Modeling Biogeochemical Processes in Leachate-Contaminated ...€¦ · MODELING BIOGEOCHEMICAL PROCESSES 409 Table I. Sequence of different redox reaction downgradient of a landﬁll

Transport in Porous Media 43: 407–440, 2001.© 2001 Kluwer Academic Publishers. Printed in the Netherlands.

407

Modeling Biogeochemical Processes inLeachate-Contaminated Soils: A Review

JAHANGIR ISLAM1, NARESH SINGHAL1� and MICHAEL O’SULLIVAN2

1Department of Civil and Resource Engineering, University of Auckland, Private Bag 92019,Auckland, New Zealand2Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland,New Zealand

(Received: 4 June 1999; in final form: 21 February 2000)

Abstract. During subsurface transport, reactive solutes are subject to a variety of hydrological, phys-ical and biochemical processes. The major hydrological and physical processes include advection,diffusion and hydrodynamic dispersion, and key biochemical processes are aqueous complexation,precipitation/ dissolution, adsorption/desorption, microbial reactions, and redox transformations. Theaddition of strongly reduced landfill leachate to an aquifer may lead to the development of differentredox environments depending on factors such as the redox capacities and reactivities of the reducedand oxidised compounds in the leachate and the aquifer. The prevailing redox environment is keyto understanding the fate of pollutants in the aquifer. The local hydrogeologic conditions such ashydraulic conductivity, ion exchange capacity, and buffering capacity of the soil are also important inassessing the potential for groundwater pollution. Attenuating processes such as bacterial growth andmetal precipitation, which alter soil characteristics, must be considered to correctly assess environ-mental impact. A multicomponent reactive solute transport model coupled to kinetic biodegradationand precipitation/dissolution model, and geochemical equilibrium model can be used to assess theimpact of contaminants leaking from landfills on groundwater quality. The fluid flow model canalso be coupled to the transport model to simulate the clogging of soils using a relationship betweenpermeability and change in soil porosity. This paper discusses the different biogeochemical processesoccurring in leachate-contaminated soils and the modeling of the transport and fate of organic andinorganic contaminants under such conditions.

Key words: modeling, biodegradation, precipitation, groundwater, redox zones, leachate, clogging.

1. Introduction

Sanitary landfills have been, and continue to be the most economical method forsolid waste disposal. Leakage of inorganic and organic pollutants from landfillsover time can influence the groundwater quality. Contamination of groundwater bylandfill leachate represents the major environmental concern associated with thelandfilling of waste. Mathematical models can serve as important tools to evaluatethe effects of infiltrating leachate and assess remedial options. In order to estimatethe environmental risk and develop strategies for groundwater protection against

� Author for correspondence: e-mail: [email protected]

408 JAHANGIR ISLAM ET AL.

contamination by landfills, an understanding of chemical transport and behaviourof pollutants in soil-groundwater system is required.

Numerous mathematical models have been developed to simulate the migrationof pollutants in soils; however, most models simulate either geochemical processesor biological transformations in soils. Relatively few models include the interactionbetween biodegradation and inorganic geochemical reactions in soils. The transportof landfill leachate in soils is controlled by complex interactions between the vari-ous physical, chemical and biological processes. A simulation model that couplesthe biogeochemical processes to the physical transport processes, under realisticboundary conditions, can be the key to understanding the movement of leachateand effectively managing the problem.

2. Basic Biogeochemical Processes in Soils

The movement of moisture through solid wastes buried in the soil at landfill sitesresults in the production of leachate. The concentrations of different constituentsof this leachate vary according to the age, composition of the waste material andthe degree of solid waste stabilisation (Chian and DeWalle, 1976). The migrationof landfill leachate is affected by the initial biochemical processes that generateleachate, and physical and chemical attenuation.

2.1. MIGRATION OF LANDFILL LEACHATE

Once leachate migrates outside the confines of the landfill, its physicochemicaland biochemical character will be altered. The most active physicochemical pro-cesses are likely to be dilution, adsorption, exchange reactions, and precipitation,with filtration for particulate matter (Bagchi, 1987; Christensen et al., 1994). Thebiochemical processes involve microbial degradation, either aerobic or anaerobic,with the latter expected to be most active, since the major part of the degradationtakes place under strictly anaerobic conditions (Lyngkilde and Christensen, 1992a).Different factors such as leachate flow rate (Alesii et al., 1980), dissolved organiccarbon (Boyle and Fuller, 1987; Christensen et al., 1996), and buffer capacity ofsoils (Yanfull et al., 1988) have considerable effects on the migration of metals inleachate contaminated soils.

Depending on the composition of the leachate, a sequence of redox zones of in-creasing redox potential may develop downgradient of a landfill; zones of methaneproduction, sulfate reduction, ferric reduction, manganic reduction, nitrate reduc-tion, and oxygen reduction will develop if the corresponding electron acceptorsare present in the aquifer (Baedecker and Back, 1979; Lyngkilde and Christensen,1992b). Table I shows the sequence of different redox reactions downgradient of alandfill. The redox zones can overlap (Wang and Van Cappellen, 1996; Baedeckerand Back, 1979; Christensen et al., 1994) and simultaneous methane production,

MODELING BIOGEOCHEMICAL PROCESSES 409

Table I. Sequence of different redox reaction downgradient of a landfill (Christensen et al.,1994)

Reactants converted to products �G0 (kcal/mol)

(pH = 7)

Methanogenic processes

2CH2O → CH3COOH CH4 + CO2 −22

4H2 + CO2 CH4 + 2H2O

Sulphate reduction

2CH2O + SO2−4 + H+ 2CO2 + HS− + 2H2O −25

Iron (ferric) reduction

CH2O + 4Fe(OH)3 + 8H+ CO2 + 4Fe2+ + 11H2O −28

Manganese (manganic) reduction

CH2O + 2MnO2 + 4H+ CO2 + 2Mn2+ + 3H2O −81

Denitrification

5CH2O + 4NO−3 + 4H+ 5CO2 + 7H2O + 2N2 −114

Aerobic respiration, oxygen reduction

CH2O + O2 CO2 + H2O −120

sulfate reduction and iron reduction has been observed in leachate plume (Bjerget al., 1995; Ludvigsen et al., 1998).

The significance of sulfate-, iron-, manganese-, and nitrate-reducing zonesdepends on local conditions. Where the amounts of iron and manganese on the sed-iment are negligible (low oxidation capacity), large horizontal zones of methano-genesis and sulfate reduction will develop (Christensen et al., 1994). High amountsof iron and manganese, as expected in reddish, oxic aquifers (high oxidation capa-city) will strongly diminish the methanogenic and sulfate-reducing zones. Mostspecific organic compounds are degraded in the anaerobic plume under metha-nogenic/sulfate-reducing or iron-reducing conditions (Lyngkilde and Christensen,1992a; Rügge et al., 1995). The sequence of redox processes strongly affects themigration of pollutants leaching from landfill and is the main key to understandingthe fate of reactive pollutants in the plume (Lyngkilde and Christensen, 1992b;Bjerg et al., 1995).

The reactions involved in pH and redox buffering processes are important incontrolling the concentrations of many major and minor chemical species in landfillleachate contaminated plume. The important pH controlling reactions in leachateare (Baedecker and Back, 1979) degradation of organic material producing CO2

and smaller amounts of NH3, which form the HCO−3 , H+ and NH4

+ ions; reductionof CO2 to CH4; and reduction of SO4

2− to H2S and additional CO2.The intro-


duction of organic matter, methane, ammonium, hydrogen sulfide, and dissolvediron into an aerobic aquifer leads to redox buffering reactions. If the aquifer con-tains carbonate minerals, it dissolves upon introduction of acid phase leachate andbuffers the pH near neutral background levels (Kehew and Passero, 1990). Thesebuffering reactions result in increased dissolved alkalinity, calcium, and magnesium,thereby increasing the saturation indices of carbonate minerals in groundwater.

2.2. EFFECT OF BIOGEOCHEMICAL PROCESSES IN SOILS

Laboratory and field studies suggest that hydraulic conductivity of the soil underthe landfill decreases with time primarily due to heavy metal precipitation and plug-ging of soil voids as a result of microbial growth (Griffin et al., 1976; Cartwrightet al., 1977; Quigley et al., 1987; Yanful et al., 1988; Brune et al., 1994; Roweet al., 1997a; Kjeldsen et al., 1998). Bacterial degradation of volatile organic acids,primarily acetic acid to CO2 accelerate the precipitation of CaCO3, the major in-organic component of ‘clog slimes’ in leachate-drainage systems (Rittmann et al.,1996). These reactions consume acidic hydrogen, causing an increase in the pH andthe total carbonates in the leachate thereby accelerating the precipitation of CaCO3.Some unlined landfills in New Zealand appear to have undergone ‘plugging’, andhave shown significant reduction in leakage of pollutants over time (Nelson, 1995).

The clogging material consists of a network of aggregates of bacteria with de-posits of inorganic material on their surfaces (Brune et al., 1994). Microscopicexamination shows that precipitation occurred only on the bacterial cells and theslime fibrils, never on the uncolonised space in-between. Chemical analysis ofthe incrustation material shows that its inorganic components consist of calcium,iron, and manganese combined with carbonate and sulfur. The precipitation andclogging of drainage material in landfills appears to be caused by two processes:bioreduction of sulfate in the vicinity of the sulfate-reducing bacteria resulting insulfur precipitating as insoluble metal sulfide, and precipitation of calcium carbon-ate onto the surface of the methane-producing and sulfate-reducing bacteria (Bruneet al., 1994).

3. Modeling Methodology

Once the landfill leachate released into the subsurface, contaminants will interacthydrologically, physically, and biochemically with both the groundwater and thesoil matrix. A complete transport model must therefore account for multispeciesphysical and biochemical transport processes. The transport processes can be de-scribed by means of a mass balance equation for each species of interest, whichbecomes a partial differential equation for transient problem and an ordinary dif-ferential equation for a steady state problem. According to Yeh and Tripathi (1989),the important steps in developing a contaminant transport with chemical reactionsare to first select the variables for the transport equations which are dependent


on chemical reactions and then select the solution algorithm for the transport andchemical reaction equations.

3.1. FLUID FLOW MODEL

The governing equation for flow in saturated and unsaturated anisotropic porousmedia can be written as (Freeze and Cherry, 1979)

Ss∂h

∂t= ∂

∂xi

(Kij

∂h

∂xj

)(saturated flow) (1)

C(ψ)∂ψ

∂t= ∂

∂xi

(Kij (ψ)

∂ψ

∂xj

)+ ∂

∂x3(Ki3(ψ)) (unsaturated flow) (2)

where t is time (T), xi are Cartesian coordinates (L), h is the hydraulic head (L),ψ is the pressure head (L), Kij is the hydraulic conductivity tensor (L/T), Ss is thecoefficient of specific storativity (1/L), and C(ψ) is the specific moisture capacity= dθ /dψ , where θ is the moisture content .

3.1.1. Numerical Solution of Fluid Flow Model

The distribution of head and velocity field can be computed explicitly for verysimple flow system, for complex flow system a numerical technique has to beused to solve the flow equation. For one dimensional steady state flow systems,velocity profiles can be simply calculated from Darcy’s equation. If the changes insolute concentration do not affect the flow field, the flow and transport equationsare uncoupled and a simultaneous solution is not required. But if the hydraulicconductivity of the media is changed due to chemical and biological process dur-ing contaminant transport, it is necessary to iterate between the fluid flow modeland the contaminant transport model. The fluid flow equation is coupled withthe contaminant transport equation through Darcy’s equation, flow velocity in theadvective term and the dependence of dispersion on flow velocity in the dispers-ive term. The main numerical approaches used are the finite difference method(Konikow and Bredehoeft, 1974), the integrated finite difference method (Narasim-han and Witherspoon, 1976), and the finite element method (Gray and Hoffman,1983a). Different numerical solutions for saturated flow is describe by Huyakornand Pinder (1983). Rowe et al. (1995) described different numerical methods withrespect to landfill hydrology.

