One-dimensional model for biogeochemical interactions and ... · growth and gas production. A two-step sequential operator splitting method isused to solve the coupled transport and

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ology 96 (2008) 32–47www.elsevier.com/locate/jconhyd

Journal of Contaminant Hydr

One-dimensional model for biogeochemical interactions andpermeability reduction in soils during leachate permeation

Naresh Singhal ⁎, Jahangir Islam 1

Department of Civil and Environmental Engineering, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

Received 8 February 2006; received in revised form 23 September 2007; accepted 26 September 2007Available online 5 October 2007

Abstract

This paper uses the findings from a column study to develop a reactive model for exploring the interactions occurring in leachate-contaminated soils. The changes occurring in the concentrations of acetic acid, sulphate, suspended and attached biomass, Fe(II), Mn(II), calcium, carbonate ions, and pH in the column are assessed. The mathematical model considers geochemical equilibrium, kineticbiodegradation, precipitation–dissolution reactions, bacterial and substrate transport, and permeability reduction arising from bacterialgrowth and gas production. A two-step sequential operator splitting method is used to solve the coupled transport and biogeochemicalreaction equations. The model gives satisfactory fits to experimental data and the simulations show that the transport of metals in soilis controlled by multiple competing biotic and abiotic reactions. These findings suggest that bioaccumulation and gas formation,compared to chemical precipitation, have a larger influence on hydraulic conductivity reduction.© 2007 Elsevier B.V. All rights reserved.

Keywords: Geochemical modeling; Leachate flow; Chemical speciation; Metal precipitation; Bacterial transport; Bioclogging; Permeability reduction

1. Introduction

The impact of leakage from landfills on the envi-ronment is governed by the transformation of inorganicand organic constituents of leachate via biogeochemicalinteractions. A variety of complex reactions occur be-tween the biological (primarily microorganisms, suchas bacteria), geological, and chemical components ofleachate contaminated soils. These reactions not onlyinfluence chemical transport but can also affect ground-water flow by altering the soil's porosity and perme-

⁎ Corresponding author. Department of Civil and EnvironmentalEngineering, University of Auckland, Private 92019, Auckland 1001,New Zealand. Tel.: +64 9 373 7599x84512; fax: +64 9 3737462.

E-mail address: [email protected] (N. Singhal).1 Presently at North Shore City Council, Private Bag 93500

Takapuna, North Shore City, New Zealand.

0169-7722/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jconhyd.2007.09.007

ability due to bacterial growth, chemical precipitation,and anaerobic gas production. Under appropriate con-ditions the combined effects of biomass growth, metalprecipitation and gas production on the soil's flow andtransport properties can be significant (e.g., Brune et al.,1994; Rowe et al., 1997).

Reactive transport modelling has evolved as a tool foranalysing the effects of complex biogeochemical interac-tions and reaction controls on soils. Quantification of theseeffects using mathematical relationships is an area ofcontinuing research with several mathematical modelshaving been developed to simulate the geochemicalprocesses (Yeh and Tripathi, 1991; Engesgaard andKipp, 1992; Walter et al., 1994) and biological transfor-mations (Borden and Bedient, 1986; Kindred and Celia,1989; Taylor et al., 1990; Clement et al., 1996a) in soils.The development and use of integrated biogeochemical

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http://dx.doi.org/10.1016/j.jconhyd.2007.09.007

33N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47

models coupling transport processes to primary reactions(i.e., organic matter degradation) and secondary reactions(e.g., redox transformation, mineral dissolution andprecipitation, sorption, and acid–base and homogeneousspeciation) is of more recent origin (Lensing et al., 1994;McNab andNarasimhan, 1994; Zysset et al., 1994; Hunteret al., 1998; Schäfer et al., 1998a; Tebes-Stevens et al.,1998; Prommer et al., 1999; Mayer et al., 2002; VanBreukelen et al., 2004). In these models geochemicalreactions are simulated assuming local equilibrium(Engesgaard andKipp, 1992), partial redox disequilibrium(McNab and Narasimhan, 1994; Brun and Engesgaard,2002), kinetic heterogeneous redox speciation (Tebes-Stevens et al., 1998; Mayer et al., 2002; Van Breukelen etal., 2004), or fully kinetic redox speciation (Hunter et al.,1998). The bacterial reactions have typically beensimulated assuming either negligible bacterial activity(Engesgaard and Kipp, 1992), prescribed zero- or first-order microbial reactions (McNab and Narasimhan, 1994;Mayer et al., 2002; Van Breukelen et al., 2004), orbacterial growth dynamics described using Monodkinetics (Schäfer et al., 1998a; Tebes-Stevens et al., 1998).

The previous biogeochemical models have ignored theeffects of biogeochemical interactions on the porosity andpermeability of soil (e.g., due to biomass accumulation,chemical precipitation or gas formation) by assuming aconstant biophase volume (e.g., Schäfer et al., 1998a) orinstantaneous degassing (e.g., Van Breukelen et al.,2004). Recent progress has beenmade in the developmentof models to describe gas bubble formation and its effecton soil permeability (e.g., see Amos and Mayer, 2006a,b)and the patterns for the flow of gas injected into saturatedporous media (Selker et al., 2007). Several models havealso been developed for permeability reduction due tobiomass accumulation in soil. Taylor et al. (1990) used the“spherical soil grains” approach of Kozeny–Carman(Carman, 1937) and the “cut-and-random-rejoining oftubes” approach of Childs and Collis-George (1950).Sarkar et al. (1994) used the effective medium theory torepresent the soil medium as a three-dimensional networkof pores and estimated the effective hydraulic conduc-tance based on the pore throat size distribution followingbacterial plugging. Clement et al. (1996a) presentedanalytical equations for changes in porosity, specificsurface area, and permeability due to biomass accumu-lation in porous media. Thullner et al. (2002,2004)described the permeability reduction in pore networksfrom biomass growing on biofilm and in discrete coloniesthat occupy pores entirely. The colony-based model waslater used by Seifert and Engesgaard (2007) to simulatebioclogging of porousmedia.While the proponents of themodels successfully calibrated their models, the limited

uptake and application of these models in other studiesmakes it difficult to identify a single model as beingsuperior to others. Furthermore, comprehensive modelsthat couple the effects of bioclogging and gas formationwith chemical speciation have not been previouslypresented in the literature.

