Addendum to the

EPA’s Composite

Model for Leachate

Migration with

Transformation

Products (EPACMTP)

Technical Background

Document 

EPACMTP Version 2.1

Draft
Office of Solid Waste (5305W)

Washington, DC 20460

September 2003

www.epa.gov/osw
Draft

Addendum to the 

EPA’s Composite Model for Leachate Migration with

Transformation Products (EPACMTP)

Technical Background Document

EPACMTP Version 2.1

Prepared for:

U.S. Environmental Protection Agency

Office of Solid Waste

Washington, DC 20460

Prepared by: RTI

3040 Cornwallis Road

Research Triangle Park, NC 27709

Under Contract No.: 68-W-03-042

HydroGeoLogic, Inc.

1155 Herndon Parkway, Suite 900

Herndon, VA 20170

Under Subcontract No.: 3-9ZU-8860

U.S. Environmental Protection Agency

Office of Solid Waste

Washington, DC 20460

September 2003
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i

TABLE OF CONTENTS

Section Page

LIST OF ACRONYMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

1.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

2.0 Expanded Site-Based Database Capability . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.1 Integration of SDF into Monte Carlo Methodology . . . . . . . . . . . . . . . 2-2

2.2 Impact on Monte Carlo Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

3.0 Incorporate Prescribed Finite Source Term Using SDF . . . . . . . . . . . . . . . . . 3-1

3.1 Use of Leachate and Water Flux Profiles from External 

Source Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

3.2 Incorporation of External Source Module into Mathematical 

Formulation of Unsaturated Zone Transport . . . . . . . . . . . . . . . . . . . . 3-3

3.3 Incorporation of External Source Module into Mathematical 

Formulation of Saturated Zone Transport . . . . . . . . . . . . . . . . . . . . . . 3-6

4.0 Add New Variables and Variable Functionalities . . . . . . . . . . . . . . . . . . . . . . 4-1

4.1 Waste Concentration ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.2 pH of Leachate (pHL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

4.3 Additional Generalized Master Variables for Metals Transport . . . . . . 4-3

4.4 Distance to Nearest Surface Water Body (New Functionality) (R4) . . 4-3

5.0 Effects of Leachate pH on Water in the Subsurface . . . . . . . . . . . . . . . . . . . . 5-1

5.1 Soil Column pH Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.2 Aquifer pH Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3

6.0 Solubility Cap at the Water Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

7.0 Add a Surface Water Body to the Modeling Domain . . . . . . . . . . . . . . . . . . . 7-1

7.1 Description of the Surface Water Body . . . . . . . . . . . . . . . . . . . . . . . . 7-1

7.2 Determining Contaminant Mass Flux from Groundwater to 

Surface Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

7.2.1 Time-Averaged Mass Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2

7.2.2 Peak Mass Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3

7.2.3 Time-to-arrival of Mass Flux . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3

7.3 Determining the Vertically Integrated Plume Profile . . . . . . . . . . . . . . 7-3

8.0 Export Results as Breakthrough Curves in Binary Format . . . . . . . . . . . . . . . 8-1

9.0 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1
ii

LIST OF TABLES

Page

Table 1.1 Documentation Changes Necessitated by the Update to EPACMTP . . . 1-3
Addendum to the EPACMTP Technical Background Document

iii

LIST OF ACRONYMS

3MRA Multi-media, Multi-pathway, and Multiple-receptor Risk

Assessment

AS EPACMTP aquifer-specific data record in input file

CCW Coal Combustion Wastes Regulatory Analysis

CS EPACMTP chemical-specific data record in input file

D&P Dyes and Pigments Risk Assessment

EPACMTP EPA’s Composite Model for Leachate Migration with

Transformation Products

HELP Hydrologic Evaluation of Landfill Performance

HGL HydroGeoLogic, Inc.

HWIR Hazardous Waste Identification Rule

IDIST EPACMTP distribution type specified in input file

LTG Laplace Transform Galerkin

MINTEQA2 EPA’s geochemical equilibrium speciation model for dilute

aqueous systems

MT EPACMTP metal-specific data record in input file

OSW Office of Solid Waste

RCRA Resource Conservation and Recovery Act

SDF source data file

SI surface impoundment

SS EPACMTP source-specific data record in input file

US EPACMTP unsaturated-zone-specific data record in input file

U.S. EPA U.S. Environmental Protection Agency

WMU waste management unit
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Addendum to the EPACMTP Technical Background Document

v

LIST OF SYMBOLS

Symbol Definition

Equation in

which the

symbol first

appears

Aaq area of vertical patch source in aquifer (m) 5.3

AnnInfili water flux from the source for year i (m/d) 3.1

Aw area of WMU footprint (m) 5.3

B thickness of the saturated zone (m) 7.5

b- function defined in Equation B.1.6 in Appendix B of the

EPACMTP Technical Background Document (U.S. EPA,

2003a) (1/m)

3.8

Csw vertically averaged concentration profile along the

groundwater-surface water interface (mg/L)

7.5

average leachate concentration during time interval [ ]

(mg/L)

3.4

c0

avg average leachate concentration (mg/L) 3.3

initial leachate concentration at the time of landfill closure

(mg/L)

4.1

waste concentration at the time of landfill closure (mg/kg) 4.1

Laplace-transformed aqueous concentration of the species (ymg/L)

3.8

Laplace transform of the source function (y-mg/L) 3.6

c0(t) prescribed annual leachate concentration in the year t (mg/L) 3.2

cp aqueous concentration of the species at the source (mg/L) 3.7

DLF landfill depth (m) 5.1

Du total depth of the unsaturated zone (m) 5.2

Dyy horizontal transverse dispersion coefficient (m2

/y) 7.5

exp(@) exponential operator (dimensionless) 3.6

FeOx iron hydroxide content (wt %) N/A

Fh volume fraction of the waste in the landfill at time of closure

(dimensionless)

5.1
LIST OF SYMBOLS (continued)

Addendum to the EPACMTP Technical Background Document

Symbol Definition

Equation in

which the

symbol first

appears

vi

foc fraction organic carbon in the saturated zone (dimensionless) N/A

Hv(@) Heaviside step function (dimensionless) 3.4

I annual areal infiltration rate (m/y) 3.1

i step index (dimensionless) 3.4

Kd distribution coefficient (sorbed and aqueous phases) (cm3

/g) N/A

Kw waste-concentration-to-leachate-concentration ratio (L/kg) 4.1

LeachFlux(t) annual average mass flux rate in the year t (g/m2

/d) 3.2

LeachFluxNY number of annual average mass flux rates (dimensionless) 3.2

LOM leachate organic matter (mg/L) N/A

(t, xsw) mass flux at time t and location xsw for species R (g/y) 7.1

time-averaged mass flux (g/y) 7.2

Ns number of steps into which co

(t) is discretized (dimensionless) 3.4

NyrMet number of annual average infiltration rates (dimensionless) 3.1

%OM percent organic matter in the unsaturated zone

(dimensionless)

N/A

p Laplace-transform variable (1/y) 3.6

pH ambient pH of water in the unsaturated and saturated zones

(standard units)

N/A

pHaq ambient pH of aquifer (standard units) 5.3

pHL pH of infiltrating leachate (standard units) 5.3

pHM pH of mixed leachate and aquifer (standard units) 5.3

average Darcy velocity (m/y) 5.3

RR retardation factor of species R (dimensionless) 5.2

Se effective saturation (dimensionless) 5.2

t time (y) 3.4
LIST OF SYMBOLS (continued)

Addendum to the EPACMTP Technical Background Document

Symbol Definition

Equation in

which the

symbol first

appears

vii

td exposure time interval of interest (y) 7.2

t

R

WT time required for the front of species R to reach water table (y) 5.2

beginning of the time interval of interest (y) 3.4

end of the time interval of interest (y) 3.4

tp leaching duration (y) 5.1

tpeak time value at which the receptor well concentration reaches its

peak (y)

