
3-15
-------
Unsaturated Zone Module Section 3.0
• a constant value (a linear isotherm) from an empirical distribution, or
• a pH-dependent linear isotherm, or
• a non-linear isotherm.
pH-dependent linear isotherms can be determined from metal-specific pH-based
empirical relationships. Non-linear isotherms were generated using a metal
speciation model, MINTEQA2, as functions of five primary geochemical variables:
pH, hydrous ferric oxide absorbent content, natural organic matter content, leachate
organic acid concentration, and carbonate level in the ambient ground water. These
non-linear isotherm functions are typically available in a tabulated form read in from
an external data file.
Further details of metals sorption coefficients can be found in Section 3.3.3 of the
EPACMTP Parameters/Data Background Document (U.S. EPA, 2003).
3.3.3.7 Chemical and Biological Transformation Coefficients
EPACMTP accounts for biochemical transformation processes using a lumped first-
order decay coefficient. The overall decay coefficient is the sum of the chemical and
biological transformation coefficients.
AO = ACU + A/,u (3.12)
where
Au = overall decay coefficient (first-order transformation) (1/y)
Acu = transformation coefficient due to chemical transformation (1/y)
\bu = transformation coefficient due to biological transformation (1/y)
The coefficients Acu and Abu are specified in the EPACMTP data input file, either as
constants or as a distribution. By default, Abu is set to zero and Acu is a derived
parameter, in which case it is calculated from the chemical-specific hydrolysis
constants:
\,Q+\2pbKd
^ • - <3'13'
where
Acu = transformation coefficient due to chemical transformation (1/y)
A1 = hydrolysis constant for dissolved phase (1/y)
9 = soil water content (dimensionless)
\2 = hydrolysis constant for sorbed phase (1/y)
pb = bulk density of the porous media (g/cm3)
Kd = liquid-solid phase distribution coefficient (cm3/g)
3-16
-------
Unsaturated Zone Module Section 3.0
The hydrolysis constants (/I, and A2) may be temperature and pH dependent. In
EPACMTP, the unsaturated-zone module uses the same ground-water temperature
and pH values as those generated for the saturated zone.
3.3.3.8 Molecular Diffusion Coefficient
EPACMTP accounts for molecular diffusion as part of hydrodynamic dispersion. For
a given solute species /', its free-water molecular diffusion coefficient D, along with
tortuosity given by Millington and Quirk (1961) are used to determine the
constituent's effective molecular diffusion coefficient in the unsaturated zone (see
Equation (3.15)).
3.3.3.9 Molecular Weight
EPACMTP accounts for concentrations of degradation products via stoichiometry. A
degradation-product concentration is determined by converting its concentration from
moles/L to mg/L using its molecular weight.
3.3.3.10 Ground-water Temperature
In a typical Monte-Carlo analysis using EPACMTP, the ground-water temperature is
assigned as a regional site-based parameter based on the location of the waste
management unit. The EPACMTP model uses the temperature of the ground water
in the aquifer as the temperature of the ground water within the unsaturated zone.
For further details, see Section 4.4.3.3.
3.3.3.11 Ground-water pH
A nationwide ground-water pH distribution was derived from STORET, the EPA's
STOrage and RETrieval database of water quality, biological, and physical data.
The EPACMTP model uses the pH of the ground water in the aquifer as the pH of
the ground water within the unsaturated zone. For further details see Section
4.4.3.4.
3.3.4 Mathematical Formulation of the Unsaturated-zone Transport
Submodule
One-dimensional transport of solute species is modeled using the following
advection-dispersion equation:
dc- M
£ 6^,QArtn (3.14)
'dzu 'dt
where
zu = depth coordinate from the base of a WMU (m)
DLu = apparent dispersion coefficient (m2/y)
3-17
-------
Unsaturated Zone Module Section 3.0
c, = aqueous concentration of species / (mg/L)
Vu = Darcy velocity obtained from solution of the flow equation
(m/y)
6 = soil water content (dimensionless)
R, = retardation factor for species i (dimensionless)
t = time (y)
Q, = coefficient to incorporate decay in the sorbed phase of species
/(defined by Equation (3.19)) (dimensionless)
Aj = first-order decay constant for species /(1/y)
^/m = stoichiometric fraction of parent m that degrades into
degradation product / (dimensionless)
Qm = coefficient to incorporate decay in the sorbed-phase of parent
m (dimensionless)
\m = first-order decay constant of parent m (1/y)
cm = aqueous concentration of parent m (mg/L)
The summation term on the right-hand side of Equation (3.14) represents the
production due to decay of parent species, where:
M = total number of parents; and
m = parent species index.