3.2. CONTAMINANT TRANSPORT MODEL

The general form of contaminant transport equation for the mobile components inthe aqueous phase is (Bear, 1979)

∂

∂t(θC)− ∂

∂xi

(θDij

∂C

∂xj

)+ ∂

∂xi(θνiC) = θR, (3)


where

νi = qi

θ= −Kij

θ

∂h

∂xi(4)

and νi is average pore fluid velocity (L/T), qi is Darcy velocity (L/T),Dij is the hy-drodynamic dispersion tensor (L2/T), θ is the moisture content (dimensionless) andR is the chemical source/sink term (M/L3/T) representing the changes in aqueouscomponent concentrations. The hydrodynamic dispersion is the sum of mechanicaldispersion and molecular diffusion. Mechanical dispersion is expressed as αiνi ,where αi is the dispersivity in the i direction (L).

3.2.1. Numerical Solution of Contaminant Transport Model

The contaminant transport model can be solved by either analytical or numericalmethods. Analytical solutions of advection–dispersion equations for one, two, andthree dimensional flow field under different boundary conditions can be found invan Genuchten and Alves (1982), Huyakorn et al. (1987), and Fetter (1993). Themain numerical methods used for solution of contaminant transport model are thefinite difference method (Kinzelbach et al., 1991; Engesgaard and Kip, 1992), theintegral finite difference method (Narasimhan et al., 1986; Steefel and Lasaga,1994), and the finite element method (Rubin and James, 1973; Yeh and Tripathi,1991). For reactive transport modeling, an upwind or upstream scheme is oftenused to avoid spurious oscillations in the vicinity of the front, which may providenegative concentration values (Kinzelbach et al., 1991; Engesgaard and Kip, 1992).

To avoid the above oscillations large numbers of alternating numerical schemehave been proposed. Daus and Frind (1985), Frind and Germain (1986), and Frindand Hokkanen (1987) used alternating direction Galerkin technique for high de-gree of spatial resolution. Cheng et al. (1984), Molz et al. (1986), and Clementet al. (1996a) used a two-stage Eulerian–Lagrangian approach which is devoid ofoscillations or numerical dispersion for larger Peclet numbers (Widdowson et al.,1988). Huyakorn et al. (1993) and Kool et al. (1994) used a Laplace-Transform-Galerkin technique developed by Sudicky (1989) that is limited to linear adsorptionand steady flow fields. Rowe and Booker (1985a,b, 1986) have proposed a finitelayer technique using a Laplace and a Fourier transform of the governing equationsfor modeling contaminant transport for 1D, 2D or 3D conditions. These techniquesare however limited to simple geometry and flow pattern of uniform properties.

3.3. EQUILIBRIUM REACTION MODEL

Two different approaches (kinetic and equilibrium based) are used to model thedistribution of chemical species. For a chemical system at equilibrium, the ionassociation equilibrium-constant approach or Gibbs free energy approach is usedto represent the geochemical equilibrium reactions (Stumm and Morgan, 1996).Gibbs free energy approach is based on the direct minimisation of the total Gibbs


free energy of a given set of species subject to constraints of mass balance equa-tions. The equilibrium approach is based on the solution of a set of nonlinearalgebraic equations obtained from the mass action and mass balance equationsfor the various components of the systems (Morel and Morgan, 1972, 1980; Reed,1982). The nonlinear algebraic equations are solved by approximation methods togive species distributions at equilibrium. In this approach equilibrium constants areneeded, whereas in the former approach free energy values are needed.

The concept of components and species as proposed by Westall et al. (1979) hasbeen used to model systems with different chemical reactions. Components are aset of linearly independent chemical entities such that every species can be writtenas the product of a reaction involving only the components, and no component canbe written in terms of components other than itself. For a given system, the setof components is not unique, but once it has been defined, the representation ofspecies in terms of this set of components is unique. The number of componentsis selected such that it is the minimum number of the set of species necessary todescribe the composition of all phases and species in the chemical system (Reed,1982). Rubin (1983) introduced the concept of tenads in chemical reactions, areacting or nonreacting chemical entity whose global mass in the system is reactionindependent or reaction invariant.

The chemical equilibrium reaction system is described by a set of nonlinear al-gebraic equations based on equilibrium constants embedded in mass balance equa-tions for the various components of the system. The concentrations of aqueous,adsorbed and precipitated species are calculated from the mass action laws. Aprecipitate is formed only when the solution is supersaturated with respect to thecomponents for that precipitate. Dissolution occurs when the solution is undersat-urated. If a species is precipitated in the solution, the solubility product equationis added to the system of equations to solve the unknown precipitated species.Similarly, when a precipitated species is completely dissolved in the solution, thesolubility product equation is removed from the system of equations.

Most chemical reaction models include a component or a master variable ora tenad and a mass balance equation for each element other than H and O. Thisleaves three equations which are referred to as mass balance on H2, mass balanceon O2 and charge balance. The choice of these three remaining equations for thecomponents or master variables that are associated with them distinguish the vari-ous aqueous chemical reaction models (Plummer et al., 1983). Nordstorm et al.(1979), Sposito (1984), Mangold and Tsang (1991), and Mattigod and Zachara(1996) reviewed and compared a number of computerised geochemical modelsfor equilibrium calculations in aqueous systems. The hydrogen ion concentrationis calculated by using either the requirement of electroneutrality (PHREEQE byParkhaurst et al., 1980; Walsh et al., 1984) or proton condition (MINTEQA2 byAllison et al., 1991; Yeh and Tripathi, 1991). In coupling the hydrological transportand chemical equilibrium, it is preferable to use the proton condition approach (Yehand Tripathi, 1989). Redox reactions are considered mathematically equivalent to


complexation reactions for equilibrium computations when the electrons are incor-porated as components in the chemical reactions. The mass conservation of oxygenis replaced by conservation of electrons. Dissolved oxygen can be treated simplyas a complexed species as follows:

O2 ⇔ 2H2O − 4H+ − 4e−. (5)

The three basic mathematical forms of adsorption reaction models, namely, iso-therm, ion exchange, and surface complexation/electrostatic models have been in-corporated in many computerised chemical reaction models (Mangold and Tsang,1991). The empirical distribution coefficient Kd approach has yielded limited suc-cess in subsurface modeling because Kd values can vary throughout the simulationas geochemical conditions change in time during solute transport (Reardon, 1981;Miller and Benson, 1983; Yeh and Tripathi, 1991; Davis et al., 1998). Weber et al.(1991) classified isotherm models as phenomenological models and ion exchange,surface complexation and hydrophobic sorption models as mechanistic models.The phenomenological models may describe sorption behaviour for a specific setof conditions but may fail to do so when the system conditions change. Mechan-istic models can provide insights into mechanisms controlling sorption reactions,and thus aid in the analysis of anticipated system responses to changes in criticalconditions.

General reviews on different adsorption models are available in the literature(Sposito, 1984; Weber et al., 1991; Goldberg, 1995). Davis and Kent (1990) andDavis et al. (1998) gave a detailed discussion on the adsorption of metals andmetal-ligand complexation on soils. Wen et al. (1998) described three commonsurface complexation models (constant capacitance model, diffuse layer model,and triple layer model) for heavy metal adsorption on natural sediments and foundthat all three models described the adsorption behaviour of the natural sedimentwell. Fein et al. (1997) and Warren and Ferris (1998) described chemical equi-librium model for the adsorption and precipitation of metals on bacterial surfacesusing surface complexation and surface precipitation theory.

3.3.1. Numerical Solution of Equilibrium Model

Typically, the nonlinear algebraic equations are solved using the Newton–Raphsonmethod (PHREEQE by Parkhurst et al., 1980; GEOCHEM by Sposito and Mat-tigod, 1980; MINTEQA2 by Allison et al., 1991). Yeh and Tripathi (1991) pro-posed a split scheme that is very effective in the case of redox reactions where theNewton–Raphson solution often fails to converge. In this split scheme, the molebalance equation for the operational electron is solved for the electron activitywith a modified bisection method (Forsythe et al., 1977) while all other molebalance equations are solved simultaneously with the Newton–Raphson method.Zyssset et al. (1994a) used a Newton–Raphson iteration to determine the primaryunknowns (activities of the components and the concentrations of the precipitated


species) and a Picard iteration for the secondary unknowns (activity coefficientsand the concentrations of all other species).

3.4. KINETIC REACTION MODEL

If the reactions are insufficiently fast due to chemical kinetics and/or mass diffu-sional processes relative to the macroscopic transport processes affecting soluteconcentration (e.g., advection, hydrodynamic dispersion), the local equilibrium as-sumptions (LEA) can not be made. Valocchi (1985) and Skopp (1986) reviewed anumber of studies in which solute transport predicted using LEA models were un-successful. James and Rubin (1979) carried out a series of soil column experimentsand concluded that LEA can not be applicable when the dispersion coefficient issignificantly larger than the diffusion coefficient. In such cases kinetic reactionmodels must be used.

3.4.1. Kinetic Adsorption Model

In case of first-order reversible sorption reaction, the rate of reaction for the sorbedcomponent S may be written as (Brusseau and Rao, 1989)

∂S

∂t= kf

n

ρC − krS, (6)

where kf and kr are the forward and reverse rate coefficients (1/T) respectively,n is the soil porosity, and ρ is the dry bulk density of soil (M/L3). A number ofother kinetic models have also been proposed to predict the non-equilibrium be-haviour. These kinetic sorption models are divided into two groups: physical non-equilibrium and chemical non-equilibrium models depending upon which mechan-ism is hypothesised as being the rate-limiting step responsible for non-equilibriumsorption (Travis and Etner, 1981; Abriola, 1987; Brusseau and Rao, 1989). Physicalnon-equilibrium sorption is assumed to be a result of mass transfer between tworegions – a mobile and a stagnant or immobile region. Advective–dispersive solutetransport is assumed to be limited to the mobile region, whereas solute transport inthe immobile region is assumed to occur only by diffusion. Solute transfer betweenthe mobile and immobile regions can be accounted for basically in either explicitlywith the use of Fick’s law to describe the physical mechanism of diffusive masstransfer or with the use of an empirical first-order mass transfer expression toapproximate solute transfer (Brusseau and Rao, 1989). Chemical non-equilibriumsorption is assumed to be the result of a time-dependent sorption reaction at thesorbent surface. The sorbent is hypothesised as having two classes of sorption sites,where sorption is instantaneous for one class and is rate-limited for the other (so-called two-site model). Sorption on the kinetics-controlled class is described bya first-order rate equation, while the other class is represented by an equilibriumisotherm equation.


3.4.2. Kinetic Precipitation Model

In groundwater the processes controlling the rates of mineral precipitation/disso-lution include mass transport, diffusion control, and surface-reaction control(Langmuir, 1997). The overall kinetics of precipitation/dissolution reactions mayinvolve several successive elementary reaction steps; in simple cases the slowestreaction is the rate-determining step. A general kinetic rate expression for the jthdissolved component of the solid is (Smith and Jaffé, 1998)

∂Cj s

∂t= aj,sks

Ns∏j=1

[uj ]aj,s −Kssp

, (7)

where ks is the precipitation rate coefficient for solid S, Ns is the number of com-ponents forming solid S, Cj is the dissolved concentration of component j, aj,sis the stoichiometric coefficient of the j th component of solid S, and Ksp is theequilibrium solubility product for solid S.

There is not much data on the kinetics of mineral precipitation or dissolutionin the literature. Table II shows the kinetic rate equations for different mineralsin aqueous solution. All of these kinetic studies were conducted in clean aqueoussystem. In natural system, the precipitation–dissolution reactions can be chemicallyinhibited by adsorbed organic compounds or inorganic ions, which block reactivesurface areas. Precipitation of calcite is completely inhibited when dissolved or-ganic carbon (DOC) is 0.3 mM or greater and when DOC is � 0.05 mM calciteprecipitates by heterogeneous nucleation instead of crystal growth and the rateis independent of calcite surface area and dependent on the DOC concentration(Lebron and Suarez, 1996). Dust particles, clay minerals, bacteria and other entit-ies in the natural environment may act as active sites to initiate precipitation byheterogeneous nucleation.