7.2

v average groundwater velocity downgradient of the WMU (m/y) 7.1

x principal Cartesian coordinate along the regional flow direction

(m)

3.8

xsw distance from downgradient edge of WMU to surface water

body (m)

7.1

XR

(xsw, t) x-direction component of the P3D solution for species R at xsw

(mg/L)

7.1

Y all locations along a line perpendicular to the groundwater

flow direction at xsw (m)

7.3

ys equivalent source width in the direction normal to the regional

flow direction on the vertical plane at the downgradient edge

of the WMU (m)

7.1

zs equivalent source depth in the vertical direction on the vertical

plane at the downgradient edge of the WMU (m)

7.1

GREEK SYMBOLS

"T horizontal-transverse dispersivity of the aquifer (m) 7.3

( first order decay rate for the species (1/y) 3.7

Dhw waste density (g/cm3

) 5.1

N total porosity (dimensionless) 5.2
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Addendum to the EPACMTP Technical Background Document

ix

ACKNOWLEDGMENTS

The report was prepared by the staff of HydroGeoLogic, Inc. (HGL) under EPA Contract

Number 68-W-03-042.
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Addendum to the EPACMTP Technical Background Document

xi

EXECUTIVE SUMMARY

The U.S. EPA Office of Solid Waste (OSW) has developed a probabilistic (Monte

Carlo) groundwater flow and transport modeling approach to assess the potential

exposure to toxic constituents in wastes that are disposed in industrial waste

management units (WMUs) subject to RCRA Subtitle D regulations. The

groundwater exposure is expressed as the concentration of a potential

contaminant at a hypothetical drinking water well (receptor well) located

downgradient of the waste disposal facility. This modeling methodology has

been incorporated into a computer code called the EPA’s Composite Model for

Leachate Migration with Transformation Products (EPACMTP; U.S. EPA, 1996a,

1996b, 1997a, 1997b, 1999a, 2002a, 2002b, 2003a, 2003b, 2003c, and 2003d). 

The U.S. EPA OSW has used EPACMTP in its groundwater pathway analysis for

a number of recent RCRA listing determinations to establish threshold

concentrations allowed in industrial wastes disposed in Subtitle D waste

management units (WMUs), including the recent groundwater pathway risk

assessments for coal combustion wastes (CCW) and dyes and pigments (D&P)

manufacturing wastes.

During the past five years, a number of advancements have been made in the

groundwater fate and transport modeling performed in support of the regulatory

efforts of the U.S. EPA OSW, including the development of several projectspecific versions of EPACMTP, created to meet the analytical requirements of

particular groundwater pathway risk assessments. In an effort to maximize the

model’s flexibility given the expected variations in data availability and analytical

requirements for regulatory applications of the model, a number of the features

that were hard-wired in previous project-specific versions of EPACMTP were

made into options in EPACMTP V2.0. Additionally, EPACMTP V2.0 includes a

computationally efficient pseudo-3D groundwater transport module and an

improved surface impoundment module.

Since some of the modeling requirements for the groundwater pathway risk

assessments for CCW and D&P are beyond the current capabilities of

EPACMTP V2.0 (the version developed, tested, and documented for the IWEM

project), the Agency has developed a new version of the model, EPACMTP

Version 2.1 (EPACMTP V2.1). The CCW and D&P analyses require a list of

correlated site-based parameters that is larger than that in the Industrial D

databases and in the regional site-based methodology incorporated in

EPACMTP. Therefore, the EPACMTP source code was modified to enable a

larger number of input parameters to be correlated with a given WMU site,

following the algorithms developed in a project-specific version of the EPACMTP

code created for an earlier RCRA listing determination. However, in addition to
Addendum to the EPACMTP Technical Background Document

xii

the site-based variable correlations permitted in the existing project-specific

version of the EPACMTP code, the new database file was extended to include all

parameters that are reasonably likely to be available as site-based parameters. 

Additionally, several other modifications to the source code were made in order

to meet the Agency’s needs for these projects: 1) additional master variables

were added and the ranges of existing master variables were widened to

accommodate the new MINTEQA2-derived adsorption isotherms that will be

used to model the groundwater transport of metal constituents; 2) data input

routines were revised to accommodate the use of external source model results

(breakthrough curve) as input to EPACMTP; 3) several new input parameters

were added; and 4) new functionality was given to the input parameter for the

distance to the nearest surface water body. This addendum to the EPACMTP

Technical Background Document (U.S. EPA, 2003a) presents the details of these

code changes as they relate to the model’s modular components, mathematical

algorithms, features, assumptions, and limitations.
Addendum to the EPACMTP Technical Background Document

1-1

1.0 Introduction

The U.S. EPA Office of Solid Waste (OSW) has developed a probabilistic (Monte

Carlo) groundwater flow and transport modeling approach to assess the potential

exposure to toxic constituents in wastes that are disposed in industrial waste

management units (WMUs) subject to RCRA Subtitle D regulations. The

groundwater exposure is expressed as the concentration of a potential

contaminant at a hypothetical drinking water well (receptor well) located

downgradient of the waste disposal facility. This modeling methodology has

been incorporated into a computer code called the EPA’s Composite Model for

Leachate Migration with Transformation Products (EPACMTP; U.S. EPA, 1996a,

1996b, 1997a, 1997b, 1999a, 2002a, 2002b, 2003a, 2003b, 2003c, and 2003d). 

The U.S. EPA OSW has used EPACMTP in its groundwater pathway analysis for

a number of recent RCRA listing determinations to establish threshold

concentrations allowed in industrial wastes disposed in Subtitle D waste

management units (WMUs), including the recent groundwater pathway risk

assessments for coal combustion wastes (CCW) and dyes and pigments (D&P)

manufacturing wastes.

During the past five years, a number of advancements have been made in the

groundwater fate and transport modeling performed in support of the regulatory

efforts of the U.S. EPA OSW. These include the development of: 1) a

computationally efficient pseudo-3D groundwater transport module for the Multimedia, Multi-pathway, and Multiple-receptor Risk Assessment (3MRA) modeling

system (U.S. EPA, 1999b); and 2) a new surface impoundment (SI) module for

the 3MRA modeling system (U.S. EPA, 1999c). In addition, several projectspecific versions of EPACMTP were developed to meet the analytical

requirements of particular groundwater pathway risk assessments, and the

Agency has received and evaluated a number of comments from public and peer

reviews regarding features and theoretical aspects of the EPACMTP model as

applied in these risk assessments. Version 2.0 of EPACMTP (EPACMTP V2.0)

was modified to incorporate the two advances listed above, to consolidate into

one code other features developed for project-specific versions of EPACMTP,

and to respond to technical comments from public and peer reviews. 

Specifically, in an effort to maximize the model’s flexibility given the expected

variations in data availability and analytical requirements for regulatory

applications of the model, a number of the features that were hard-wired in

previous project-specific versions of EPACMTP were made into options in

EPACMTP V2.0. The details of the comprehensive testing and verification that

was conducted during the development of EPACMTP V2.0 are presented in U.S.

EPA, 2001. 
Addendum to the EPACMTP Technical Background Document

1-2

Since some of the modeling requirements for the groundwater pathway risk

assessments for CCW and D&P are beyond the current capabilities of

EPACMTP V2.0 (the version developed, tested, and documented for the IWEM

project), the Agency has developed a new version of the model, EPACMTP

Version 2.1 (EPACMTP V2.1). The CCW and D&P analyses require a list of

correlated site-based parameters that is larger than that in the Industrial D

databases and in the regional site-based methodology incorporated in

EPACMTP. Therefore, the EPACMTP source code was modified to enable a

larger number of input parameters to be correlated with a given WMU site,

following the algorithms developed in a project-specific version of the EPACMTP

code created for an earlier RCRA listing determination. However, in addition to

the site-based variable correlations permitted in the existing project-specific

version of the EPACMTP code, the new database file was extended to include all

parameters that are reasonably likely to be available as site-based parameters. 

