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Journal of Contaminant Hydrology 96 (2008) 32–47 www.elsevier.com/locate/jconhyd
One-dimensional model for biogeochemical interactions and permeability 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 2007 Available 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, kinetic biodegradation, precipitation–dissolution reactions, bacterial and substrate transport, and permeability reduction arising from bacterial growth and gas production. A two-step sequential operator splitting method is used to solve the coupled transport and biogeochemical reaction equations. The model gives satisfactory fits to experimental data and the simulations show that the transport of metals in soil is 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 ability due to bacterial growth, chemical precipitation, and anaerobic gas production. Under appropriate con- The impact of leakage from landfills on the envi- ditions the combined effects of biomass growth, metal ronment is governed by the transformation of inorganic precipitation and gas production on the soil's flow and and organic constituents of leachate via biogeochemical transport properties can be significant (e.g., Brune et al., interactions. A variety of complex reactions occur be- 1994; Rowe et al., 1997). tween the biological (primarily microorganisms, such Reactive transport modelling has evolved as a tool for as bacteria), geological, and chemical components of analysing the effects of complex biogeochemical interac- leachate contaminated soils. These reactions not only tions and reaction controls on soils. Quantification of these influence chemical transport but can also affect ground- effects using mathematical relationships is an area of water flow by altering the soil's porosity and perme- continuing research with several mathematical models having been developed to simulate the geochemical ⁎ Corresponding author. Department of Civil and Environmental processes (Yeh and Tripathi, 1991; Engesgaard and Engineering, University of Auckland, Private 92019, Auckland 1001, Kipp, 1992; Walter et al., 1994) and biological transfor- New Zealand. Tel.: +64 9 373 7599x84512; fax: +64 9 3737462. E-mail address: [email protected] (N. Singhal). mations (Borden and Bedient, 1986; Kindred and Celia, 1 Presently at North Shore City Council, Private Bag 93500 1989; Taylor et al., 1990; Clement et al., 1996a)insoils. Takapuna, North Shore City, New Zealand. The development and use of integrated biogeochemical
0169-7722/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jconhyd.2007.09.007 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 33 models coupling transport processes to primary reactions uptake and application of these models in other studies (i.e., organic matter degradation) and secondary reactions makes it difficult to identify a single model as being (e.g., redox transformation, mineral dissolution and superior to others. Furthermore, comprehensive models precipitation, sorption, and acid–base and homogeneous that couple the effects of bioclogging and gas formation speciation) is of more recent origin (Lensing et al., 1994; with chemical speciation have not been previously McNab and Narasimhan, 1994; Zysset et al., 1994; Hunter presented in the literature. et al., 1998; Schäfer et al., 1998a; Tebes-Stevens et al., This paper presents a mathematical model for the 1998; Prommer et al., 1999; Mayer et al., 2002; Van biogeochemical interactions occurring during leachate Breukelen et al., 2004). In these models geochemical permeation in packed columns. The model considers reactions are simulated assuming local equilibrium kinetic precipitation–dissolution and equilibrium aqueous (Engesgaard and Kipp, 1992), partial redox disequilibrium geochemical speciation, kinetic biodegradation, chemical (McNab and Narasimhan, 1994; Brun and Engesgaard, and bacterial transport, and biomass accumulation in soils. 