# Addendum to the EPA’s Composite Model for Leachate Migration with Transformation Products (EPACMTP) Technical Background Document EPACMTP Version 2.1 DraftOffice 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 2003This page intentionally left blank.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 ( pH L ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 4.3 Additional Generalized Master Variables for Metals Transport . . . . . . 4-3 4.4 Distance to Nearest Surface Water Body (New Functionality) ( R

4 ) . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1ii LIST OF TABLES
Page
Table 1.1 Documentation Changes Necessitated by the Update to EPACMTP . . . 1-3Addendum to the EPACMTP Technical Background Document

iii LIST OF ACRONYMS

3MRA Multi-media, Multi-pathw ay, 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 C omposite M odel for Leachate Migration with T ransformation P roducts 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. Environm ental Protection Agency
WMU waste management unitThis page intentionally left blank.Addendum to the EPACMTP Technical Background Document

v LIST OF SYMBOLS

Symbol Definition Equation in which the symbol first

appears A aq area of vertical patch source in aquifer (m) 5.3
AnnInfil i water flux from the source for year i (m/d) 3.1
A w 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

C sw vertically averaged concentration profile along the groundwater-surface water interface (mg/L) 7.5

average leachate concentration during time interval [ ] (mg/L) 3.4

c 0 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) 4.1Laplace-transformed aqueous concentration of the species (ymg/L) 3.8

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

c 0 (t) prescribed annual leachate concentration in the year t (mg/L) 3.2

c

p aqueous concentration of the species at the source (mg/L) 3.7
D LF landfill depth (m) 5.1
D utotal depth of the unsaturated zone (m) 5.2
D yy horizontal transverse dispersion coefficient (m 2 /y) 7.5 exp(
@ ) exponential operator (dimensionless) 3.6
F e O x iron hydroxide content (wt %) N/A

F

h volume fraction of the waste in the landfill at time of closure (dimensionless) 5.1LIST OF SYMBOLS (continued) Addendum to the EPACMTP Technical Background Document

Symbol Definition Equation in which the symbol first

appears

vi f oc fraction organic carbon in the saturated zone (dimensionless) N/A
H v (
@ ) Heaviside step function (dimensionless) 3.4

I annual areal infiltration rate (m/y) 3.1
i step index (dimensionless) 3.4
K d distribution coefficient (sorbed and aqueous phases) (cm 3 /g) N/A
K

w waste-concentration-to-leachate-concentration ratio (L/kg) 4.1 LeachFlux(t) annual average mass flux rate in the year t (g/m 2 /d) 3.2
LeachFluxNY number of annual average mass flux rates (dimensionless) 3.2 LOM leachate organic matter (mg/L) N/A

( t, x sw ) mass flux at time t and location x sw

for species R (g/y) 7.1 time-averaged mass flux (g/y) 7.2
N

s number of steps into which c o (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

pH aq ambient pH of aquifer (standard units) 5.3 pH L pH of infiltrating leachate (standard units) 5.3 pH M 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
S e effective saturation (dimensionless) 5.2
t time (y) 3.4LIST OF SYMBOLS (continued) Addendum to the EPACMTP Technical Background Document

Symbol Definition Equation in which the symbol first

appears

vii t d 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
t p leaching duration (y) 5.1
t peak 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 al ong the regional flow direction (m) 3.8

x

sw distance from downgradient edge of WMU to surface water body (m) 7.1

X R ( x sw , t ) x-direction component of the P3D solution for species R at x sw (mg/L) 7.1

Y all locations along a line perpendicular to the groundwater flow direction at x sw (m) 7.3

y

s 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

z s 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

D

hw waste density (g/cm 3 ) 5.1 N total porosity (dimensionless) 5.2This page intentionally left blank.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.This page intentionally left blank.Addendum to the EPACMTP Technical Background Document

xi 

### EXECUTIVE SUMMARY
The U.S. EPA Office of Solid Waste (O SW) has developed a probabilistic (Monte Carlo) groundwater flow and transport m odeling 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 drinki ng water well (receptor well) located downgradient of the waste disposal fac ility. This modeling methodology has been incorporated into a computer code called the EPA ’s C omposite M odel for Leachate Migration with T ransformation P roducts (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 wa stes disposed in Subtitle D waste management units (WMUs), including t he 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 per formed in support of the regulatory efforts of the U.S. EPA OSW, includi ng the development of several projectspecific versions of EPACMTP, created to meet the analytical requirements of particular groundwater pathway risk assessment s. In an effort to maximize the model’s flexibility given the expected variat ions in data availability and analytical requirements for regulatory applications of the model, a number of the features that were hard-wired in previous proj ect-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 requirem ents for the groundwater pathway risk assessments for CCW and D&P are bey ond 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 s ource 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 proj ect-specific version of the EPACMTP code created for an earlier RCRA listing determination. However, in addition toAddendum to the EPACMTP Technical Background Document