3.4.3. Kinetic Biodegradation Model

Three conceptual methods exist for mathematical modeling of bacterial growth andbiologically reacting solute transport in saturated porous media – the strictly mac-roscopic, discrete microcolony, and continuous biofilm approaches (Baveye andValocchi, 1989). The strictly macroscopic approach assumes no particular biomassconfiguration and the bacteria are assumed to respond to the macroscopic bulk fluidsubstrate concentration (see Corapcioglu and Haridas, 1984; Borden and Bedient,1986; Kindred and Celia, 1989; MacQuarrie et al., 1990; Clement et al., 1996a).The microcolony approach assumes the microorganisms grow in small discretemicrocolonies attached to particle surfaces, and diffusional mass transport throughthe immobile water phase (see Molz et al., 1986; Widdowson et al., 1988; Chenet al., 1992; Kinzelbach et al., 1991; Lensing et al., 1994). The biofilm approachassumes that the microorganism form a continuous layer covering the entire surfaceof the porous media and considers diffusional mass transport between aqueous


Tabl

eII

.K

inet

icra

teeq

uati

ons

ford

iffe

rent

min

eral

sin

aque

ous

solu

tion

Min

eral

sR

ate

equa

tion

sR

ate

cons

tant

,KS

olub

ilit

yR

efer

ence

s

prod

uct,

Ksp

Cal

cite

For

pH(2

−7.

7),p

CO

2(1

0−3.

5−

1.0)

atm

k1

=0.

051

1×

10−8.4

8P

lum

mer

(CaC

O3)

R=k

1[H

+ ]+k

2[H

2C

O∗ 3]+

k3

[H2O

]−k

2=

3.45

×10

−5et

al.(

1978

)

K4

[Ca2+

][H

CO

− 3]

k3

=1.

19×

10−7

K4

=K

2/K

sp(k

′ 1+

1/[H

+ ](k

2[H

2C

O∗ 3]

k′ 1

=10k

1

+k3

[H2O

]))

mm

ole/

cm2/s

For

pH>

8an

dpC

O2<

0.01

atm

k=

118.

2±

14.7

Insk

eep

R=k

([C

a2+][

CO

2− 3]−K

sp)

mol

e/m

2/s

dm6/m

ole/

m2/s

and

Blo

om(1

985)

Sid

erit

eR

=k({[

Fe2+

][CO

2− 3]}1/

2−K

1/2

sp)2

391.

81

×10

−10.

78G

reen

berg

and

(FeC

O3)

mol

e/m

2/s

L2/m

ole/

m2 /

sTo

mso

n(1

992)

Rho

doch

rosi

teR

=K

([M

n2+][

CO

2− 3]/K

sp−

1)n

k=

1.56

±0.

39×

10−1

5×

10−1

1S

tern

beck

(199

7)

(MnC

O3)

µm

ole/

h/m

2µ

mol

e/h/

m2

n=

1.72

4±

0.06

7

Iron

Sul

fide

R=k

[H2S

]m

ole/

lite

r/s

k=

90±

10s−

11

×10

−11.

65R

icka

rd(1

995)

(FeS

)

[]=

activ

ity.


phase and bacteria within the biofilm (see Rittmann and McCarty, 1980; Rittmannet al., 1980; Bouwer and Cobb, 1987; Taylor and Jaffé, 1990; Zysset et al., 1994b).The macroscopic approach does not make any unwarranted assumption concerningthe spatial distribution of the biomass (Baveye and Valocchi, 1989). However, toinvestigate the effects of bacterial growth on groundwater flow, it may be essentialto apply the microcolony or biofilm approach.

Yates and Yates (1988) and De Blanc et al. (1996) gave a comprehensive re-view of modeling bacterial growth and biodegradation kinetics in the subsurfaceenvironment. Modeling geochemical interactions between organic biodegradationand inorganic species is a current research topic. Lensing et al. (1994), Zyssetet al. (1994b), McNab and Narasimhan (1994, 1995), Rittmann and Van Briesen(1996), Hunter et al. (1998), Salvage and Yeh (1998), Tebes-Stevens et al. (1998),Van Breukelen et al. (1998), and Schäfer et al. (1998) described the developmentof reactive solute transport coupling organic biodegradation kinetics and the localinorganic geochemistry.

Assuming macroscopic approach, that is, absence of diffusional resistance, bio-degradation of the substrate and microbial growth can be represented by the fol-lowing system of equations (Clement et al., 1996a):

∂S

∂t= −µmax

Y

S

Ks + S

Cea

Kea + Cea

(Xa + ρXs

n

), (8)

∂Xa

∂t= µmax

S

Ks + S

Cea

Kea + CeaXa −KdecX

a −KattXa + ρKdetX

s

n, (9)

∂Xs

∂t= µmax

S

Ks + S

Cea

Kea + CeaXs −KdecX

s −KdetXs + nKattX

a

ρ, (10)

where S is the substrate concentration in the bulk (mobile) fluid (M/L3), Xa isthe aqueous-phase biomass concentration (M/L3), Xs is the solid-phase biomassconcentration (M/M),Cea is the concentration of terminal electron acceptor (M/L3),Kdec is the first-order endogenous decay coefficient (1/T), Katt is the biomass at-tachment coefficient (1/T), Kdet is the biomass detachment coefficient (1/T), µmax

is the maximum specific growth rate of the biomass (1/T), Y is the yield coefficientfor the biomass (cell mass produced per mass of substrate consumed), and Ks andKea are the saturation constant for substrate and electron acceptor (M/L3), definedas the concentration for which the specific growth rate is equal to µmax/2.

3.4.4. Numerical Solution of Kinetic Model

The mathematical formulation of the kinetic reactions leads to a nonlinear sys-tem of ordinary differential equations, which may be stiff due to its numericalbehaviour. There are several methods for solving system of ordinary differentialequations. Kinzelbach et al. (1991) and Schäfer et al. (1998) used Gear method(Gear, 1971) for the solution of kinetic biodegradation model. Zysset et al. (1994a,


1994b) used an iterative predictor-corrector scheme introduced by Young and Boris(1977) for the solution of kinetic reversible adsorption and biodegradation model.Clement et al. (1996a) and Van Breukelen et al. (1998) used the fourth-orderRunge–Kutta method for solving the set of kinetic biodegradation equations. Anumber of ODE (ordinary differential equation) solvers are now available whichcan solve the stiff systems of ordinary differential equations. Steefel and MacQuar-rie (1996) gave a list of available packages for solving sets of ordinary differentialequations and differential algebraic equations (those consisting of both kinetic andequilibrium reactions). Clement et al. (1998) used LSODEA differential equationsolver (Hindmarsh and Petzold, 1995) for solving the kinetic reaction equations inRT3D model. Borden and Bedient (1986) used an adaptive time step solver for stiffequations CSMP III (IBM, 1976) for solving the set of kinetic equations.

3.5. PERMEABILITY REDUCTION MODEL

Precipitation of solids and bacterial growth can affect the porosity and permeabilityof the medium. To develop a ‘fully coupled’ model of reactive solute transport wemust consider temporal changes in porosity and permeability, and how they in turncan modify subsurface flow. This is sometimes referred to as ‘feedback’ coup-ling. The porosity changes caused by chemical precipitation or bacterial growthcan be related to precipitated or biomass volume. The permeability change as-sociated with this change in porosity is a complex problem because the porosity–permeability correlation depend on many geometric factors such as pore size distri-bution, pore shapes, and connectivity (Verma and Pruess, 1988). The relationshipbetween porosity (as well as other geometrical properties of a porous medium)and permeability is a fundamental area of study in hydrogeology. Many differentmodeling approaches for the treatment of single-phase permeability have beendescribed in the literature. The simplest model of the relation between permeab-ility and pore-level properties is the Kozeny–Carman equation. This equation hashistorically been used to explain the fundamental causes of permeability because itprovides a link between media attributes and flow resistance.

Since its inception, the Kozeny–Carman model has had many modifications toimprove the estimation of permeability. Recently, Panda and Lake (1994) proposeda modified Kozeny–Carman model to estimate the single-phase permeability of apermeable medium from the bulk physical properties of the interconnected poresystem (e.g., porosity and tortuosity) and the statistics of its particle size distribu-tion. Steefel and Lasaga (1990) used the Kozeny–Carman equation where porosityis modeled as a bundle of capillary tubes of equal length. In general, however,this model is only applicable to simple granular materials (Bear, 1972), and canbe very inaccurate for more complex media. Verma and Pruess (1988) used ideal-ised models of porous media to correlate the relative changes in permeability tothe relative changes in porosity caused by mineral redistribution. Their geometricmodel considers the medium as a set of non-intersecting flow channels of varying


cross-sectional shape. Weir and White (1996) developed a theoretical model ofpermeability and porosity changes resulting from surface deposition or dissolutionin an initial rhombohedral array of uniform spheres. They found at late times anapproximately quadratic dependence between relative changes in permeability andporosity preceded by an initial rapid reduction in permeability.

Taylor et al. (1990) proposed a number of models on the basis of Kozeny–Carman equation and ‘cut-and-random-rejoin’ approach introduced by Childs andCollis-George (1950). Clement et al. (1996b) developed analytical equations basedon macroscopic approach to model changes in porosity, specific surface area, andpermeability caused by biomass accumulation in porous media. Vandevivere et al.(1995) evaluated a number of existing mathematical models and suggested thatnone of the existing models could predict satisfactorily the saturated permeabilityreductions observed in fine sands, whereas they are somewhat better in coarser ma-terials. It is argued that this inadequacy of existing models is due to the continuousbiofilm assumption on which they are founded.

3.6. COUPLING THE REACTION AND TRANSPORT MODEL

Two main solution methods have been proposed to solve the coupled set of equa-tions. In the one-step method, transport and biochemical reaction equations aresolved simultaneously (Rubin and James, 1973; Valocchi et al., 1981; Jenningset al., 1982; Miller and Benson, 1983; Lichtner, 1985; Steefel and Lasaga, 1994;Shen and Nikolaidis, 1997; García-Delgado and Koussis, 1997). In the two-stepmethod, the transport equations are separated from the biochemical reaction equa-tions and solved sequentially at each time step, with or without iterations in between(Grove and Wood, 1979; Walsh et al., 1984; Kirkner et al., 1985; Cederberg et al.,1985; Bryant et al., 1986; Kinzelbach et al., 1991; Schäfer et al., 1998; Salvageand Yeh, 1998; Tebes-Stevens et al., 1998). The one-step method is generally morecomplicated to formulate than the two-step procedure and models can not be easilymodified to deal with mixed kinetic and equilibrium reactions. These models arenot suitable for addressing realistic two- and three-dimensional problems. Two-step methods enable the use of appropriate numerical methods for the transportand the chemical model part separately and is favourable in terms of computer costand flexibility for complex systems.

Sequential iterative approach (SIA), of two-step methods are implemented indifferent ways by different researchers. In the sequential non-iterative approach(SNIA), also called the operator splitting or time splitting approach, a transportstep is followed by a reaction step using the transported concentrations in eachtime step. This method is used in mixing cell models (Schultz and Reardon, 1983;Appelo and Willemsen, 1987). McNab and Narasimhan (1994, 1995) used SNIAfor modeling geochemical interactions between organic and inorganic species. En-gesgaard and Kip (1992) and Walter et al. (1994) demonstrated the SIA and SNIAfor test cases. The results show that SNIA compares favorably to SIA. Walter


et al. (1994) recommended that for cases conforming to the local equilibriumassumption, two-step sequential non-iterative approach can be used efficiently tosimulate hydrogeological systems with realistic aquifer properties and boundaryconditions under complex geochemical conditions. Recently, Tebes-Stevens et al.(1998) used an alternative sequential iterative approach (SIA-1) which improvesthe convergence behaviour of the traditional SIA through the inclusion of an addi-tional first-order term from the Taylor Series expansion of the kinetic reaction rateexpressions. The use of SIA-1 method results in a significant reduction in the CPUtime.

Another alternating operator splitting method referred to as Strang splittingproposed by Strang (1968) has been used by Zysset et al. (1994a) in modelingof chemically reactive groundwater transport. In this method the reaction stepis centred between two transport steps, that is, in each time step transport over�t/2, reaction over�t , and transport over�t/2 are computed. Zysset and Stauffer(1992) compared SIA, SNIA and Strang sequence scheme to an analytical solutionin a test case and concluded that an iterative method does not necessarily achievehigher accuracy though it requires more computer time than the Strang sequencescheme. Valocchi and Malmstead (1992) used a slightly different scheme, tworeaction steps of �t/2 in between two transport steps of �t/2, and found operatorsplitting error of O(�t2) for the case of radioactive decay. Harzer and Kinzelbach(1989) and Barry et al. (1996) presented discretisation errors in two-step methodsfor different types of reactions. It was shown that maximum errors arise in thecase of heterogeneous equilibrium reactions and the truncation error leads to theintroduction of additional numerical dispersion, proportional to �t (Harzer andKinzelbach, 1989). Either small time steps or iteration between the two sets ofequations must be applied to obtain accurate solutions.