This paper presents a mathematical model for thebiogeochemical interactions occurring during leachatepermeation in packed columns. The model considerskinetic precipitation–dissolution and equilibrium aqueousgeochemical speciation, kinetic biodegradation, chemicaland bacterial transport, and biomass accumulation in soils.In particular, the model accounts for the effects of thebiophase, chemical precipitate, and separate phase gas onthe soil's permeability. To the authors' knowledge this isthe first study to consider the above mentioned biogeo-chemical processes in an integrated manner, althoughprevious studies have tackled subsets of the currentsystem. Experimental data obtained from laboratoryexperiments with soil columns (Islam and Singhal,2004) is used to assess the strengths and weaknesses ofthe proposedmodel and identify areas for further research.

2. Laboratory study

Laboratory experiments were conducted by pumpingleachate collected from a local municipal landfill throughpacked columns to investigate the effects of leachatepermeation and interactions between the soil media,bacteria and leachate constituents on soil permeability(details presented in Islam andSinghal, 2004). The columnswere 50 cm long and 5 cm in diameter and were packedwith 0.21–0.61 mm sized sand. The porosity of the packedmedia was estimated as 0.41 by gravimetric analysis. Aflow of 0.23ml/min wasmaintained in the columns and thehead loss data was used to estimate the average saturatedhydraulic conductivity as 8.8×10−3 cm/s. A pulse of 0.5Msodium bromide solution was then injected into a columnand an analytical solution of the advective–dispersiveequation was fitted to the observed bromide breakthroughdata to obtain a dispersivity of 0.12 cm. The bacterialinoculum used to seed the columns was obtained bycentrifuging 24 L of landfill leachate and re-suspending thecentrifugate in 2 L of raw leachate. This microbe-enrichedsolution was pumped into three columns at 5 ml/min, andwas followed by 12 h of no flow to promote bacterialattachment to the soil. One of the columns was thendismantled to determine the initial distribution of attachedbiomass in soil. The remaining two columns were fedleachate, amendedwith acetic acid to give a final acetic acidconcentration of 1750mg/L (equivalent to 350mg-C/L), inupflow mode at 0.23 ml/day for 58 days (Phase 1). To put

34 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47

this acetic acid concentration in perspective, the dissolvedorganic carbon concentrations in leachate contaminatedgroundwater typically range up to 120mg-C/L (Bjerg et al.,1995; Nielsen et al., 1995), but in selective regions withinthe aquifer the concentration can be as large as 480mg-C/L(Brun et al., 2002). The acetic acid concentration used,therefore, lies at the high end of the reported dissolvedorganic carbon concentrations in contaminated aquifers. Arelatively large concentration of acetic acid is used in thisstudy to promote biological growth and gas formation sothat their effects can be observed over short durations. After58 days one of the columns was dismantled to determinethe spatial distribution of attached biomass and precipitatedmetals. The last column was operated with an increasedinfluent acetic acid concentration of 2900mg/L for 16 days,followed by a further increased influent acetic acidconcentration of 5100 mg/L for an additional 52 days(Phase 2). After 126 days of operation this column wasdismantled and the soil analysed for attached biomass andprecipitated metals.

In the columns acetic acid was principally biode-graded via methanogenesis, resulting in gas productionof up to 1440 ml/day. The acetic acid degradation wasaccompanied by a rapid increase in pH, inorganiccarbon (dissolved carbonate), and biomass accumula-tion in the inlet region of the columns. This led tocarbonate supersaturation, which promoted the precip-itation of iron, manganese, and calcium as carbonate inthe 0–2 cm section of the columns. Biomass accumu-lation, metal precipitation, and gas production reducedthe hydraulic conductivity in the inlet region of thecolumns by over two orders of magnitude.

3. Model development

The model consists of two submodels — one forchemical transport and the other for permeabilityreduction. The chemical transport submodel describesthe transport and transformation of dissolved leachateconstituents in soil, and the permeability reductionsubmodel describes the change in soil permeability dueto biomass accumulation, chemical precipitation and gasproduction. The reactive transport model is written interms of the total aqueous concentrations of a specified setof components, which are defined as linearly independentchemical entities such that every species in the system canbe expressed as the product of a reaction involving onlythe components, and no component can be written interms of components other than itself (Yeh and Tripathi,1989). For a given system, the set of components is notunique, but once it has been defined, the representation ofspecies in terms of this set of components is unique.

3.1. Reactive transport model

The transport of dissolved components is describedusing the general one-dimensional form of the contam-inant transport equation for mobile components in theaqueous phase as follows (Bear, 1979):

∂∂t

nCj

� �� ∂∂x

nD∂Cj

∂x

� �þ ∂∂x

nvCj

� �¼nRj; j¼ 1; N ;Nc

ð1Þ

v ¼ qn¼ �K

n∂h∂x

ð2Þ

where n is the porosity (dimensionless), q is the Darcyvelocity (L/T), t is time (T), v is average pore fluidvelocity (L/T), x is a unit vector pointed verticallyupwards (L), Cj is the total dissolved concentration ofcomponent j (M/L3), D is the hydrodynamic dispersioncoefficient (L2/T), K (=kikrw) is hydraulic conductivity(L/T) and ki and krw are respectively the saturated (L/T)and relative permeabilities, Nc is the total number ofdissolved components, and Rj is the source/sink term(M/L3/T) representing the changes in total aqueousconcentration of component j due to chemical andbiological reactions. Eqs. (1) and (2) predict theconcentrations of the dissolved inorganics, dissolvedorganic substrates, dissolved electron acceptors, andsuspended biomass.

