Contaminated Ground Water and Sediment - Chapter 4 potx

Parker, Lily Sehayek CONTENTS 4.1 Introduction and Overview4.2 Basic Concepts and Equations4.2.1 Multiphase Fluid Flow4.2.1.1 Darcy’s Law for Multiphase Flow4.2.1.2 Capillary Pressure an

4 Modeling Fate and

Transport of Chlorinated Organic Compounds

in the Subsurface

prepared by Brent E Sleep

with contributions by Neal D Durant, Charles R Faust, Joseph G Guarnaccia, Mark R Harkness, Jack C Parker, Lily Sehayek

CONTENTS

4.1 Introduction and Overview4.2 Basic Concepts and Equations4.2.1 Multiphase Fluid Flow4.2.1.1 Darcy’s Law for Multiphase Flow4.2.1.2 Capillary Pressure and Relative Permeability Relations4.2.2 Multicomponent Mass Transport

4.2.2.1 Mass Balance and Transport Flux Equations4.2.2.2 Interphase Mass Transfer

4.2.3 Modeling Biotic and Abiotic Transformations4.2.3.1 Review of Chlorinated Solvent

Transformation Mechanisms4.2.3.2 Petroleum Hydrocarbon Biodegradation Models4.2.3.3 Chlorinated Solvent Biodegradation Models4.2.4 Computational Issues

4.2.4.1 Spatial Discretization4.2.4.2 Temporal Discretization4.2.4.3 Linearization of Nonlinear Equations of Multiphase

Flow and Transport4.2.4.4 Solution of Linear Equations4.3 Modeling DNAPLs — State of Practice4.3.1 Roles of Modeling

4.3.1.1 Research and EducationL1667_book.fm Page 179 Tuesday, October 21, 2003 8:33 AM

Appendix A:

Workshop Panels

PANEL 1 MIXING ZONE: DISCHARGE OF CONTAMINATED GROUND WATER INTO SURFACE WATER BODIES

E XPERT P ANEL L EADER

Miguel A Medina, Jr., Duke University

A SSISTANT E XPERT P ANEL L EADER

Nancy R Grosso, DuPont Company

E XPERT P ANEL M EMBERS

Robert L Doneker, Oregon Graduate Institute of Science and TechnologyHenk Haitjema, Indiana University

D Michael Johns, Windward Environmental LLCWu-Seng Lung, University of Virginia

Steven C McCutcheon, USEPA National Exposure Research LaboratoryFarrukh Mohsen, Gannett Fleming, Inc

Aaron I Packman, Northwestern University Philip J Roberts, Georgia Institute of Technology

J Bart Ruiter, DuPont Company

PANEL 2 CONTAMINATED SEDIMENT: ITS FATE AND TRANSPORT

E XPERT P ANEL L EADER

Danny D Reible, Louisiana State University

A SSISTANT E XPERT P ANEL L EADER

Richard H Jensen, DuPont Company

E XPERT P ANEL M EMBERS

Sam Bentley, Louisiana State University

Mimi B Dannel, USEPA Headquarters

Joseph V DePinto, Limno-Tech, Inc

James A Dyer, DuPont Company

Kevin J Farley, Manhattan College

Marcelo H Garcia, University of Illinois

David Glaser, Quantitative Environmental Analysis

John M Hamrick, Tetra Tech, Inc

Wilbert J Lick, University of California at Santa Barbara

Robert A Pastorok, Exponent Environmental Group

Richard F Schwer, DuPont Company

C Kirk Ziegler, Quantitative Environmental Analysis

PANEL 3

OPTIMIZATION MODELING FOR REMEDIATION AND MONITORING

E XPERT P ANEL L EADER

George F Pinder, University of Vermont

A SSISTANT E XPERT P ANEL L EADER

Robert B Genau, DuPont Company

E XPERT P ANEL M EMBERS

Robert M Greenwald, GeoTrans, Inc

Hugo A Loaiciga, University of California at Santa Barbara

George P Karatzas, Technical University of Crete

Peter K Kitanidis, Stanford University

Reed M Maxwell, Lawrence Livermore National Laboratory

Alexander S Mayer, Michigan Technological University

Dennis B McLaughlin, Massachusetts Institute of TechnologyRichard C Peralta, U.S Air Force Reserve and Utah State UniversityChristine A Shoemaker, Cornell University

Brian J Wagner, U.S Geological Survey

Kathleen M Yager, USEPA Technology Innovation OfÞce

William W.-G Yeh, University of California at Los Angeles

PANEL 4

SIMULATION OF HALOGENATED HYDROCARBONS

IN THE SUBSURFACE

E XPERT P ANEL L EADER

Charles R Faust, GeoTrans, Inc

A SSISTANT E XPERT P ANEL L EADERS

Neal D Durant, GeoTrans, Inc

Craig L Bartlett, DuPont Company

E XPERT P ANEL M EMBERS

Robert C Borden, North Carolina State University

Ronald J Buchanan, Jr., DuPont Company

Randall Charbeneau, University of Texas

Eva L Davis, USEPA Kerr Laboratory

Joseph G Guarnaccia, CIBA-Geigy Specialty Chemicals

Mark R Harkness, General Electric Corporation

Jack C Parker, Oak Ridge National Laboratory

Hanadi Rafai, University of Houston

Lily Sehayek, Penn State Great Valley

Brent E Sleep, University of Toronto

Jon F Sykes, University of Waterloo

Albert J Valocchi, University of Illinois

4.3.1.2 Policy Development4.3.1.3 Site Assessment and Remedial Design4.3.2 Overview of Existing Models

4.3.2.1 Three-Phase Models4.3.2.2 Two-Phase Models4.3.2.3 Single-Phase Models4.3.2.4 Chlorinated Solvent Biodegradation Models4.3.3 Model Selection and Limitations

4.4 Site Applications4.4.1 Gulf Coast EDC DNAPL Release4.4.2 DNAPL Source Area Characterization Coastal Plain of New Jersey4.5 Research Needs

4.5.1 Constitutive Relationships for Multiphase Flow, Transport, and Interphase Mass Transfer

4.5.1.1 k–S–P Relationships4.5.1.2 Mass Transfer Relationships4.5.1.3 Summary

4.5.2 DNAPLs In Fractured Media4.5.2.1 Unsaturated Water Flow4.5.2.2 NAPLs

4.5.2.3 Summary4.5.3 Impact of Biodegradation on DNAPL Dissolution4.5.3.1 Model Development

4.5.3.2 Reductive Dechlorination Rates at High

Concentrations of Dissolved PCE4.5.3.3 Reductive Dechlorination in the Presence of DNAPL4.5.3.4 Summary

4.5.4 Plume Attenuation4.5.4.1 Biotransformation Kinetics4.5.4.2 Halorespiration

4.5.4.3 Spatial Variability in Redox Conditions4.5.4.4 Complex Mixtures

4.5.4.5 Bioavailability and Mass Transfer from Sorbed Phase4.5.4.6 Summary

4.6 Technology Transfer4.6.1 Approach4.6.1.1 QA Standards4.6.1.2 Expert Decision Support System4.6.1.3 Model Application Archive and Database Support4.6.1.4 Training Support

4.6.2 Implementation Recommendations4.7 Summary, Conclusions, and Recommendations4.7.1 Multiphase Flow and Transport4.7.2 Chlorinated Hydrocarbon Biodegradation4.7.3 Technology Transfer

4.1 INTRODUCTION AND OVERVIEW

Halogenated organic compounds such as chlorinated aliphatic and aromatic pounds have been used widely as solvents since the early 1940s As a result ofwidespread production, transportation, use, and disposal, these compounds are com-mon ground water contaminants Due to their limited but environmentally signiÞcantaqueous phase solubilities, spills of these compounds typically result in the formationand migration of a separate organic phase that is denser than water This densenonaqueous phase liquid (DNAPL) can move signiÞcant distances in the subsurface,contaminating large volumes of the subsurface environment The residual DNAPLleft in the wake of DNAPL ßow can persist as a source of contamination for decades,slowly dissolving into the water phase and volatilizing into the soil–gas phase inthe vadose zone

com-Chlorinated organic compounds are among the most serious ground water taminants because of their mobility and persistence in the subsurface, their wide-spread use, and their health effects Consequently, billions of dollars are being spent

con-in efforts to remediate ground water contamcon-ination from chlorcon-inated organic pounds Developing and applying reliable, accurate, and readily available fate andtransport models is greatly needed to assess the risks posed by spills of thesecompounds to the subsurface and to aid in evaluating and designing remediationprograms to address these spills A variety of sophisticated research level models topredict chlorinated organic compound fate and transport in the subsurface have beendeveloped The use of these models is limited, however, due to mathematical com-plexity, signiÞcant data demands, and the inability to validate the many assumptionsinherent in these models Research on the physics, chemistry, and biology of thesecompounds and the prediction of their fate and transport in a complex, heterogeneoussubsurface is ongoing, with many questions yet to be answered

The panel discussed issues associated with simulating chlorinated organic pound behavior in the subsurface Presentations by panel members focused onmodeling chlorinated organic compound fate and transport under natural conditionsrather than under enhanced remediation conditions The uncertainty associated withconstitutive relationships appropriate for use in Þeld-scale modeling was identiÞed

com-as an area for continued research Aspects of modeling DNAPL source dissolutionand volatilization were covered, and practical techniques for modeling source-termbehavior at the Þeld scale were presented The problems of dealing with subsurfaceheterogeneities in simulating Þeld-scale DNAPL behavior were identiÞed, and theneed for upscaling methods and robust inverse modeling techniques were empha-sized Several presentations addressed the current practices for modeling the naturalattenuation of chlorinated compounds Chlorinated compound biodegradation mod-els of varying levels of complexity were reviewed The need for a framework forchoosing the appropriate level of simpliÞcation in modeling was discussed, and theneed for technology transfer to end users of models was emphasized

The objective of this chapter is to review the state of the art with respect tothe simulation of chlorinated organic compounds in the subsurface and to presentthe conclusions and recommendations of the panel with respect to basic researchneeds and issues of technology transfer Basic concepts and equations underlyingmodels for chlorinated organic compound behavior in the subsurface are reviewed

in Section 4.2 The current state of practice with respect to modeling chlorinatedorganic compound fate and transport is described in Section 4.3 Section 4.4contains Þeld applications presented by the panel Research needs identiÞed bythe panel are discussed in Section 4.5, while Section 4.6 examines aspects oftechnology transfer required for the effective promulgation of simulation modelsfor chlorinated organic compounds

4.2 BASIC CONCEPTS AND EQUATIONS

Halogenated organic compounds exhibit a broad range of physical and chemicalproperties Those of particular concern as ground water contaminants include indus-trial solvents, such as tetrachloroethylene (also known as perchloroethylene or PCE),trichloroethylene (TCE), and carbon tetrachloride (CT), and a variety of polychlo-rinated biphenyl (PCB) oils used in various industrial applications (Pankow andCherry, 1996) These compounds are liquids at normal subsurface temperatures andhave limited solubility in water and speciÞc gravities greater than water They thusfall under the deÞnition of DNAPLs (Schwille, 1988) The speciÞc gravity of chlo-rinated aliphatic hydrocarbons can be as high as 1.6 (Mercer and Waddell, 1993).Low solubility and relatively high density are key properties that lead to the com-plexity of their distribution in the subsurface In this section, these and other impor-tant factors are discussed

The transport and fate of halogenated organic compounds in the subsurface arecontrolled by complex phenomena in a wide variety of hydrologic settings Halo-genated organic compounds can occur as a nonaqueous phase liquid (NAPL) and

as species in the aqueous, vapor, and soil phases (Figure 4.1) The phenomena thatgovern the behavior of halogenated organic compounds in the subsurface can beclassed into two broad categories that control the following:

• Fluid-phase distributions and bulk ßow of NAPL, water, and vapor phases

in the subsurface as affected by gravity, capillary and buoyancy forces,pore geometry, and larger-scale heterogeneity

• Interphase mass transfer, transport, and attenuation of halogenated pounds and their by-products through dissolution, volatilization, sorp-tion/desorption, colloidal transport, diffusion–dispersion, and chemicaland biological reactions

com-In general, modeling halogenated organic compounds involves simulating surface systems composed of more than one ßuid phase and requires a conceptualunderstanding of the relevant chemical, physical, and biological processes that con-trol the distributions, interactions, and reactions within all phases

sub-Mathematical models for multiphase migration of organic contaminants in soilsand aquifers were presented by numerous authors beginning in the 1980s (e.g.,Abriola and Pinder, 1985; Faust, 1985; Osborne and Sykes, 1986; Kuppusamy etal., 1987; Faust et al., 1989; Sleep and Sykes, 1989, 1993) based on earlier modelsdeveloped for petroleum reservoir engineering (Aziz and Settari, 1979).