Additionally, several other modifications to the source code were made in order

to meet the Agency’s needs for these projects: 1) additional master variables

were added and the ranges of existing master variables were widened to

accommodate the new MINTEQA2-derived adsorption isotherms that will be

used to model the groundwater transport of metal constituents; 2) data input

routines were revised to accommodate the use of external source model results

(breakthrough curve) as input to EPACMTP; 3) several new input parameters

were added; and 4) new functionality was given to the input parameter for the

distance to the nearest surface water body. This addendum to the EPACMTP

Technical Background Document (U.S. EPA, 2003a) presents the details of these

code changes as they relate to the model’s modular components, mathematical

algorithms, features, assumptions, and limitations. Table 1.1 is a crosswalk

between the sections of this addendum and the existing EPACMTP V2.0

documentation.
1-3

Table 1.1 Documentation Changes Necessitated by the Update to EPACMTP

Code Changes Made to Create EPACMTP V2.1 Project Parameters/Data Background Document Technical Backgroun

Main Document Addendum Main Document 

Expand site-based database capability (SDF) D&P CCW Update many subsections of § 2, 3, 4, 5 and 6 § 2.1 and 2.2 Update § 5.5.2 New § 5.6 § 2

§ 2

Incorporate input of leaching and/or infiltration profiles as source term using SDF D&P Update § 2.3.6, 2.4.9, 2.5.2, & 2.6.2 Update § 3.2.3 Update § 4.3 § 3.2 § 3.2 § 3.1 New § 2.1.3 Update § 3.3.4 Update § 4.4.5.2.1 § 3

§ 3§ 3

Add a single surface water body to modeling domain D&P CCW Update 2.4.8 § 4.4 Update 2.2.2.2.7 New § 4.4.3.7 Update §4.4.7 Replace App F § 4

§ 7§ 7§ 7

Export receptor well results as breakthrough curves in binary format D&P NA Update § 4.4.6 Update § 4.4.6.1-3 § 8 Export surface water results as breakthrough curve in binary format D&P NA Update § 4.4.7 § 8 Add pH of leachate as a newvariable

CCW New § 3.3.3.3 § 4.2 Update many

subsections of §2.2and §3.3.3

§ 4

Add waste concentration as a newvariable

CCW New § 2.3.7 § 4.1 New 2.2.1.2.12 § 4

Add generalized extra mastervariables for metals transport

CCW New § 3.3.3.2.8 § 4.3 Update § 3.3.3.6 § 4

Add soil column pH determination CCW NA Update § 3.3.3.11 § 5Add mixed aquifer pHdetermination

CCW NA Update § 4.4.3.4 § 5

Add solubility cap at water table CCW NA Update § 4.4.4.7 § 6

Acronyms:CCW - Coal Combustion Wastes Regulatory Analysis D&P - Dyes and Pigments Listing Determination SDF - Source Data File
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Addendum to the EPACMTP Technical Background Document

2-1

2.0 Expanded Site-Based Database Capability

As described in Section 5.3.3 of the EPACMTP Technical Background Document

(U.S. EPA, 2003a), the regional site-based approach is used in the EPACMTP

model to generate (for each Monte-Carlo realization) a random, yet internally

consistent, set of the required site-specific values without requiring the

exhaustive sampling that would be required to actually gather these data from

waste sites around the country. For each Monte-Carlo realization, EPACMTP

selects a site, at random, from the appropriate WMU-specific data set. The

corresponding climatic and hydrogeologic indices and the generated soil type are

then used by the model to generate random, but internally consistent, sets of

values for the climatic, soil and aquifer parameters. Thus, the use of the regional

site-based methodology which links together these correlated data sets serves to

reduce the probability that the generated data set contains a physically

infeasible, unrealistic, or highly unlikely set of parameter values. This approach

is based on several correlated databases comprising data for WMU

characteristics, default infiltration and recharge rates, soil characteristics, and

aquifer characteristics. For use with the EPACMTP model, these databases

have been compiled into the so-called “site data files”, one for each WMU type

(i.e., LFsite.dat, SIsite.dat, etc.). Note that in the regional site-based

methodology, not all of the EPACMTP input parameters need to be specified as

site-related; input parameters such as leachate concentration or receptor well

location can be specified using any of the standard probability distribution types

available in EPACMTP.

However, the list of correlated site-based parameters in the regional site-based

methodology incorporated in EPACMTP V2.0 is limited to a specific set of

parameters. Therefore, during the development of EPACMTP V2.1, the source

code was modified to enable a larger number of input parameters to be

correlated with a given WMU site. The algorithms developed for this purpose in

an earlier project-specific version of the EPACMTP code were adapted to include

all numeric EPACMTP input parameters. This new database file is called the

source data file (SDF), and its filename generally is the same as the

corresponding input data file, but its extension must be “.dat.” Additionally, the

functionality of this SDF was expanded so that the records in this file can either

be read sequentially or randomly. 

The advantages of using the SDF include: 1) achieving a higher degree of

correlation in the site-based data, 2) providing coordination with external source

modules (as described in Section 3), and 3) providing the means to efficiently

perform a number of deterministic EPACMTP model runs in batch mode. Any or

all of the numeric input parameters in EPACMTP V2.1 (that is, all the parameters
Addendum to the EPACMTP Technical Background Document

2-2

in the SS, CS, MT, US, and AS record groups for all WMU types) can be directly

specified in the SDF, and the SDF can also be used in conjunction with the site

data file to provide additional flexibility in specifying, correlating, and constraining

parameter values.

2.1 Integration of SDF into Monte Carlo Methodology

As summarized above, the regional site-based methodology for performing a

Monte Carlo analysis enables parameter values to be specified using either

empirical or parametric distributions of values; however, use of the SDF enables

parameter values to be specified using correlated, tabular distributions of values. 

Note that the SDF can be used either instead of the regional, site-based

methodology or in conjunction with it (as described below in Section 2.2).

The records in the SDF can be read either sequentially or randomly with

replacement; this option is controlled by an input parameter in the header of the

SDF. If sufficient data are available (or can be generated) for the entire universe

of sites, then the sequential record selection can be used. In this case the

number of Monte Carlo realizations will be the same as the number of records in

the SDF. For instance, sequential record selection is typically used to efficiently

perform a number of deterministic model runs in batch mode. Alternatively, if

data are available for only some sites, then the option for random record

selection with replacement can be used. In this way, a statistically valid set of

Monte Carlo realizations can be constructed that is larger than the number of

records in the SDF. Note that even if the same site is sampled more than once

during the course of a Monte Carlo analysis in EPACMTP, the specific values of

infiltration rate, hydrogeologic parameters, and receptor well location may still

vary; likewise, the resulting receptor well concentration value will likely change,

as well.

In a Monte Carlo modeling analysis, each variable that is treated as random must

be assigned one of the probability distribution types that are available in

EPACMTP. In addition to the 13 distribution types listed in Table 5.1 of the

EPACMTP Technical Background Document (U.S. EPA, 2003a), a new

distribution type has been created in EPACMTP V2.1 to signify that a parameter

value should be drawn from the SDF. Therefore, if the appropriate data are

tabulated in the SDF, any of EPACMTP’s numeric input parameters can be

specified in the input data file with the new distribution type indicating that the

given parameter value should be drawn from the SDF. For any parameter

specified in the input file with this new distribution type, the other values in the

input record for that parameter (mean, standard deviation, minimum, and

maximum) are ignored. Note that the default distribution type for each Monte-
Addendum to the EPACMTP Technical Background Document

2-3

Carlo variable is discussed in the EPACMTP Parameters/Data Background

Document (U.S. EPA, 2003b).