2002), kinetic heterogeneous redox speciation (Tebes- In particular, the model accounts for the effects of the Stevens et al., 1998; Mayer et al., 2002; Van Breukelen et biophase, chemical precipitate, and separate phase gas on al., 2004), or fully kinetic redox speciation (Hunter et al., the soil's permeability. To the authors' knowledge this is 1998). The bacterial reactions have typically been the first study to consider the above mentioned biogeo- simulated assuming either negligible bacterial activity chemical processes in an integrated manner, although (Engesgaard and Kipp, 1992), prescribed zero- or first- previous studies have tackled subsets of the current order microbial reactions (McNab and Narasimhan, 1994; system. Experimental data obtained from laboratory Mayer et al., 2002; Van Breukelen et al., 2004), or experiments with soil columns (Islam and Singhal, bacterial growth dynamics described using Monod 2004) is used to assess the strengths and weaknesses of kinetics (Schäfer et al., 1998a; Tebes-Stevens et al., 1998). the proposed model and identify areas for further research. The previous biogeochemical models have ignored the effects of biogeochemical interactions on the porosity and 2. Laboratory study permeability of soil (e.g., due to biomass accumulation, chemical precipitation or gas formation) by assuming a Laboratory experiments were conducted by pumping constant biophase volume (e.g., Schäfer et al., 1998a)or leachate collected from a local municipal landfill through instantaneous degassing (e.g., Van Breukelen et al., packed columns to investigate the effects of leachate 2004). Recent progress has been made in the development permeation and interactions between the soil media, of models to describe gas bubble formation and its effect bacteria and leachate constituents on soil permeability on soil permeability (e.g., see Amos and Mayer, 2006a,b) (details presented in Islam and Singhal, 2004). The columns and the patterns for the flow of gas injected into saturated were 50 cm long and 5 cm in diameter and were packed porous media (Selker et al., 2007). Several models have with 0.21–0.61 mm sized sand. The porosity of the packed also been developed for permeability reduction due to media was estimated as 0.41 by gravimetric analysis. A biomass accumulation in soil. Taylor et al. (1990) used the flow of 0.23 ml/min was maintained in the columns and the “spherical soil grains” approach of Kozeny–Carman head loss data was used to estimate the average saturated (Carman, 1937) and the “cut-and-random-rejoining of hydraulic conductivity as 8.8×10−3 cm/s. A pulse of 0.5 M tubes” approach of Childs and Collis-George (1950). sodium bromide solution was then injected into a column Sarkar et al. (1994) used the effective medium theory to and an analytical solution of the advective–dispersive represent the soil medium as a three-dimensional network equation was fitted to the observed bromide breakthrough of pores and estimated the effective hydraulic conduc- data to obtain a dispersivity of 0.12 cm. The bacterial tance based on the pore throat size distribution following inoculum used to seed the columns was obtained by bacterial plugging. Clement et al. (1996a) presented centrifuging 24 L of landfill leachate and re-suspending the analytical equations for changes in porosity, specific centrifugate in 2 L of raw leachate. This microbe-enriched surface area, and permeability due to biomass accumu- solution was pumped into three columns at 5 ml/min, and lation in porous media. Thullner et al. (2002,2004) wasfollowedby12hofnoflowtopromotebacterial described the permeability reduction in pore networks attachment to the soil. One of the columns was then from biomass growing on biofilm and in discrete colonies dismantled to determine the initial distribution of attached that occupy pores entirely. The colony-based model was biomass in soil. The remaining two columns were fed later used by Seifert and Engesgaard (2007) to