The immobile components are not transported andare therefore treated using mass balance as follows:

∂Mm

∂t¼ Rm; m ¼ 1; N ;Nm ð3Þ

where Mm is the concentration of immobile phase m,Nm is the number of immobile components and Rm is therate of change of immobile phases due to chemical andbiological reactions. The concentration array Mm in Eq.(3) represents the concentration of immobile compo-nents, i.e., precipitated species, adsorbed species andsoil-attached biomass.

The generic source/sink terms, Rj and Rm, are used todescribe a variety of reactions, which are modelled bythe following modules.

3.1.1. Geochemical equilibrium reactions moduleThis module uses the equilibrium speciation model

MINTEQA2 (Allison et al., 1991) to model thehomogeneous chemical reactions, such as aqueous spe-ciation, acid–base interactions, and oxidation–reduction.In addition, adsorption reactions are also assumed tooccur at equilibrium. The equilibrium reactions are solved


using the ion association equilibrium-constant approach,which involves setting up non-linear algebraic equationsusing equilibrium constants embedded in mass balanceequations for the various components in the system. Theconcentrations of the aqueous, adsorbed and precipitatedspecies are calculated from the mass action laws and theresulting set of non-linear algebraic equations is solved byNewton–Raphson approximation method for the individ-ual ion activities, which are used to calculate thecomponent concentrations at equilibrium.

3.1.2. Kinetic precipitation–dissolution moduleThis module considers the precipitation and dissolu-

tion of the four dominant minerals — calcite (CaCO3),siderite (FeCO3), rhodochrosite (MnCO3), and ironsulphide (FeS), which are modelled using the followingrate expression (Smith and Jaffé, 1998):

∂Cj;s

∂t¼ �aj;sks jNs

l¼l u1½ �al;s � Ksp;s

� � ð4Þ

where aj,s and al,s are the stoichiometric coefficients ofcomponents j and l forming precipitate species s, ks is theprecipitation rate coefficient, ul is the free ion activity ofcomponent k in solution, Cj,s is the concentration ofaqueous components j forming precipitate, Ksp,s is theequilibrium solubility product of the precipitated species,and Ns is the number of components in the precipitate.The precipitation–dissolution kinetic rate expressionsused in the study are presented in Table 1.

3.1.3. Biotransport and kinetic biodegradation moduleThis module describes the transport and accumula-

tion of bacteria in soil, and the biodegradation of organicchemicals. No assumptions are made on the structureand distribution of microorganisms degrading the or-ganic compounds. The acetate degradation and micro-bial growth is expressed as follows (e.g., Clement et al.,1996b):

∂Cs

∂t¼ � lmax

YCs

Ks þ Cs

Cea

Kea þ CeaXa þ qsXs

ng

� �kj

mIFm

ð5Þ

∂Xs

∂t¼ lmax

Cs

Ks þ Cs

Cea

Kea þ CeaXskgj

mIFm

� KdecXs � KdetXs þ nKattXa

qsð6Þ

∂Xa

∂t¼ lmax

Cs

Ks þ Cs

Cea

Kea þ CeaXakj

mIFm

� KdecXa � KattXa þ qsKdetXs

nð7Þ

where η is the effectiveness factor, λ is the metabolicpotential function, μmax is the maximum specific growthrate of biomass (1/T), ρs is the bulk density of aquifersolids (M/L3), Cea is the concentration of terminalelectron acceptor (M/L3), Cs is the acetate concentrationin the bulk (mobile) fluid (M/L3), IFm is the inhibitionfunction for inhibiting species m, Katt is the biomassattachment coefficient (1/T), Kdec is the first-orderendogenous decay coefficient (1/T), Kdet is the biomassdetachment coefficient (1/T), Ks and Kea are the half-saturation constants for organic substrate and electronacceptors, respectively (M/L3), Xa is the suspendedbiomass concentration (M/L3), Xs is the soil-attachedbiomass concentration (M/M), and Y is the yieldcoefficient for the biomass (cell mass produced permass of substrate consumed). The attachment coefficient(Katt) is expressed as a function of the volume fraction ofattached biomass (ns) as follows (Taylor and Jaffé, 1990):

Katt ¼ 75 ns day�1� � ð8Þ

The metabolic potential function λ is used to modelthe lag time, observed in some biological processes, asfollows (Wood et al., 1994):

k ¼0; t V sL

s� sLsE � sL

; sL V t V sE

1; t N sE

8><>: ð9Þ

where τ is the time for which microorganisms have beenin contact with the substrates (T), τL is the lag time (T),and τE is the time required to reach exponential growth(T).

The effectiveness factor η is defined by Zysset et al.(1994) as:

g ¼ Xmax � Xs

Xmaxð10Þ

where Xmax is the maximum capacity for the biomass tobe attached (M/M).

The inhibition functions are used to model thesequential use of stronger to weaker electron acceptorsand are expressed as follows (Van Cappellen andGaillard, 1996):

IFm ¼ ICm

ICm þ EAmð11Þ

where EAm is the concentration of the inhibitingelectron acceptor m (M/L3) and ICm is the inhibitionconstant (M/L3).

The biodegradation reactions for acetic acid in differentredox environments are presented in Eqs. (12)–(15) and the

Table 1Precipitation–dissolution rate formulations

Precipitating/dissolving mineral Kinetic rate expressions Solubility product, Ksp Calibrated rate constant

Calcite (CaCO3) k1m ([Ca2+][CO3

2−]−Ksp) 10−8.47 5.0×103 mol−1 l d−1

Dolomite (CaMg(CO3)2) k2m ([Ca2+][Mg2+][CO3

2−]2−Ksp) 10−17.00 5.0×109 mol−1 l d−1

Siderite (FeCO3) k3m ([Fe2+][CO3

2−]−Ksp) 10−10.55 2.0×10−1 mol−1 l d−1

Rhodochrosite (MnCO3) k4m ([Mn2+][CO3

2−]−Ksp) 10−10.41 1.0×10−1 mol−1 l d−1

Iron Sulphide (FeS) k5m ([Fe2+][HS−] / [H+]−Ksp) 10−3.91 2.0×10−2 mol−1 l d−1

Solid Fe(III) reduction −k1Fe(III) [CH3COOH] – 1.5×10−2 d−1

−k2Fe(III) [TS] [Fe(OH)3] – 2.5×101 mol−1 l d−1

Solid Mn(IV) reduction −k1Mn(IV) [CH3COOH] – 5.0×10−4 d−1

−k2Mn(IV) [TS] [MnO2] – 5.5×101 mol−1 l d−1

−k3Mn(IV) [Fe2+] [MnO2] – 5.0×10−1 mol−1 l d−1

Note: [TS]=[H2S]+[HS]+[S2−].


overall reaction R, including the oxidation of organicmatter, reduction of inorganic compound and bacterial cellsynthesis, is given in Eq. (16) (Criddle et al., 1991).