2.2 Impact on Monte Carlo Module

Fundamentally, the approach used for a regional site-based Monte-Carlo

analysis consists of conducting the modeling analysis for the sites in a waste site

database on the assumption that these sites are an adequate representation of

the universe of possible waste sites in the geographic region of interest (usually

the entire United States). Summarized below is the actual procedure of the

regional site-based Monte-Carlo simulation, highlighting the manner in which the

SDF can be used in conjunction with the site data file. These steps describe the

general procedure used at the time of preparation of this document and reflect

the currently available databases commonly used by the U.S. EPA. Some of the

specifics may vary for individual projects as the Agency updates its databases,

but the steps below will still illustrate the essence of the methodology:

STEP 1: Select a Waste Site

The first step involves selecting a site, at random, from the list of waste sites;

these waste sites can be tabulated in the standard site data file or in the SDF. 

The data set is treated as an empirical distribution, with each site having a

defined probability of occurrence. When the model selects a site, the data read

into EPACMTP include the appropriate characteristics for that site, including unit

area, unit depth, an index that specifies the nearest climate center, and an index

that specifies the underlying soil type (and landfill cover type) and aquifer type. 

So any or all of these inputs can be individually specified for each waste unit

using the SDF, or they can be specified according to the default distribution types

typically used with the regional site-based methodology. 

STEP 2: Generate Recharge and Infiltration for the Selected Waste Site

Several options are available for specifying the recharge and infiltration rates.

First, these rates (or in the case of composite-lined surface impoundments, the

leak density) can be directly specified in the input file as constant values or

empirical or statistical distributions of values. For instance, an empirical

distribution of infiltration rates can be used to model a composite liner scenario

for a landfill or waste pile; for composite-lined surface impoundments, an

empirical distribution of leak densities is specified and the infiltration rate is then

calculated. Second, the soil type at the chosen waste site (and cover type for

landfills) and the specified liner scenario can be used along with the climate

center index to determine the appropriate values for recharge and infiltration at
Addendum to the EPACMTP Technical Background Document

2-4

the site by querying the database of HELP-modeled recharge and infiltration

rates (note that there are no HELP-modeled infiltration rates for the composite

liner scenario). Third, the recharge and infiltration rates can be tabulated in the

SDF.

STEP 3: Generate Hydrogeologic Variables for Selected Site in the

Industrial Subtitle D Facility Study

As explained above, given the resolution of available hydrogeological databases

and acknowledging the uncertainty in the effective local values of hydrogeological

site characteristics, the regional site-base approach is generally implemented by

using the aquifer type assigned to the chosen site in the WMU database. The

input values for the four hydrogeologic parameters for the chosen site are then

determined from the probability distributions that define the corresponding aquifer

type. That is, a correlated set of hydrogeologic parameter values is randomly

chosen from among those available in the hydrogeologic database for the

chosen aquifer type. If the selected ground-water parameter set is missing any

values, a joint distribution of the parameters (derived for each environment) is

used to fill in the missing values. The details of the procedure used to generate

missing values are presented in Section 5.5.3 of the EPACMTP Technical

Background Document (U.S. EPA, 2003a). Alternatively, values for either the

aquifer type or the four hydrogeologic parameters can be tabulated in the SDF. If

the four hydrogeologic parameters are specified in the SDF, then all values for

each input must be greater than zero. If the aquifer type is specified in the SDF,

then the model uses (as needed) the standard procedure to generate missing

values (those that are specified with values less than zero).

STEP 4: Generate Remaining Parameters for the Selected Waste Site

The remaining parameters for the waste site that are not assigned as site-related

(e.g., x, y, and z coordinates of the receptor well) are typically generated by using

one of the probability distributions described in Section 5.4 of the EPACMTP

Technical Background Document (U.S. EPA, 2003a). Any derived parameters

are calculated as described in Section 5.4.10 of the EPACMTP Technical

Background Document (U.S. EPA, 2003a). However, any numeric EPACMTP

input parameter can be tabulated in the SDF by specifying for that parameter a

distribution type of “88" in the input data file.
Addendum to the EPACMTP Technical Background Document

2-5

STEP 5: Calculate the Predicted Receptor Well Concentration Value for the

Selected Waste Site

Given the complete set of input parameter values generated in the previous four

steps, and the chemical-specific characteristics (e.g., leachate concentration,

adsorption coefficient and exponent, and degradation rate), the EPACMTP flow

and transport modules are executed to compute the receptor well concentration

(and groundwater to surface water mass flux, if appropriate) for this Monte-Carlo

realization. Note that the chemical-specific input parameters can also be

tabulated in the SDF.

STEP 6: Repeat Steps 1 Through 5 a Specified Number of Times, and

Estimate the National Distribution of Receptor Well Concentrations

After Step 5, the receptor well concentration for a specific realization is obtained.

The process is then repeated as many times as is specified by the user. The

result of the Monte-Carlo modeling analysis is a groundwater concentration for

each model realization; these results represent the nationwide distribution of

drinking water exposure concentrations. Likewise, if specified in the input file,

the groundwater to surface water mass flux can be generated for each model

realization; these results represent the nationwide distribution of contaminant

mass fluxes to nearby surface water bodies and can be used to calculate surface

water concentrations to be compared to ambient water quality criteria.

In most cases, the number of Monte-Carlo realizations will be much greater than

the number of sites used in the regional, site-based analysis, and because the

selection of sites as described in Step 1 above is random, each site is expected

to be picked more than once. However, because there’s generally an additional

random component to the process of assigning values to all of the EPACMTP

parameters (e.g., well location), repeated selection of the same waste site in the

Monte-Carlo process generally will not result in the same predicted receptor well

exposure concentration and contaminant mass flux.
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Addendum to the EPACMTP Technical Background Document

3-1

3.0 Incorporate Prescribed Finite Source Term Using SDF

As described above, the SDF functionality was introduced to facilitate the

coupling of external source modules with EPACMTP and to maintain the

correlation among common site-specific and Monte Carlo parameters. Transient

external source modules are likely to generate time series of leachate

concentrations, mass fluxes, water fluxes, et cetera, while EPACMTP V2.0 is

limited to single scalar values to represent long-term average leachate

concentrations and/or infiltration rates. To advance the degree of coupling

between EPACMTP and external source models (and reduce prediction errors

introduced through time-averaging), EPACMTP V2.1 includes updates to read

mass and/or water flux time series data (in the form of an auxiliary input binary

file) and the option to apply the time series either to the top of the soil column or

directly to the water table. That is, in addition to the two source-term modules

available within EPACMTP (continuous source and finite source) and described

in Section 2.1.1 and 2.1.2 of the EPACMTP Technical Background Document

(U.S. EPA, 2003a), EPACMTP V2.1 has the capability to use the output of a

transient external source module as input to EPACMTP. External time series

data are stored in auxiliary input files using a binary format, and access to the

data in the binary files is controlled through the SDF: the parameter of interest,

either leachate concentration or source infiltration rate, must be included as a

field in the SDF and the value in that field must be less than zero. When a record

of the SDF is processed and a negative value is encountered for either of the

above parameters, EPACMTP looks to the binary file for the appropriate time

series. The time series data may be used to specify either water or mass flux

source boundary conditions.

EPACMTP allows the user to separately specify whether the vadose zone or the

saturated zone are to be included in the Monte-Carlo simulation. When the

vadose zone is included in the Monte-Carlo simulation, and the SDF requires

time series data from the binary file, the time series data are incorporated into the

flow and/or transport boundary conditions applied to the top of the soil column

that represents the vadose zone. If the vadose zone is omitted in the preceding

scenario, the time series data are incorporated into the flow and/or transport

boundary conditions applied to the top of the watertable. Some instances may

arise where the vadose zone is included and, depending upon the WMU scenario

being modeled, the selected suite of input parameter values describes a WMU

that is hydraulically connected to the aquifer; that is, the base of the WMU is

below the water table. So, for any iterations in which the WMU is hydraulically

connected to the aquifer and a transient external source module is being used as

input to EPACMTP, the vadose zone is automatically bypassed, and the source

boundary conditions are applied to the watertable.
Addendum to the EPACMTP Technical Background Document

3-2

(3.1)

(3.2)

3.1 Use of Leachate and Water Flux Profiles from External Source

Module

In addition to the input specifications for infiltration rate described in Sections

2.2.1.2.6, 2.2.2.2.3, 2.2.3.2.2, and 2.2.4.2.2 of the EPACMTP Technical

Background Document (U.S. EPA, 2003a), the infiltration rate can be specified

through the use of an input binary file containing time series data generated by

an external source module. The EPACMTP model requires as input: 1) an

effective steady state rate of vertical downward percolation from the source

through the unsaturated zone and to the water table (the infiltration rate in m/y),

and 2) annual average leachate concentrations (mg/L). The long-term annual

average infiltration rate (I) is calculated such that mass is conserved, and the full

time-series of annual average water fluxes are used in the calculation. The

infiltration rate is calculated as:

where

I = annual areal infiltration rate (m/y)

NyrMet = number of annual average infiltration rates

(dimensionless)

AnnInfili = water flux from the source for year i (m/d)

Note that NyrMet and AnnInfili are specified in the input binary file and that this

method of specifying the infiltration rate can be used with any of the four WMU

types.