simulate leachate, amended with acetic acid to give a final acetic acid bioclogging of porous media. While the proponents of the concentration of 1750 mg/L (equivalent to 350 mg-C/L), in models successfully calibrated their models, the limited upflow 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 dissolved 3.1. Reactive transport model organic carbon concentrations in leachate contaminated groundwater typically range up to 120 mg-C/L (Bjerg et al., The transport of dissolved components is described 1995; Nielsen et al., 1995), but in selective regions within using the general one-dimensional form of the contam- the aquifer the concentration can be as large as 480 mg-C/L inant transport equation for mobile components in the (Brun et al., 2002). The acetic acid concentration used, aqueous phase as follows (Bear, 1979): therefore, lies at the high end of the reported dissolved ∂ ∂ ∂Cj ∂ organic carbon concentrations in contaminated aquifers. A nCj nD þ nvCj ¼nRj; j ¼ 1; N ; Nc relatively large concentrationofaceticacidisusedinthis ∂t ∂x ∂x ∂x study to promote biological growth and gas formation so ð1Þ that their effects can be observed over short durations. After 58 days one of the columns was dismantled to determine q K ∂h v ¼ ¼ ð2Þ the spatial distribution of attached biomass and precipitated n n ∂x metals. The last column was operated with an increased where n is the porosity (dimensionless), q is the Darcy influent acetic acid concentration of 2900 mg/L for 16 days, velocity (L/T), t is time (T), v is average pore fluid followed by a further increased influent acetic acid velocity (L/T), x is a unit vector pointed vertically concentration of 5100 mg/L for an additional 52 days upwards (L), C is the total dissolved concentration of (Phase 2). After 126 days of operation this column was j component j (M/L3), D is the hydrodynamic dispersion dismantled and the soil analysed for attached biomass and coefficient (L2/T), K (=k k ) is hydraulic conductivity precipitated metals. i rw (L/T) and k and k are respectively the saturated (L/T) In the columns acetic acid was principally biode- i rw and relative permeabilities, N is the total number of graded via methanogenesis, resulting in gas production c dissolved components, and R is the source/sink term of up to 1440 ml/day. The acetic acid degradation was j (M/L3/T) representing the changes in total aqueous accompanied by a rapid increase in pH, inorganic concentration of component j due to chemical and carbon (dissolved carbonate), and biomass accumula- biological reactions. Eqs. (1) and (2) predict the tion in the inlet region of the columns. This led to concentrations of the dissolved inorganics, dissolved carbonate supersaturation, which promoted the precip- organic substrates, dissolved electron acceptors, and itation of iron, manganese, and calcium as carbonate in suspended biomass. the 0–2 cm section of the columns. Biomass accumu- The immobile components are not transported and lation, metal precipitation, and gas production reduced are therefore treated using mass balance as follows: the hydraulic conductivity in the inlet region of the columns by over two orders of magnitude. ∂M m ¼ R ; m ¼ 1; N ; N ð3Þ ∂t m m 3. Model development where Mm is the concentration of immobile phase m, The model consists of two submodels — one for Nm is the number of immobile components and Rm is the chemical transport and the other for permeability rate of change of immobile phases due to chemical and reduction. The chemical transport submodel describes biological reactions. The concentration array Mm in Eq. the transport and transformation of dissolved leachate (3) represents the concentration of immobile compo- constituents in soil, and the permeability reduction nents, i.e., precipitated species, adsorbed species and submodel describes the change in soil permeability due soil-attached biomass. to biomass accumulation, chemical precipitation and gas The generic source/sink