4.2.1 M ULTIPHASE F LUID F LOW

4.2.1.1 Darcy’s Law for Multiphase Flow

When an organic ßuid enters the subsurface, it ßows downward due to gravity andcapillary forces and moves laterally due to capillary forces In the vadose zone, theorganic displaces the air and water as it moves through the soil pores DNAPLs canmove below the water table, whereas LNAPLs pool on the water table Below thewater table, a DNAPL displaces the water phase as it moves downward The move-ment of the organic phase through the soil pores is affected by the organic ßuiddensity, viscosity, interfacial tension with water and air, contact angle of the phaseinterface with the aquifer solids (i.e., wettability), and by the soil porosity, perme-ability, and pore-size distribution The inßuence of these factors is manifested in thefollowing generalized form of Darcy’s law that can be used to describe continuumlevel multiphase ßow in porous media:

(4.1)

FIGURE 4.1 Fate and transport of chlorinated organic compound releases in the subsurface.

Ground Water Flow

DNAPL Vapor

DNAPL Release

Dissolved DNAPL Plume Residual DNAPL Low-permeability layer

In this equation, qbis the Darcy velocity of phase b (b = g for gas, w for water,and n for NAPL), k rb is the relative permeability of phase b, k is the intrinsicpermeability tensor, mbis the viscosity of phase b, Pbis the phase pressure,rbis thephase mass density, g is the gravitational acceleration constant, and z is the elevation.Intrinsic permeability is so called because it is generally assumed to be aninherent characteristic of the porous medium This assumption is usually valid incoarse-grained media but can be a poor assumption in certain cases in which inter-actions between ßuids and soil grains result in temporal changes in the pore structure

or if the porosity or pore structure are affected by changes in pore pressure (e.g.,consolidation, shrink-swell, hydraulic fracturing) Although in most applicationspermeability is assumed to be constant over time for a given porous medium, incertain cases consideration of possible relationships to present or historical phasepressures or species concentrations may be necessary for accurate predictions Thetensorial nature of permeability reßects anisotropy that may develop due to a non-random spatial orientation of the pore structure or ßuid distributions or of largerscale heterogeneities (e.g., fractures, layering)

Fluid densities vary as a function of respective ßuid pressures For liquidssubjected to small pressure variations, ßuid compressibility can often be safelydisregarded Gas-phase compressibility is signiÞcantly greater than that of liquids,and, if gas ßow is modeled, compressibility should be considered Gas compress-ibility can be easily modeled based on ideal gas theory Density effects may besigniÞcant in the vapor transport of dense volatile organics in permeable porousmedia (Sleep and Sykes, 1989)

The mobility of NAPLs is inßuenced by viscosity Less viscous NAPLs tend tomigrate farther and more rapidly than others (Cohen and Mercer, 1993) Capillarypressures (i.e., the pressure differences between phases) are related to interfacialtension between the phases, wettability, and pore geometry Decreases in interfacialtension or increases in contact angle decrease capillary pressures between phasesfor a given pore geometry Decreases in interfacial tension or increases in contactangle thus decrease entry pressures for nonwetting phases into Þne-grained media,increasing the mobility of the nonwetting phase

In general, ßuid density, viscosity, and interfacial tensions vary as functions oftemperature and phase composition (Ma and Sleep, 1997) In isothermal, noncompo-sitional models, the dependence of ßuid properties on temperature and ßuid compo-sition and their temporal and spatial variations are disregarded However, where theseeffects are expected to be signiÞcant, they should be taken into account Temperatureeffects on these properties are well understood, and mixture theories exist to computecompositional effects In cases where the effects of surfactants may be under consid-eration, speciÞc experimental studies are required to characterize the behavior

4.2.1.2 Capillary Pressure and Relative Permeability Relations

In multiphase systems, pressure differences (i.e., capillary pressures) exist betweenphases as a result of interfacial tension between phases and curvature of the phaseinterfaces The capillary pressure across a curved interface with principal radii r 1

and r 2 is given by the following Laplace–Young Equation (Hunter, 1991):

where p≤ and p¢ are pressures on opposite sides of the interface The principal radiifor an interface in a soil pore are related to pore shape, the location of the phaseinterface in the pore, and the contact angle between the phase interface and theaquifer solids

The contact angle, measured through the denser ßuid, is determined by thechemical nature of the ßuids and the solid Wetting ßuids have contact anglesless than 90°, while nonwetting ßuids have contact angles greater than 90° Inthe vadose zone, liquids (i.e., NAPLs or water) are usually wetting ßuids com-pared with air In the saturated zone, most natural porous media are stronglywater-wet (Anderson, 1986); the exception may be when signiÞcant quantities ofnatural organic matter, graphite, silicates, and many sulÞdes are present in theporous medium When determining the wettability of multiphase systems con-taining NAPLs, several factors should be considered, including water chemistry,NAPL chemical composition, presence of natural organic matter, presence ofother agents (e.g., surfactants), aquifer saturation history, and mineral composi-tion of the porous medium

For a three-phase (i.e., gas, water, NAPL) system, water is usually the mostwetting phase, gas the least wetting, and NAPL the intermediate (Parker et al., 1987).The physically relevant capillary pressures are thus:

where subscripts g, w, and n designate gas, water, and NAPL, respectively Formonotonically changing ßuid saturations, the gas–NAPL interface curvature, and,thus, the gas–NAPL capillary pressure, is expected to be a function of gas-phasesaturation The gas-phase saturation controls gas-relative permeability Similarly,NAPL–water capillary pressure is expected to be a function of water saturation,which controls water-relative permeability

Various mathematical functions have been proposed to describe ßuid tion–capillary pressure (k–S–P) relationships for two-phase and three-phase ßuidsystems (Aziz and Settari, 1979; Corey, 1986; Parker et al., 1987) For example, for

satura-a two-phsatura-ase NAPL–wsatura-ater system, the Brooks–Corey relsatura-ationship for NAPL–wsatura-atercapillary pressure is as follows:

=ÊËÁ

where S ew is the effective water saturation calculated from the water saturation, S w;the maximum water saturation, S m;and the irreducible water saturation, S wr:

(4.5)

where p dow is the entry or bubbling pressure for the nonwetting (i.e., NAPL) phase,and l is an empirical constant termed the pore size index In contrast, Lenhardand Parker (1987) used relationships based on the following van Genuchten (1980)formulation:

(4.6)

where a, m, and n are empirical parameters It should be noted that theBrooks–Corey model incorporates a distinct entry pressure for the onset of non-wetting-phase displacement of the wetting phase, whereas the van Genu-chten–based model does not

As ßuid saturations change in multiphase systems, the relative permeability ofthe phase changes Stone (1973) proposed a method for computing three-phaserelative permeabilities from measured two-phase air–NAPL and NAPL–water rela-tive permeabilities assuming the water relative permeability to be a function of watersaturation only, air relative permeability to be a function of air saturation only, andNAPL relative permeability to be a function of air and water saturations Relativepermeability expressions based on ßuid saturations and the parameters from thecapillary pressure saturation relationships also have been developed for theBrooks–Corey relationship by using the Burdine (1953) pore size distribution model

by integrating the capillary pressure saturation relationships over the range of able saturations The Mualem (1976) model was used with the van Genuchten model

allow-to develop corresponding relative permeability expressions For given organic-phasesaturations, the Burdine relative permeability is always smaller than the Mualemrelative permeability (Oostrom and Lenhard, 1998)

Oostrom and Lenhard (1998) compared results from one-dimensional columnLNAPL inÞltration experiments with predictions of a simulator by using theBrooks–Corey and the van Genuchten models They found that the Brooks–Coreymodel gave a better match to experimental data than did the van Genuchten model.This match was attributed to the Þnite entry pressure of the Brooks–Corey model

as well as to differences in the relative permeability expressions associated withthe two models

Direct measurement of three-phase k–S–P relations is difÞcult and tedious, andthree-phase relations are generally predicted theoretically from two-phase data.Relative permeabilities are seldom measured but are predicted using the parametersdetermined from capillary pressure saturation measurements Leverett (1941) wasthe Þrst to propose that three-phase air–NAPL–water k–S–P functions could bepredicted from two-phase relationships (i.e., air–NAPL and NAPL–water functions)

assuming ßuid wettability in the order of water > NAPL > air such that NAPL occurs

as Þlms between water and gas phases Similar arguments supported by experimentaldata suggest that water saturation may be regarded as a function of NAPL–watercapillary pressure only and air saturation may be regarded as a function of air–NAPLcapillary pressure Furthermore, two-phase S–P functions for different ßuids should

be scalable by the respective ßuid–ßuid interfacial tensions Parker et al (1987)presented a method for estimating three-phase relations from two-phase air–watercapillary pressure–saturation data using a scaling approach air–water andNAPL–water interfacial tension data

The Leverett (1941) scaling approach used by Parker et al (1987) assumesthat the spreading coefÞcients for the systems are zero The spreading coefÞcient,

S, is calculated from the interfacial tensions between the phases (Oren and zewski, 1995):

where saw,san, and snware the air–water, air–NAPL, and NAPL–water interfacialtensions, respectively Some NAPLs have positive spreading coefÞcients, whereasothers, including many chlorinated solvents, have negative spreading coefÞcients.For those with positive spreading coefÞcients, the organic phase forms a Þlmbetween the air and the water phases in a three-phase system, resulting in a systemthat effectively has a spreading coefÞcient of zero (Oren and Pincewski, 1995).The existence of this Þlm has important implications for residual NAPL saturations

in three-phase systems

For NAPLs with negative spreading coefÞcients, discontinuities in the NAPLphase may be more pronounced in three-phase systems, leading to higher residualNAPL saturations in the vadose zone (Zhou and Blunt, 1997) Hofstee et al (1997)found that Leverett scaling could be applied only to a small portion of water–PCE–airretention curves Below a critical PCE saturation, the total liquid content appeared

to become a function of the capillary pressure across the air–water interface ratherthan a function of capillary pressure across the air–PCE interface as implied byLeverett scaling Below the critical saturation, PCE breakup into microlenses wasobserved These microlenses constituted a signiÞcant fraction of the PCE saturation,resulting in higher residual PCE saturations than would be expected for spreadingNAPLs (Hofstee et al., 1997)