xii the site-based variable correlations permi tted in the existing project-specific version of the EPACMTP code, the new dat abase 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 pr ojects: 1) additional master variables were added and the ranges of existing master variables were widened to accommodate the new MINTEQA2-deriv ed 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 EPACMT P; 3) several new input parameters were added; and 4) new functionality was gi ven 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 m odel’s modular components, mathematical algorithms, features, a ssumptions, and limitations.Addendum to the EPACMTP Technical Background Document

1-1 1.0 Introduction The U.S. EPA Office of Solid Waste (O SW) has developed a probabilistic (Monte Carlo) groundwater flow and transport m odeling 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 drinki ng water well (receptor well) located downgradient of the waste disposal fac ility. This modeling methodology has been incorporated into a computer code called the EPA ’s C omposite M odel for Leachate Migration with T ransformation P roducts (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 wa stes disposed in Subtitle D waste management units (WMUs), including t he 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 per formed in support of the regulatory efforts of the U.S. EPA OSW. Thes e include the development of: 1) a computationally efficient pseudo-3D gr oundwater transport module for the Multimedia, Multi-pathway, and Multiple-rec eptor Risk Assessment (3MRA) modeling system (U.S. EPA, 1999b); and 2) a new su rface 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 adv ances listed above, to consolidate into one code other features developed for proj ect-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 anal ytical 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 requirem ents for the groundwater pathway risk assessments for CCW and D&P are bey ond 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 s ource 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 proj ect-specific version of the EPACMTP code created for an earlier RCRA listing determination. However, in addition to the site-based variable correlations permi tted in the existing project-specific version of the EPACMTP code, the new dat abase 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 pr ojects: 1) additional master variables were added and the ranges of existing master variables were widened to accommodate the new MINTEQA2-deriv ed 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 EPACMT P; 3) several new input parameters were added; and 4) new functionality was gi ven 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 m odel’s modular components, mathematical algorithms, features, assumptions, and lim itations. Table 1.1 is a crosswalk between the sections of this addendum and the existing EPACMTP V2.0 documentation.1-3 Addendum to the EPACMTP Technical Background DocumentTable 1.1 Documentation Changes Necessitated by the Update to EPACMTPCode Changes Made toCreate EPACMTP V2.1 ProjectParameters/Data BackgroundDocument Technical Background DocumentMain Document Addendum Main Document AddendumExpand site-based databasecapability (SDF)D&PCCWUpdate manysubsections of § 2, 3,4, 5 and 6§ 2.1 and 2.2 Update § 5.5.2New § 5.6§ 2.2§ 2.1Incorporate input of leachingand/or infiltration profiles as sourceterm using SDFD&P Update § 2.3.6,2.4.9, 2.5.2, & 2.6.2Update § 3.2.3Update § 4.3§ 3.2§ 3.2§ 3.1New § 2.1.3Update § 3.3.4Update § 4.4.5.2.1§ 3.1§ 3.2§ 3.3Add a single surface water body tomodeling domainD&PCCWUpdate 2.4.8 § 4.4 Update 2.2.2.2.7New § 4.4.3.7Update §4.4.7Replace App F§ 4.4§ 7.1§ 7.2§ 7.3Export receptor well results asbreakthrough curves in binaryformatD&P NA Update § 4.4.6Update § 4.4.6.1-3§ 8Export surface water results asbreakthrough curve in binaryformatD&P NA Update § 4.4.7 § 8Add pH of leachate as a newvariableCCW New § 3.3.3.3 § 4.2 Update manysubsections of §2.2and §3.3.3§ 4.2Add waste concentration as a newvariableCCW New § 2.3.7 § 4.1 New 2.2.1.2.12 § 4.1Add generalized extra mastervariables for metals transportCCW New § 3.3.3.2.8 § 4.3 Update § 3.3.3.6 § 4.3Add soil column pH determination CCW NA Update § 3.3.3.11 § 5.1Add mixed aquifer pHdeterminationCCW NA Update § 4.4.3.4 § 5.2Add solubility cap at water table CCW NA Update § 4.4.4.7 § 6Acronyms:CCW - Coal Combustion Wastes RegulatoryAnalysis D&P - Dyes and Pigments Listing Determination SDF - Source Data FileThis page intentionally left blank.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-s pecific values without requiring the exhaustive sampling that would be requir ed to actually gather these data from waste sites around the country. For eac h Monte-Carlo realization, EPACMTP selects a site, at random, from the appr opriate WMU-specific data set. The corresponding climatic and hydrogeologic i ndices 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 param eters. Thus, the use of the regional site-based methodology which links together these correlated data sets serves to reduce the probability thatthe 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 re charge 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 inputparameters 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-bas ed 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 fil ename generally is the same as the corresponding input data file, but its extens ion must be “.dat.” Additionally, the functionality of this SDF was expanded so thatthe 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) prov iding 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 par ameters in EPACMTP V2.1 (t hat is, all the parametersAddendum 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 al so 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 va lues to be specified using either empirical or parametric distributions of values; however, use of the SDF enables parameter values to be specified using corre lated, 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 (o r 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 r uns 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 construct ed 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 analysi s in EPACMTP, the specific values of infiltration rate, hydrogeologic parameter s, 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 va riable that is treated as random must be assigned one of the probability distribut ion 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 EPACMT P 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 bel ow 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 pr eparation 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 st andard 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 t he model selects a site, the data read into EPACMTP include the appropriate charac teristics for that site, including unit area, unit depth, an index that specifie s 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 i ndividually 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 co mposite-lined surface impoundments, an empirical distribution of leak densities is specified and the infiltration rate is then calculated. Second, the soil type at t he chosen waste site (and cover type for landfills) and the specified liner scenar io can be used along with the climate center index to determine the appropriate values for recharge and infiltration atAddendum 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 in filtration 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 resoluti on of available hydrogeological databases and acknowledging the uncertainty in the e ffective local values of hydrogeological site characteristics, the regional si te-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 par ameters (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 paramet ers can be tabulated in the SDF. If the four hydrogeologic paramet ers 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 si te that are not assigned as site-related (e.g., x, y, and z coordinates of the rec eptor 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 tabul ated 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 paramet er values generated in the previous four steps, and the chemical-specific characte ristics (e.g., leachate concentration, adsorption coefficient and exponent, and degradation rate), the EPACMTP flow and transport modules are executed to co mpute 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 time s as is specified by the user. The result of the Monte-Carlo modeling anal ysis is a groundwater concentration for each model realization; these results represent the nationwide distribution of drinking water exposure concentrations. Like wise, if specified in the input file, the groundwater to surface water mass flux can be generated for each model realization; these results represent t he 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-Ca rlo realizations will be much greater than the number of sites used in the regi onal, 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 a ssigning values to all of the EPACMTP parameters (e.g., well location), repeated sele ction of the same waste site in the Monte-Carlo process generally will not resultin the same predicted receptor well exposure concentration and contaminant mass flux.This page intentionally left blank.Addendum to the EPACMTP Technical Background Document