The parameters Qm, and \m pertain to parent species m. The coefficient £jm is a
constant related to the decay reaction stoichiometry. It expresses the fraction of a
parent species that decays to each degradation species. For instance consider the
following hydrolysis reaction whereby parent constituent A produces degradation
product B:
2A + 3H2O - 3B (OH)- + 3H+
In the above reaction, parent species A is species 1 and degradation product B is
species 2. The speciation factor for degradation product B, £21 is equal to 3/2 = 1.5.
The speciation factor depends also on the units used to express concentration, e.g.,
mg/L versus Molar concentration will result in different values for £jm. This is
because ^m relates to the number of molecules reacting not the masses.
The dispersion coefficient DLU in Equation (3.14) is defined as:
where
DLu = apparent dispersion coefficient (m2/y)
ocLu = longitudinal (along the vertical flow direction) dispersivity in the
unsaturated zone defined by Equation (3.9) (m)
Vu = Darcy velocity obtained from solution of the flow equation
(m/y)
3-18
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Unsaturated Zone Module Section 3. 0
9 = soil water content (dimensionless)
Dj0/ = effective molecular diffusion coefficient (m2/y)
The effective molecular diffusion coefficient is determined from
D = D
where:
DM = effective molecular diffusion coefficient (m2/y)
9 = soil moisture content (dimensionless)
D, = molecular diffusion coefficient in free water for species / (m2/y)
(|)eu = effective porosity for the unsaturated zone (dimensionless)
The first expression on the right hand side of the above equation is referred to as
tortuosity and is derived by Millington and Quirk (1961).
The effect of equilibrium sorption is expressed through the retardation coefficient R-.
cte,-
'' • *; <3 17)
where
R, = retardation factor for species / (dimensionless)
pfau = soil bulk density of the unsaturated zone (g/cm3)
9 = soil water content (dimensionless)
f, = slope of the adsorption isotherm for species / (L/kg)
s, = sorbed constituent concentration for species / (mg
constituent/kg dry soil)
Cj = aqueous concentration of species / (mg/L)
When the adsorption isotherm expressed in Equation (3.17) is linear, /;• is equal to the
solid-liquid phase distribution coefficient, Kd. Alternatively, EPACMTP allows the use
of a nonlinear Freundlich adsorption isotherm
8, = /C1/C/n'
nr1
3-19
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Unsaturated Zone Module Section 3.0
where
s, = sorbed concentration of species / (mg constituent/kg dry soil)
kVl = nonlinear Freundlich parameter for species / (mg/kg)
Cj = aqueous concentration of species / (mg/L)
rji = nonlinear Freundlich exponent for species / (dimensionless)
In the special case of a linear Freundlich isotherm (that is, when the exponent 77 =
1.0), the parameter kVl is the same as the distribution coefficient Kd.
For nonlinear metals transport, the model accommodates tabular isotherm data from
external sources. The existing database in EPACMTP was generated using the
MINTEQA2 speciation model. Further details of the derivation and use of distribution
coefficients for metals can be found in Section 3.3.3 of the EPACMTP
Parameters/Data Background Document (U.S. EPA, 2003).
EPACMTP accounts for biochemical transformation processes using a lumped first
order decay coefficient derived from the hydrolysis constants of the sorbed and
dissolved phases.
To account for degradation in both the dissolved and sorbed phase, the lumped
degradation coefficient A, is multiplied by the coefficient Q,, which is given by
Q,= ^ + k (3.19)
D
where
Q, = coefficient to incorporate decay in the sorbed phase for
species / (dimensionless)
pfau = soil bulk density for the unsaturated zone (g/cm3)
9 = soil water or moisture content (dimensionless)
/f1(. = nonlinear Freundlich parameter for species / (mg/kg)
c, = aqueous concentration of species / (mg/L)
/7, = non-linear Freundlich exponent for species / (dimensionless)
When sorption is linear, Q, is the same as the retardation coefficient, R,.