CH3COO− þ 4ð1−fsÞMnO2 þ 0:4fsNH

þ4

þð9−8:4fsÞHþ¼N 0:4fsC5H7O2Nþ2ð1−fsÞH2CO

⁎3 þ 4ð1−fsÞMn2þ

þð4−2:8fsÞH2O ð12ÞCH3COO

− þ 8ð1−fsÞFeðOHÞ3 þ 0:4fsNHþ4


⁎3 þ 8ð1−fsÞFe2þ

þð20−18:8fsÞH2O ð13Þ

CH3COO− þ ð1−fsÞSO2−

4 þ 0:4fsNHþ4


⁎3 þ ð1−fsÞHS−

þ1:2fsH2O ð14ÞCH3COO

− þ 0:4fsNHþ4 þ ð1−2:2fsÞH2O

þð1−0:4fsÞHþ¼N 0:4fsC5H7O2Nþð1−fsÞH2CO

⁎3 þ ð1−fsÞCH4 ð15Þ

R ¼ Rd þ fe Ra þ fs Rc ð16Þwhere Rd, Ra, and Rc are the half-reactions for the electrondonor, acceptor, and bacterial cell synthesis respectively, fsis the fraction of electrons diverted for synthesis, fe is thefraction of electrons used for energy generation, and thesum of fs and fe equals 1. The values for fs are 0.40, 0.07,0.06, and 0.05 with Fe(III), Mn(IV), SO4

2−, and CO2,respectively, as electron acceptors (Criddle et al., 1991).The changes in concentrations of the electron acceptors,pH, and inorganic carbon due to biodegradation reactionsare computed from the stoichiometry of the microbialmediated redox reactions given in Eqs. (12)–(15).

Following the approach used by Wang and VanCappellen (1996) primary reactions, i.e., reactions involv-ing biodegradation of acetate using Fe(III) and Mn(IV) aselectron acceptors, are represented as first-order kinetic

reactions, while the secondary abiotic redox reactions (e.g.,those betweenFe(III),Mn(IV) and dissolved sulphides, andbetween Mn(IV) and dissolved Fe(II)) are formulated asbimolecular kinetic rate expressions in terms of thedissolved and solid concentrations of the respective species.This representation assumes that growth substrate concen-tration is limiting the primary reactions, while the sec-ondary reactions are controlled by the interactions betweenthe dissolved species and the corresponding solid phase.The secondary abiotic redox reactions for the reductionof Fe(III) and Mn(IV) are presented in Eqs. (17)–(19).Accordingly, the kinetic expressions for microbially me-diated reactions in Eqs. (12) and (13) are presented inEqs. (20) and (21), respectively, and for abiotic reactions inEqs. (17)–(19) by Eqs. (22)–(24), respectively. The sul-phate reduction (Eq. (14)) and methanogenesis (Eq. (15))reactions do not involve solid minerals and are representedusing the Monod kinetic relationship in Eq. (5). The cou-pling of the kinetic and equilibrium expressions isdescribed later in the manuscript.

Abiotic reactions:

2FeðOHÞ3ðsÞ þ H2S þ 4Hþ⇒2Fe2þ þ So þ 6H20

ð17ÞMnO2ðsÞ þ H2S þ 2Hþ⇒Mn2þ þ So þ 2H20 ð18Þ

MnO2ðsÞ þ 2Fe2þ þ 4H2O⇒Mn2þ þ 2FeðOHÞ3ðsÞ þ 2Hþ

ð19Þ

Rate expressions:

∂ðMnO2Þ=∂t ¼ −kMnðIVÞ1 ½CH3COOH� ð20Þ

∂ðFeðOHÞ3Þ=∂t ¼ −kFeðIIIÞ1 ½CH3COOH� ð21Þ

∂ðFeðOHÞ3Þ=∂t ¼ −kFeðIIIÞ2 ½TS�½FeðOHÞ3� ð22Þ


∂ðMnO2Þ=∂t ¼ −kMnðIVÞ2 ½TS�½MnO2� ð23Þ

∂ðMnO2Þ=∂t ¼ −kMnðIVÞ3 ½Fe2þ�½MnO2� ð24Þ

where So is sulphide in solid state and TS is the sum of[H2S], [HS

−], and [S2−].

Table 2Densities of precipitating minerals (CRC Press, 1998)

Minerals Mineral density (g/cm3)

Calcite (CaCO3) 2.71Dolomite (CaMg(CO3)2) 2.86Siderite (FeCO3) 3.90Rhodochrosite (MnCO3) 3.70Iron Sulphide (FeS) 4.70

3.2. Permeability reduction model

This model consists of two modules — one forpredicting the effect of bioaccumulation and chemicalprecipitation–dissolution, and the other for the effect ofgas formation, on the soil's porosity and permeability. Thecombined effect of bioaccumulation, metal precipitation,and gas formation on hydraulic conductivity is modelledas a multiple of the amended intrinsic permeability(reduced by solids formation via bioaccumulation andmetal precipitation) and the relative permeability to water(to account for the presence of a gaseous phase).