3-1 3.0 Incorporate Prescribed Finite Source Term Using SDF
As described above, the SDF functiona lity 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 flux es, et cetera, while EPACMTP V2.0 is limited to single scalar values to represent long-term average leachate concentrations and/or infiltration rate s. 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 i nput 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 va lue 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 us ed 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 app lied 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 inco rporated into the flow and/or transport boundary conditions applied to the top of the watertable. Some instances may arise where the vadose zone is in cluded and, depending upon the WMU scenario being modeled, the selected suite of inputparameter 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 iter ations 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 fo r 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 c ontaining 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) AnnInfil i = water flux from the source for year i (m/d)

Note that NyrMet and AnnInfil i are specified in the inputbinary 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 cont aining time series data output from an external source module. In this case, the prescribed annual average leachate concentration, c 0 (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
c 0 (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/m 2 /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 concent ration is required, as is the case for non-linear metals transport in the vados e zone, an average concentration can be calculated from c 0 (t) as follows:

where

c 0 avg = average leachate concentration (mg/L) LeachFluxNY = number of annual average mass flux rates
c 0 (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. Al so 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 va ry 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 prof ile generated by an external model to be applied as a transient source concent ration boundary condition, as described inAddendum 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 c o 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) N

s = number of steps into which c o (t) is discretized (dimensionless) = average leachate concentration during the time interval [ , ] (mg/L) H v (
@ ) = 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

H v (
@ ) = Heaviside step function (dimensionless) t = time (y) = beginning of the time interval of interest (y)