In addition to the input specifications for leachate concentration described

Sections 2.2.1.2.7, 2.2.2.2.8, 2.2.3.2.3, and 2.2.4.2.3 of the EPACMTP Technical

Background Document (U.S. EPA, 2003a), this input parameter can be specified

through the use of an input binary file containing time series data output from an

external source module. In this case, the prescribed annual average leachate

concentration, c0

(t), is calculated from the long-term infiltration rate and mass

fluxes from the source model as follows:
Addendum to the EPACMTP Technical Background Document

3-3

(3.3)

where 

c0(t) = prescribed annual leachate concentration in the

year t (mg/L)

I = annual areal infiltration rate (m/y)

LeachFlux(t) = annual average mass flux rate in the year t

(g/m2/d)

LeachFluxNY = number of annual average mass flux rates

(dimensionless)

Note that LeachFlux(t) and LeachFluxNY are specified in the input binary file. In

the event that a constant leachate concentration is required, as is the case for

non-linear metals transport in the vadose zone, an average concentration can be

calculated from c0

(t) as follows:

where

c0

avg = average leachate concentration (mg/L)

LeachFluxNY = number of annual average mass flux rates

c0(t) = prescribed annual leachate concentration in the

year t (mg/L)

When the leachate concentration is specified using an input binary file, the initial

leachate concentration becomes a function of time for the constituent. Note that

this option is not available for any degradation products produced through

biodegradation or chemical hydrolysis. Also note that when this option is used,

the leaching duration is set equal to the duration of the breakthrough curve

presented in the input binary file.

3.2 Incorporation of External Source Module into Mathematical

Formulation of Unsaturated Zone Transport

The semi-analytical solution used for transient or steady-state decay chain

simulations in the unsaturated zone with linear sorption in EPACMTP V2.0 did

not allow the source concentration to vary as an arbitrary function of time, as

specified in Equation B.1.2c in Appendix B of the EPACMTP Technical

Background Document (U.S. EPA, 2003a). For EPACMTP V2.1, that solution

was modified to allow the leachate profile generated by an external model to be

applied as a transient source concentration boundary condition, as described in
Addendum to the EPACMTP Technical Background Document

3-4

(3.4)

(3.5)

Equation 3.22 of the EPACMTP Technical Background Document (U.S. EPA,

2003a). To make this case amenable to solution by the Laplace transform

method, the source function co

R

(t) is approximated as a sequence of Heaviside

step functions. Dropping the species subscript R to simplify the notation, this can

be expressed as

where

= prescribed annual leachate concentration in the year t (mg/L)

i = step index (dimensionless)

Ns = number of steps into which co(t) is discretized (dimensionless)

= average leachate concentration during the time interval 

[ , ] (mg/L)

Hv (@) = Heaviside step function (dimensionless) (see Equation 3.5

below)

t = time (y)

= beginning of the time interval of interest (y)

= end of the time interval of interest (y)

The Heaviside step function is defined as

where

Hv (@) = Heaviside step function (dimensionless)

t = time (y)

= beginning of the time interval of interest (y)

The Laplace transform of the source function, then becomes
Addendum to the EPACMTP Technical Background Document

3-5

(3.6)

(3.7)

(3.8)

where

= Laplace transform of the source function (y-mg/L)

p = Laplace-transform variable (1/y)

i = step index (dimensionless)

Ns = number of steps into which co

(t) is discretized

(dimensionless)

= average leachate concentration during time interval [ ]

(mg/L)

= beginning of the time interval of interest (y)

= end of the time interval of interest (y)

exp(@) = exponential operator (dimensionless)

 replaces the rational term 

in Equation B.1.6 in Appendix B of the EPACMTP Technical Background

Document (U.S. EPA, 2003a), so the general solution becomes

where

= Laplace transform of the source function (y-mg/L)

cp = constant aqueous concentration of the species at the source

(mg/L)

p = Laplace-transformation variable (1/y)

( = first order decay rate for the species (1/y)
Addendum to the EPACMTP Technical Background Document

3-6

= Laplace-transformed aqueous concentration of the species

(y-mg/L)

exp(@) = exponential operator (dimensionless)

b- = function defined in Equation B.1.6 in Appendix B of the

EPACMTP Technical Background Document (U.S. EPA,

2003a)

x = principal Cartesian coordinate along the regional flow

direction (m)

3.3 Incorporation of External Source Module into Mathematical

Formulation of Saturated Zone Transport

The Laplace Transform Galerkin (LTG) solution used for simulating transport in

the saturated zone allows the concentration at the water table to vary arbitrarily

with time. In general, the arbitrary profile is determined by the unsaturated zone

transport module. If, however, the unsaturated zone is not simulated, a leaching

profile generated by an external source model may be substituted without any

modification to the solution formulation.
Addendum to the EPACMTP Technical Background Document

4-1

4.0 Add New Variables and Variable Functionalities

The enhanced capabilities of EPACMTP Version 2.1 necessitated the addition of

the following input parameters:

• waste concentration (available for the landfill scenario only)

• leachate pH

• a number of additional generalized master variables

These new inputs are described below in Sections 4.1 through 4.3. Additionally,

in EPACMTP Version 2.1, the functionality of an existing input parameter

(distance to surface water) was extended, as described in Section 4.4.

The new methodology to model the fate and transport of metals with nonlinear

sorption isotherms which necessitated the addition of two model inputs (leachate

pH and additional generalized master variables) includes consideration of how

the leachate pH affects the pH of water in the vadose zone and the aquifer, and

thus the transport behavior of metals. Although changes in the pH of water in the

vadose zone and the aquifer due to the influence of leachate pH may also affect

the hydrolysis rates of degrading organic constituents, this modeling capability

was not required for any current or upcoming application of EPACMTP. Hence,

this functionality for organic constituents was not included in EPACMTP V2.1.

4.1 Waste Concentration ( )

In addition to the landfill input parameters described in Section 2.2.1.2 of the

EPACMTP Technical Background Document (U.S. EPA, 2003a), the waste

concentration is now an explicit input parameter for the landfill, depleting source

option; that is, it is not used for other WMU types or for the landfill continuous

source or pulse source scenarios.

The waste concentration (mg/kg), represents the total mass fraction of

constituent in the waste which may eventually leach out. Therefore, in the

context of the depleting (finite) source methodology, 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 but these methods may not

measure the “leachable” waste concentration very precisely. Thus, the waste

concentration 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. 
Addendum to the EPACMTP Technical Background Document

4-2

(4.1)

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. On the

other hand, ignoring these other loss pathways will be protective for the

groundwater pathway analysis. 

In order to model a landfill using EPACMTP’s depleting source option, values for

both the waste concentration, , and the leachate concentration are

required. In EPACMTP V2.0, 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

where

Kw = waste-concentration-to-leachate-concentration ratio (L/kg)

= waste concentration at the time of landfill closure (mg/kg)

= 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.