When subjected to nonmonotonic saturation histories, relative permeability vs.saturation and capillary pressure vs saturation functions exhibit signiÞcant hysteresis.This is especially signiÞcant for NAPL due in part to the occurrence of residual NAPLthat has been hydraulically immobilized as occluded blobs or disconnected Þlmsinduced by incomplete NAPL displacement by water or air Hysteresis in two-phasesystems has been studied extensively, and reasonably reliable models have beendeveloped to predict two-phase hysteric functions from primary drainage and imbi-bition path measurements (e.g., Mualem, 1974; Gillham et al., 1976; Scott et al.,1983; Kool and Parker, 1987) However, whereas only 2 directions of saturationchange are possible in two-phase systems (i.e., wetting-phase drainage or imbibition),

12 path directions are possible in three-phase systems (i.e., IID, IDI, IDD, DII, DID,

DDI, CDI, CID, ICD, DCI, IDC, and DIC), where I, D, and C designate imbibition,

drainage, and constant saturation, respectively, of water, NAPL, and air (Saraf et al.,

1982) This complexity effectively precludes characterizing three-phase hysteretic

k–S–P functions based solely on direct experimental observations and requires

pre-dictive models to be quite complicated to handle all circumstances properly

Mathematical models for hysteretic three-phase k–S–P relations have been

pre-sented for petroleum reservoir applications by Evrenos and Comer (1969) and

Killough (1976) Parker et al (1987), Lenhard and Parker (1987), Lenhard et al

(1989), and Guarnaccia et al (1997) presented relationships of environmental interest

based on the van Genuchten model These models involve Þve parameters to describe

the main air–water drainage and imbibition S–P functions (including maximum

residual water and air saturations), two ßuid-dependent scaling factors, and two

additional residual saturations The Parker–Lenhard model considers the maximum

residual NAPL saturation for displacement by water and the maximum residual air

saturation for displacement by NAPL Residual NAPL caused by displacement by

air is not considered The Guarnaccia model considers residual NAPL saturations

caused by displacement by water or air Air entrapment is assumed to be the same

for displacement by water or NAPL

Hysteresis in k–S–P relations introduces a signiÞcant degree of complexity

and uncertainty to the characterization of three-phase ßow Incorporating hysteresis

into multiphase ßow models increases programming complexity The need to

change k–S–P curves with reversals between drainage and imbibition creates

instabilities in nonlinear iterations of these models, often requiring small time

steps to be resolved

4.2.2 M ULTICOMPONENT M ASS T RANSPORT

4.2.2.1 Mass Balance and Transport Flux Equations

The general macroscopic mass balance equation for species a within phase b(=g

for gas, w for water, n for NAPL) may be written as follows:

(4.8)

where f is porosity, Sb is phase saturation, rbis phase molar density, Xab is the

mole fraction of species a in phase b, qbis the Darcy velocity for phase b

described by Equation 4.1,Jab is the diffusive–dispersive mass ßux for species

a in phase b, rab is the net mass transfer of species a to (positive) or from

(negative) phase b, andGab represents the net sources (or sinks if negative) for

species a representing internal reactions and external sources/sinks A mass

balance for the adsorbed phase, assuming no transport in the adsorbed phase,

may be written as follows:

where X as is the adsorbed mass per mass of solids, rs is the density of soil solids,

and r as andGas are mass transfer rates and source/sink terms for the adsorbed phase

Equations 4.8 and 4.9 are subject to the following physical constraints:

(4.10a)

(4.10b)

(4.10c)

where the summations are over the indicated phases or chemical species

It is often assumed that the porous medium is incompressible and, hence, thatporosity is temporally invariant However, in certain situations, it may be warranted

to regard porosity as a function of ßuid pressure and/or temperature (e.g., caserelevant compressibility or thermal expansion coefÞcients would be required) Thedispersive–diffusive ßux is described by the following:

4.2.2.2 Interphase Mass Transfer

The interphase transfer of organic mass occurs by several processes (Figure 4.1),including NAPL dissolution, NAPL volatilization, and partitioning between waterand adsorbed phases and water and gas phases The simplest approach to phasepartitioning is to assume local equilibrium between phases In this case, the concen-tration in a given phase can be written as a function of the concentration in anotherphase multiplied by a partitioning coefÞcient Typically, for sparingly soluble organiccompounds such as the chlorinated organics, Henry’s law is used for equilibriumpartitioning between the water and the gas phases, and Raoult’s law is used for

partitioning from the organic phase to the water and gas phases In a three-phasesystem, the mole fractions of an organic species a in the water, gas, and organicphases at equilibrium would be governed by the following (Sleep and Sykes, 1993):

(4.13)

where H is the Henry’s law coefÞcient (Pa), P g is the gas phase pressure (Pa), and

Pa0 is the pure component vapor pressure (Pa) of the organic species From thisequation, it can be seen that the mole fraction of the organic in the water phase (andtherefore the effective solubility of the organic in the water phase) in equilibriumwith a multicomponent organic phase is proportional to the mole fraction of theorganic in the organic phase Molar concentrations of each NAPL components areoften unknown In such cases, the mass fraction or volume fraction of the component

of interest can be used as a surrogate for its mole fraction (Mackay et al., 1991).More soluble components preferentially dissolve from NAPL mixtures over time,resulting in an asymptotic reduction in their mole fraction and hence effectivesolubility (Mackay et al., 1991) It has been argued that removal of more solublespecies from a NAPL mixture can lead to a stabilized source for which naturalattenuation processes can contain the dissolution of the remaining sparingly solublecomponents (Adeel et al., 1997)

Raoult’s law and Henry’s law are based on ideal phase behavior The activitycoefÞcient quantiÞes the degree of nonideality experienced by a component due tointermolecular interactions in a NAPL or aqueous solution For ground water withtypical contaminant concentrations, the activity coefÞcients are governed primarily

by water–solute interactions For NAPL mixtures, the degree of nonideality can beassociated with the similarity of components (Mackay et al., 1991) For example, ifall the components in a NAPL mixture are alkanes, then the activity coefÞcient can

be assumed to be unity (i.e., the NAPL behaves as an ideal mixture and followsRaoult’s law) The use of nonideal phase partitioning relationships becomes partic-ularly necessary when dealing with surfactants and cosolvents In most practicalsituations, the activity coefÞcients of individual components in complex, aged liquidmixtures cannot be accurately measured Several methods are available in publishedliterature for estimating activity coefÞcients (e.g., Fredenslund et al., 1977; van Nessand Abbot, 1982)

In addition to deviations from ideality due to chemical interactions, deviationsfrom equilibrium between phases are expected when ßuid ßow rates are high such

as during pump-and-treat or soil vapor extraction operations Sleep and Sykes (1989)showed that rate limitations on mass transfer between phases could have a signiÞcantimpact on the fate and transport of volatile organics in variably saturated porousmedia In particular, the rates of removal of organics from the subsurface by pump-and-treat or soil vapor extraction are lower than predicted when using an equilibriumpartitioning model As contact areas between the organic phase and the water andgas phases are expected to decrease with mass removed, the rates of organic removalare expected to decline with time, resulting in very long times required to achievecleanup goals

HXaw =X Pag g =X Pa ao 0

The model of Sleep and Sykes (1989) assumed that kinetic interphase masstransfer could be simulated as a Þrst-order process, governed by the following:

(4.14)

where r aij is the mass transfer rate of species a from phase i to phase j per porous media volume (or from phase j to phase i if r aij < 0), gij is the mass transfer coefÞcient

between phase i and phase j, rj is the density of phase j, f is porosity, S j is the

saturation of phase j, Xa is the actual mass fraction of species a in phase j, and is

the mass fraction in phase j that would occur if equilibrium existed with phase i.

In recent years, several studies have been published that demonstrate the tance of rate-limited organic-phase dissolution and propose a variety of correlations

impor-to predict Þrst-order mass transfer coefÞcients for NAPL dissolution from residualsaturations of organics Mass transfer coefÞcients were calculated from Sherwoodnumbers The Sherwood number is a dimensionless mass transfer number deÞned

in terms of the Þrst-order mass transfer coefÞcient; the molecular diffusion

coefÞ-cient, D; and a length scale, l, of the porous medium (typically d50):

(4.15)

The Sherwood number in turn is related to ßuid velocities, diffusion coefÞcients,and organic ßuid saturations For example, Miller et al (1990) found that Sher-wood numbers describing NAPL dissolution in centimeter-scale sand columnscould be Þt by the following:

(4.16)

where f is porosity, qn is the nonwetting-phase volume fraction, Rew is the

water-phase Reynolds number, and Sc w is the water-phase Schmidt number (i.e., ratio ofwater-phase velocity to water-phase diffusion coefÞcient of organic species) Miller

et al (1998) summarized correlations found by others such as Powers et al (1992,1994) It is likely that the empirical coefÞcients and exponents of the mass transfercorrelations are sensitive to organic-phase emplacement techniques and soil poresize distributions It must also be stressed that these models were developed formillimeter- or centimeter-scale experiments Testing these models at the Þeld scalehas not been attempted, and it is certain that an upscaling procedure would berequired before applications in models discretized at the Þeld scale

Investigations of mass transfer between the water and gas phases indicate thatthis process is rapid compared with the partitioning between organic and waterphases Miller et al (1998) summarize correlations published for rate constants forgas–water and gas–organic partitioning

The partitioning of chlorinated organic compounds to the soil phase (adsorption)can also have a very signiÞcant impact on fate and transport in the subsurface

(Schwarzenbach et al., 1993) In recent years, sorption mechanisms have been the focus

of a numerous investigations Brusseau and Rao (1989) and Weber et al (1991) marize current concepts of adsorption in subsurface systems In many systems (e.g.,those involving nonionic hydrophobic solute sorbing from the water phase to naturalsoils with signiÞcant organic content), linear sorption models may be appropriate (Miller

sum-et al., 1998) When sorption behavior deviates from linearity, models such as theFreundlich model or the Langmuir model are often used (Weber et al., 1991).Recent investigations have found that sorption and desorption processes can takefrom months to years to reach equilibrium Cornelissen et al (1997) examined thetemperature dependence of slow adsorption and desorption in batch experimentswith chlorobenzenes, PCBs, polycyclic aromatic hydrocarbons (PAHs), and labora-tory- and Þeld-contaminated sediments The laboratory-contaminated sedimentswere maintained in contact with the chemicals of interest for 34 d Cornelissen et

al (1997) identiÞed three stages of desorption: a rapid stage corresponding to theÞrst few hours of desorption, an intermediate stage corresponding to a few weeks,and a slow stage corresponding to several months of desorption time

Rate limitations of sorption and desorption are usually attributed to slow diffusionwithin soil grains, or within soil aggregates (Brusseau and Rao, 1989) Some modelsassume that this process can be described by a Þrst-order model, whereas others use

a diffusion-based model incorporating assumptions about soil grain or aggregategeometry Both Þrst-order models and diffusion-based models cannot reproduce therapid initial sorption rates observed experimentally As a result, a number of two-sitemodels have been proposed that include both equilibrium and kinetic sorption sites

(e.g., Nkedi-Kizza et al., 1984; van Genuchten and Wagenet, 1989).