3.2.1. Biomass production and chemical precipitationmodule

The models for estimating changes in soil properties(such as, porosity, permeability and surface area) due tobiomass accumulation (e.g., Taylor et al., 1990; Sarkaret al., 1994; Clement et al., 1996a)) have not beenextensively tested in the laboratory or the field. Themodels make different assumptions and incorporatevarying levels of complexity to estimate the permeabil-ity by relating biomass to the reduction in pore spaceavailable for flow. As stated previously, no singlebioclogging model has been shown to better representthe underlying processes or more accurately predict thechanges in permeability reduction. In this study, giventhe need to adopt a permeability reduction model thatcould be readily interfaced with the geochemicalspeciation module, the model proposed by Clementet al. (1996a) was adopted. To estimate the permeabilityand porosity reduction by bioaccumulation and chem-ical precipitation the Clement model was modified byincluding the reduction in pore volume from precipita-tion as follows:

ki;bpki;0

¼ 1� nb þ npn0

� �196

ð25Þ

nbp ¼ n0 � nb þ np� � ð26Þ

where ki,bp is the biomass plus metal precipitationaffected intrinsic permeability (L2), ki,0 is the initialintrinsic permeability (L2), n0 is the initial soil porosity,nbp is the biomass plus precipitation affected porosity,

np is the volume fraction of the precipitated minerals(L3/L3), nb is the volume fraction of the soil-attachedbiomass (=Xsρs /ρb) (L

3 biomass/L3 total), and ρb is theattached biomass density (M/L3). Assuming 50% ofcellular carbon is protein (Luria, 1960) and solid phasebiomass density is 70 mg-volatile solids/cm3 (Cookeet al., 1999), the attached biomass density (ρb) isestimated as 35 mg-protein/cm3. The densities of thevarious precipitating minerals modelled in this study arelisted in Table 2. The large difference in biomass andmineral densities can have a significant influence on therelative contribution of biomass growth and mineralprecipitation to permeability reduction.

3.2.2. Gas formation moduleThe rate degradation of acetate to gaseous products,

methane and carbon dioxide is described by Eqs. (5),(14) and (15). Acetate degradation in the column isquick and results in vigorous production of methane,which being poorly soluble in water, forms separatephase gas bubbles. Carbon dioxide has high solubility inwater and its contribution to the gaseous phase isignored. It is assumed that the bubbles coalesce over asufficiently short interval (estimated from methaneproduction rates to be less than 10 cm) of the columnso that a separate gas phase can be assumed to prevail inthe entire column. The effect of gas flow on soilpermeability is modelled using the generalised Darcy'sLaw (modified after Huyakorn and Pinder, 1983).

qa ¼ � ki;bpkrala

∂pa∂x

þ qa g ̂� �

; a ¼ w; g ð27Þ

where μα is the dynamic viscosity of fluid (M/LT), ρα isthe density of fluid (M/L3), ĝ is the acceleration due togravity (L/T2), krα is the relative permeability thataccounts for the reduction in the permeability to waterdue to the presence of a second phase (i.e., gas), pα is thepressure (M/LT2), and qα is the Darcy flux (L/T) for thewater (α=w) and gaseous (α=g) phases.

To parallel the assumption of gas coalescence over shortdistances, it is assumed that water saturation is relatively

Table 3Values of the model simulation parameters

Parameter Value

Column length, L 50 cmColumn diameter 5 cmTime step, Δt 0.0125 daySpace discretisation, Δx 0.5 cmDarcy flux, q 16.9 cm/dayDispersivity, α 0.12 cmInitial porosity, n 0.41Saturated hydraulic conductivity, Ks 8.8×10−3 cm/s


constant over most of the column, i.e., a constant capillarypressure prevails over the entire column. Therefore,

dpcdx

¼ dpgdx

� dpwdx

¼ 0 ð28Þ

where pc is the capillary pressure (M/LT2). Thus,

lwqwkrw

� lgqgkrg

þ ki;bpg qw � qg� � ¼ 0 ð29Þ

The relative permeabilities to water and gas are givenas (Parker et al., 1987; Parker, 1989):

krwðθwÞ ¼ θ1=2e ð1−ð1−θ1=me ÞmÞ2 ð30Þ

krgðθwÞ ¼ ð1−θeÞ1=2ð1−θ1=me Þ2m ð31Þwhere he ¼ hw�hwr

hws�hwris the normalised water content

(ignoring the effects of bioaccumulation and chemicalprecipitation on θw and θws), θw is the water content, θwris the residual water content, θws is the saturated watercontent,m=1−1/n, and n is the van Genuchten equationparameter. As the effect of bioaccumulation and chemicalprecipitation on θw and θws is ignored, a single value ofwater content is obtained for the entire column byminimising the sum of squares of the residuals from(μwqw / krw−μaqa / kra) plus ki,bpg(ρw−ρa) using theLevenberg–Marquardt algorithm (Morris, 1993). Thereduction in hydraulic conductivity is calculated as:

Reduction in K kð Þ ¼ 1� ki;bpkrwki;0

� �100 ð32Þ

The above model is a simple, but approximaterepresentation of the processes by which gas bubbleform, coalesce, and then escape by forming a continuousgas phase. Furthermore, the model neglects hystereticeffects of periodic gas accumulation and venting. Assuch, the model represents an averaged effect of gasformation over the long-term; a more accurate repre-sentation of the short-term effect of gas formation onsoil permeability can be developed by following Amosand Mayer (2006b).

4. Numerical solution and coupling of modules

The one-dimensional advection–dispersion equation issolved using a finite difference scheme with centralweighting in space and time as discussed by Islam andSinghal (2002). A two-step sequential operator splittingmethod, similar to that used byWalter et al. (1994), is used

to solve the coupled transport model and biogeochemicalreaction equations. The mathematical formulation of thekinetic biodegradation reactions gives a system ofordinary differential equations, which is solved by thestiff ordinary differential equation system solver SFODE(Morris, 1993).