terms, Rj and Rm, are used to production. The reactive transport model is written in describe a variety of reactions, which are modelled by terms of the total aqueous concentrations of a specified set the following modules. of components, which are defined as linearly independent chemical entities such that every species in the system can 3.1.1. Geochemical equilibrium reactions module be expressed as the product of a reaction involving only This module uses the equilibrium speciation model the components, and no component can be written in MINTEQA2 (Allison et al., 1991)tomodelthe terms of components other than itself (Yeh and Tripathi, homogeneous chemical reactions, such as aqueous spe- 1989). For a given system, the set of components is not ciation, acid–base interactions, and oxidation–reduction. unique, but once it has been defined, the representation of In addition, adsorption reactions are also assumed to species in terms of this set of components is unique. occur at equilibrium. The equilibrium reactions are solved N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 35 using the ion association equilibrium-constant approach, where η is the effectiveness factor, λ is the metabolic which involves setting up non-linear algebraic equations potential function, μmax is the maximum specific growth using equilibrium constants embedded in mass balance rate of biomass (1/T), ρs is the bulk density of aquifer 3 equations for the various components in the system. The solids (M/L ), Cea is the concentration of terminal 3 concentrations of the aqueous, adsorbed and precipitated electron acceptor (M/L ), Cs is the acetate concentration 3 species are calculated from the mass action laws and the in the bulk (mobile) fluid (M/L ), IFm is the inhibition resulting set of non-linear algebraic equations is solved by function for inhibiting species m, Katt is the biomass Newton–Raphson approximation method for the individ- attachment coefficient (1/T), Kdec is the first-order ual ion activities, which are used to calculate the endogenous decay coefficient (1/T), Kdet is the biomass component concentrations at equilibrium. detachment coefficient (1/T), Ks and Kea are the half- saturation constants for organic substrate and electron 3 3.1.2. Kinetic precipitation–dissolution module acceptors, respectively (M/L ), Xa is the suspended 3 This module considers the precipitation and dissolu- biomass concentration (M/L ), Xs is the soil-attached tion of the four dominant minerals — calcite (CaCO3), biomass concentration (M/M), and Y is the yield siderite (FeCO3), rhodochrosite (MnCO3), and iron coefficient for the biomass (cell mass produced per sulphide (FeS), which are modelled using the following mass of substrate consumed). The attachment coefficient rate expression (Smith and Jaffé, 1998): (Katt) is expressed as a function of the volume fraction of attached biomass (ns)asfollows(Taylor and Jaffé, 1990): ∂C ; j s ¼ jNs ½ al;s ð Þ aj;sks l¼l u1 Ksp;s 4 1 ∂t Katt ¼ 75 ns day ð8Þ where a and a are the stoichiometric coefficients of j,s l,s The metabolic potential function λ is used to model components j and l forming precipitate species s, k is the s the lag time, observed in some biological processes, as precipitation rate coefficient, u is the free ion activity of l follows (Wood et al., 1994): component k in solution, Cj,s is the concentration of 8 aqueous components j forming precipitate, Ksp,s is the > 0; t V s < L equilibrium solubility product of the precipitated species, s sL k ¼ ; sL V t V sE ð9Þ and N is the number of components in the precipitate. :> sE sL s ; N The precipitation–dissolution kinetic rate expressions 1 t sE used in the study are presented in Table 1. where τ is the time for which microorganisms have been in contact with the substrates (T), τ is the lag time (T), 3.1.3. Biotransport and kinetic biodegradation module L and τE is the time required to reach exponential growth This module describes the