The truncation error analysis by Barry et al. (1996) shows that Strang split-operator method leads to increased error (first order in time) for the equilibriumreaction (linear retardation), but for radioactive decay and linear interphase masstransfer model it is second-order accurate in the temporal discretisation. Steefeland MacQuarrie (1996) presented numerical comparisons for different types ofcoupling schemes. It was shown that in case of realistic one-dimensional probleminvolving Monod kinetic reactions, the Strang splitting approach is computation-ally more efficient than the SIA method, but for equilibrium adsorption reactions(whether linear or nonlinear) the SIA method appears to be more efficient, althoughconvergence difficulties in some problems may make it harder to use.

4. Biogeochemical Models

This section reviews the different biogeochemical transport models reported in theliterature to simulate the transport of landfill leachate in subsurface soil systems.The section is divided into two subsections, the first section focuses on chemicalspeciation modeling for closed system, and the second on solute transport models


coupled with biochemical reaction models for open system. The present paper doesnot review the moisture flow and gas transport models in landfills. A number ofmoisture flow model have been developed to simulate leachate flow and transportprocesses in a landfill (Straub and Lynch, 1982; Schroeder et al., 1984; Demetraco-poulos et al., 1986; Lu and Bai, 1991; Khanbilvardi et al., 1995). A comprehensivereview on gas simulation models for landfills is given by El-Fadel et al. (1997).

4.1. CHEMICAL SPECIATION MODELING

Many studies have used geochemical speciation models to calculate the speci-ation of metals with respect to inorganic and organic complexes. Jensen et al.(1998) used geochemical speciation model MINTEQA2 to calculate the distri-bution of dissolved Fe(II) and Mn(II) among aqueous species in the leachate-contaminated groundwater and showed that model results were consistent withthe experimental ion-exchange speciation results. MINTEQA2 model speciationpredicted that Fe(II) and Mn(II) in the dissolved fraction in the leachate-pollutedgroundwater were primarily as free divalent ions (about 80%), and about 20% Fe(II) and Mn(II) were present as bicarbonate complexes. MINTEQA2 calculationsindicated only negligible complexation with dissolved organic matter for Mn(II)(< 5%).

Calculations with MINTEQA2 indicated that the leachate-polluted groundwa-ter samples were strongly supersaturated with respect to siderite (FeCO3) andmoderately supersaturated with respect to rhodochrosite (MnCO3) (Jensen et al.,1998). Supersaturation of carbonate minerals persists possibly because of slowprecipitation kinetics and/or inhibited by complexation of cations with organicligands in solution. MINTEQA2 calculations by Bjerg et al. (1995) in landfillpollution plume also indicated supersaturation with respect to FeS (mackinaw-ite/monosulfide), FeCO3, CaCO3 (calcite), CaMg(CO3)2 (dolomite), and MnCO3

at the border of the landfill to a distance of around 60–90 m from the landfill.Gounaris et al. (1993) also used geochemical speciation model MINTEQA2 tocalculate the possible precipitates in landfill leachate. Geochemical model calcula-tions suggested that the inorganic components of the colloids were predominantlycarbonate and phosphate precipitates. Magnesium was mostly dissolved, while ironand calcium were found in colloidal fractions and the dissolved phase.

Barker et al. (1986) used the geochemical speciation model GEOCHEM toevaluate the possible importance of organic complexation in speciation of Fe andother cations in landfill leachate-polluted groundwater. A mixture of simple or-ganic compounds already in the GEOCHEM thermodynamic database representedthe measured dissolved organic carbon (DOC). Even though the leachate-pollutedgroundwaters were rich in Fe and Mn and in DOC, little organic complexing ofthese metals was predicted by the model calculations. Much of the Ni and signi-ficant proportion of Cd and Zn were organically bound. Batch sorption studies byChristensen et al. (1996) showed that although DOC formed complexes with Cd,


Ni and Zn, the migration velocity of the metals were still be very low (< 1.2% ofthe water migration velocity). In earlier studies, Pease and Adrian (1978) foundthe extent of organic complexation of iron to be too small to alter significantlythe chemical reactivity of the metal species in landfill leachate, whereas Knox andJones (1979) found significant complexation of cadmium by organic componentsof landfill leachate.

Recent studies by Christensen et al. (1999) found that at low DOC concen-trations (40 mg/l) in a leachate-polluted groundwater more than 85% of the Cuand Pb in solution were bound in DOC complexes, and at higher concentrations(> 60 mg/l) at least 90% of the Cu and Pb were bound in DOC complexes. TheMINTEQA2 model and its default database provided excellent predictions of Cuand Pb complexation by DOC compared to the experimental results. Adjusting thedefault Cu and Pb binding constants for fulvic acids in the WHAM model (Tip-ping, 1994) database, good agreement was obtained between model predictionsand experimental results.

4.2. LEACHATE TRANSPORT MODELING

Pickens and Lennox (1976), Gureghian et al. (1981), and Gray and Hoffman(1983a,b) applied a two-dimensional solute transport model to simulate the tran-sient movement of landfill leachate in saturated groundwater flow. The numericalformulations of these models were based on the Galerkin finite element technique.A linear equilibrium sorption equation was used by Pickens and Lennox (1976) todescribe the retardation of the movement of contaminants in soils. Because of lackof observed reliable water quality data, sensitivity tests were run to determine howerrors in boundary condition specification, pumping rates, permeability, porosity,dispersivity, and distribution coefficient affect computed results.

A number of numerical model studies have been carried out to simulate flowand contaminant migration in groundwater at the Canadian Forces Base Bordenlandfill near Toronto (Sykes et al., 1982a,b; Dance and Reardon, 1983; Schulzand Reardon, 1983; Frind and Hokkanen, 1987). A three-dimensional finite differ-ence model was used by Sykes et al. (1982a) to demonstrate the use of model insynthesis, interpretation, and simulation of contaminant transport systems. An av-erage annual leachate volume was used in the simulation. Sensitivity runs indicatedthat seasonal effects were of importance. Frind and Hokkanen (1987) used a two-dimensional finite element model to simulate the evolution of chloride plume atthe Borden landfill. To handle the high-resolution grid that was necessary becauseof the large contrasts between longitudinal and transverse vertical dispersivity, thealternating direction Galerkin technique was used. A time-varying source concen-tration function satisfactorily reproduced concentration peaks that were observedin the field.

Sykes et al. (1982b) used a two-dimensional Galerkin finite element model tosimulate the migration of leachate organic as chemical oxygen demand in ground-


water below the Borden landfill. Simultaneous Michaelis–Menten substrate util-ization and microbial mass production equations were used for modeling of bio-degradation. For substrate concentration less than 25% of the half utilization ratecoefficient and for microbial populations approaching a steady state the Michaelis–Menten equations are reduced to a first-order reaction kinetic model. Due to bac-terial growth and active gas production, an effective porosity of 0.25 was used forthe Michaelis–Menten zone and a value of 0.40 for the remaining spatial domain.Model results indicated substantial removal of leachate organics (90%) within shortdistance (2 m) of the landfill even under the conditions of widely varying biologicalparameters.

A one-dimensional mixing-cell model coupled to the chemical equilibrium sub-routine for complexation, ion exchange, and calcite precipitation/dissolution reac-tions was developed by Dance and Reardon (1983) to simulate the results of thenatural-gradient tracer test at the Borden landfill site. Model results for the distri-bution of Na+ and K+ due to release of Ca2+ from exchange sites provided goodagreement with those from field experiments. However, the model showed pooragreement for Mg2+ concentration profile. The model predicted Na+ to be slightlyretarded and K+ to be strongly retarded with respect to chloride ion. Schulz andReardon (1983) used a combined two-dimensional mixing cell/analytical modelto describe multiple reactive solute transport in unidirectional groundwater flowregimes. The application of the model to simulate the field injection experimentyielded results in reasonable agreement with field observations.

Bütow et al. (1989) used a geochemical equilibrium code MINEQL and a two-dimensional finite difference transport code FAST to model the transport of leachatefrom an abandoned landfill site. The two codes were linked by elemental dis-tribution coefficients (Kd) calculated by MINEQL and used by FAST to modeltransport of leachate. Sorption was taken into account according to a simple surfacecomplexation model. Three steps were carried out: Cl− was used to calibrate para-meters of the transport code, Na+ to check the calibration and Ni2+ to characterizethe maximal spreading of toxic heavy metals. Sensitivity analysis with numericalmodel showed that within the usual range of parameters no considerable increaseof concentration can be expected in a distance of more than 2500 m from thelandfill.

A conceptual colloids-metal transport model (COMET) was developed by Millset al. (1991) and incorporated into EPA’s CML model that simulates the solutemigration from a landfill in the unsaturated zone to a receptor (i.e., drinking-waterwell) in the saturated zone. Solute transport is simulated using one-dimensionaltransport equations in the unsaturated zone and three-dimensional transport equa-tions in the saturated zone. By using the principle of flux conservation, the unsatur-ated and saturated zone solutions are linked in a mixing zone directly beneath thewaste facility. The model equations are solved using quasi-analytical techniques.The simulation results indicate that mobile phase metal concentrations (dissolvedconcentration plus concentration adsorbed to mobile colloids) increase as colloid


concentrations increase, and arrival times of soluble metal species to stationaryreceptors decrease.

A composite modeling approach was presented by Kool et al. (1994) for simu-lating the three-dimensional subsurface transport of contaminants from land wastedisposal sites. The approach was based on one-dimensional vertical infiltration andcontaminant transport in the unsaturated zone and 3-D groundwater flow and con-taminant transport in the saturated zone. The coupling between the unsaturated-and saturated-zone submodels was at the water table based on continuity of wa-ter and solute flux. The unsaturated-zone transport equation was solved analytic-ally for linear sorption but in case of nonlinear sorption a fully numerical finiteelement method was employed. The saturated-zone transport equation with lin-ear sorption was solved numerically using the Laplace transform–Galerkin tech-nique, in case of nonlinear sorption a standard Galerkin finite element numericaltechnique was used. Model formulations and solution schemes were verified bycomparison against a fully 3-D variably saturated flow and transport code for anon-degrading, non-sorbing contaminant leaching from a hypothetical landfill. Ap-plication of the model to a controlled release field experiment showed reasonableagreement between model predictions and groundwater monitoring results.

Wu and Li (1998) used a multicomponent reactive solute transport model tostudy the migration of four heavy metals (Cd2+, Pb2+, Cu2+, and Zn2+) and othermajor chemical species in a sand/bentonite clay barrier. Numerical results indicatethat under a nearly neutral leachate, the mobility of four heavy metals followsthe order Cu2+>Zn2+>Pb2+>Cd2+. The mobility of Cd2+ and Pb2+ is greatlyretarded by mostly because of the precipitation of CdCO3 and PbCO3, but themigration of Cu2+ and Zn2+ is only retarded by cation exchange. For a moreacidic leachate, the mobility order changes to Cd2+>Zn2+>Cu2+>Pb2+. Cationexchange is the only factor retarding the migration of the heavy metals under acidicleachate. The leachate pH has a significant effect on the migration of Cd2+ andPb2+, but has only limited effect on the mobility of Cu2+ and Zn2+.

Rowe and Booker (1990) developed a one-dimensional finite layer contaminanttransport model POLLUTE in soils which was used in a number of studies for po-tential contaminant impact assessment of an engineered landfill on the underlyingaquifer. Contaminant transport through both fractured and unfractured soils can bemodeled. Both linear and nonlinear sorption, and radioactive (or other first-order)decay can be considered. Rowe and Fraser (1993a) showed that size of the landfilland the infiltration rate through the cover have a substantial impact on the peakconcentrations of contaminants released from the landfill and the required servicelife of the leachate collection systems. Rowe (1991) discussed the potential impactof fracturing of soil beneath a landfill. Rowe and Fraser (1993b) examined theeffects of four barrier designs on the peak contaminant concentration for a rangeof aquifer heads. A site where the aquifer head is above the base of the landfill wasshown to provide a better barrier to contaminant migration. Rowe et al. (1996)illustrated the impact of chloride and dichloromethane for two barrier systems


using the values of diffusion coefficients determined from experiments. A designfor composite liners involving a geomembrane, compacted clay and a minimumgeologic barrier was performed very well.