The Þndings of Cornelissen et al (1997) that a range of sorption coefÞcientswere required to model kinetic sorption has been addressed by several other research-ers Connaughton et al (1993); Pedit and Miller (1994); Chen and Wagenet (1995);and Culver et al (1997) presented models that employed distributions of Þrst-orderrate constants to characterize sorption kinetics Culver et al (1997) used both log-normal and gamma distributions for sorption rate constants Cunningham et al.(1997) developed a model that attributed sorption to intergranular diffusion Diffu-sion was characterized by a gamma distribution of diffusion coefÞcients rather than

by a distribution of rate constants The model was Þt to TCE sorption experimentsconducted at 15, 30, and 60°C with silica gel and natural sediments

Considerable research has been performed on vapor sorption to low moisturecontent soils and the effect of humidity on sorption In the case of vapor sorption tolow moisture content soils, nonlinear sorption isotherms are required that incorporatethe effects of soil humidity on sorption (Chiou and Shoup, 1985; Unger et al., 1996a).Comprehensive modeling of organic vapor transport in low moisture content soils thusrequires nonlinear sorption models as well as predictions of water vapor transport.Research both at the laboratory and the Þeld scales indicates that sorption rates oftenoccur at rates slow enough to warrant the use of a kinetic model that accounts for atleast two sorption regimes Methods for determining the appropriate effective Þeld-scaleparameters for these models has not been developed, and scaling issues have not yetbeen adequately addressed (Miller et al., 1998) The multisite models also introduceadditional variables that must be solved, increasing the computational cost of modeling

4.2.3 M ODELING B IOTIC AND A BIOTIC T RANSFORMATIONS

4.2.3.1 Review of Chlorinated Solvent

Transformation Mechanisms

4.2.3.1.1 Biodegradation Mechanisms

Once dissolved into ground water, CAHs may be subject to a variety of mation mechanisms depending on the redox chemistry and availability of other carbonsources (e.g., natural organic matter or petroleum cocontaminants) The three generalbiodegradation mechanisms are reductive dehalogenation, oxidation, and aerobiccometabolism Of these three mechanisms, reductive dehalogenation is believed to

biotransfor-be the most effective and perhaps the most important mechanism contributing to thenatural destruction of CAHs in aquifers The state-of-the-science regarding the poten-tial for CAH biodegradation under various conditions is summarized in Table 4.1

TABLE 4.1

Conditions for Biotic and Abiotic Transformations of Chlorinated Solvents

Compound

Anaerobic Biodegradation Potential

Aerobic Biodegradation

Degradation Potential

Primary Substrate

metabolic

Co-Primary Substrate

metabolic

Notes: 0 = Very small (if any) potential; X = Some potential; XX = Fair potential; XXX = Good potential;

XXXX = Excellent potential; 1,1-DCE = 1,1-Dichlorethene; t-DCE = trans-1,2-Dichloroethene; c-DCE

= cis-1,2-Dichloroethene; VC = Vinyl chloride; PCA = Tetrachloroethane; 1,1,2-TCA =

1,1,2-Trichloro-ethane; 1,1,1-TCA = 1,1,1-Trichloro1,1,2-Trichloro-ethane; 1,1-DCA = 1,1-Dichloro1,1,2-Trichloro-ethane; 1,2-DCA = hane; CA = Chloroethane; CF = Chloroform; DCM = Dichloromethane; CM = Chloromethane.

1,2-Dichloroet-Source: After McCarty and Semprini, 1994; McCarty, 1997; Butler and Hayes, 1999; Lorah and Olsen,

1999; Bradley and Chapelle, 2000; Maymo-Gatell et al., 2001

Names of speciÞc CAHs are abbreviated in the discussion below Table 4.1 provides

an index of name abbreviations for each of the CAHs considered here

4.2.3.1.2 Reductive Dehalogenation

Under certain anaerobic conditions, a variety of bacteria can use chlorinated solventsfor respiration, transforming them in a process known as halorespiration (McCarty,1997) In this process, halogenated compounds such as PCE and TCE are biode-graded by reductive dehalogenation Reductive dehalogenation is a reaction in whichone or more chlorine atoms are replaced with hydrogen atoms, reducing the carbonatom on the CAH molecule Certain bacteria that mediate this reaction can gainenergy and grow through mediation of reductive dehalogenation (Maymo-Gatell etal., 1997, 2001) Reducing equivalents for this process are supplied by hydrogenproduced by the biodegradation of naturally occurring or anthropogenic carboncompounds The biodegradation of the organic matter is thought to be carried out

by fermentative organisms, not by the dechlorinating organisms Most microbialdechlorinating consortia also contain methanogens that compete with dechlorinatorsfor hydrogen (Fennel and Gossett, 1998)

Figure 4.2 illustrates the common pathways for reductive dehalogenation ofchlorinated compounds For PCE, reductive dehalogenation follows the order ofPCE Æ TCE Æ c-DCE Æ VC Æ ethene The rate of reductive dehalogenation tends

to decrease as the number of chlorine substituents on the CAH molecule decreases(Vogel, 1994) In addition, the rate and extent of dehalogenation depends on the

FIGURE 4.2 Natural degradation pathways for CAHs.

Notes:

Pathways shown are for anaerobic biological reductive dehalogenation unless noted Oxidation = both aerobic and anaerobic biooxidation.

2E = biologically mediated dichloroelimination.

Abiotic-E = abiotic elimination.

Abiotic-H = abiotic hydrolysis.

redox conditions, with DCE and VC dehalogenation occurring more rapidly undermore reducing (i.e., sulfate-reducing or methanogenic) conditions.

Complete reductive dehalogenation is most commonly reported at those siteswhere signiÞcant concentrations of codisposed petroleum contaminants or leachateare also present (Semprini et al., 1995) Conversely, PCE, TCE, and DCE tend topersist at sites where organic electron donors are absent and redox potentials arerelatively high (i.e., microaerobic or nitrate-reducing conditions) (Sturchio et al.,1998) At some sites, intermediates such as DCE or CF can accumulate as evidence

of past reductive dehalogenation that occurred prior to exhaustion of the electrondonor supply Accordingly, one important step in constructing chlorinated solventbiodegradation models is to consider the amount of electron donor available tosustain reductive dehalogenation (National Research Council [NRC], 2000), as well

as inhibition effects from transformation products such as CF

DCE, CF, and VC can also persist due to an absence of halorespiring bacteria.Halorespirers are not ubiquitous in nature, and not all subsurface bacteria are able

to mediate complete halogenation (e.g., PCE Æ ethene) In most laboratory studieswhere complete dehalogenation of PCE and TCE has been observed, a microbial

consortium has mediated the CAH transformation sequence To date,

Dehalococ-coides ethenogenes is the only microorganism known to be capable of completely

dechlorinating PCE (Magnuson et al., 2000)

In addition to occurring via halorespiration, reductive dehalogenation of CAHscan also occur cometabolically During cometabolic reductive dehalogenation, trans-formation of a given CAH occurs fortuitously during microorganism growth onanother substrate Many methanogenic and sulfate-reducing bacteria are able tomediate cometabolic reductive dehalogenation, which effectively can result in thedehalogenation of PCE and TCE but not DCE (Bagley and Gossett, 1990; Gantzerand Wackett, 1991) In this process, dehalogenation of the CAH molecule occursdue to reactions with bacterial cofactors (e.g., porphyrins containing redox-sensitivemetals), but the cell does not derive energy for growth The relatively slow reductivedehalogenation that results from this cometabolic reaction may be the cause of theincomplete dehalogenation that is observed at many sites Recently, evidence has

been presented that the degradation of VC by D ethenogenes is cometabolic

(Maymo-Gatell et al., 2001)

4.2.3.1.3 Oxidation

Because chlorine atoms are electronegative by nature, the susceptibility of CAHs todegradation via direct oxidation decreases as the number of chlorine substituentsincreases (Figure 4.2) Consequently, polychlorinated ethenes such as hexachlo-robenzene (HCB), PCE, TCE, CT, and CF are largely recalcitrant to direct oxidation.However, it has been shown that lightly chlorinated ethenes such as VC and DCEcan be biodegraded oxidatively under aerobic, iron-reducing, and methanogenicconditions (Hartmans and de Bont, 1992; Bradley and Chapelle, 1996, 1997, 1999;Bradley et al., 1998) When used as the sole electron donor, VC can serve as a

growth substrate (Verce et al., 2000), and c-DCE can support cell metabolism

(Bradley and Chapelle, 2000) Consequently, the rate and extent of natural subsurfaceCAH destruction does not depend on reductive dehalogenation alone DCE and VC

that are produced in reducing zones of an aquifer may be oxidized when the plumeenters zones where sulphate, nitrate, iron, or oxygen can act as electron acceptors.

4.2.3.1.4 Aerobic Cometabolism

During aerobic cometabolism, the destruction of TCE, DCE, and/or VC is coupled

to the biooxidation of a more easily degraded primary substrate such as methane orammonia Of the three mechanisms for CAH biodegradation, aerobic cometabolism

is likely the least signiÞcant under natural subsurface conditions (NRC, 2000).Aerobic cometabolism is most often characteristic of engineered bioremediationsystems, where oxygen and a primary substrate such as methane, toluene, phenol,butane, or ammonia are introduced to promote chlorinated ethene biodegradation.However, aerobic cometabolism can occur intrinsically where CAHs come intocontact with methane in slightly aerated zones of an aquifer, as has been suggested

by Bradley and Chapelle (1998) and Lorah and Olsen (1999)

4.2.3.1.5 Abiotic Transformations

In general, biodegradation is the most important natural process governing thedestruction of CAHs in the subsurface For those CAHs that have been observed todegrade abiotically under natural conditions, abiotic degradation rates are typicallymuch slower than biodegradation rates However, these reactions can still be signif-icant within the time scales commonly associated with ground water movement

A variety of investigations have shown chloroethenes to be resistant to abioticdegradation A growing body of evidence suggests, however, that PCE; TCE; PCA;1,1,1-TCA; and CT can be degraded abiotically in the presence of ferrous sulÞdesthat are common in reduced aquifers and wetlands (Kriegman-King and Reinhard,1992; Curtis and Reinhard, 1994; Devlin and Muller, 1999; Butler and Hayes,

1999, 2000) CT can also be reduced abiotically in the presence of dissolved phase

Fe2+, HS_, and pyrite Natural organic matter that coats aquifer material canaccelerate this process signiÞcantly by acting as an electron shuttle The effect ofiron sulÞde and organic matter could play an important role in CT reduction forplumes that intercept bogs or wetlands In addition, green rust, a naturally occur-ring iron hydroxide, can also promote the degradation of CT (Heron et al., 1994;Erbs et al., 1999)

The chemical pathway(s) for the natural abiotic degradation of PCE and TCEcan differ from the biodegradation pathway in that acetylene (C2H2) is a majorabiotic transformation intermediate for both PCE and TCE Therefore, detectingC2H2 in chlorinated solvent plumes can serve as evidence that abiotic degradation

is occurring

Relative to chloroethenes, chloroethanes are more susceptible to abiotic radation 1,1,1-TCA and 1,2-dichloroethane (1,1-DCA) are both susceptible todegradation via hydrolysis 1,1,1-TCA can also be degraded via an abiotic elim-ination (alkane => alkene) reaction to form 1,1-DCE (Figure 4.2) This abioticdegradation of 1,1,1-TCA likely is the primary source of 1,1-DCE in contaminatedaquifers PCA degrades to TCE by the same type of abiotic reaction (Lorah andOlsen, 1999) The CA that forms as a result of TCA biotransformation also can

deg-be transformed abiotically

4.2.3.2 Petroleum Hydrocarbon Biodegradation Models

Early fate and transport models that described contaminant biodegradation wereprimarily developed for simulating the aerobic biodegradation of petroleum hydro-carbons (Sykes et al., 1982; Borden and Bedient, 1986; Molz et al., 1986) Subse-quently, a variety of biodegradation models have been published in the literature,including models for both aerobic and anaerobic biodegradation processes, as well

as saturated and unsaturated zone transport (Srinivasan and Mercer, 1988;