However, in EPACMTP V2.1, the user also has the option to provide the required

data in the form of the initial leachate concentration and the initial waste

concentration. In this case, the waste-to-leachate concentration ratio, Kw, is

calculated using Equation 4.1.
Addendum to the EPACMTP Technical Background Document

4-3

4.2 pH of Leachate (pHL)

In addition to the source-specific input parameters described in Section 2.2 of the

EPACMTP Technical Background Document (U.S. EPA, 2003a), the leachate pH

is now an input parameter that can be used when modeling the subsurface fate

and transport of a metal constituent with a nonlinear sorption isotherm, and can

be used to model any of the four WMU types. This parameter is used in

determining the sorption behavior of metals with non-linear isotherms in both the

unsaturated and saturated zones by potentially changing the pH value that is

used to select the appropriate sorption isotherm. The algorithms by which the

model determines the extent to which leachate pH affects the pH of water in

vadose zone and aquifer are described below in Sections 5 and 6.

4.3 Additional Generalized Master Variables for Metals Transport

In addition to the seven metal-specific input parameters used in conjunction with

the nonlinear adsorption isotherms that are described in Section 3.3.3.2 of the

EPACMTP Parameters/Data Background Document (U.S. EPA, 2003b) (i.e.,

metal identification number, pH, FeOX, LOM, %OM, foc, and groundwater type),

EPACMTP V2.1 allows specification of up to 10 additional master variables. 

These are generalized variables that can be populated with any new sorptionsensitive parameters that influence metal transport and that were used as

MINTEQA2 model inputs (e.g., ionic strength in the CCW modeling analysis). 

These input parameters can be used with any of the four WMU types.

Random values of all specified geochemical master variables are generated by

the EPACMTP code to be used in Monte-Carlo simulations. These values are

generated for the user-specified hydrogeochemical environment expressed in

terms of the distribution type (IDIST) and statistical parameters (mean, standard

deviation, and parameter upper and lower bounds). Once generated, these

parameter values are then used to choose the appropriate sorption isotherm for

modeling metals transport and may be output in a modeling summary file for

metal simulation parameters.

4.4 Distance to Nearest Surface Water Body (New Functionality) (R4)

In EPACMTP V2.0, the distance to the nearest surface water body, xsw, is used

as one method to prevent the generation and use of an excessively high

infiltration rate and is used in the surface impoundment (SI) scenario only (as

described in Section 2.4.8 of the EPACMTP Parameters/Data Background

Document (U.S. EPA, 2003b)). In EPACMTP V2.1, the following additional

functionality has been assigned to this variable: it has been extended to all four
Addendum to the EPACMTP Technical Background Document

4-4

WMU types for the use of placing a hypothetical surface water body onto the

model grid and allowing the output of contaminant mass fluxes at the interface

between the aquifer and this surface water body. These mass fluxes can then be

used to perform a screening-level ecological risk assessment by converting the

contaminant mass fluxes to water concentrations within the surface water body

and comparing these concentrations to ambient water quality criteria.

The modeled surface water body is assumed to be fully-penetrating, of infinite

extent (that is, it extends beyond the lateral grid boundaries of EPACMTP), and

oriented perpendicular to the regional groundwater flow direction.
Addendum to the EPACMTP Technical Background Document

5-1

5.0 Effects of Leachate pH on Water in the Subsurface

As mentioned above, prior to the creation of EPACMTP V2.1 the impacts of

leachate pH upon the ambient pH conditions have largely been neglected in

groundwater pathway analyses because the variability of the pH in the modeled

wastes was usually small. For CCW wastes, the variability in leachate pH was

found to be very high. Therefore, the potential for pH changes in the subsurface

was very likely. The constraints for incorporating such considerations into

EPACMTP were: (1) to not impair the computational efficiency of the

probabilistic tool; (2) to use easily available data to support the decision; and (3)

to ensure that the approach is defensible in the face of uncertainty regarding the

true impacts of leachate pH on the subsurface. In the development of EPACMTP

V2.1, two new algorithms were developed to account for the effect of leachate pH

on the ambient pH of water in the subsurface: (1) to determine the governing pH

in the soil column (either the pH of the leachate or that of the native soils); and

(2) to determine the resulting pH of the saturated zone as a result of the

infiltrating leachate mixing with pristine water in the aquifer.

Note that these pH adjustments are options that can be used only when

modeling metals with non-linear sorption isotherms. Although changes in the pH

of water in the vadose zone and the aquifer due to the influence of leachate pH

may also affect the hydrolysis rates of degrading organic constituents, this

modeling capability was not required for any current or upcoming application of

EPACMTP. Hence, this functionality for organic constituents was not included in

EPACMTP V2.1.

5.1 Soil Column pH Determination

To determine the governing pH of the soil column beneath the WMU when

modeling metals with non-linear sorption isotherms, the duration of leaching is

compared to an estimate of the first arrival time of the contaminant front at the

water table (a surrogate for the residence time of the contaminant in the soil

column).

For all WMU types other than a LF, the leaching duration (tp) must be prescribed

as a constant value or a distribution of values. Since clean closure is assumed

for these WMU types, the leaching duration generally corresponds to the

operational life of the unit. The leaching duration for landfills can be prescribed;

however, landfills are typically modeled using the depleting source option in

which it is assumed that a LF is a permanent WMU with leachate generation

continuing until the waste is depleted. In this case, the leaching duration (tp) is
Addendum to the EPACMTP Technical Background Document

5-2

(5.1)

(5.2)

derived based on the LF characteristics (rather than being determined a priori)

using the following equation:

where

tp = leaching duration (y)

= constituent concentration in the waste (mg/kg)

DLF = landfill depth (m)

Fh = volume fraction of the waste in the landfill at time of closure

(dimensionless)

Dhw = waste density (g/cm3)

= leachate concentration (mg/L)

I = annual areal infiltration rate (m/y)

The first arrival time of the contaminant front at the water table (a surrogate for

the residence time of the contaminant in the soil column) is estimated using the

following equation:

where:

= time required for the front of species R to reach water table

(y)

Du = total depth of the unsaturated zone (m)

RR = retardation factor of species R (dimensionless)

N = total porosity (dimensionless)

Se = effective saturation (dimensionless)

I = annual areal infiltration rate (m/y)
Addendum to the EPACMTP Technical Background Document

5-3

(5.3)

If the leaching duration is relatively long compared to the time required for the

contaminant to migrate to the water table, the likelihood that the leachate

permeates the soil column is high; in this case, it is assumed that the pH

environment would be governed by the leachate. Conversely, a relatively short

leaching duration and retarded contaminant migration would favor the ambient

characteristics over the length of the soil column. 

An analysis of the relationship between operational life and travel time indicated

that using a value of about five as the decision criteria for this ratio (leaching

duration over travel time) would, in most cases, result in a balanced selection of

leachate pH governing versus soil pH governing over the course of a Monte

Carlo simulation of approximately 10,000 iterations. For this reason, the Agency

has decided to use a factor of five as the decision criteria for determining the

governing pH in the soil column. This comparison of operational life and travel

time is performed for each model realization as follows. For a given realization,

the leachate pH and the remainder of the geochemical master variable values

generated for that realization are used to select the appropriate metal-specific

sorption isotherm. The model then calculates an average distribution coefficient

(Kd) from this isotherm; Kd is used to calculate the retardation factor (RR

)

according to Equations 3.16 and 3.17 of the EPACMTP Technical Background

Document (U.S. EPA, 2003a); and RR is used to calculate the travel time, t

R

WT

according to Equation 5.2 (above). This series of calculations is then repeated

using the ambient soil pH. These two travel times are then averaged, and the

resulting average travel time is compared to the leaching duration. If the ratio is

greater than five, the pH of the leachate is assumed to govern; thus, the pH of

the leachate is used to select the isotherm for transport in the unsaturated zone. 

If the ratio is equal to or less than five, the soil pH is used to select the isotherm.