Rowe et al. (1997b) developed a model for predicting the rate of clogging ofleachate collection systems caused by biological growth and biochemically drivenprecipitation. The model used a time marching algorithm to model the evolutionof the influent and effluent organic concentration, biofilm thickness, inert biofilmplus mineral (CaCO3) film thickness and porosity at any position or time. A linearrelationship between COD and CaCO3 precipitation was used to calculate the rateof mineral precipitation of CaCO3. The non-steady state biofilm growth and lossalgorithm was combined with equations to model the change in the porosity andspecific surface as the biofilm and mineral film grow, mass balance equations andshearing equations. The model was developed to simulate both one-dimensionalcolumn tests and drainage layers where there is two-dimensional flow.

5. The Composite Model

Models for leachate transport in soils must include the various physical, chemicaland biological processes that affect the eventual concentration of pollutants in soilsand groundwater. The flow and transport of leachate leaking from landfill in theunsaturated zone can be assumed one-dimensional downward direction only. Thisassumption will minimize the estimated unsaturated-zone residence time and there-fore lead to conservative assessments of eventual groundwater impacts (Kool et al.,1994). For unsaturated contaminant transport Rowe (1987) recommends a simpleranalysis that assumes the soil be saturated to estimate the design contaminationbased on the worst case. In the vicinity of the waste source, although non-uniformgroundwater flow requires 3-D flow and transport solutions but fairly accurate ap-proximations of the contaminant plume in the saturated zone can be obtained formany cases when the effect of horizontal transverse flow is ignored (Kool et al.,1994). A two-dimensional vertical cross-section flow and transport representationis most appropriate when the areal extent of the waste disposal facility is large anda thick saturated zone underlies it.

The microbial sequences of redox reaction downgradient of a landfill are ana-logous to that of the marine sediments (Baedecker and Back, 1979). There arenumerous models developed for diagenetic processes in sediments that include theinteractions between biodegradation and inorganic geochemical reactions (Dhakarand Burdige, 1996; Wang and Van Cappellen, 1996; Park and Jaffé, 1996; Smithand Jaffé, 1998). Several researchers used inhibition functions which suppress thereduction of some terminal electron acceptors in the presence of others (Kindredand Celia, 1989; Kinzelbach et al., 1991; Dhakar and Burdige, 1996, Schäfer et al.,1998). Wang and Van Cappellen (1996) defined a set of limiting concentrationsfor the successive external electron acceptors of the five respiratory pathways O2,NO−

3 , Mn(IV), Fe(III), and SO−4 . When the concentration of an external electron


Table III. Limiting concentrations of terminal electron acceptors in respiration path-ways (after, Van Cappellen and Wang, 1995)

Pathway Limiting reactant Limiting concentration Environment

Aerobic respiration Dissolved O2 1 – 10 µM Marine

Freshwater

Denitrification Dissolved NO3 50 – 80 µM Marine

4 – 20 µM Freshwater

Mn reduction Solid Mn(IV) 1 – 10 µmol/g Marine

Freshwater

Fe reduction Solid Fe(III) 1 – 50 µmol/g Marine

Freshwater

Sulfate reduction Dissolved SO4 1600 µM Marine

60 – 300 µM Freshwater

acceptor exceeds its limiting value, the rate of corresponding pathway is assumedto be independent of the concentration of the electron acceptor. When the concen-tration of the electron acceptor drops below its limiting value, the correspondingrate decreases linearly with the oxidant concentration, and bacteria start utilizingorganic carbon oxidation pathways with a lower intrinsic energy yield. Table IIIlists the ranges of the limiting concentrations reported for natural aquatic environ-ment compiled by Van Cappellen and Wang (1995). This computational schemecan be used to model overlap of redox zones downgradient of a landfill.

The geochemical equilibrium models such as MINTEQA2 or PHREEQE canbe coupled with the transport model for chemical speciation, acid-base reactions,aqueous complexation, mineral precipitation–dissolution, oxidation–reduction, andadsorption reactions. The microbially mediated sequence of reactions can bemodeled using multiple Monod-type expressions with different functional bac-terial groups. For microbial mediated sequence of redox processes that are notat equilibrium, the redox potential (pE) can be approximated to that of the domin-ant redox couple (Morel and Hering, 1993). According to Park and Jaffé (1996),redox potential (pE) can be estimated at each location of the domain based on theconcentrations of the dominant terminal electron acceptor and its correspondingreduced species from the transport and kinetic biodegradation model. Togetherwith other computed species’ concentrations the estimated pE can then be usedin the chemical equilibrium model to calculate the equilibrium state towards whichthe system should be driven (Smith and Jaffé, 1998). Precipitation can be allowedto take place at any location for which the chemical equilibrium model predicts thepresence of that solid at equilibrium, and dissolution can be allowed for which thechemical equilibrium model predicts the absence of that solid at equilibrium. Basedon the speciation calculation and specified rate expressions, rates of adsorption andprecipitation can be calculated. Finally the mass of each mineral phase of interest is


Figure 1. A simple flow diagram for the sequential solution scheme of the composite model.

updated and the aqueous solutions are re-equilibrated with the geochemical equi-librium model. A simple flow diagram of the sequential solution scheme of thecomposite model is illustrated in Figure 1.

In reactive transport modelling, a good knowledge of biological reaction kin-etics and stoichiometry is required for evaluating changes in the physical andchemical properties of microbial environments. Microbial transformations mayproduce or consume alkalinity, thereby initiating innumerable changes in solutionchemistry. Criddle et al. (1991) and Rittmann and Van Briesen (1996) gave a detail


Table IV. The overall biodegradation reactions for different microbial pathways

Reactants converted to products

Aerobic respiration

CH2O + (1 − fs) O2 + 0.2fs NH+4 0.2fs C5H7O2N + (1 − fs) H2CO∗

3 + 0.2fs H++0.6fs H2O

Denitrification

CH2O + 0.8 (1 − fs) NO−3 + 0.2fs 0.2fs C5H7O2N +(1 − fs) H2CO∗

3 + 0.4(1 − fs)N2+NH+

4 + (0.8 − fs) H+ (0.4 + 0.2fs) H2O

Manganese reduction

CH2O +2(1 − fs) MnO2 + 0.2fs 0.2fs C5H7O2N +(1 − fs) H2CO∗3 + 2(1 − fs)

NH+4 + (4 − 4.2fs) H+ Mn2+ + (2 − 1.4fs) H2O

Iron reduction

CH2O +4(1 − fs) Fe(OH)3 + 0.2fs 0.2fs C5H7O2N +(1 − fs) H2CO∗3 + 4(1 − fs)

NH+4 + (8 − 8.2fs) H+ Fe2+ + (10 − 9.4fs) H2O

Sulphate reduction

CH2O +0.5(1 − fs) SO2−4 + 0.2fs 0.2fs C5H7O2N +(1 − fs) H2CO∗

3 + 0.5

NH+4 + (0.5 − 0.7fs) H+ (1 − fs) HS− + 0.6fs H2O

Methanogenic processes

CH2O +0.2fs NH+4 + (0.5 − 1.1fs) 0.2fs C5H7O2N +0.5(1 − fs) H2CO∗

3 + 0.5(1 − fs)

H2O CH4 + 0.2fs H+

H2CO∗3: dissolved CO2, CH4: methane, SO2−

4 : sulphate, HS−: hydrogen sulphide.

description on biological reaction kinetics and stoichiometry, and the pathways ofbiotransformation. Table IV shows the overall biodegradation reaction of organicmatter expressed as CH2O in leachate for different microbial pathways. The overallreaction R is given by the expression (Criddle et al., 1991)

R = Rd + feRa + fsRc, (11)

where Rd, Ra, and Rc are the half reaction for electron donor, acceptor, and bac-terial cell synthesis respectively, fs is the fraction of electrons diverted for syn-thesis, fe is the fraction of electrons used for energy generation, and fs + fe = 1.Typical values of maximum fs for aerobic and anaerobic systems are given inTable V. Typically, the volatile fatty acids were found to contribute over 90% of thetotal organics in the high strength landfill leachate (Johansen and Carlsen, 1976;Harmsen, 1983). The values of fs for fatty acids given in Table V can be used. Ifyield data are available, values of maximum fs can be calculated from the followingrelationship (Criddle et al., 1991):

fs(max) = Ymmd

mb, (12)

where Ym is the maximum organism yield (mg organisms/mg substrate), md isthe electron equivalent mass of the electron donor (gm), and mb is the electron


Table V. Typical values of maximum fs for bacterialreactions (Criddle et al., 1991)

Electron donor Electron acceptor fs(max)

Carbohydrate O2 0.68

Carbohydrate NO−3 0.60

Carbohydrate SO−4 0.30

Carbohydrate CO2 0.28

Protein O2 0.64

Protein CO2 0.08

Fatty acid O2 0.55

Fatty acid NO−3 0.45

Fatty acid SO−4 0.06

Fatty acid CO2 0.05

Methanol O2 0.43

Methanol NO−3 0.36

Methanol SO−4 0.26

Methanol CO2 0.15

equivalent mass of biomass (5.65 gm when ammonia is the nitrogen source, and4.04 gm when nitrate is the nitrogen source).

Change in concentrations of different terminal electron acceptors, pH, and gasproduction due to kinetic biodegradation reactions can be computed from the stoi-chiometry of the microbial mediated redox reactions (Table IV). This allows themechanistic modelling of the influence of biological activities on the local inor-ganic geochemistry. A two-step iterative or sequential operator splitting methodcan be applied to solve the coupled solute transport model, kinetic biochemicalmodel, and geochemical equilibrium model. If iteration is not performed betweenthe transport and biochemical reaction equation small time steps can be used fortwo-step sequential operator splitting method. To simulate the evolution of clog-ging processes of soils under the leaking landfill, the fluid flow model is coupledto the transport model with a feedback effect through some relationship betweenpermeability and changes in porosity of the soil.

6. Application and Conclusion

Different complex interactions involving physical, chemical and biological pro-cesses control the transport of landfill leachate in soils. Relatively few models existthat include complex interactions between the physical, chemical and biologicalprocesses in soils. Field and laboratory studies show that many geochemical pro-cesses in leachate-contaminated soils are kinetically controlled. Inadequate kinetic


data coupled with insufficient understanding of the complexities of biogeochem-ical interactions associated with leachate transport processes prevent the devel-opment of a comprehensive composite model having significant predictive cap-ability. Moreover, general lack of quality field data for calibration and validationpurposes also affects a comprehensive composite model for better environmentalmanagement. The overall conclusion of the present review is that although inform-ation is available on several aspects of biogeochemical interactions in leachate-contaminated soils, further research is required before the transport of leachateconstituents in soils is fully understood.

This study has reviewed the current scientific literature pertaining to variousaspects of leachate migration in soils and presented a framework to develop acomprehensive composite model. Such composite models may be used to assessthe impact of contaminants leaking from landfills on groundwater quality. Themodel can also serve as a management tool and used to evaluate environmental riskscenarios and develop strategies for groundwater protection against contamination.

References

Abriola, L. M.: 1987, Modeling contaminant transport in the subsurface: An interdisciplinarychallenge, Rev. Geophys. 25, 125–134.

Alesii, B. A., Fuller, W. H. and Boyle, M. V.: 1980, Effect of leachate flow rate on metal migrationthrough soil, J. Environ. Qual. 9, 119–126.

Allison, J. D., Brown, D. S. and Nova-Gradac, K. J.: 1991, MINTEQA2/PRODEFA2, A GeochemicalAssessment Model for Environmental Systems: Version 3.0 User’s Manual, Environ. Res. Lab.Off. of Res. and Dev., U.S. Environ. Prot. Agency, Athens, GA.

Appelo, C. A. J. and Willemsen, A.: 1987, Geochemical calculations and observations on saltwaterintrusions, I. A combined geochemical/mixing cell model, J. Hydrol. 94, 313–330.

Baedecker, M. J. and Back, W.: 1979, Modern marine sediments as a natural analog to the chemicallystressed environments of a landfill, J. Hydrol. 43, 393–413.

Bagchi, Amalendu: 1987, Natural attenuation mechanisms of landfill leachate and effects of variousfactors on the mechanisms, Waste Manage. Res. 5, 453–464.