Widdow-son et al., 1988; MacQuarrie et al., 1990; Chen et al., 1992; McClure and Sleep,

1996; Rathfelder et al., 2000) In recent years, emphasis on anaerobic biodegradationhas grown, and models have been developed that simulate biodegradation undermultiple electron-accepting conditions including nitrate-reducing, iron-reducing,sulfate-reducing, and methanogenic conditions (Lu et al., 1999; Waddill and Wid-dowson, 2000)

Most of these models incorporate substrate-limited biodegradation by usingMonod kinetics In addition, electron acceptor limitations are incorporated by addingextra Monod terms based on electron acceptor concentrations and electron acceptorhalf-saturation constants (dual Monod kinetics) For example, Borden and Bedient(1986) modeled hydrocarbon biodegradation coupled to biomass growth and decayusing versions of the following two expressions:

(4.17)

(4.18)

where C D is the aqueous-phase concentration of hydrocarbon (or electron donor),

X t represents the total active biomass concentration, k is the maximum hydrocarbon utilization rate, K D is the hydrocarbon half-saturation constant, A is the electron acceptor (oxygen) concentration, K A is the electron acceptor half-saturation constant,

Y is the microbial yield coefÞcient (cell mass created per unit substrate consumed),

and b is the microbial decay and endogenous respiration coefÞcient Widdowson et

al (1988) incorporated additional Monod terms to include the impact of nutrientlimitation on hydrocarbon biodegradation Complete mineralization of hydrocarbon

to carbon dioxide and water is usually assumed in hydrocarbon biodegradationmodeling, although Malone et al (1993) included the formation of intermediateproducts in the biodegradation of aromatic hydrocarbons

Most of the hydrocarbon biodegradation models simulate only aqueous-phasetransport with the exception of the McClure and Sleep (1996) model, which includesfull three-phase ßow and transport with equilibrium interphase partitioning Rath-felder et al (2000) modeled aqueous and gaseous-phase transport to allow bioventingsimulation Malone et al (1993) and Rathfelder et al (2000) included kinetic NAPLdissolution from residual NAPL sources Recent laboratory experiments have shown

ûú

û

úÈ +Î

û

ú

-that PCE biodegradation can occur in the presence of the organic phase and -thatthis can enhance the rate of PCE DNAPL dissolution (Yang and McCarty, 2000;Cope and Hughes, 2001) These empirical Þndings conÞrm the predictions of Sea-gren et al (1994), who were among the Þrst to provide a quantitative description ofenhanced NAPL dissolution resulting from biodegradation Mass transfer limitationsfrom both the NAPL and sorbed phases can also limit the biodegradation rate in theaqueous phase (Ghoshal et al., 1996; Bosma et al., 1997) Because substrates aretypically hydrolyzed prior to biodegradation, nonaqueous and sorbed-phase hydro-phobic organic contaminants generally are thought to be unavailable for biodegra-dation (Zhang et al., 1998) Consequently, the impact of biodegradation on NAPLand plume attenuation is often limited by the rate of NAPL dissolution and/ordesorption from aquifer solids.

Most hydrocarbon biodegradation models are based on the recognition thatbiomass predominantly is present as a bioÞlm in a porous medium; however,there is some variation in the representation of the bioÞlm and the substrateuptake processes of the bioÞlm Baveye and Valocchi (1989) reviewed the threemost common representations of bioÞlm processes in porous media The ÞrstbioÞlm model (Rittmann et al., 1980; Bouwer and McCarty, 1984) describes thebioÞlm as having uniform thickness, covering all solid surfaces The transfer ofsolutes into the bioÞlm occurs across a stagnant boundary layer into a thinbioÞlm that is conceptualized to be fully penetrated so that mass transfer limi-tations are all associated with the stagnant boundary layer Therefore, this model

requires solution of algebraic equations to determine bioÞlm concentrations and

also requires assumptions about the stagnant boundary thickness and bioÞlmsurface area

The second class of bioÞlm models (Molz et al., 1986; Widdowson et al., 1988;Chen et al., 1992) assumes that biomass grows in microcolonies that are constant

in size but increase in number as substrate consumption occurs A stagnant boundarylayer governing mass transfer to the microcolonies is hypothesized as with the Þrstclass, thereby requiring solution for microcolony substrate concentrations andassumptions about boundary-layer thickness and microcolony geometry

The third class of bioÞlm models (Sykes et al., 1982; Borden and Bedient, 1986;Kindred and Celia, 1989; MacQuarrie et al., 1990; Wood et al., 1994; McClure andSleep, 1996) makes no assumption about bioÞlm conÞguration and assumes thatdiffusion limitations in stagnant boundary layers and in the bioÞlm may be neglectedand that biodegradation kinetics are based directly on bulk water phase concentra-tions Although this is a simpliÞcation of the pore-scale processes, at present there

is no sufÞcient experimental evidence to discount the practical value of this simpliÞedmodel (Baveye and Valocchi, 1989)

The models of Molz et al (1986); Widdowson et al (1988); and Chen et al.(1992) assume a stationary biomass phase with no bacterial transport In contrast,the models of Borden and Bedient (1986), MacQuarrie et al (1990), and McClureand Sleep (1996) assume advective–dispersive transport of bacteria with attachment

of biomass to aquifer solids modeled as a linear sorption process Sorption cients are typically chosen so that 95% of the biomass is attached to the soil (Bordenand Bedient, 1986)

coefÞ-It is recognized that the process of attached microbial growth, bacterial tion in porous media, and bioÞlm shearing is much more complex than can besimulated with a linear sorption model Complex models incorporating biomassattachment and detachment as a function of bioÞlm aqueous-phase concentration,bioÞlm thickness, and shear forces related to ground water velocity have beendeveloped (Taylor and Jaffe, 1990; Cunningham et al., 1991) Most of these modelsassume an idealized geometry of soil particles and of uniform bioÞlm growth Thesemodels incorporate changes in soil permeability, porosity, and dispersivity as afunction of bioÞlm thickness and have been applied to laboratory-scale experiments(Taylor and Jaffe, 1990), but no Þeld-scale veriÞcation has been performed Includingthe effects of bioÞlm growth on permeability, porosity, and dispersivity in a biodeg-radation model may be necessary in engineered remediation systems where biomassstimulation through nutrient addition and high carbon loading produce high rates ofbiological growth Such models can also be used to optimize nutrient and substrateaddition to minimize formation plugging (Taylor and Jaffe, 1991).

deposi-4.2.3.3 Chlorinated Solvent Biodegradation Models

For the reasons discussed in Section 4.2.3.1, modeling chlorinated solvent radation can be substantially more complex than modeling petroleum hydrocarbonbiodegradation Model selection depends on a variety of factors, including the type

biodeg-of dechlorinating microorganisms present, the type and amount biodeg-of electron donorpresent, and the redox conditions in the aquifer In general, the practice of modelingchlorinated solvent biodegradation is less well established than that for modelingpetroleum hydrocarbon biodegradation Nevertheless, the following three basic types

of chlorinated solvent biodegradation models have emerged:

• Monod models that simulate halorespiration

• Monod models that simulate cometabolic biodegradation

• Sequential transformation models that assume a Þrst-order kinetics foreach sequential transformation

Fennel and Gossett (1998) and Bagley (1998) presented some of the Þrst modelsfor simulating halorespiration In the batch model of Bagley (1998), dual Monodkinetics based on chlorinated ethene concentration and hydrogen concentration wasused to simulate each of the transformation steps from PCE to ethene For example,the biodegradation of PCE was represented by the following:

(4.19)

where X PCE is the biomass concentration of PCE degraders, c PCE and c H2 are the

water-phase concentrations of PCE and hydrogen, respectively, and K PCE and K H2

are the half-saturation constants for PCE and hydrogen, respectively The production

of hydrogen from the fermentation of ethanol to acetic acid and propionic acid and

ùû

úú

2

from the fermentation of propionic acid was included, as was the use of acetic acidand hydrogen by methanogens In addition to the simulation of 10 chemical species,

the model includes the growth of 2 dechlorinating species (PCE to c-DCE and c-DCE

to ETH), ethanol and propionic acid fermenters, and aceticlastic and genotrophic methanogens Inhibition terms were also included in the Monod terms

hydro-to account for VC degradation inhibition by the other chlorinated ethenes andthermodynamic limitations on fermentation reactions

The batch model of Bagley (1998) has been incorporated into the compositionalmodel of McClure and Sleep (1996) as described in Aschwanden (2001) Theresulting model involves solution for concentrations of 10 chemical species and 5microbial species and is therefore not readily applicable to multidimensional Þeld-scale modeling of anaerobic PCE biodegradation In addition to metabolic dehalo-genation, many chlorinated organics can be biodegraded cometabolically Becausethe organisms do not derive any beneÞt from this cometabolic biodegradation butgrow on other substrates, modeling cometabolic biodegradation involves simulatingthe chlorinated contaminant and growth substrate

Many chlorinated compounds create intermediates that are toxic to isms For example, the aerobic biodegradation of TCE and VC produces epoxidesthat inactivate microorganisms (Wackett et al., 1989) Chang and Alvarez-Cohen(1995), building on the work of Criddle (1993), developed a model that includedbiodegradation of a growth substrate and a chlorinated organic by oxygenase-expressing cultures Cell growth, reducing energy limitation, product toxicity, com-petition between growth substrate, and cometabolic substrate for oxygenase enzymeswere all included in the model The resulting equations for degradation of growthsubstrate and chlorinated contaminant are as follows:

microorgan-(4.20a)

(4.20b)

where X is the biomass concentration, R is the reducing energy electron equivalent concentration, K R is the half-saturation constant for reducing energy, S g is the con-

centration of growth substrate, S c is the concentration of chlorinated organic, K Sg is

the half-saturation constant for growth substrate, and K Sc is the half-saturation

con-stant for chlorinated organic The terms S c /K Sc and S g /K Sg account for competitiveinhibition between growth substrate and chlorinated organic

Growth is modeled by the following:

-where T c is the transformation capacity of the cometabolic substrate, representingthe amount of cometabolic substrate degraded divided by the amount of cells inac-tivated due to product toxicity An additional equation is also involved to predictchanges in reducing equivalents due to consumption from chlorinated organic deg-radation and regeneration from external sources.