At each location in the modelled domain the redoxpotential (pE) is estimated using the concentrations ofthe dominant terminal electron acceptor and itscorresponding reduced species calculated from thetransport and kinetic biodegradation model (Smith andJaffé, 1998). The estimated pE is used in the equilibriumspeciation model to determine the speciation of tracemetals and non-dominant redox species at that location,and the equilibrium state towards which the system isdriven. The rate expressions in Table 1 are then used tocalculate the rates of the non-dominant redox reactions(not applicable to the present study) and precipitation ordissolution of minerals. At locations where the chemi-cal equilibrium model predicts that the ion activityproduct exceeds the solubility product (Ksp) precipita-tion occurs, and where the converse applies dissolutionoccurs. Finally, the masses of all mineral phases areupdated and the dissolved species re-equilibrated at eachtime step.

A grid spacing (Δx) of 0.25 cm, giving a Pecletnumber (Δx /α) of 2 using the measured dispersivity (α)of 0.12 cm, is used to meet the Peclet criterion, and atime step (Δt) of 0.00625 days is chosen to satisfy theCourant criterion (v Δt /Δx≤1). Model simulations areperformed for 126 days to cover Phases 1 and 2 ofcolumn operation. The transport simulations involveone organic compound (acetic acid) and 14 dissolvedinorganic components (yielding 42 inorganic species inthe MINTEQA2 chemical equilibrium speciationmodel) and 7 solid mineral phases. The simulationparameters are summarised in Table 3 and thebiochemical parameters (i.e., growth rates, yield coeffi-cients, and half saturation constants), obtained during

Table 4Calibrated values for kinetic microbial transformation parameters

Biological parameters Calibrated parameters Literature values References

Maximum microbial capacity for attachment (Xmax), mol-cell/g-sand 8×10−5 – –Biomass density (ρs), g-protein/cm

3 35 – –Detachment coefficient (Kdet), day

−1 0.02 0–5.36 7, 18, 21Attachment coefficient (Katt), day

−1 75 nb 7.4–410 7, 18, 21

Sulphate reducing bacteria:Maximum growth rate (μmax), day

−1 0.034 0.001–30 2, 4, 5, 8, 9, 12, 14–16, 19, 20Decay coefficient (Kdec), day

−1 0.003 1×10−6–0.4 2, 4, 5, 12, 14, 15, 17, 19, 20Half-saturation constant for acetic acid (Ks), mol HAc/l 2×10−4 1×10−4–4 4, 5, 8, 12, 15, 20Half-saturation constant for sulphate (Kea), mol SO4/l 1×10−4 1×10−6–1×10−3 4, 14, 15Yield coefficient for acetic acid (Y), mol-cell/mol-HAc 0.006 0.003–0.125a 5, 8, 9, 12, 15, 20

Methanogenic bacteria:Maximum growth rate (μmax), day

−1 0.062 1×10−4–1.69 1–5, 9–11, 13, 16–17, 20Decay coefficient (Kdec), day

−1 0.006 1×10−6–0.05 2–5, 9–11, 13, 16–17, 20Half-saturation constant for acetic acid (Ks), mol HAc/l 2.0×10−3 5×10−5–4×10−2 1–5, 9–11, 13, 16–17, 20Inhibition constant for sulfate (IC), mol SO4/l 1.0×10−3 – –Yield coefficient for acetic acid (Y), mol-cell/mol-HAc 0.007 0.005–0.023 a 1–3, 5, 9–11, 13, 16–17, 20

Notes: References listed are: (1) Aguilar et al., 1995; (2) Angelidaki et al., 1999; (3) Bernard et al., 2001; (4) Brun et al., 2002; (5) Demirekler et al.,2004; (6) El-fadel et al., 1996; (7) Hornberger et al., 1992; (8) Ingvorsen et al., 1984; (9) Isa et al., 1986; (10) Kugelman and Chin, 1971; (11)Lawrence and McCarty, 1969; (12) Middleton and Lawrence, 1977; (13) Peiking et al., 1998; (14) Schäfer et al., 1998a; (15) Schäfer et al., 1998b;(16) Speece, 1996; (17) Sykes et al., 1982; (18) Tan et al., 1994; (19) Uberoi and Bhattacharya, 1997; (20) Yoda et al., 1987; (21) Zysset et al., 1994.a Estimated by converting mg-VSS/mg-COD to mol-cell/mol-HAc.


model calibration by fitting the predictions to experi-mental observations, are presented in Table 4.

5. Simulation results and discussion

5.1. Biochemical reactions

The initial biomass concentration of sulphate reducersand methanogens, estimated by adjusting their relativeproportions to match the observed and simulated

Fig. 1. Comparison of observed and simulated concentratio

sulphate and acetic acid concentrations, indicates thatthe initial concentration of sulphate reducers is small (5%of the measured initial total biomass concentration). Asshown on Figs. 1 and 2 the agreement between thesimulated and observed acetic acid and sulphate profilesin both phases is good; however, the fits for Phase 2 aresomewhat poorer than those for Phase 1. A comparisonof the simulated and observed concentrations of attachedand suspended biomass concentrations (Fig. 3) showsthat the attached and suspended biomass profiles fit the

ns of (a) acetic acid and (b) sulphate during Phase 1.

Fig. 2. Comparison of observed and simulated concentrations of (a) acetic acid and (b) sulphate during Phase 2.


data satisfactorily, with the exception of day 93. Themodel did not fully capture the decrease in suspendedbiomass concentrations at later times, which is likelycaused by a lowering in detachment rates under slowmicrobial growth conditions (Hornberger et al., 1992;Tan et al., 1994).

The observed and simulated changes in Fe (II) andMn(II) concentrations resulting from the reduction ofMn(IV) and Fe(III) oxides in sand due to redox reactionswith dissolved sulphide ions and the microbial oxidationof organic carbon are shown on Fig. 4. The rateconstants obtained by fitting the data are presented inTable 1. Model simulations indicate that Mn(IV) oxidereduction by Fe(II) oxidation is a minor abioticreduction pathway. The Fe(II) concentrations decreaseat the column inlet due to precipitation as FeS, but thenincrease further into the column due to the microbialreduction of Fe(III) oxide in sand. The precipitation rateof Fe(II) as FeCO3 is found to be small, consistent with

Fig. 3. Comparison of observed and simulated concentr

the reported slow rate of FeCO3 precipitation (Wajonet al., 1985; Greenberg and Tomson, 1992).