5.2 Aquifer pH Determination

In the saturated zone, the impacts of leachate pH can be handled using a simple

homogeneous mixing calculation. As shown in the equation below, the volume of

leachate released from the WMU is mixed with a volume of the aquifer that is

likely to be impacted by a plume:
Addendum to the EPACMTP Technical Background Document

5-4

where 

pHM = pH of mixed leachate and groundwater in the aquifer

(standard units)

pHL = pH of infiltrating leachate (standard units)

I = annual areal infiltration rate (m/y)

Aw = area of WMU footprint (m)

pHaq = ambient pH of aquifer (standard units)

= average Darcy velocity (m/y)

Aaq = area of vertical patch source in aquifer (m)

= ys * zs

ys = equivalent source width in the direction normal

to the regional flow direction on the vertical

plane at the downgradient edge of the WMU

(m)

zs = equivalent source depth in the vertical direction

on the vertical plane at the downgradient edge

of the WMU (m)

The resulting mixed pH is then used to select the isotherm for transport in the

saturated zone with one limitation: in carbonate environments, the mixed pH in

the aquifer is not allowed to drop below a pH of six. Such acid conditions would

likely result in significant dissolution of the soil matrix.
Addendum to the EPACMTP Technical Background Document

6-1

6.0 Solubility Cap at the Water Table

As explained in Appendix B of the EPACMTP Technical Background Document

(U.S. EPA, 2003a), each isotherm is comprised of equilibrium concentrations of

the three contaminant phases (dissolved, sorbed, and precipitated) over a range

of total concentration values. An examination of the change in the dissolved

phase concentrations relative to changes in the total concentration in any

isotherm reveals solubility behavior for that contaminant: if the dissolved

component does not change with increasing total concentration, a limit on the

solubility has been achieved. If, however, the dissolved component increases

along with the total concentration, then capacity for more dissolved mass

remains in the groundwater.

EPACMTP uses this information contained in each isotherm to determine if a

solubility limit should be imposed in the saturated zone. Once an isotherm has

been selected (after pH considerations have been addressed), the equilibrium

states corresponding to the three highest total concentrations are examined. If

the dissolved concentration changes more than one tenth of one percent over the

last three points, then EPACMTP assumes the solubility limit has not been

identified and the leachate concentration entering the saturated zone at the

watertable is unchanged. However, if the change in dissolved concentration is

less than one tenth of one percent, EPACMTP assumes a solubility limit has

been reached and caps the concentration of the leachate entering the saturated

zone at the watertable to that limit.
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Addendum to the EPACMTP Technical Background Document

7-1

7.0 Add a Surface Water Body to the Modeling Domain

In EPACMTP V2.0, a groundwater-to-surface-water pathway analysis could be

performed, but only as a separate post-processing step. So one of the upgrades

included in EPACMTP V2.1 was to incorporate into the code a more refined

methodology for evaluating the mass flux at the interface between the saturated

zone and a hypothetical surface water body. The following subsections describe

in detail this new capability.

7.1 Description of the Surface Water Body

The EPACMTP V2.1 can evaluate the contaminant mass flux at the interface

between the saturated zone and a hypothetical surface water body. In the

model, the groundwater-surface water interface is located at some distance

downstream of the WMU along the plume centerline (see Figure 7.1). In adding

this functionality to the model, several protective simplifying assumptions have

been made for the following reasons: (1) to successfully represent what is

known to be a dynamic process between the groundwater and surface water

within a Monte Carlo modeling framework; (2) to evaluate the risks associated

with exposure to contaminated surface water; and (3) to maintain computational

efficiency. The primary simplifying assumptions are these: (1) the groundwatersurface water interface is assumed to be perpendicular to the regional

groundwater flow direction; (2) the interface is infinite in its lateral extent so as to

intercept the entire width of the dissolved contaminant plume; and (3) the

intercepting surface water body fully penetrates the saturated region of the

subsurface.

7.2 Determining Contaminant Mass Flux from Groundwater to Surface

Water

Contaminant mass fluxes generated by the pseudo three-dimensional (P3D)

transport module of EPACMTP V2.1 at the groundwater-surface water interface

are calculated from a time series of concentration values evaluated where the

interface intersects the plume center line. The distance down gradient of the

WMU to this intersection is designated as xsw (see Section 4.4 above). These

transient point concentrations, XR

(xsw, t), represent the mean dissolved

concentration of a constituent inside a virtual footprint representing the WMU at a

time t in years and distance xsw in meters (see discussion of pseudo-3D transport

module of EPACMTP in the Technical Background Document (U.S. EPA 2003a)

for more details). XR

(xsw, t), in mg/L, is convenient for calculating the total mass

flux to the intercepting water body at time t and distance xsw by using the

following equation:
Addendum to the EPACMTP Technical Background Document

7-2

(7.1)

(7.2)

where

= mass flux at time t and location xsw for species R (g/y)

t = time (y)

xsw = distance from downgradient edge of WMU to surface

water body (m)

XR

(xsw, t) = x-direction component of the P3D solution for species

R at xsw (mg/L)

ys = equivalent source width in the direction normal to the

regional flow direction on the vertical plane at the

downgradient edge of the WMU (m)

zs = equivalent source depth in the vertical direction on the

vertical plane at the downgradient edge of the WMU

(m)

v = average groundwater velocity downgradient of the

WMU (m/y)

Implicit in the above equation is the conversion factor (1000L@g) / (m3

@1000mg)

which evaluates to unity.

7.2.1 Time-Averaged Mass Flux

When time-averaged contaminant mass fluxes are required, a two-step

procedure is used. The first step is to determine the time value at which the

mass flux reaches its peak (tpeak). For the P3D transport solution, tpeak for the

groundwater-to-surface water mass flux is found directly from the breakthrough

curve. Denoting the exposure time interval of interest as td, the time-averaged

mass flux is then computed as:

where

 = time-averaged mass flux (g/y)

td = exposure time interval of interest (y)
Addendum to the EPACMTP Technical Background Document

7-3

tpeak = time value at which the receptor well concentration

reaches its peak (y)

 = mass flux at time t and location xsw for species R (g/y)

t = time (y)

In EPACMTP V2.1, up to 10 values of the exposure duration of interest (td) may

be specified for each modeled chemical constituent, and the exposure

duration(s) is/are then applied at all receptor locations, including the surface

water body, if specified.

7.2.2 Peak Mass Flux

For the P3D transport solution, a complete breakthrough curve (mass flux versus

time) is determined for the surface water body in each model realization. The

peak mass flux at the interface of the aquifer and the surface water body is found

by performing a direct search for the maximum mass flux value in the

breakthrough curve.

7.2.3 Time-to-arrival of Mass Flux

For the P3D transport equation, the time-to-arrival of the peak mass flux at the

interface of the aquifer and the surface water body is determined by directly

searching the breakthrough curve. 

7.3 Determining the Vertically Integrated Plume Profile

The post-processing procedure described in this section can be used to convert

the mass flux data output by EPACMTP V2.1 into a depth-wise averaged

concentration profile along the interface between the aquifer and the surface

water body. These data, along with volume and flow data for the surface water

body, could then be used to calculate water concentrations in the lake or river to

be compared with ambient water quality criteria.

Surface water bodies are commonly modeled by assuming that WMUs behave

as non-point sources of pollution. Therefore, to receive the mass dissolved in the

groundwater leaching from a WMU, this type of surface water model would

require the distribution of dissolved constituent concentrations along the interface

between the aquifer and the surface water body. Essentially, this distribution

represents a cross-section of the plume intercepting the surface water body. 

Further, it is assumed that the common boundary fully penetrates the saturated

region of the subsurface, as defined by the groundwater model. This

conservative assumption implies that the entire dissolved contaminant plume in
Addendum to the EPACMTP Technical Background Document

7-4

(7.3)

the aquifer is intercepted by the surface water body at the common boundary. 

This assumption relaxes the need to have detailed knowledge of how the

concentration changes with depth: a depth-wise averaged concentration along

the common boundary will suffice.