The model of Chang and Alvarez-Cohen (1995) was veriÞed with laboratorybatch experiments As with the model for chlorinated ethene biodegradation, thismodel involves many parameters, including rate constants, yields, half-saturationconstants, transformation capacity, stoichiometric constants for reducing energyproduction and consumption, initial reducing energy electron equivalent concentra-tions, and initial microbial population Although incorporating this model into amultiphase ßow and transport model is straightforward algorithmically and mathe-matically, determining the appropriate parameters and initial conditions for reducingenergy and biomass is difÞcult in the Þeld For cometabolic biodegradation models,perhaps the most important point of consideration is that these models have limitedutility for modeling chlorinated solvent fate in nonengineered systems Althoughthese models have been useful for analyzing cases where a primary substrate hasbeen introduced to enhance biodegradation (Semprini and McCarty, 1992; Travisand Rosenberg, 1997), there are few natural conditions for which these models would

be appropriate (NRC, 2000) Methane generation at landÞlls provides a primarysubstrate source to support methanotrophic chloroethene degradation, but halores-piration is expected to be a more dominant process when landÞll leachate is present.When biomass levels, microbial community composition, and electron donor oracceptor concentrations are relatively constant at a particular site, the multipleMonod expressions of Equations 4.19, 4.20a, and 4.20b reduce to single Monodkinetics expressions Under conditions of high-chlorinated organic concentrationsrelative to the substrate half-saturation constant, Monod kinetics reduces to zero-order kinetics At low-chlorinated organic concentrations, the Monod model reduces

to Þrst-order kinetics Biokinetic studies by Haston and McCarty (1999) found that

a Þrst-order kinetic approximation could be appropriate for reductive dehalogenationwhen chloroethene concentrations are in the microgram per liter (µg/l) range Thoseresearchers also concluded, however, that Monod kinetics offer the best approachfor modeling chloroethene biodegradation

First-order biokinetic models are appropriate for certain cases, particularly whenchloroethene concentrations are sufÞciently low to warrant this approach Clement

et al (1998) developed the code RT3D, a three-dimensional (3-D) numerical fateand transport model that simulates the sequential transformation of PCE to VC using

a series of Þrst-order transformation expressions The kinetics of the biologicalreactions are represented in RT3D as follows:

(4.25)

where Y TCE/PCE is a yield coefÞcient whose value is determined stoichiometrically

based on the parent–daughter decay of PCE to TCE, and k PCE represents the order decay coefÞcient A variety of methods are available for deriving a site-speciÞcestimate of sequential transformation decay coefÞcients (U.S Environmental Pro-tection Agency [USEPA], 1998) Use of the Þrst-order approximation requires care-ful consideration of the potential errors implicit in the approach Further discussion

The equations of multiphase ßow are classiÞed as parabolic partial differentialequations As the capillary pressure gradients are decreased, the problem becomesmore hyperbolic in nature, giving way to the propagation of sharp fronts (e.g., theBuckley–Leverett solution) Solving multiphase ßow equations, whether with Þniteelement or Þnite difference methods, usually necessitates using a method that hassufÞcient numerical dissipation to guarantee convergence to the correct method Themost common method is one point upstream weighting of relative permeabilities,which guarantees unconditional convergence to the correct solution as the grid isreÞned (Aziz and Settari, 1979) This guaranteed convergence comes at the price ofnumerical dispersion that smears sharp fronts (Aziz and Settari, 1979) Higher-ordermethods of relative permeability weighting have also been applied, such as two-point and third-order upstream weighting (Sleep and Sykes, 1993) and ßux limiters(Unger et al., 1996b) The major difÞculty with the higher-order spatial discretizationtechniques is that they introduce a higher-order connection pattern, decreasing thesparsity of the Jacobian matrix formulated with Newton linearization

The solution of the compositional equations for both ßuid ßow and transportcan be accomplished with similar techniques as those used for simulating multiphaseßow Additional discretizations are needed for solute advection and dispersion withinthe ßuid phases Although it is common to use upstream weighted methods for

-advection terms, this technique introduces numerical dispersion that can be muchmore signiÞcant than that introduced in multiphase ßow simulation The samehigher-order methods used for relative permeability weighting can be used fordiscretizing solute advection terms (Sleep and Sykes, 1993; Unger et al., 1996b).

4.2.4.2 Temporal Discretization

The most robust method for temporal discretization is the fully implicit method(Aziz and Settari, 1979) The fully implicit method is unconditionally stable,although there is still a time-step limitation associated with converging the nonlineariterations in multiphase ßow and transport The disadvantage of the fully implicitmethod is that the mass balance equations for ßow and transport are fully coupled,and, consequently, a large set of coupled equations must be solved simultaneously

It has been commonplace in the petroleum industry (Aziz and Settari, 1979) touse an approach termed “implicit in pressure, explicit in saturations” (IMPES), whichallows governing equations to uncouple, forming a set of equations that can besolved implicitly for pressures, followed by an explicit solution of a second set ofequations for ßuid saturations This method is signiÞcantly less computationallyexpensive than the fully implicit method for a given time step However, the IMPESmethod is only conditionally stable The allowable time-step size decreases as theimportance of capillarity increases in the problem, making it particularly unsuitablefor simulating three-phase ßow and transport problems

Adaptive time-stepping methods developed for petroleum reservoir simulation(Thomas and Thurmau, 1983) have also been applied to simulations of multiphaseßow and transport in ground water systems (Sleep and Sykes, 1993) In thesemethods, cells are adaptively switched from IMPES to fully implicit when changes

in saturations or concentrations or ßow rates are too large This method allowsthe use of larger time steps than allowable in a fully IMPES simulation but atlower computational cost than a fully implicit method In addition to reducingcomputational times, the use of adaptive implicit methods allows the use of higher-order weighting schemes at IMPES nodes without changing the sparsity of thesystem matrix The major drawback of using adaptive implicit methods is theabsence of easily calculated criteria for switching cells from IMPES to implicit(Fung et al., 1989)

4.2.4.3 Linearization of Nonlinear Equations of Multiphase

Flow and Transport

The equations of multiphase ßow are highly nonlinear due to the nonlinear dependence

of relative permeability and capillary pressure on ßuid saturations Solving multiphaseßow equations requires a linearization technique The simplest approach is successiveiteration or Picard iteration, where the discretized equations are solved using relativepermeabilities and capillary pressures calculated from current values of saturations Theiteration process is started with an initial guess of saturations, usually equal to the initialsaturations or the saturations at the end of the previous time step This method ofsuccessive iteration is not very robust because it is sensitive to initial guesses of satura-

tions and does not perform well for systems with highly nonlinear relative permeabilityand capillary pressure relationships (typical of most soils) or systems with rapidly chang-ing saturations due to high ßow rates In these cases, the lack of robustness of this methodleads to a requirement of extremely small time steps or to complete failure to converge.

A more robust method for solving the nonlinear multiphase ßow and transportequations is the use of Newton linearization (i.e., the Newton Raphson method),which requires computing the Jacobian of the coefÞcient matrix of the mass balanceequations This computation makes code development more difÞcult because massbalance equation derivatives with respect to the solution variables are required.However, numerical differentiation methods can be used to eliminate the need foranalytical derivative determination

Solving equations of multiphase ßow and transport in compositional simulators

is complicated by equations changing depending on the number and types of phasespresent in a discretized element This necessitates a change in the solution variableswhen there is a change in the ßuids present Sleep and Sykes (1993) discuss theprimary variable substitution for a three-phase compositional simulator In theirmodel for a system composed of water, air, and one organic species, there are threedegrees of freedom for each discrete element (Þnite difference block in this case)

In systems with all three phases present, the solution variables are water head, watersaturation, and total liquid saturation (i.e., water plus organic-phase saturations) Incontrast, regions containing only water and total liquid saturations are the same.However, the water phase may contain dissolved organic, so it is necessary to solvefor the concentration of organic in the water phase In addition, the air or organicphase can enter the region at some time, which necessitates the calculation of watersaturations to detect the condition of water desaturation Because water velocitiesare also required, it is necessary to compute water heads Thus, when air and organicphases enter a water-saturated region, the solution variables are changed from waterhead, water saturation, and organic concentration in the water phase to water head,water saturation, and total liquid saturation Choices of solution variables for otherphase conditions and criteria for switching solution variables are given by Sleep andSykes (1993) It has been demonstrated that the variable substitution methods withthe appropriate choice of solution variables can impact solution times for unsaturatedßow by an order of magnitude (Forsyth et al., 1995) For multiphase ßow andtransport problems, improvements in performance of factors of three to Þve wereobtained with optimal variable substitution (Forsyth et al., 1998)

4.2.4.4 Solution of Linear Equations

SigniÞcant advances in algorithms for solving large sets of sparse linear equationsgenerated by applying Þnite differences and Þnite elements were made in the 1980sand early 1990s Iterative methods are the most powerful of these algorithms andrely on incomplete factorization methods coupled with acceleration methods Incom-plete lower upper factorization using Gaussian elimination has been shown to be aneffective method and has been combined with orthomin acceleration (Behie andVinsome, 1982) and stabilized biconjugate gradients (van der Vorst, 1992) to producerobust solvers applicable to large systems

4.3 MODELING DNAPLS — STATE OF PRACTICE

The speed and memory capacity of computational resources has grown nally over the past 50 years and is likely to continue growing at a similar pace As

phenome-a result, computphenome-ationphenome-al tphenome-asks thphenome-at were onerous 10 yephenome-ars phenome-ago cphenome-an be performed withlittle effort today; tasks that were virtually impossible 20 years ago are within easygrasp today; and problems that are impractical today will become increasinglytractable, if not trivial, as the years pass Thus, the state of practice in modeling is

a very transient one, with great promise for advances in the years ahead

Of course, powerful computers do not guarantee efÞcient and accurate models.Advances in the fundamental understanding and ability to quantify physical, chem-ical, and biological processes and their interactions in the subsurface have been made

in recent years, although many issues remain poorly understood and difÞcult toquantify at the present time

In this section, the role that models play in research, policy, and engineering isreviewed The types of models and speciÞc computer codes available at this timeare discussed, as well as some of the limitations of present models

4.3.1 R OLES OF M ODELING

4.3.1.1 Research and Education

Soils and aquifers are very complex systems that involve interactions of numerousphysical, chemical, and biological processes Computer models are an important means

of cataloging our current understanding and expanding the limits of our understanding

As the number of variables and processes that are considered and the

sophisti-cation of their mathematical description increase, the ability to make “intuitive” a

priori projections of system behavior, even in the most qualitative manner, becomes

tenuous Models become the necessary roadmaps that allow calculation through thetortuous paths of interacting phenomena

Computer models are powerful research tools Beginning from a foundation ofwell-tested theories and methods, a tier is built one at a time, checking the soundness

of the structure during building and tearing down and rebuilding as necessary Thisapproach follows the classical mode of scientiÞc inquiry:

The foregoing process is incremental and iterative Often, apparent success

is achieved during initial model testing under a relatively limited range of

conditions, only to discover that the model deviates from observations undermore complex conditions.

For example, measurements of ßuid saturation–pressure relations can bedescribed accurately and consistently by monotonic functions for experiments inwhich an NAPL displaces water from core samples However, the same functionsfail to accurately describe NAPL displacement by water Laboratory measurements

on a wide variety of porous media have shown that mass transfer coefÞcients can

be estimated from correlations with grain size and pore velocity However, scale observations generally indicate that these correlations fail miserably Whensuch failures occur, researchers may pine for a world controlled by linear lawswith constant coefÞcients Nevertheless, such Þndings are valuable because theyrepresent the Þrst step toward developing an improved understanding of the pro-cesses that occur below the ground surface

Þeld-Some of the most pressing issues in subsurface modeling involve uncertainty

in the scaling up of constitutive relations from the laboratory scale, which isrelatively well understood, to the Þeld scale, which is less well quantiÞed Anotherresearch paradigm that has broad application for investigating this and other issues

is as follows:

• Model at Low Resolution

Develop a course-scale model of the phenomena of interest and ment it to predict large-scale behavior for deÞned conditions

imple-• Model at High Resolution

Perform “numerical experiments” with a Þne-scale distributed ter model to predict large-scale averaged phenomena under a range ofconditions

parame-• Modify Low-Resolution Model

Evaluate the accuracy of the large-scale model predictions Accept orreject the model, and modify or reÞne it as appropriate

This approach is predicated on an assumption that processes in the Þne-scalemodel and parameter distribution can be accurately represented and that there are

no additional processes at the large scale Validation of the Þne-scale model must

be predicated on the Model–Measure–Modify paradigm Advantages of the “LowModel–High Model–Modify” approach are as follows:

• A much wider range of conditions can be studied in a shorter periodbecause the approach does not rely on nature

• Much greater precision is possible than in Þeld studies where ment error and uncertainty in site characterization can obscure results

measure-• It is much less costly

Model sensitivity analyses are a valuable means of gaining insight into ena Numerical experiments allow researchers to study the effects of individualvariables that may be difÞcult or impossible to isolate with conventional experimentsand that would certainly be more time-consuming and costly without complications

phenom-attributed to measurement error Such studies often point to issues that warrant moredetailed study numerically or experimentally.