Barker, J. F., Tessmann, J. S., Plotz, P. E. and Reinhard, M.: 1986, The organic geochemistry of asanitary landfill leachate plume, J. Contam. Hydrol. 1, 171–189.

Barry, D. A., Miller, C. T. and Culligan-Hensley, P. J.: 1996, Temporal discretization errors in non-iterative split-operator approaches to solving chemical reaction/groundwater transport models, J.Contam. Hydrol. 22, 1–17.

Baveye, P. and Valocchi, A.: 1989, An evaluation of mathematical models of the transport ofbiologically reacting solutes in saturated soils and aquifers, Water Resour. Res. 26, 1413–1421.

Bear, J.: 1972, Dynamics of Fluids in Porous Media, Elsevier, New York.Bear, J.: 1979, Hydraulics of Groundwater, McGraw-Hill, New York.Bjerg, P. L., Rügge, K., Pedersen, J. K. and Christensen, T. H.: 1995, Distribution of redox sensitive

groundwater quality parameters downgradient of a landfill (Grindsted, Denmark), Environ. Sci.Technol. 29, 1387–1394.

Borden, R. C. and Bedient, P. B.: 1986, Transport of dissolved hydrocarbon influenced by oxygen-limited biodegradation, 1, Theoretical development, Water Resour. Res. 22, 1973–1982.

Bouwer, E. J. and Cobb, G. B.: 1987, Modeling of biological processes in the subsurface, Water Sci.Technol. 19, 769–779.


Boyle, M. and Fuller, W. H.: 1987, Effect of municipal solid waste leachate composition on zincmigration through soils, J. Environ. Qual. 16, 357–360.

Brune, M., Ramke, H. G., Collins, H. J. and Hanert, H. H.: 1994, Incrustation problems in landfilldrainage systems, In: T. H. Christensen, R. Cossu and R. Stegmann (eds), Landfilling of Waste:Barriers, E & FN Spon, London, pp. 569–605.

Brusseau, M. L. and Rao, P. S. C.: 1989, Sorption nonideality during organic contaminant transportin porous media, CRC Crit. Rev. Environ. Cont. 19, 33–99.

Bryant, S. L., Schechter, R. S. and Lake, L. W.: 1986, Interaction of precipitation/dissolution wavesand ion exchange in flow through permeable media, AIChE J. 32, 751–764.

Bütow, E., Holzbecher, E. and Koß, V.: 1989, Approach to model the transport of leachates froma landfill site including geochemical processes, In: H. E. Kobus and W. Kinzelbach (eds),Contaminant Transport in Groundwater, A.A. Balkema, Rotterdam, pp. 183–190.

Cartwright, K., Griffin, R. A. and Gilkeson, R. H.: 1977, Migration of landfill leachate through glacialtills, Ground Water 15, 294–305.

Cederberg, G. A., Street, R. L. and Leckie, J. O.: 1985, A groundwater mass transport and equilibriumchemistry model for multicomponent systems, Water Resour. Res. 21, 1095–1104.

Chen, Y. M., Abriola, L. M., Alvarez, P. J. J., Anid, P. J. and Vogel, T. M.: 1992, Modeling trans-port and biodegradation of benzene and toluene in sandy aquifer material: Comparison withexperimental measurements, Water Resour. Res. 28, 1833–1847.

Cheng, R. T., Casulli, B. and Milford, S. N.: 1984, Eularian-Lagrangian solution of the convection–dispersion equation in natural coordinates, Water Resour. Res. 20, 944–952.

Childs, E. C. and Collis-George, N.: 1950, The permeability of porous materials, Proc. R. Soc.London, Ser. A, 201, 392–405.

Chian, S. K. and Dewalle, F. B.: 1976, Sanitary landfill leachates and their treatment. J. Environ.Engrg. Div. ASCE 102, 411–431.

Christensen, T. H., Kjeldsen, P., Albrechtsen, H., Heron, G., Nielsen, P. H., Bjerg, P. L. and Holm, P.E.: 1994, Attenuation of landfill leachate pollutants in aquifers, Crit. Rev. Environ. Sci. Technol.24, 119–202.

Christensen, J. B., Jensen, D. L. and Christensen, T. H.: 1996, Effect of dissolved organic carbonon the mobility of cadmium, nickel and zinc in leachate polluted groundwater, Water Res. 30,3037–3049.

Christensen, J. B., Jelle, J. B. and Christensen, T. H.: 1999, Complexation of Cu and Pb by DOCin polluted groundwater: A comparison of experimental data and predictions by computerspeciation models (WHAM and MINTEQA2), Water Res. 33, 3231–3238.

Clement, T. P., Hooker, B. S. and Skeen, R. S.: 1996a, Numerical modeling of biologically reactivetransport near nutrient injection well, J. Environ. Engrg. 122, 833–839.

Clement, T. P., Hooker, B. S. and Skeen. R. S.: 1996b, Macroscopic models for predictingchanges in saturated porous media properties caused by microbial growth, Ground Water 34,934–942.

Clement, T. P., Sun, Y., Hooker, B. S. and Petersen, J. N.: 1998, Modeling multispecies reactivetransport in ground water, Ground Water Monit. Remed. 18, 79–92.

Corapcioglu, M. Y. and Haridas, A.: 1984, Transport and fate of microorganisms in porous media:theoretical investigation, J. Hydrol. 72, 149–169.

Criddle, C. S., Alvarez, L. M. and McCarty, P. L.: 1991, Microbial processes in porous media, In:J. Bear and M. Y. Corapcioglu (eds), Transport Processes in Porous Media, Kluwer AcademicPublishers, Dordrecht, Boston, pp. 641–691.

Dance, J. T. and Reardon, E. J.: 1983, Migration of contaminants in groundwater at a landfill: A casestudy, 5. Cation migration in the dispersion test, J. Hydrol. 63, 109–130.

Daus, A. D. and Frind, E. O.: 1985, An alternating direction Galerkin technique for simu-lation of contaminant transport in complex groundwater systems, Water Resour. Res. 21,653–664.


Davis, J. A. and Kent, D. B.: 1990, Surface complexation modeling in aqueous geochemistry,In: M. F. Hochella and A. F. White (eds), Mineral-Water Interface Geochemistry, Reviews inMineralogy 23, Mineralogical Society of America, Washington, D.C., pp. 177–260.

Davis, J. A., Coston, J. A., Kent, D. B. and Fuller, C. C.: 1998, Application of the surfacecomplexation concept to complex mineral assemblages, Environ. Sci. Technol. 32, 2820–2828.

De Blanc, P. C., McKinney, D. C. and Speitel, G. E. Jr.: 1996, Modeling subsurface biodegrada-tion of non-aqueous phase liquids, In: M. Y. Corapcioglu (ed.), Advances in Porous Media 3,1–86.

Demetracopoulos, A. C., Sehayek, L. and Erdogan, H.: 1986, Modeling leachate production frommunicipal landfills, J. Environ. Engrg. Div. ASCE 112, 849–866.

Dhakar, S. P. and Burdige, D. J.: 1996, A coupled, non-linear, steady state model for early diageneticprocesses in pelagic sediments, Am. J. Sci. 296, 296–330.

El-Fadel, M., Findikakis, A. N., Leckie, J. O.: 1997, Gas simulation models for solid waste landfills,Crit. Rev. Environ. Sci. Technol. 27, 237–283.

Engesgaard, P. and Kip, K. L.: 1992, A geochemical model for redox-controlled movement of min-eral fronts in ground-water flow systems: A case of nitrate removal by oxidation of pyrite, WaterResour. Res. 28, 2829–2843.

Fein, J. B., Daughney, C. J., Yee, N. and Davis, T. A.: 1997, A chemical equlibrium model for metaladsorption onto bacterial surfaces, Geochim. Cosmochim. Acta 61, 3319–3328.

Fetter, C. W.: 1993, Contaminant Hydrology, MacMillan, New York.Freeze, R. A. and Cherry, J. A.: 1979, Groundwater, Prentice-Hall, Englewood Cliffs, N.J.Forsythe, G., Malcolm, M. A. and Moler, C. B.: 1977, Computer Methods for Mathematical

Computations, Prentice-Hall, Englewood Cliffs, N.J. pp. 259.Frind, E. O. and Germain, D.: 1986, Simulation of contaminant plumes with large dispersive contrast:

Evaluation of alternating direction Galerkin models, Water Resour. Res. 22, 1857–1873.Frind, E. O. and Hokkanen, G. E.: 1987, Simulation of the borden plume using the alternating

direction Galerkin technique, Water Resour. Res. 23, 918–930.García-Delgado, R.A. and Koussis, A. D.: 1997, Ground-water solute transport with hydrogeochem-

ical reactions, Ground Water 35, 243–249.Gear, C. W.: 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-

Hall, Englewood Cliffs, N.J.Goldberg, S.: 1995, Adsorption models incorporated into chemical equilibrium models, In: R. H.

Loeppert, A. P. Schwab and S. Goldberg (eds), Chemical Equilibrium and Reaction Models, SoilScience Society of America and American Society of Agronomy, Madison, Wisconsin, USA, pp.75–95.

Gounaris, V., Anderson, P. R. and Holsen, T. M.: 1993, Characteristics and environmental signific-ance of colloids in landfill leachate, Environ. Sci. Technol. 27, 1381–1387.

Gray, W. G. and Hoffman, J. L.: 1983a, A numerical model study of ground-water contamina-tion from Price’s landfill, New Jersey, I. Data base and flow simulation, Ground Water 21,7–14.

Gray, W. G. and Hoffman, J. L.: 1983b, A numerical model study of ground-water contaminationfrom Price’s landfill, New Jersey, II. Sensivity analysis and contaminant plume simulation,Ground Water 21, 15–21.

Greenberg, J. and Tomson, M.: 1992, Precipitation and dissolution kinetics and equilibria of aqueousferrous carbonate vs temperature, Appl. Geochem. 7, 185–190.

Griffin, R. A, Shimp, N. F., Steele, J. D., Ruch, R. R., White, W. A. and Hughes, G. M.: 1976,Attenuation of pollutants in municipal landfill leachate by passage through clay, Environ. Sci.Technol. 10, 1262–1268.

Grove, D. B. and Wood, W. W.: 1979, Prediction and field verification of subsurface-water qualitychanges during artificial recharge, Lubbock, Texas, Ground Water 17, 250–257.


Gureghian, A. B., Ward, D. S. and Cleary, R. W.: 1981, A finite element model for the migration ofleachate from a sanitary landfill in Long Island, New York – II: Application, Water Resour. Bull.17, 62–66.

Harmsen, J.: 1983, Identification of organic compounds in leachate from a waste tip, Water Res. 17,699–705.

Harzer, J. and Kinzelbach, W.: 1989, Coupling of transport and chemical processes in numericaltransport models, Geoderma 44, 115–127.

Hering, J. G. and Stumm, W.: 1990, Oxidative and reductive dissolution of minerals, In: M. F.Hochella and A. F. White (eds), Mineral-Water Interface Geochemistry, Reviews in Mineralogy23, Mineralogical Society of America, Washington, D.C., pp. 427–465.

Hindmarsh, A. C. and Petzold, L. R.: 1995, Algorithm and software for ordinary differential equa-tions and differential algebraic equations, Part II: Higher order methods and software packages,Comput. Phys. 9, 148–155.

Hunter, K. S., Wang, Y. and Van Cappellen, P.: 1998, Kinetic modeling of microbially-drivenredox chemistry of subsurface environments: coupling transport, microbial metabolism andgeochemistry, J. Hydrol. 209, 53–80.

Huyakorn, P. S. and Pinder, G. F.: 1983, Computational Methods in Subsurface Flow, Academic, SanDiego, California.

Huyakorn, P. S., Ungs, M. J., Mulkey, L. A. and Sudicky, E. A.: 1987, A three-dimensional analyticalmethod for predicting leachate migration, Ground Water 25, 588–598.

Huyakorn, P. S., Kool, J. B. and Blandford, T. N.: 1993, An overview of modeling technique forsolute transport in groundwater, In: H. E. Allen, E. M. Perdue and D. S. Brown (eds), Metals inGroundwater, Lewis publishers, MI, pp. 139–172.

IBM Canada Ltd.: 1976, Continuous System Modeling Program III (5734–X39), Program ReferenceManual, IBM Canada Ltd., Ont.