The observed and simulated concentration profiles fordissolved and total solid calcium are shown in Fig. 5, andfor dissolved carbonate and solution pH in Fig. 6. Thedissolved Ca(II) simulations show a gradual decreasealong the column, instead of the observed quick decreasein the 0–5 cm section followed by a relatively constantconcentration in the remainder of the column— a patternsimilar to that observed for Mg(II) concentrations (datanot presented here). The observed rapid decrease indissolved calcium occurs in the inlet region, where a largeattached biomass concentration is present. This rapiddecrease in dissolved calcium may have resulted fromenhanced precipitation of calcium via nucleation on thereactive sites of bacterial cell surfaces (Brune et al., 1994;Fortin et al., 1997; Fortin and Ferris, 1998). Thesimulations for total calcium match the observations atday 58, but significantly overpredict those at day 126.

ations of (a) attached and (b) suspended biomass.

Fig. 4. Comparison of observed and simulated concentrations of dissolved (a) iron and manganese.


5.2. Porosity and permeability reduction

The soils were initially saturated, but gradually be-came unsaturated due to gas production in the columns.The piezometric head measurements were affected bygas formation and flow in the columns, especiallyduring Phase 2 when the gas production rates werelarger. Awater content of 0.373 and 0.370 at days 80 and86, respectively, was estimated using Eq. (29) with aresidual water content (θwr) of 0.045, van Genuchtenparameter n of 2.68 for sand (Carsel and Parrish, 1988),soil porosity of 0.41, saturated hydraulic conductivity of8.8×10−3 cm/s, and observed gas flow rates of 1080and 1440 ml/day and a water flow rate of 331 ml/day.The above estimates give a gas saturation of approxi-mately 10%, which corresponds to a reduction in hy-draulic conductivity of 60% (i.e., krw=0.4).

The simulated porosity values are shown on Fig. 7,which suggest that the most significant changes inporosity over a short distance from the inlet. Over58 days the predicted decrease in porosity was 32% and

Fig. 5. Comparison of observed and simulated concentra

limited to the 0–1.5 cm section of the column. With timethere was an increase in the amount as well as the lengthof column-zone affected by porosity reduction. By126 days the porosity was predicted to reduce by 70% inthe 0–5 cm section of the column.

Fig. 7 also shows the observed and simulatedhydraulic conductivity (with and without the consider-ation of gas phase) values. The simulations presented fordays 56, 73 and 126 consider only the effect ofbioaccumulation on hydraulic conductivity and showsimilar trends as porosity. The simulated hydraulicconductivities are larger than those observed, and whilethe simulations better approximate the observations atlarger times, an observable difference between thesevalues remains. After 126 days of operation a reductionin hydraulic conductivity of 99.6% (decrease from8.8×10−3 cm/s to 3.5×10−5 cm/s) was observed in the2–6 cm section of the column. The model simulationsshow that hydraulic conductivity reduction due to metalprecipitation is under 1% and can be ignored. Also,when only bioaccumulation is considered (i.e., the gas

tions of (a) dissolved and (b) precipitated calcium.

Fig. 6. Comparison of observed and simulated concentrations of (a) total dissolved carbonate and (b) pH.


phase is ignored), the simulations show decreases inhydraulic conductivity in the 0–2 cm and 2–6 cmsections of the column of 97% and 67%, respectively.Simulations accounting for the effects of gas productionon hydraulic conductivity show a smaller differencebetween the observations and predictions in the inletsection of the column, but a consistently lower predictedhydraulic conductivity than observed in the remainderof the column. When bioaccumulation and gas forma-tion are both considered, the simulated decreases inhydraulic conductivity are 99% and 87% in the 0–2 cmand 2–6 cm sections, respectively. The combination ofbioaccumulation and continuous gas flow predicts a62% decrease in hydraulic conductivity in the 10–50 cmsection of the column, instead of the 80% and 11%observed at 22 cm and 37 cm, respectively. Asbioaccumulation accounts for only 6% of the simulatedhydraulic conductivity decrease, the predicted conduc-tivity decrease is largely due to gas flow in the column.

The differences between the observed and simulatedvalues are attributed to the use of simple uncalibrated

Fig. 7. (a) Simulated porosity and (b) observe

models for permeability reduction by bioaccumulationand gas formation. Also of significance is the assump-tion of continuous gas flow in the simulations; in theexperiments gas flow is seen to occur intermittently,suggesting that during the intervening period gasbuildup occurs within the column until the gas-pressureincreases to force gas escape from the column. A similarsituation is encountered during water infiltration inunsaturated soil where gas saturation builds up beforeair can escape (Wang et al., 1997). The model does notinclude the above phenomena and ignores permeabilityreduction due to bubble formation and entrapment dueto organic biodegradation in soil. Additionally, the useof discontinuous gas flow in the simulations will lessenthe predicted decrease in hydraulic conductivity in thetail section of the column. Despite the underestimationof hydraulic conductivity reduction in the inlet regionand overestimation in the tail section of the column, themodel's performance is deemed acceptable for itssimple formulation. The permeability reduction modelcan be further improved by calibrating the exponent in

d and simulated hydraulic conductivity.

Fig. 8. Simulated (a) porosity and (b) hydraulic conductivity for different substrate loadings.


the bioaccumulation module and including gas bubbleformation and entrapment in the gas formation module.

While the findings of the study may not be directlyapplicable to the field due to the small scale of thephysical model, one-dimensional vertical flow, andlarge acetic acid concentration, it does however provideclues on the effects of interactions occurring in selectiveportions of a leachate contaminated aquifer. Of theprocesses considered, bioclogging would appear to havethe most significant effect on permeability reduction.Under anaerobic conditions gas formation would alsocontribute to permeability reduction by decreasing theamount of pore space available to flow. Furthermore,chemical precipitation is unlikely to contribute signif-icantly to permeability reduction. It must be noted thatpermeability reduction will occur in selective regions asexcessive bioaccumulation and gas formation onlyoccur significantly in areas containing large concentra-tions of organic matter. Although the issue of soilheterogeneity is not considered in this paper, bacterialand gas accumulation are likely to homogenise the

Fig. 9. Simulated concentration profiles of (a) attached biom

media at the small scale by decreasing the effective sizeof larger pores available for water flow. However, atlarger scales there may be an increase in heterogeneitydue to formation of preferential flow paths as the flowcircumvents regions with reduced permeability.