In addition to their utility as research tools, models serve as a valuable teachingtool by providing a hands-on, boots-off means of “observing” how complex systemsrespond to various external factors and system properties Especially when deployedwith interactive graphical pre- and postprocessors, the virtual reality laboratorybecomes a powerful learning environment

4.3.1.2 Policy Development

Regulatory policy development is another broad area in which subsurface modelsplay a key role Models provide a means of assessing the reasonableness of policies,developing design standards, evaluating emerging concepts and technologies, andestablishing cleanup criteria

Protocols for developing risk-based cleanup levels (RBCLs) rely heavily on

models RBCLs represent the maximum contaminant concentration at a

compli-ance point in a given media (e.g., soil, ground water) at a given location that will

result in a human health risk or ecological risk less than a speciÞed probability(e.g., fewer than one additional death per 1 million people) To make such anassessment, it is necessary to Þrst identify all potential exposure pathways (e.g.,ingestion or contact with contaminated ground water, breathing of air contaminated

by vapor migration through soil into buildings) Next, the magnitude of the

taminant concentrations at the potential exposure points (e.g., ground water

con-centration at a water supply well, vapor concon-centration in indoor air) are estimatedover a speciÞed potential exposure period (e.g., the average time individuals stay

in a residence), which is then used to compute the risk based on toxicologicalstudies For each potential exposure pathway, an estimate is made of the averageattenuation over the exposure period between the compliance point and the expo-sure point Models are critical for determining attenuation factors, which canincrease or decrease with time

Various approaches have been adopted for determining RBCLs At one end ofthe spectrum, site-speciÞc values can be determined by using relatively sophisti-cated models in conjunction with detailed site characterization data Regulatoryguidance may or may not exist for speciÞc modeling approaches or models Atthe opposite extreme, predetermined RBCLs may be speciÞed for certain ranges

in site conditions (e.g., depth to ground water, distance to water supply wells, soil

or aquifer type) based on results from generic model scenarios using conservativeparameter values Intermediate methodologies for determining site-speciÞc RBCLsinvolve the use of simpliÞed models with generic (i.e., conservative) parametersbased on limited site data

Regulations for land disposal are strongly linked to modeling for systems rangingfrom common landÞlls, which are designed on the basis of hydrologic controlmodels, to high-level radioactive waste disposal, which must consider the potentialfor transport over millennia Models also play an important role in new technologyevaluation and guideline development for assessing and implementing monitorednatural attenuation

4.3.1.3 Site Assessment and Remedial Design

Models serve a critically important role in site assessment and remedial designactivities During site assessment investigations, models facilitate meaningful inter-pretation of site characterization data to identify migration pathways and rates,estimate potential exposure, determine appropriate cleanup levels, and set projectpriorities Sensitivity analyses with preliminary site models at the early investigationstages allow data gaps to be identiÞed and characterization efforts to be optimized

to meet project needs with minimum cost

Remedial technology selection and design generally involve numerous steps.First, remedial technologies are screened for feasibility and appropriateness con-sidering site conditions (e.g., types and amounts of contamination and media,soil/aquifer properties) Following a preliminary screening, a more detailed assess-ment of the effectiveness and cost of feasible alternatives is performed SimpliÞedmodels can be used at this stage to estimate system requirements and operatingtimes for comparison If a Þnal remedy selection cannot be clearly identiÞed atthis point, sensitivity analyses can help identify critical data requirements to narrowthe decision and design pilot tests or establish other site characterization needs.Following model reÞnement using the additional data, the models can be used toextrapolate results from the pilot test to the full-scale system and select a Þnalremedy selection

Final system design (and, in some cases, Þnal remedy selection) involves lishing optimum values for a number of design parameters (e.g., number and loca-tions of wells, ßow rates) Models are uniquely suited for design optimization.Extrapolating pilot test results to full-scale operation is a nonlinear and frequentlynonintuitive problem Furthermore, only one full-scale system can be implemented;therefore, models provide the only possible means to evaluate the cost effectiveness

estab-of multiple full-scale options in a short period estab-of time and inexpensively

As an example, Table 4.2 presents a study of remedial options for a fuel spill(Parker et al., 1997) For each of the four remedial strategies, designs were developedbased on a simple direct interpretation of pilot test data or by optimizing designparameters based on model analyses results Estimated total costs for the variousmethods (i.e., capital plus discounted operating cost) illustrate the beneÞt of usingmodels for remedy selection and design

TABLE 4.2

Estimated Remediation Costs for Various Options and Design Protocols

Total Cost (Dollars in Thousands)

4.3.2 O VERVIEW OF E XISTING M ODELS

4.3.2.1 Three-Phase Models

Models capable of simulating transient ßow of three ßuid-phase soil and groundwater systems made their Þrst appearance in the mid-1980s (e.g., Faust, 1985).Facilitated by advances in basic understanding of multiphase ßow and transport andnumerical techniques (e.g., Abriola and Pinder, 1985; Parker, 1989; Mercer andCohen, 1990) and by advances in computer hardware, numerous multiphase numer-ical models were introduced in the 1990s (Table 4.3)

Multiphase ßow models are sophisticated numerical codes that incorporatehighly nonlinear three-phase relative permeability–ßuid saturation–capillary pres-sure (k–S–P) relations to simulate the transient ßow of water, air, and/or NAPL.Various formulations are employed to describe the k–S–P relations, with morerigorous models considering complexities due to nonwetting ßuid entrapment andhysteresis (Lenhard et al., 1989; Guarnaccia et al., 1997) In some models, airmobility is assumed to be sufÞciently great so that air pressure remains at atmo-spheric, allowing the air ßow equation to be eliminated (Richards’ assumption)

In addition to bulk ßuid ßow, many multiphase models simulate the transport

of one or more chemical species partitioning among vapor, aqueous, NAPL, andsolid (i.e., adsorbed) phases In the simplest models, local equilibrium phase parti-

TABLE 4.3

Overview of Available Three-Phase Flow and Transport Models

FEHM 3-D three-phase ßow; multispecies transport; heat

transport; dual porosity

Zyvoloski et al., 1995; Dash et al., 1997 MAGNUS 3-D three-phase ßow; single species transport Huyakorn et al., 1994 MOFAT 2-D three-phase ßow; multispecies transport Katyal et al., 1991 MUFTE 3-D three-phase ßow; single species transport Helmig et al., 1994 NAPL 3-D three-phase ßow; single species transport;

nonequilibrium interphase mass transfer coefÞcients as functions of NAPL saturation

Guarnaccia et al., 1997

NUFT 3-D three-phase ßow; multispecies transport; heat

transport; dual porosity; steam injection

Nitao, 1996 STOMP 3-D three-phase ßow; multispecies transport; dual

porosity; heat transport

Lenhard et al., 1995; White and Oostrom, 1996 COMPFLOW 3-D three-phase ßow; multispecies transport; dual

porosity; discrete fractures

Unger et al., 1995 COMPSIM 3-D three-phase ßow; multispecies transport; dual

porosity; biodegradation; heat transport

Sleep and Sykes, 1993; Sehayek et al., 1999; Sleep et al., 2000 UTCHEM 3-D three-phase ßow; multispecies transport;

nonequilibrium interphase mass transfer; various reaction models; surfactant effects

Pope et al., 1999

tioning is assumed More sophisticated models consider nonequilibrium exchangedescribed by Þrst-order mass transfer functions Mass transfer coefÞcients in suchmodels are commonly user-speciÞed, but in some cases can be computed internally

as functions of ßuid saturations and velocities and other factors These functions arenot well understood at the Þeld scale at the present time Some models considernonequilibrium mass transfer between “mobile” pore regions (e.g., fractures or othermacropores) and “immobile” pore regions, which is usually described by a Þrst-order mass transfer function SpeciÞcation of three-phase k–S–P relations that areaccurate and consistent with multiregion transport models is a problematic issue atthis time

Reported models range from those that simulate only one species subject tolinear partitioning and Þrst-order decay to those that model multiple species subject

to a variety of equilibrium or kinetically controlled reactions Of particular cance for chlorinated solvents are models that consider the production and decay of

signiÞ-a series of dsigniÞ-aughter products of the originsigniÞ-al contsigniÞ-aminsigniÞ-ant (i.e., chsigniÞ-ain decsigniÞ-ay) A fewmodels account for relationships between phase concentrations of chemicals (indi-vidually or in total) and bulk ßuid properties (e.g., density, viscosity, surface andinterfacial tensions), other chemical properties (e.g., cosolvent effects on solubility),and/or k–S–P relations (e.g., residual NAPL saturations) The resulting coupling ofthe ßow model to the transport model increases the nonlinearity of the numericalproblem but can be critical to predict certain behavior, such as the effects of surfactantinjection on remediation

Several models have been developed and simulate heat transport to enablethe assessment of thermal-assisted remediation technologies (e.g., steam injec-tion) or radioactive waste burial In addition to solving a heat transport equationand ßow and chemical transport equations, further nonlinearity is induced due

to the temperature-dependence of equilibrium-phase partitioning relations andbulk ßuid properties

4.3.2.2 Two-Phase Models

For many problems of practical importance, NAPLs exist in the vadose zone at aresidual saturation that is essentially immobile under ambient Þeld conditions Insuch cases, two-phase air–water models may be appropriate tools to assess volatilechemical emissions or evaluate remediation involving vapor extraction, soil heating,

or steam injection (Table 4.4) The simplest models of this class simulate unsaturatedwater ßow based on Richard’s assumption (i.e., gas phase at constant pressure),which eliminates the need to solve an airßow equation Depending on the numericalformulation used to solve the water-ßow equation, the solution can be limited tosimulations of vadose zone problems in which the domain remains unsaturated (i.e.,unsaturated ßow models), or the solution can allow simulation of fully saturatedmedia as a special case (i.e., variably saturated models)

In contrast to the Richard’s unsaturated ßow formulation, true two-phase ßowmodels simulate gas-phase ßow explicitly For example, a dynamic gas phase mustclearly be considered in certain circumstances to model soil vapor extraction or steaminjection or to assess the effects of natural air pressure ßuctuations on vapor transport

Transport analyses in air–water models range from single species formulationswith simple linear adsorption and Þrst-order decay to multispecies formulations withcomplex kinetically controlled biological and geochemical species transformations.Some models consider nonequilibrium, interphase mass transfer; diffusion-limited,matrix-fracture mass transfer; or heat transport By deÞnition, unsaturated ßow modelscannot consider gas-phase advection, although they can consider vapor-phase diffusionwithout adding signiÞcantly to the computational burden True two-phase ßow modelsmust be used to predict advective transport in both vapor and aqueous phases.Some air–water models consider an immobile NAPL phase with phase parti-tioning that can be modeled as equilibrium controlled or as a Þrst-order mass transferprocess However, because the quantity and distribution of NAPL is rarely knownwith any degree of certainty, NAPL is often not explicitly modeled In the lattercase, NAPL dissolution and volatilization are handled as boundary conditions byeither specifying species concentrations in dissolved and/or vapor phases or rates ofdissolution or volatilization within a source area (i.e., region with residual NAPL).