The initial and boundary conditions of the one-dimensional transport problem may be
expressed as:
c/z^O) = c/n (3.20)
3-20
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Unsaturated Zone Module Section 3.0
where
Ci(zu, 0) = initial aqueous concentration of species / at depth zu (mg/L)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
c-n = initial concentration in the soil column (mg/L) (In EPACMTP, it
is assumed that the unsaturated zone is initially contaminant-
free, and so this parameter is set to zero).
and either a prescribed source flux condition, assuming a perfectly mixed influent
= Vu(c°(t)-c) (3.21)
where
DLu = apparent dispersion coefficient (m2/y)
c, = aqueous concentration of species / (mg/L)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
t = time (y)
V = Darcy velocity (m/y)
c, = aqueous concentration of species / at the source (mg/L)
or a prescribed source concentration condition
c,(0,0 = c°(t) (3.22)
where
c, (0,t) = aqueous concentration of species / at zu = 0 (mg/L)
c° (f) = leachate concentration of species/emanating from the WMU
(mg/L)
and a zero concentration gradient condition at the bottom of the unsaturated zone
!!! ^ =" ° (3.23a)
where
C; (lu, t) = aqueous concentration of species / at time t at the bottom of
the saturated zone (mg/L)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
3-21
-------
Unsaturated Zone Module
Section 3.0
t
bottom of the unsaturated zone (m)
time (y)
Analytical or semi-analytical solutions for the transport equation for the unsaturated
zone are based on an assumption that the flow and transport domain is semi-infinite.
In other words, the flow and transport domain along the positive zu direction is
extended to infinity. However, concentration of species / at the water table is still
determined as zu = lu. When either the analytical steady-state transport or
semi-analytical multi-species transport solutions are used (see Section 3.3.5), the
boundary condition shown in Equation (3.23a) is prescribed at the new extreme end
of the flow and transport domain instead of at zu = lu, i.e.,
do, M)
5z..
= 0
(3.23b)
where
c, (°<>, t) = aqueous concentration of species / at zu -°° (mg/L)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
t = time (y)
The source concentration c° (t) can be either constant in time, or may represent a
decaying source. In the latter case, the source concentration of the /-th species is
given by Bateman's equation:
M
dt
mCm
(3.24a)
where
t
Y,
m
M
Ym
_o
aqueous concentration of species / in the source (mg/L)
time (y)
first-order decay rate for species / in the source (1/y)
index of the parent species (dimensionless)
total number of parent species (dimensionless)
stoichiometric fraction of parent m that degrades into
degradation product / (dimensionless)
first-order decay rate for parent m (1/y)
aqueous concentration of parent m (mg/L)
Subject to
= c
(3.24b)
3-22
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Unsaturated Zone Module Section 3.0
where
0° = aqueous concentration of species / (mg/L)
t = time (y)
dj = initial aqueous concentration of species / in the source (mg/L)
3.3.5 Solution Methods for Transport in the Unsaturated Zone
The transport module incorporates three solution options for the transport equation.
An analytical solution is used for steady-state, single species simulations involving a
linear adsorption isotherm. A semi-analytical solution is used for transient or
steady-state decay chain simulations with linear sorption. A semi-analytical solution
is used for all cases involving metals that have nonlinear sorption. The three
solution methods are discussed below.
3.3.5.1 Steady-state. Single Species Analytical Solution
The analytical solution considers the unsaturated zone as a layered system with
constant seepage velocity and uniform saturation in each layer. These layers
correspond to the segments used in the steady-state flow solution. Each segment or
layer is assigned an average water content. The governing equation for steady-state
transport in the i-th layer is
1 — - A'c =0
- 12 a
dZu dZu
where
a'Lu = longitudinal dispersivity for the /-th layer (m)
c = aqueous concentration of the constituent of interest (mg/L)
zu' = local depth coordinate measured from the top of the /-th layer
(m)
u ' = retarded seepage velocity in the /-th layer (m/y)
A' = first order decay constant (1/y)
The retarded seepage velocity of the constituent of interest, it, is given by
V1
u1 = — — (3.25b)
6'R'
3-23
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Unsaturated Zone Module
Section 3.0
where
u'
V1
vu
R
retarded seepage velocity in the /-th layer (m/y)
ground-water velocity in the /-th layer (m/y)
water content in the i-th layer (dimensionless)
retardation factor in i-th layer (dimensionless)