The Laplace transform of the source function, then becomesAddendum 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) N

s = number of steps into which c o (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)
c

p = 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 prof ile is determined by the unsaturated zone transport module. If, however, the unsatur ated 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 Sect ions 4.1 through 4.3. Additionally, in EPACMTP Version 2.1, the functi onality 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 wate r 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 upc oming 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 parameter s 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 par ameter for the landfill, depleting source option; that is, it is not used for ot her 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 event ually leach out. Therefore, in the context of the depleting (finite) sour ce methodology, is the total leachable waste concentration. From a practical per spective, it is important to know how this property will be measured for actual wa ste samples. There are established procedures to measure the leachate c oncentration but these methods may not measure the “leachable” waste concentrati on 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 wast e 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 enter ing the landfill, and the waste-to-leachate concentration ratio, K w . The latter input parameter can be calculated by the user from waste characterization data as

where

K w = 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 t hese 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 leachat e concentration and the initial waste concentration. In this case, the waste-to-leachate concentration ratio, K w , is calculated using Equation 4.1.Addendum to the EPACMTP Technical Background Document

4-3 4.2 pH of Leachate ( pH L )
In addition to the source-specific input par ameters 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 wit h a nonlinear sorption isotherm, and can be used to model any of the four WM U types. This parameter is used in determining the sorption behavior of metals with non-linear isotherms in both the unsaturated and saturated zones by potent ially changing the pH value that is used to select the appropriate sorption is otherm. The algorithms by which the model determines the extent to which l eachate 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 ar e 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, f oc , 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 st rength in the CCW modeling analysis). These input parameters can be used with any of the four WMU types. Random values of all specified geochem ical master variables are generated by the EPACMTP code to be used in Monte-Carlo simulations. These values are generated for the user-specified hydr ogeochemical environment expressed in terms of the distribution type (IDIST) and statistical param eters (mean, standard deviation, and parameter upper and lowe r bounds). Once generated, these parameter values are then used to choos e 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) ( R

4 ) In EPACMTP V2.0, the distance to the nearest surface water body, x sw , is used as one method to prevent the generat ion and use of an excessively high infiltration rate and is used in the su rface 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 fourAddendum 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 cont aminant 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 conc entrations 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 t he lateral grid boundaries of EPACMTP), and oriented perpendicular to the regi onal 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 creat ion of EPACMTP V2.1 the impacts of leachate pH upon the ambient pH c onditions have largely been neglected in groundwater pathway analyses because the va riability of the pH in the modeled wastes was usually small. For CCW wa stes, 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 t he 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 subsur face. 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 subs urface: (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 ar e 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 rate s of degrading organic constituents, this modeling capability was not required for any current or upcoming application of EPACMTP. Hence, this functionality fo r 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 is otherms, the duration of leaching is compared to an estimate of the first arriva l 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 ( t p ) 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 ( t p ) isAddendum 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

t p = leaching duration (y) = constituent concentration in the waste (mg/kg) D LF = landfill depth (m) F

h = volume fraction of the waste in the landfill at time of closure (dimensionless) 

### D

hw = waste density (g/cm 3 ) = 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) D u= total depth of the unsaturated zone (m) RR = retardation factor of species R (dimensionless) 

### N = total porosity (dimensionless) S e = 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 t able, 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 leachat e. 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 oper ational 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 mostcases, result in a balanced selection of leachate pH governing versus soil pH gov erning over the course of a Monte Carlo simulation of approximately 10,000 iter ations. 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 calc ulates an average distribution coefficient ( K d ) from this isotherm; K d 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 isot herm 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 mix ed 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
pH M = pH of mixed leachate and groundwater in the aquifer (standard units) pH L = pH of infiltrating leachate (standard units) I = annual areal infiltration rate (m/y) A w = area of WMU footprint (m) pH aq = ambient pH of aquifer (standard units) = average Darcy velocity (m/y) A aq = area of vertical patch source in aquifer (m)

= y s * z s y

s = equivalent source width in the direction normal to the regional flow direction on the vertical plane at the downgradient edge of the WMU (m)

z s = 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 ex amination 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 assu mes the solubility limit has not been identified and the leachate concentration entering the saturated zone at the watertable is unchanged. However, if t he change in dissolved concentration is less than one tenth of one percent, EPAC MTP assumes a solubility limit has been reached and caps the concentration of the leachate entering the saturated zone at the watertable to that limit.This page intentionally left blank.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-pr ocessing 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 cont aminant 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 betw een the groundwater and surface water within a Monte Carlo modeling framework; (2) to evaluate the risks associated with exposure to contaminated surface wa ter; and (3) to maintain computational efficiency. The primary simplifying assu mptions 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 disso lved 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 t he groundwater-surface water interface are calculated from a time series of concentration values evaluated where the interface intersects the plume center li ne. The distance down gradient of the WMU to this intersection is designated as x sw