4.3.2.3 Single-Phase Models

The most common use of models to date for assessing chlorinated solvent transporthas focused on analyzing ground water transport under natural and engineeredconditions Because DNAPL in aquifers is expected to occur primarily at residualsaturations that are immobile under ambient conditions and because the quantityand distribution of DNAPL is usually unknown, most ground water solvent transportmodels do not consider DNAPL explicitly As with unsaturated zone models, most

TABLE 4.4

Overview of Unsaturated Flow and True Two-Phase Flow and Transport Models

CHAIN_2D 2-D unsaturated ßow and multispecies transport; chain

decay

Simunek and van Genuchten, 1994 HBGC123D +

FEMWATER

3-D variably saturated ßow; multispecies transport; heat transport; bio- and geochemical reactions; dual porosity

Yeh et al., 1998 3DMURF

+3DMURT

3-D unsaturated ßow and single species transport; dual porosity

Gwo et al., 1994, 1995 R-UNSAT 1-D vertical or 2-D radial unsaturated ßow; multispecies

dissolved transport with vapor diffusion; NAPL source model; chain decay

Lahvis and Baehr, 1997

SUTRA 2-D variably saturated ßow, single species transport Voss, 1984

TOUGH2

+T2VOC

3-D two-phase ßow; multispecies transport; chain decay;

heat transport; dual porosity; steam injection

Pruess, 1991;

Pruess et al., 1999 VLEACH 1-D unsaturated ßow; single species transport with vapor

diffusion

Turin, 1990 VS2DI 2-D variably saturated ßow, single species transport or

heat transport

Lappala et al., 1987; Healy and Ronan, 1996

ground water transport models treat NAPL dissolution implicitly by specifying thedissolved species concentration or dissolution rate at the source area Availablemodels that have been utilized for simulating dissolved-phase chlorinated hydrocar-bon transport in ground water are summarized in Table 4.5 It should be noted thatmodels designated as variably saturated ßow codes in Table 4.4 can be used to modelsaturated ßow with computational efÞciency comparable with single-phase groundwater models Furthermore, some two- and three-phase ßow models allow specialcases in which the solution of speciÞed phases is eliminated to reduce the compu-tational burden of the rigorous solution.

Single-phase gas ßow models have also been developed that are appropriatefor modeling forced air remediation in which temporal variations in water satu-rations can be reasonably disregarded Numerically, single-phase air ßow modelsare very similar (or in some cases identical) to single-phase ground water ßowmodels (e.g., the air ßow model AIR3D is actually a modiÞcation of the groundwater ßow model MODFLOW)

Similar variations in single-phase transport model formulations (e.g., number ofspecies modeled, types of reactions, equilibrium- vs nonequilibrium-phase transfer)occur as those found in two- and three-phase models SimpliÞed solutions have alsobeen developed for use as preliminary assessment tools (e.g., the BIOCHLOR model)for screening-level analyses

4.3.2.4 Chlorinated Solvent Biodegradation Models

Most chlorinated solvents are biodegraded under a variety of terminal electronaccepting processes and can serve as electron donors under anaerobic conditions

TABLE 4.5

Overview of Single-Phase Flow and Transport Models

AIR3D 3-D transient air ßow model (could be coupled

with MT3D or RT3D to model vapor transport)

Joss and Baehr, 1995 BIOCHLOR 1-D steady-state uniform ground water ßow with

3-D multispecies transport; chain decay with option for two zones of decay coefÞcients

Aziz et al., 2000

HST3D 3-D ground water ßow, single-species transport;

heat transport

Kipp, 1986, 1997 MOCDENSE +

MODFLOW

2-D ground water ßow; transport for two species;

ßuid properties as linear function of Þrst species

Sanford and Konikow, 1985

3-D ground water ßow; multispecies transport;

chain decay; rate-limited sorption; Monod kinetics; electron receptor limited decay; user- deÞnable reaction models

Clement, 1997

In addition, chlorinated solvent biodegradation often produces transformation ucts that are of as much environmental concern as the parent compounds At present,BIOCHLOR and RT3D are the only two publicly available models that are com-monly used for modeling chlorinated solvent biodegradation (Table 4.5).

prod-Both BIOCHLOR and RT3D model the chain decay of contaminants, butRT3D allows the use of multiple electron acceptors and Monod kinetics Microbialgrowth is not modeled in either model, so kinetic rate constants used are lumpedparameters that implicitly include microbial population Thus, the models arelimited to sites at which the microbial population is relatively stable In addition,because microbial activity and population can vary signiÞcantly from site to site,kinetic constants must be determined from site-speciÞc contaminant concentrationdata The DECHLOR model of Shoemaker et al (2001) includes microbial growthand the production and consumption of hydrogen, with thermodynamic limits onhydrogen production This model is more comprehensive than RT3D and BIO-CHLOR but has had limited Þeld application

4.3.3 M ODEL S ELECTION AND L IMITATIONS

Selecting the most suitable model for a given problem is an exercise in compromisethat requires careful consideration of the objectives of the analysis and the costs,beneÞts, and drawbacks of various modeling approaches On initial consideration,

it may appear self-evident that the most rigorous model will always be the “best”model However, all models are, by deÞnition, simpliÞcations of reality that can bepeeled away to Þnd yet another layer of complexity beneath From a practicalstandpoint, the best model is the one that can answer the question posed to it withacceptable accuracy for the least cost Because accuracy and cost are often inverselyrelated, model selection imposes tradeoffs

In principle, more rigorous models are capable of making predictions withgreater accuracy, i.e., answering the questions posed with less uncertainty Theproblem when selecting a model is to determine to which processes and parametersthe answers are sensitive and to which they are not In some cases, this is self-evident (e.g., no need to model gas advection to evaluate a ground water pump-and-treat system), while in other cases it is not intuitively obvious (e.g., the need

to model seasonal temperature ßuctuations to design a soil vapor extraction system

in Michigan) These nonintuitive issues can be resolved by performing sensitivityanalyses with relatively simple models In some cases, the only way to answerthe question is to make comparisons between the simpler and more complexmodels for prototype problems to assess sensitivity vis à vis the problem underconsideration For example, if the problem is to optimize a remediation systemdesign, the concern is the sensitivity of the design decision to model results, whichmay not relate to primary model output (e.g., ßuxes, concentrations, cleanup goaltime) in a linear manner

Although more complex and rigorous models theoretically are capable of greateraccuracy, in practice, complex nonlinear models become increasingly subject tonumerical errors in their solutions These errors can be reduced by the Þnesse ofimproved numerical solution techniques, or, up to a point, by brute strength of

computer power through Þner spatial and temporal discretization Numerical errorcan be difÞcult to detect in complex models that can (correctly) respond in waysthat are intuitive Avoiding or at least minimizing numerical error in complex modelsgenerally requires signiÞcant skill and experience by the user In addition to requiringmore experienced personnel to operate, complex models require more effort to set

up and run, more computer resources to execute, and more supporting effort to obtainrequired input data This all translates to additional cost, which must be balancedagainst the potential beneÞts of more complex models

Improvements in the robustness and efÞciency of numerical methods andcomputer performance will gradually reduce the effort and cost of using morecomplex models Developing increasingly sophisticated pre- and postprocessingsoftware will also make complex models easier and faster to operate by personnelwith less experience

In addition to the foregoing computational issues, signiÞcant knowledge gapsremain in the basic understanding of Þeld-scale subsurface processes The knowl-edge of transport processes at the laboratory scale is generally good However,substantial uncertainty exists regarding the mathematical representation of pro-cesses at the Þeld scale With currently available computer resources and Þeldcharacterization technology, it is impractical to model Þeld heterogeneity at a Þneresolution However, attempts to scale up by averaging small-scale parameters orfunctions often lead to apparent phenomena at the larger scale A well-knownexample of an apparent process due to scaleup is hydrodynamic dispersion.Another well-known problem (especially in petroleum reservoir modeling) is thescaleup of k–S–P relations This scaleup is a particularly difÞcult problem whendealing with DNAPLs in ground water due to complications associated withunstable ßow in heterogeneous media Whether this issue can be resolved sufÞ-ciently to enable quantitative prediction of DNAPL movement for practical cases

is not clear at this time

Another important scaleup issue involves the quantiÞcation of Þeld-scale masstransfer kinetics This is a basic problem that spans the range in models fromsimple single-phase dissolved models to the most complex three-phase models Aconsiderable volume of research exists regarding the quantiÞcation of mass trans-port at the laboratory scale for a wide range of porous and other systems (e.g.,Cussler, 1984; Miller et al., 1990) However, it is likely that heterogeneity inporous media properties and phase distributions (i.e., spatial distributions of NAPLsaturations and their interfacial areas with other phases) will induce apparentprocesses at the Þeld scale that are not observed in the laboratory (e.g., Guarnaccia

Using the last quarter of the 20th century as a gauge, great advances in thecapability of subsurface computer models are expected to solve important environ-mental problems in the 21st century

4.4 SITE APPLICATIONS

The practical research objective of organic simulation in the subsurface is to providetools for solving environmental problems at the Þeld scale To illustrate how modelsand theory have been used in practice, two example applications are summarizedbelow The two approaches were radically different: one used a compositionalsimulator and the other a ground water ßow model and empirical relationships Bothapproaches led to evaluations that permitted the companies involved and the regu-lating agencies to make informed decisions regarding remediation at the two sites.Likewise, each of these applications shows that complex mathematical models arelimited by the availability of data at the Þeld scale

4.4.1 G ULF C OAST EDC DNAPL R ELEASE

In 1994, approximately 15,000 gal of DNAPL were released from a pipeline to anearby drainage ditch on a site located in the U.S Gulf Coast The DNAPL wascomposed of 1,2-dichloroethane (EDC) Emergency actions were taken to remediatethe ditch area and impacted sediments; however, EDC DNAPL remained in shallowwater-bearing units in the vicinity of the ditch To address long-term concern related

to the DNAPL and dissolved-phase EDC, detailed site investigations and modelingwere performed to achieve the following:

• ConÞrm conceptualization of the hydrologic system

• Simulate ßow in water-bearing zones

• Provide input for conceptual containment system design

• Evaluate the potential for EDC DNAPL to reach the regional aquifer

• Provide worst-case scenario input for modeling dissolved-phase EDCtransport in the regional aquifer

• Estimate exposure concentrations

A combination of models was applied to focus on different issues and scales of interest

A 3-D ground water ßow model was developed to simulate ßow over a wideareal extent and in multiple hydrostratigraphic units The ßow model provided theframework for a two-dimensional (2-D) (i.e., cross section) compositional model ofthe EDC DNAPL transport Results of the DNAPL simulations were used as a basisfor source conditions to assess dissolved EDC transport in the regional aquifer.The modeling approach used information and concepts from Þeld investigationsand observations conducted concurrently with and after emergency actions Theseinvestigations characterized the hydrogeologic conditions as well as the nature, fate,and extent of EDC in the subsurface From the ground surface down, the stratigraphicunits at the site consisted of a 40-ft sand; upper interbedded clays, sands, organic silts,peat; interbedded sands, silts, and clays; a gumbo clay; sandy clay; and the Upper Chicot(a sandy aquifer) Early Þndings of the Þeld investigations concluded the following:

• Immobile DNAPL was present in the organic/silt peat and inorganic clay

• Mobile DNAPL was present in the 40-ft sand only