Inskeep, W. P. and Bloom, P. R.: 1985, An evaluation of rate equations for calcite precipitationkinetics at pCO2 less than 0.01 atm and pH greater than 8, Geochim. Cosmochim. Acta 49,2165–2180.

James, R. V. and Rubin, J.: 1979, Applicability of the local equilibrium assumption to transportthrough soils of solutes affected by ion exchange, In: Chemical Modeling in Aqueous Systems,ACS Symposium Series 93, American Chemical Society, Washington, D.C., USA, pp. 225–235.

Jennings, A. A., Kirkner, D. J. and Theis, T. L.: 1982, Multicomponent equilibrium chemistry ingroundwater quality models. Water Resour. Res. 18, 1089–1096.

Jensen, D. L., Boddum, J. K., Redemenn, S. and Christensen, T. H.: 1998, Speciation of dis-solved iron(II) and manganese(II) in a groundwater pollution plume, Environ. Sci. Technol. 32,2657–2664.

Johansen, O. J. and Carlson, D. A.: 1976, Characterization of sanitary landfill leachates, Water Res.10, 1129–1134.

Kehew, A. E. and Passero, R. N.: 1990, pH and redox buffer mechanisms in a glacial drift aquifercontaminated by landfill leachate, Ground Water 28, 728–737.

Khanbilvardi, R. M., Ahmed, S. and Gleason, P. J.: 1995, Flow investigation for landfill leachate(FILL), J. Environ. Engrg. 121, 45–57.

Kindred, J. S. and Celia, M. A.: 1989, Contaminant transport and biodegradation, 2. Conceptualmodel and test simulations, Water Resour. Res. 25, 1149–1159.

Kinzelbach, W., Schäfer, W. and Herzer, J.: 1991, Numerical modeling of natural and enhanceddenitrification processes in aquifers, Water Resour. Res. 27, 1123–1135.

Kirkner, D. J., Jennings, A. A. and Theis, T. L.: 1985, Multi-solute mass transport with chemicalinteraction kinetics, J. Hydrol. 76, 107–117.

Kjeldsen, P., Bjerg, P. L., Rügge, K., Christensen, T. H. and Pedersen, J. K.: 1998, Characterizationof an old municipal landfill (Grindsted, Denmark) as a groundwater pollution source: Landfillhydrology and leachate migration, Waste Manage. Res. 16, 14–22.


Knox, K and Jones, P. H.: 1979, Complexation characteristics of sanitary landfill leachates, WaterRes. 13, 839–846.

Konikow, L. F. and Bredehoeft, J. D.: 1974, Modeling flow and chemical quality changes in anirrigated stream-aquifer system, Water Resour. Res. 10, 546–562.

Kool, J. B., Huyakorn, P. S., Sudicky, E. A. and Saleem, Z. A.: 1994, A composite modeling approachfor subsurface transport of degrading contaminants from land-disposal sites, J. Contam. Hydrol.17, 69–90.

Langmuir, D.: 1997, Aqueous Environmental Geochemistry, Prentice Hall, New Jersey.Lensing, H. J., Vogt, M. and Herrling, B.: 1994, Modelling of biologically mediated redox processes

in the subsurface, J. Hydrol. 159, 125–143.Lichtner, P. C.: 1985, Continuum model for simultaneous chemical reactions and mass transport in

hydrothermal systems, Geochim. Cosmochim. Acta 49, 779–800.Lu, C. and Bai, H.: 1991, Leaching from solid waste landfills Part I: Modeling, Environ. Technol. 12,

545–558.Ludvigsen, L., Albrechtsen, H. J., Bjerg, P. L. and Christensen, T. H.: 1998, Anaerobic microbial

processes in a leachate contaminated aquifer (Grindsted, Denmark), J. Contam. Hydrol. 33,173–291.

Lyngkilde, J. and Christensen, T. H.: 1992a, Fate of organic contaminants in the redox zones of alandfill leachate pollution plume (Vejen, Denmark), J. Contam. Hydrol. 10, 291–307.

Lyngkilde, J. and Christensen, T. H.: 1992b, Redox zones of a landfill leachate pollution plume(Vejen, Denmark), J. Contam. Hydrol. 10, 273–289.

MacQuarrie, K. T. B., Sudicky, E. A. and Frind, E. O.: 1990, Simulation of biodegradable organiccontaminants in groundwater 1. Numerical formulation in principal directions, Water Resour.Res. 26, 207–222.

Mangold, D. C. and Tsang, C. F.: 1991, A summary of subsurface hydrological and hydrochemicalmodels, Rev. Geophys. 29, 51–79.

Mattigod, S. V. and Zachara, J. M.: 1996, Equilibrium modeling in soil chemistry, In: J. M. Bigham(ed.), Methods of Soil Analysis. Part 3. Chemical Methods, Soil Science Society of America, andAmerican Society of Agronomy, Madison, Wisconsin, USA, pp. 1309–1358.

McNab, W. W. Jr. and Narasimahan, T. N.: 1994, Modeling reactive transport of organic com-pounds in groundwater using a partial redox disequilibrium approach, Water Resour. Res. 30,2619–2635.

McNab, W. W. Jr. and Narasimhan, T. N.: 1995, Reactive transport of petroleum hydrocarbon con-stituents in a shallow aquifer: Modeling geochemical interactions between organic and inorganicspecies, Water Resour. Res. 31, 2027–2033.

Miller, C. W. and Benson, L. V.: 1983, Simulation of solute transport in a chemically reactiveheterogeneous system: Model development and application, Water Resour. Res. 19, 381–391.

Mills, W. B., Liu, S. and Fong, F. K.: 1991, Literature review and model (COMET) for colloid/metalstransport in porous media, Ground Water 29, 199–208.

Molz, F. J., Widdowsen, M. A. and Benefield, L. D.: 1986, Simulation of microbial growth dy-namics coupled to nutrient and oxygen transport in porous media, Water Resour. Res. 22,1207–1216.

Morel, F. M. M. and Hering, J. G.: 1993, Principles and Applications of Aquatic Chemistry, Wlley,New York, p. 588.

Morel, F. and Morgan, J.: 1972, A numerical method for computing equilibria in aqueous chemicalsystems, Environ. Sci.Technol. 6, 58–67.

Narasimhan, T. N. and Witherspoon, P. A.: 1976, An integrated finite difference method for analyzingfluid flow in porous media, Water Resour. Res. 12, 57–64.

Narasimhan, T. N., White, A. F. and Tokunaga, T.: 1986, Groundwater contamination from an inact-ive uranium mill tailings pile, 2, Application of a dynamic mixing model, Water Resour. Res. 22,1820–1834.


Nelson, A.: 1995, Landfill leakage and biofilms – can we rely on self clogging mechanisms, Proc.of the 7th annual conf. of the Waste Management Institute NZ, Auckland, New Zealand, pp.431–442.

Nicholson, R. V., Cherry, J. A. and Reardon, E. J.: 1983, Migration of contaminants in groundwaterat a landfill: A case study, VI. Hydrogeochemistry, J. Hydrol. 63, 131–142.

Nordstorm, D. K. et al.: 1979, A comparison of computerized chemical models for equilibriumcalculations in aqueous systems, In: Chemical Modeling in Aqueous Systems, ACS SymposiumSeries 93, American Chemical Society, Washington, D.C., USA. pp. 857–892.

Panda, M. N. and Lake, L. W.: 1994, Estimation of single-phase permeability from parameters ofparticle-size distribution, Am. Assoc. Petrol. Geol. Bull. 78, 1028–1039.

Park, S. S. and Jaffé, P. R.: 1996, Development of a sediment redox potential model for theassessment of postdepositional metal mobility, Ecol. Modell. 91, 169–181.

Parkhurst, D. L., Thorstensen, D. C. and Plummer, L. N.: 1980, PHREEQE: A Computer Programfor Geochemical Calculations, U.S. Geol. Surv. Water Resour. Invest., PB81–167801.

Pease, R. W. and Adrian, D. D.: 1978, Complexation between organic molecules and iron in anaer-obic landfill leachate, Proceedings of the 33rd Industrial Waste Conference, Purdue University,Lafayette, Indiana, pp. 219–224.

Pickens, J. F. and Lennox, W. C.: 1976, Numerical simulation of waste movement in steadygroundwater flow systems, Water Resour. Res. 12, 171–180.

Plummer, L. N., Wigley T. M. L. and Parkhurst, D. L.: 1978, The kinetics of calcite dissolution inCO2 water systems at 5 to 60◦C and 0.0 to 1.0 atm CO2, Am. J. Sci. 278, 179–216.

Plummer, L. N., Parkhurst, D. L. and Thorstensen, D. C.: 1983, Development of reaction models forgroundwater systems, Geochim. Cosmochim. Acta 47, 665–686.

Postma, D., Boesen, C., Kristiansen, H. and Larsen, F.: 1991, Nitrate reduction in an unconfinedsandy aquifer: Water chemistry, reduction processes and geochemical modeling, Water Resour.Res. 27, 2027–2046.

Quigley, R. M., Fernandez, F., Yanful, E., Helgason, T., Margaritis, A. and Whitby, J. L.: 1987,Hydraulic conductivity of contaminated natural clay directly below a domestic landfill, Can.Geotech. J. 24, 377–383.

Reardon, E. J.: 1981, Kd’s – Can they be used to describe reversible ion sorption reaction incontaminant migration? Ground Water 19, 279–286.

Reed, M. H.: 1982, Calculation of multicomponent chemical equilibria and reaction processesin systems involving minerals, gases, and an aqueous phase, Geochim. Cosmochim. Acta 46,513–528.

Rickard, D.: 1995, Kinetics of FeS precipitation: Part 1. Competing reaction mechanisms, Geochim.Cosmochim. Acta 59, 4367–4379.

Rittmann, B. E. and McCarty, P. L.: 1980, Model of steady-state-biofilm kinetics, Biotechnol. Bioeng.22, 2343–2357.

Rittmann, B. E. and VanBriesen, J. M.: 1996, Microbiological processes in reactive modeling, In:P. C. Lichtner, C. I. Steefel and E. H. Oelkers (eds), Reactive Transport in Porous Media,Reviews in Mineralogy, 34, Mineralogical Society of America, Washington, D.C., pp. 311–334.

Rittmann, B. E., McCarty, P. L. and Roberts, P. V.: 1980, Trace-organics biodegradation in aquiferrecharge, Ground Water 18, 236–243.

Rittmann, B. E., Fleming, I. R. and Rowe, R. K.: 1996, Leachate chemistry: Its implication forclogging, North American Water and Environment Congress ’96, Anaheim, CA. June, paper 4(CD Rom) 6p, Session GW-1, Biological Processes in Groundwater Quality.

Rowe, R. K.: 1987, Pollutant transport through barriers, In: R. D. Woods (ed.), Geotechnical Practicefor Waste Disposal, Geotechnical Special Publication No. 13, ASCE, pp. 159–181.

Rowe, R. and Booker, J. R.: 1985a, 1-D pollutant migration in soils of finite depth, J. Geotech. Engrg.ASCE, 111, 479–499.


Rowe, R. and Booker, J. R.: 1985b, 2-D pollutant migration in soils of finite depth, Can. Geotech. J.22, 429–436.

Rowe, R. and Booker, J. R.: 1986, A finite layer technique for calculating three-dimensional pollutantmigration in soil, Geotechnique 36, 205–214.

Rowe, R. K. and Booker, J. R.: 1990, Program POLLUTE v.5 – 1D Pollutant Migration through aNon-homogeneous Soil: User’s Manual, Geotechnical Research Centre, University of WesternOntario, London, Canada.

Rowe, R. K. and Fraser, M. J.: 1993a, Long-term behaviour of engineered barrier systems,Proceedings Sardinia 93, 4th International Landfill Symposium, Cagliari, Italy, 397–406.

Rowe, R. K. and Fraser, M. J.: 1993b, Service life of barrier systems in the assessment of contaminantimpact, Proceedings of Joint CSCE-ASCE National Conference on Environmental Engineering,Montreal, Canada, pp. 1217–1224.

Rowe, R. K.: 1991, Contaminant impact assessment and the contaminating lifespan of landfills, Can.J. Civ. Eng. 18, 244–253.

Rowe, R. K., Quigley R. M. and Booker, J. R.: 1995, Clayey Barrier Systems for Waste DisposalFacilities, E & FN Spon, London, UK.