The source boundary condition for the uppermost layer is given by
where
c(0,t) =
c(Q,t) = c°
aqueous-phase concentration at zu1 = 0 (mg/L)
aqueous-phase source concentration (mg/L)
(3.26)
Using the bottom layer boundary condition (Equation (3.23)) and continuity of
concentration between layers, the analytical steady-state transport solution for the
multi-layered system is
c(zu) = c°exp
u'\
4a!,,^l
u"\
(3.27)
where
a
Lu
U1
u
aqueous concentration of the constituent of interest at zu
(mg/L)
aqueous concentration at the source (mg/L)
index of the layer of interest (dimensionless)
index of a layer from the top layer to the layer immediately
above the layer of interest (dimensionless)
thickness of layer / (m)
longitudinal dispersivity for the /-th layer (m)
first order decay constant (1/y)
retarded seepage velocity in the /-th layer (m/y)
first order decay constant in the /c-th layer (1/y)
retarded seepage velocity in the /c-th layer (m/y)
3-24
-------
Unsaturated Zone Module
Section 3.0
zu = depth coordinate which is taken positive downward from the
base of a waste management unit, in this case it corresponds
to a location within the /c-th layer (m)
z0fc = local depth coordinate measured from the top of the /c-th layer
(m) (m)
If the effect of either dispersion or decay is very small, i.e., cr/l/ty, < < 1, Equation
(3.27) reduces to the steady-state solution for purely advective transport
where
c(zu) = c°exp
u'
(3.28)
where
u
u'
aqueous concentration of the constituent of interest (mg/L)
aqueous concentration at the source (mg/L)
index of the layer of interest (dimensionless)
index of a layer from the top layer to the layer immediately
above the layer of interest (dimensionless)
first order decay constant (1/y)
thickness of layer / (m)
retarded seepage velocity in the /-th layer (m/y)
first order decay constant (1/y)
local depth coordinate measured from the top of the /c-th layer
(m) (m)
retarded seepage velocity in the /c-th layer (m/y)
3.3.5.2 Transient. Decay Chain Semi-analytical Solution
A semi-analytical transport solution is used for steady-state or transient problems
involving multi-species chained decay reactions, but linear sorption. The Laplace
transformation is applied to the governing transport equation. The resulting ordinary
differential equation in the spatial coordinate is solved analytically, followed by
numerical inversion of the Laplace transformed solution using the de Hoog algorithm
(de Hoog et al., 1982). Transient boundary conditions reflecting pulse input of
contaminants are accommodated using the superposition method. The
semi-analytical solution for chain-decay transport is given in Appendix B.1 of this
report.
3.3.5.3 Semi-analytical Solution for Metals with Non-linear Sorption
The general advection-dispersion solute transport equation can be written as:
3c
~dt
ds
+ u
dZ.,
dz,.
dc
'dz..
(3.29)
3-25
-------
Unsaturated Zone Module Section 3.0
where
c = aqueous phase concentration of the constituent of interest
(mg/L)
t = time (y)
pbu = soil bulk density for the unsaturated zone (g/cm3)
9 = moisture content (dimensionless)
s = sorbed phase concentration of the constituent of interest
(mg/kg)
U = seepage velocity (m/y)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
DLu = dispersion coefficient (m2/y)
Assuming equilibrium and reversible sorption, the sorbed phase and dissolved phase
concentrations are related through:
s = Kdc (3.30)
where
s = sorbed phase concentration (mg/kg)
Kd = distribution coefficient (L/kg)
c = aqueous phase concentration (mg/L)
When Kd is a function of c, as in the metals case, the governing equation (Equation
(3.29)) becomes nonlinear. An exact analytical solution to Equation (3.29) in general
form is intractable because of the nonlinear adsorption term. In order to solve the
problem, some approximations are required. If the solute transport is advection-
dominated, we may ignore the dispersion term in Equation (3.29). In that case, the
transport equation (Equation (3.29)) can be written as
a-??- + [1 + f'(C)]— = 0
dzu ^ ' dt
f'(c) = (3.32)
where
U = seepage velocity (m/y)
c = aqueous phase concentration (mg/L)
zu = depth coordinate which is taken positive downward from the
base of a waste management unit (m)
3-26
-------
Unsaturated Zone Module Section 3.0
f(c) = nonlinear function representing the adsorption isotherm
(mg/kg)
f'c = derivative of f(c) with respect to s (dimensionless)
t = time (y)
s = sorbed phase concentration (mg/kg)
The semi-analytical solution for metals transport is given in Appendix B.2 of this
report. In addition, the solution of Equation (3.32) requires that Kd be a monotonic
function of c. Details relating to the monotonicity treatment of Kd are given in
Appendix B.2.
3-27
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