5.3. Case studies

The rate of clogging under a landfill is a function ofthe flow rate, soil grain size, temperature and leachatecomposition (e.g., organic content, suspended solids,and calcium content) (Rowe, 1998). A sensitivity analy-sis was performed using the model developed in thisstudy to assess the effects of substrate loading, leachateflow rate, particle size, and mineral precipitation on theclogging of soils underlying landfills. A one-dimension-al vertical flow of leachate is assumed beneath the land-fill. Unless stated otherwise, simulations are done usingthe calibrated parameter values for the controls listed inTable 3. Five test cases were simulated: Cases 1, 2 and 3assess the effect of influent acetic acid at concentrations

ass and (b) acetic acid for different substrate loadings.

Fig. 10. Simulated (a) porosity and (b) hydraulic conductivity showing the effects of flow rate (Case 4) and particle size (Case 5).


of 3000 mg/L, 6000 mg/L, and 9000 mg/L, respectively;Case 4 simulates permeability reduction in soils for aninfluent acetic acid concentration of 6000 mg/L (same asCase 2) and a flow rate of 0.11 ml/min (corresponding tohalf the flow rate for Cases 1, 2 and 3); and, Case 5simulates permeability reduction in soils with a particlesize of 0.2 mm, half the size of particles used in theprevious cases, for an influent acetic acid concentrationof 6000 mg/L. The attachment coefficients (Katt) werecalculated using the filtration theory (Tien et al., 1979).Accordingly, in Case 4 the attachment was decreased by50% and in Case 5 it was increased by 217%. Thedetachment coefficient (Kdet) value was kept the same forall the cases. Model simulations were run for a totalsimulation time of 180 days. In addition, two simulationswere done to examine the effect of calcium and mag-nesium precipitation with influent calcium and magne-sium concentrations of 400 and 240 mg/L, and 1200 and730 mg/L, respectively, at pH 8. The simulated maxi-mum reduction in permeability due to mineral precipi-tation was only 8% and the results are not presentedhere.

Fig. 11. Simulated (a) attached biomass and (b) acetic acid showin

Simulation results for the Cases 1 to 3 showing theeffects of substrate loading on porosity and hydraulicconductivity are presented in Fig. 8 and for attachedbiomass and acetic acid in Fig. 9. Increasing substrateloading results in further lowering of porosity andhydraulic conductivity by only 4%; however, the zoneaffected by these reductions is increased by approxi-mately 4 cm for every 3000 mg/L increase in theinfluent acetic acid concentration. The simulatedattached biomass profiles show that permeabilityreduction is due to biomass growth and retention insoil, and that the higher influent acetic acid concentra-tion increases the length of the zone over which aceticacid is available to bacteria. Figs. 10 and 11 compare theeffects of reducing the flow rate (Case 4) and sand size(Case 5) with Case 1, noting that mass influx of acetatein Cases 1 and 4 is the same. Case 4 gives very similarresults to Case 1 for porosity and permeability reduction(Fig. 10) as well as the attached biomass (Fig. 11) in soil.Reducing the particle size increases the attachmentcoefficient. In Case 5 the increase in the attachmentcoefficient and a larger biomass buildup for an influent

g the effects of flow rate (Case 4) and particle size (Case 5).


acetate concentration of 6000 mg/L lead to greaterreductions in porosity and hydraulic conductivity. Case5 results suggest that hydraulic conductivity reductionsof more than three orders of magnitude can result in soilsunder specific conditions.

6. Conclusions

The biogeochemical model developed in this studyshows satisfactory agreement with experimental data foracetic acid, sulphate, suspended and attached biomass,Fe(II), Mn(II), dissolved and total calcium, carbonateions, pH, and the soil's hydraulic conductivity. Themodel for permeability reduction by gas formation issimplistic and can be improved by incorporating a gasbubble formation and entrapment mechanism. While thefitted parameters are within the range of values reportedin literature, the diversity range of values reported in theliterature and the large number of calibrated parameterssuggests that issues of non-uniqueness may remain andwill need addressing via on-going research. Thesimulations show that bioaccumulation causes thelargest reduction in permeability. Gas formation canalso be a significant contributor to permeabilityreduction, but metal precipitation in comparison has anegligible effect. Simulations also show that highersubstrate concentrations may increase the length of thezone experiencing hydraulic conductivity reduction, butmay not lead to further decreasing the conductivity.Also, conductivity reductions are likely to be larger infiner-grained soils than larger-grained soils.

The main implication of this study for engineeringpractice is the need to consider permeability reductionduring anaerobic and aerobic in-situ remediationapplications. Significant permeability reduction canresult from bioaccumulation as well as gas formationin these applications; mineral precipitation is generally asmall contributor to permeability reduction. However,depending on the specific situation, e.g., around leachatecollection pipes in landfills, mineral precipitation maybe a significant contributor to permeability reduction.The use of integrated biogeochemical models in the fieldcan serve a useful purpose in assessing such impacts;however, developing two- or three-dimensional modelsfor full-scale field use remains a challenge as theintegration of the equilibrium (e.g. MINTEQ) and non-equilibrium geochemical models with groundwater flowand chemical transport, gas production and accumula-tion, and permeability reduction models is madedifficult by the lack of adequately tested models andpresence of several model parameters for whichestimates are unavailable. As the model convergence

to solutions is slow, successful adoption of such modelswould require the development of efficient numericalschemes coupled with rigorous testing and validation ofthe integrated approaches.

Acknowledgements

We would like to acknowledge the comments andsuggestions from the journal editor, E.O. Frind, and oneanonymous reviewer.

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