Rowe, R. K., Hrapovic, L. and Armstrong, M. D.: 1996, Diffusion of organic pollutants throughHDPE geomembrane and composite liners and its influence on groundwater quality, Proceedingsof 1st European Geosynthetics Conference, Maastricht, pp. 737–742.

Rowe, R. K., Fleming, I. R., Armstrong, M. D., Cooke, A. J., Cullimore, D. R., Rittmann, B. E.,Bennestt, P. and Longstaffe, F. J.: 1997a, Recent advances in understanding the clogging ofleachate collection systems, Proceedings Sardinia 97, 6th International Landfill Symposium,Cagliari, Italy, 3, pp. 383–390.

Rowe, R. K., Cooke, A. J., Rittmann, B. E. and Fleming, I.: 1997b, Some considerations in numericalmodelling of leachate collection system clogging, Proceedings of 6th International Symposiumson Numerical Models in Geomechanics – NUMOG VI, Montreal, Canada, pp. 277–282.

Rubin, J.: 1983, Transport of reacting solutes in porous media: Relation between mathematicalnature of problem formulation and chemical nature of reactions, Water Resour. Res. 19, 1231–1252.

Rubin, J. and James, R. V.: 1973, Dispersion-affected transport of reacting solutes in saturated por-ous media: Galerkin method applied to equilibrium controlled exchange in unidirectional steadywater flow, Water Resour. Res. 9, 1332–1356.

Rügge, K., Bjerg, P. L. and Christensen, T. H.: 1995, Distribution of organic compounds from muni-cipal solid waste in the groundwater downgradient of a landfill (Grindsted, Denmark), Environ.Sci. Technol. 29, 1395–1414.

Salvage, K. M. and Yeh, G. T.: 1998, Development and application of a numerical model of kin-etic and equilibrium microbiological and geochemical reactions (BIOKEMOD), J. Hydrol. 209,27–52.

Schäfer, D., Schäfer, W. and Kinzelbach, W.: 1998, Simulation of reactive processes relative to bio-degradation in aquifers 1. Structure of the three-dimensional reactive transport model, J. Contam.Hydrol. 31, 167–186.

Schroeder, P. R., Gibson, A. C. and Smolen, M. D.: 1984, The Hydrologic Evaluation of LandfillPerformance (HELP) Model, Vol II, Documentation for Version 1, U.S. Environ. Prot. Agency,Cincinnati, Ohio.

Schulz, H. D. and Reardon, E. J.: 1983, A combined mixing cell/analytical model to describe two-dimensional reactive solute transport for unidirectional groundwater flow, Water Resour. Res. 19,493–502.

Shen, H. and Nikolaidis, N. P.: 1997, A direct substitution method for multicomponent solutetransport in ground water, Ground Water 35, 67–78.

Skopp, J.: 1986, Analysis of time-dependent chemical processes in soils, J. Environ. Qual. 15,205–213.


Smith, S. L. and Jaffé, P. R.: 1998, Modeling the transport and reaction of trace metals in water-saturated soils and sediments. Water Resour. Res. 34, 3135–3147.

Sposito, G.: 1984, Chemical models of inorganic pollutants in soils, CRC Crit. Rev. Environ. Cont.15, 1–24.

Sposito, G. and Mattigod, S. V.: 1980, GEOCHEM: A Computer Program for the Calculation ofChemical Equilibria in Soil Solutions and other Natural Water Systems, Kearney Foundation ofSoil Science, Univ. of Calif., Riverside, California.

Steefel, C. I. and Lasaga, A. C.: 1990, Evolution of dissolution patterns: permeability change dueto coupled flow and reaction, In: D. C. Melchoir and R. L. Bassett (eds), Chemical Mod-eling of Aqueous Systems II, ACS Symposium Series 416, American Chemical Society, pp.212–225.

Steefel, C. I. and Lasaga, A. C.: 1994, A coupled model for transport of multiple chemical speciesand kinetic precipitation/dissolution reactions with application to reactive flow in single phasehydrothermal systems, Am. J. Sci. 294, 529–592.

Steefel, C. I. and MacQuarrie, K. T. B.: 1996, Approaches to modeling of reactive transport in porousmedia, In: P.C. Lichtner, C. I. Steefel and E. H. Oelkers (eds), Reactive Transport in PorousMedia, Reviews in Mineralogy, 34, Mineralogical Society of America, Washington, D.C., pp.83–129.

Sternbeck, J.: 1997, Kinetics of rhodochrosite crystal growth at 25◦C: The role of surface speciation,Geochim. Cosmochim. Acta 61, 785–793.

Strang, G.: 1968, On the construction and comparison of difference schemes, SIAM J. Numer. Anal.5, 506–517.

Straub, W. A. and Lynch, D. R.: 1982, Models of landfill and leaching: Moisture flow and inorganicstrength, J. Environ. Engrg. Div. ASCE 108, 231–250.

Stumm, W. and Morgan, J. J.: 1996, Aquatic Chemistry, Chemical Equilibria and Rates in NaturalWaters, Wiley, New York.

Sudicky, E. A.: 1989, The Laplace transform Galerkin tecnique: A time-continuous finite ele-ment theory and application of mass transport in groundwater, Water Resour. Res. 25, 1833–1846.

Sykes, J. F., Pahwa, S. B., Lantz, R. B. and Ward, D. S.: 1982a, Numerical simulation of flow andcontaminant migration at an extensively monitored landfill, Water Resour. Res. 18, 1687–1704.

Sykes, J. F., Soyupak, S. and Farquhar, G. J.: 1982b, Modeling of leachate organic migration andattenuation in groundwaters below sanitary landfills, Water Resour. Res. 18, 135–145.

Taylor, S. W. and Jaffé, P. R.: 1990, Substrate and biomass transport in a porous medium, WaterResour. Res. 26, 2181–2194.

Taylor, S. W., Milly, P. C. D. and Jaffé, P. R.: 1990, Biofilm growth and the related changes in thephysical properties of a porous medium, 2. Permeability. Water Resour. Res. 26, 2161–2169.

Tebes-Stevens, C., Valocchi, A. J., VanBriesen, J. M. and Rittmann, B.E.: 1998, Multicompon-ent transport with coupled geochemical and microbiological reactions: model description andexample simulations, J. Hydrol. 209, 8–26.

Tipping, E.: 1994, WHAM: a chemical equilibrium model and computer code for waters, sedimentsand soils incorporating a discrete site/electrostatic model of ion binding by humic substances,Comput. Geosci. 20, 973–1023.

Travis, C. C. and Etnier, E. L.: 1981, A survey of sorption relationships for reactive solutes in soil,J. Environ. Qual. 10, 8–17.

Valocchi, A. J.: 1985, Validity of the local equilibrium assumption for modeling sorbing solutetransport through homogeneous soils, Water Resour. Res. 21, 808–820.

Valocchi, A. J. and Malmstead, M.: 1992, Accuracy of operator splitting for advection–dispersion-reaction problems, Water Resour. Res. 28, 1471–1476.

Valocchi, A. J., Street, R. L. and Roberts, P. V.: 1981, Transport of ion-exchanging solute ingroundwater: chromatographic theory and field simulation. Water Resour. Res. 17, 1517–1527.


Van Breukelen, B. M., Appelo, C. A. J. and Olsthoorn, T. N.: 1998, Hydrogeochemical transportmodeling of 24 years of Rhine water infiltration in the dunes of the Amsterdam Water Supply,J. Hydrol. 209, 281–296.

Van Cappellen, P. and Wang, Y.: 1995, Metal cycling in surface sediments: modeling the interplay oftransport and reaction, In: H.E. Allen (ed.), Metal Contaminated Aquatic Sediments, Ann ArborPress, London, pp. 21–64.

van Genuchten, M. T. and Alves, W. J.: 1982, Analytical solutions of the one-dimensionalconvective–dispersive solute transport equation. USDA-ARS Tech. Bull. 1661, U.S. Dept. ofAgriculture, Washington, D.C.

Verma A. and Pruess, K.: 1988, Thermohydrological conditions and silica redistribution nearhigh-level nuclear wastes emplaced in saturated geological formations, J. Geophys. Res. 93,1159–1173.

Vandevivere, P., Baveye, P., de Lozada, D. S. and Deleo, P.: 1995, Microbial clogging of satur-ated soils and aquifer materials: Evaluation of mathematical models, Water Resour. Res. 31,2173–2180.

Wang, Y. and Van Cappellen, P.: 1996, A multicomponent reactive transport model of early diagen-esis: application to redox cycling in coastal marine sediments, Geochim. Cosmochim. Acta 60,2993–3014.

Walsh, M. P., Bryant, S. L., Schechter, R. S. and Lake. L. W.: 1984, Precipitation and dissolution ofsolids attending flow through porous media, AIChE J. 30, 317–328.

Walter, A. L., Frind, E. O., Blowers, D. W., Ptacek, C. J. and Molson, J. W.: 1994, Modeling ofmulticomponent reactive transport in groundwater - 1. Model development and evaluation, WaterResour. Res. 30, 3137–3148.

Warren, L. A. and Ferris, F. G.: 1998, Continuum between sorption and precipitation of Fe(III) onmicrobial surfaces, Environ. Sci. Technol. 32, 2331–2337.

Weber, W. J. Jr., McGinley, P. M. and Katz, L. E.: 1991, Sorption phenomena in subsurface systems:Concepts, models and effects on contaminant fate and transport, Water Res. 25, 499–528.

Weir, G. J. and White, S. P.: 1996, Surface deposition from fluid flow in a porous medium, Transportin Porous Media 25, 79–96.

Wen, X., Du, Q. and Tang, H.: 1998, Surface complexation model for the heavy metal adsorption onnatural sediment, Environ. Sci. Technol. 32, 870–875.

Westall, J. C., Zachary, J. L. and Morel, F. M. M.: 1976, MINEQL: A Computer Program for theCalculation of Chemical Equilibrium Composition of Aqueous System, Tech. Note 18, Dept. ofCiv. Eng., MIT, Cambridge.

Widdowson, M. A., Molz, F. J. and Benefield, L. D.: 1988, A numerical transport model for oxygen-and nitrate-based respiration linked to substrate and nutrient availability in porous media, WaterResour. Res. 24, 1553–1565.

Wu, G. and Li, L. Y.: 1998, Modeling of heavy metal migration in sand/bentonite and the leachatepH effect, J. Contam. Hydrol. 33, 313–336.

Yanful, E. K., Quigley, R. M. and Nesbitt, H. W.: 1988, Heavy metal migration at a landfill site,Sarnia, Ontario, Canada-2: Metal partitioning and geotechnical implications, Appl. Geochem. 3,623–629.

Yates, M. V. and Yates, S. R.: 1988, Modeling microbial fate in the subsurface environment, CRCCrit. Rev. Environ. Cont. 17, 307–345.

Yeh, G. T. and Tripathi, V. S.: 1989, A critical evaluation of recent developments in hydro-geochemical transport models of reactive multichemical components, Water Resour. Res. 25,93–108.

Yeh, G. T. and Tripathi, V. S.: 1991, A model for simulating transport of reactive multispeciescomponents: Model development and demonstration, Water Resour. Res. 27, 3075–3094.


Young, T. R. and Boris, J. P.: 1977, A numerical technique for solving stiff ordinary differentialequations associated with the chemical kinetics of reactive-flow problems, J. Phys. Chem. 81,2424–2427.

Zysset, A. and Stauffer, F.: 1992, Modeling of microbial processes in groundwater infiltrationsystems, In: T. F. Russell, R. E. Ewing, C. A. Brebbia, W. G. Gray and G. F. Pinder (eds),Mathematical Modeling in Water Resources, Computational Mechanics Publications, Billerica,Mass., pp. 325–332.

Zysset, A., Stauffer, F. and Dracos, T.: 1994a, Modeling of chemically reactive groundwatertransport, Water Resour. Res. 30, 2217–2228.

Zysset, A., Stauffer, F. and Dracos, T.: 1994b, Modeling of reactive groundwater transport governedby biodegradation, Water Resour. Res. 30, 2423–2434.

Documents

Modeling Biogeochemical Processes in Leachate-Contaminated ...€¦ · MODELING BIOGEOCHEMICAL PROCESSES 409 Table I. Sequence of different redox reaction downgradient of a landﬁll