Groundwater exposures generated by the P3D flow and transport module of

EPACMTP consist of a time series of exposure concentrations at location directly

down gradient of the WMU along the plume center line. This location

corresponds to the down gradient (xrw) distance of the receptor location. The

time series is then modified to reflect the two remaining orthogonal directions that

define the receptor location: the distance of the receptor location from the plume

centerline (yrw), and the depth of the receptor beneath the watertable (z*rw).

To accommodate the requirements of the surface water model in an efficient

manner, a simplified solution can be used that utilizes the output generated by

EPACMTP to calculate a depth-averaged transverse profile of concentration

along the common boundary, assuming that the region of the concentration

profile beyond the edges of the virtual footprint of the WMU are normally

distributed. This assumption is valid for the following condition:

where

Y = all locations along a line perpendicular to the groundwater

flow direction at xsw (m)

ys = equivalent source width in the direction normal to the

regional flow direction on the vertical plane at the

downgradient edge of the WMU (m)

"T = horizontal-transverse dispersivity of the aquifer (m)

xsw = distance from downgradient edge of WMU to surface water

body (m)
Addendum to the EPACMTP Technical Background Document

7-5

(7.4)

(7.5)

The region of interest at xSW is defined as

where

Y = all locations along a line perpendicular to the groundwater

flow direction at xsw (m)

ys = equivalent source width in the direction normal to the

regional flow direction on the vertical plane at the

downgradient edge of the WMU (m)

"T = horizontal-transverse dispersivity of the aquifer (m)

xsw = distance from downgradient edge of WMU to surface water

body (m)

The concentration profile (Csw) at any time t can be defined as:

where

Csw = vertically averaged concentration profile along the

groundwater-surface water interface (mg/L)

t = time (y)

xsw = distance from downgradient edge of WMU to surface water

body (m)

Y = all locations along a line perpendicular to the groundwater

flow direction at xsw (m)

XR = x-direction component of the P3D solution

ys = equivalent source width in the direction normal to the

regional flow direction on the vertical plane at the

downgradient edge of the WMU (m)
Addendum to the EPACMTP Technical Background Document

7-6

"T = horizontal-transverse dispersivity of the aquifer (m)

zs = equivalent source depth in the vertical direction on the

vertical plane at the downgradient edge of the WMU (m)

B = thickness of the saturated zone (m)

Dyy = horizontal transverse dispersion coefficient (m2

/y)

v = average groundwater velocity down stream of the WMU

(m/y)

Depending upon the spacing of successive Y locations, the mass flux can be

derived from Csw(t, xsw, Y), v, and B.
Addendum to the EPACMTP Technical Background Document

8-1

8.0 Export Results as Breakthrough Curves in Binary Format

In order to meet the Agency’s analytical requirements, additional flexibility

regarding receptor locations and modeling output have been incorporated in

EPACMTP V2.1. In the previous version of the model, the only modeled receptor

location is a groundwater well. In EPACMTP V2.1, the capability to specify a

surface water body as a receptor location was added. Since the EPACMTP

modeling output for a surface water body receptor location is typically used as

input to a surface water modeling effort, EPACMTP’s output data must be

consistent with the conceptual model for the surface water model. As modeled in

EPACMTP, the receptor well is a single, fixed point in space that can be

represented by a unique set of x, y, and z coordinates. However, the conceptual

model for surface water modeling performed by the Agency typically assumes

that WMUs behave as non-point sources and that the groundwater plume fully

penetrates the intercepted surface water body. Therefore, to receive the

contaminant mass dissolved in the groundwater leaching from the WMU, the

surface water model requires the distribution of dissolved constituent

concentrations along the boundary common to the groundwater pathway and the

surface water body. Essentially, this distribution represents a cross-section of

the plume that intercepts the surface water body.

In order to meet these requirements, the following modifications were made

during development of EPACMTP V2.1: 1) added the capability to specify a

surface water body as a receptor location, 2) for a groundwater well, added the

capability to generate output groundwater concentrations in the form of a

breakthrough curve (these data are written to a binary file with the extension

“rwb”); and 3) for a surface water body, added the capability to generate

breakthrough curve data describing the distribution of groundwater

concentrations along a cross-section of the plume where it intercepts the surface

water body (these data are written to a binary file with the extension “swb”).

Note that the capability to generate breakthrough curves at a receptor location

was added to the code and tested during development of EPACMTP V2.0 as part

of adding the new P3D saturated zone flow and transport module. These

breakthrough curve data were generated in order to determine the peak and

maximum time-averaged concentrations that are reported to the *.sat file. 

However, in EPACMTP V2.0, the complete set of breakthrough curve data were

not part of the model’s output. For EPACMTP V2.0, the accuracy of the

breakthrough curve data was verified against that produced by the 3MRA Aquifer

module; during the development and testing of EPACMTP V2.1, it was verified

that the breakthrough curve data are correctly output to the binary file.
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Addendum to the EPACMTP Technical Background Document

9-1

9.0 References

U.S. EPA, 1996a. EPA's Composite Model for Leachate Migration with

Transformation Products (EPACMTP) Background Document for Metals

Transport in the Subsurface, Volume 1: Methodology. Office of Solid

Waste. U.S. Environmental Protection Agency, Washington, D.C. 20460.

U.S. EPA, 1996b. EPA's Composite Model for Leachate Migration with

Transformation Products (EPACMTP) Background Document for the Finite

Source Methodology. Office of Solid Waste. U.S. Environmental

Protection Agency, Washington, D.C. 20460.

U.S. EPA, 1997a. EPA's Composite Model for Leachate Migration with

Transformation Products (EPACMTP) User's Guide. Office of Solid Waste.

U.S. Environmental Protection Agency, Washington, D.C. 20460.

U.S. EPA, 1997b. Analysis of EPA’s Industrial Subtitle D Databases used in

Groundwater Pathway Analysis of the Hazardous Waste Identification

Rule (HWIR). Office of Solid Waste. U.S. Environmental Protection

Agency, Washington, D.C. 20460.

U.S. EPA, 1999a. EPA's Composite Model for Leachate Migration with

Transformation Products (EPACMTP) Background Document for Metals

Transport in the Subsurface, Volume 2: Sorption Isotherms. Office of Solid

Waste. U.S. Environmental Protection Agency, Washington, D.C. 20460.

U.S. EPA, 1999b. Vadose and Aquifer Modules Extracted from EPACMTP for

HWIR99. U.S. EPA, OSW, Washington, DC.

U.S. EPA, 1999c. Source Modules for Tanks and Surface Impoundments:

Background and Implementation for the Multi-media, Multi-pathway, and

Multi-receptor Risk Assessment (3MRA) for HWIR99, U.S. EPA, OSW,

Washington, DC.

U.S. EPA, 2001. Testing and Verification of EPACMTP Version 2. Office of Solid

Waste. U.S. Environmental Protection Agency, Washington, D.C. 20460. 

November, 2001.

U.S. EPA, 2002a. IWEM User’s Guide. Office of Solid Waste. U.S. Environmental

Protection Agency, Washington, D.C. 20460. U.S. EPA 530-R-02-013.
Addendum to the EPACMTP Technical Background Document

9-2

U.S. EPA, 2002b. IWEM Technical Background Document. Office of Solid

Waste. U.S. Environmental Protection Agency, Washington, D.C. 20460. 

U.S. EPA 530-R-02-012.

U.S. EPA, 2003a. EPACMTP Technical Background Document. Office of Solid

Waste, Washington, DC. 20460. U.S. EPA 530-R-03-002.

U.S. EPA, 2003b. EPACMTP Parameters/Data Background Document. Office

of Solid Waste, Washington, DC. 20460. U.S. EPA 530-R-03-003.

U.S. EPA, 2003c. Addendum to the EPACMTP Technical Background

Document. Office of Solid Waste, Washington, DC. 20460.

U.S. EPA, 2003d. Addendum to the EPACMTP Parameters/Data Background

Document. Office of Solid Waste, Washington, DC. 20460.