(see Section 4.4 above). These transient point concentrations , X R ( x sw , t ), represent the mean dissolved concentration of a constituent inside a virt ual footprint representing the WMU at a time t in years and distance x sw

in meters (see discussion of pseudo-3D transport module of EPACMTP in the Technical Background Document (U.S. EPA 2003a) for more details). X R ( x sw , t ), in mg/L, is convenient for calculating the total mass flux to the intercepting water body at time t and distance x sw

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 x sw

for species R (g/y) t = time (y)
x

sw = distance from downgradient edge of WMU to surface water body (m) X R ( x sw , t ) = x-direction component of the P3D solution for species R at x sw

(mg/L) y

s = equivalent source width in the direction normal to the regional flow direction on the vertical plane at the downgradient edge of the WMU (m)
z s = 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) / (m 3

@ 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 ( t peak ). For the P3D transport solution, t peak for the groundwater-to-surface water mass flux is found directly from the breakthrough curve. Denoting the exposure ti me interval of interest as t d , the time-averaged mass flux is then computed as:

where = time-averaged mass flux (g/y) t d = exposure time interval of interest (y)Addendum to the EPACMTP Technical Background Document

7-3 t peak = time value at which the re ceptor well concentration reaches its peak (y) = mass flux at time t and location x sw

for species R (g/y) t = time (y)
In EPACMTP V2.1, up to 10 values of the exposure duration of interest (t d ) may be specified for each modeled chemical constituent, and the exposure duration(s) is/are then applied at all re ceptor locations, including the surface water body, if specified.

7.2.2 Peak Mass Flux
For the P3D transport solution, a comple te 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 t he 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. Theref ore, to receive the mass dissolved in the groundwater leaching from a WMU, this type of surface water model would require the distribution of dissolved consti tuent concentrations along the interface between the aquifer and the surface water body. Essentially, this distribution represents a cross-section of the plum e intercepting the surface water body. Further, it is assumed that the co mmon boundary fully penetrates the saturated region of the subsurface, as defi ned by the groundwater model. This conservative assumption implies that the entire dissolved c ontaminant plume inAddendum 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 dept h-wise averaged concentration along the common boundary will suffice. Groundwater exposures generated by t he P3D flow and transport module of EPACMTP consist of a time series of ex posure concentrations at location directly down gradient of the WMU along the pl ume center line. This location corresponds to the down gradient ( x rw ) 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 ( y rw ), and the depth of the rec eptor beneath the watertable ( z* rw ).
To accommodate the requirements of t he surface water model in an efficient manner, a simplified solution can be us ed that utilizes t he output generated by EPACMTP to calculate a depth-averaged tr ansverse 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 x sw

(m) y

s = 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)
x

sw = 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 x sw (m) y

s = 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)
x

sw = distance from downgradient edge of WMU to surface water body (m) The concentration profile ( C sw ) at any time t can be defined as:

where

C sw = vertically averaged concentration profile along the groundwater-surface water interface (mg/L) t = time (y)
x

sw = distance from downgradient edge of WMU to surface water body (m) Y = all locations along a line perpendicular to the groundwater flow direction at x sw (m) X

R = x-direction component of the P3D solution y

s = 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)
z s = 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) D yy = horizontal transverse dispersion coefficient (m 2 /y)
v = average groundwater velocitydown stream of the WMU (m/y) Depending upon the spacing of successive Y locations, the mass flux can be derived from C sw ( t, x sw

, 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 analytic al requirements, additional flexibility regarding receptor locations and mode ling 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 source s and that the groundwater plume fully penetrates the intercepted surface water body. Therefore, to receive the contaminant mass dissolved in the groundw ater leaching from the WMU, the surface water model requires the di stribution of dissolved constituent concentrations along the boundary common to the groundwater pathway and the surface water body. Essentially, this di stribution 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 loca tion, 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 break through 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 t hat 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 agains t that produced by the 3MRA Aquifer module; during the development and testi ng of EPACMTP V2.1, it was verified that the breakthrough curve data are co rrectly output to the binary file.This page intentionally left blank.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 Protec tion 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 A gency, Washington, D.C. 20460.
U.S. EPA, 1997b. Analysis of EPA’s Industrial Subtitle D Databases used in Groundwater Pathway Analysis of t he 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 Protec tion Agency, Washington, D.C. 20460.
U.S. EPA, 1999b. Vadose and Aquifer M odules 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 (3 MRA) 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 Protec tion 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 Protec tion 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.