transport and accumula- (T). tion of bacteria in soil, and the biodegradation of organic The effectiveness factor η is defined by Zysset et al. chemicals. No assumptions are made on the structure (1994) as: and distribution of microorganisms degrading the or- ganic compounds. The acetate degradation and micro- X X g ¼ max s ð10Þ bial growth is expressed as follows (e.g., Clement et al., Xmax 1996b): where Xmax is the maximum capacity for the biomass to ∂ Cs lmax Cs Cea qsXs be attached (M/M). ¼ Xa þ g k j IFm ∂t Y Ks þ Cs Kea þ Cea n m The inhibition functions are used to model the ð5Þ sequential use of stronger to weaker electron acceptors and are expressed as follows (Van Cappellen and ∂ Gaillard, 1996): Xs ¼ Cs Cea j lmax Xskg IFm ∂t Ks þ Cs Kea þ Cea m IC IF ¼ m ð11Þ nKattXa m þ KdecXs KdetXs þ ð6Þ ICm EAm qs where EAm is the concentration of the inhibiting ∂ 3 Xa ¼ Cs Cea j electron acceptor m (M/L ) and ICm is the inhibition lmax Xak IFm 3 ∂t Ks þ Cs Kea þ Cea m constant (M/L ). qsKdetXs The biodegradation reactions for acetic acid in different K X K X þ ð7Þ dec a att a n redox environments are presented in Eqs. (12)–(15) and the 36 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47
Table 1 Precipitation–dissolution rate formulations
Precipitating/dissolving mineral Kinetic rate expressions Solubility product, Ksp Calibrated rate constant m 2+ 2− − 8.47 3 − 1 −1 Calcite (CaCO3) k1 ([Ca ][CO3 ]−Ksp)10 5.0×10 mol ld m 2+ 2+ 2− 2 − 17.00 9 − 1 −1 Dolomite (CaMg(CO3)2) k2 ([Ca ][Mg ][CO3 ] −Ksp)10 5.0×10 mol ld m 2+ 2− − 10.55 −1 −1 − 1 Siderite (FeCO3) k3 ([Fe ][CO3 ]−Ksp)10 2.0×10 mol ld m 2+ 2− − 10.41 −1 −1 − 1 Rhodochrosite (MnCO3) k4 ([Mn ][CO3 ]−Ksp)10 1.0×10 mol ld m 2+ − + − 3.91 −2 − 1 − 1 Iron Sulphide (FeS) k5 ([Fe ][HS ]/[H ]−Ksp)10 2.0×10 mol ld Fe(III) −2 − 1 Solid Fe(III) reduction −k1 [CH3COOH] – 1.5×10 d Fe(III) 1 − 1 −1 −k2 [TS] [Fe(OH)3] – 2.5×10 mol ld Mn(IV) −4 − 1 Solid Mn(IV) reduction −k1 [CH3COOH] – 5.0×10 d Mn(IV) 1 − 1 −1 −k2 [TS] [MnO2] – 5.5×10 mol ld Mn(IV) 2+ −1 −1 − 1 −k3 [Fe ] [MnO2] – 5.0×10 mol ld 2− Note: [TS]=[H2S]+[HS]+[S ]. overall reaction R, including the oxidation of organic reactions, while the secondary abiotic redox reactions (e.g., matter, reduction of inorganic compound and bacterial cell those between Fe(III), Mn(IV) and dissolved sulphides, and synthesis, is given in Eq. (16) (Criddle et al., 1991). between Mn(IV) and dissolved Fe(II)) are formulated as bimolecular kinetic rate expressions in terms of the − þ ð − Þ þ : þ CH3COO 4 1 fs MnO2 0 4fsNH4 dissolved and solid concentrations of the respective species. þð − : Þ þ¼N : 9 8 4fs H 0 4fsC5H7O2N This representation assumes that growth substrate concen- þ ð − Þ ⁎ þ ð − Þ 2þ 2 1 fs H2CO3 4 1 fs Mn tration is limiting the primary reactions, while the sec- þð − : Þ ð Þ 4 2 8fs H2O 12 ondary reactions are controlled by the interactions between − þ ð − Þ ð Þ þ : þ the dissolved species and the corresponding solid phase. CH3COO 8 1 fs Fe OH 3 0 4fsNH4 þð − : Þ þ¼N : The secondary abiotic redox reactions for the reduction 17 16 4fs H 0 4fsC5H7O2N ⁎ 2þ of Fe(III) and Mn(IV) are presented in Eqs. (17)–(19). þ2ð1−f ÞH2CO þ 8ð1−f ÞFe s 3 s Accordingly, the kinetic expressions for microbially me- þð20−18:8f ÞH2O ð13Þ s diated reactions in Eqs. (12) and (13) are presented in − þð − Þ 2− þ : þ Eqs. (20) and (21), respectively, and for abiotic reactions in CH3COO 1 fs SO4 0 4fsNH4 þð − : Þ þ¼N : Eqs. (17)–(19) by Eqs. (22)–(24), respectively. The sul- 2 1 4fs H 0 4fsC5H7O2N ⁎ − phate reduction (Eq. (14)) and methanogenesis (Eq. (15)) þ2ð1−f ÞH2CO þð1−f ÞHS s 3 s reactions do not involve solid minerals and are represented þ1:2f H2O ð14Þ s using the Monod kinetic relationship in Eq. (5). The cou- − þ : þ þð − : Þ CH3COO 0 4fsNH4 1 2 2fs H2O pling of the kinetic and equilibrium expressions is þð − : Þ þ¼N : 1 0 4fs H 0 4fsC5H7O2N described later in the manuscript. þð − Þ ⁎ þð − Þ ð Þ 1 fs H2CO3 1 fs CH4 15 Abiotic reactions:
þ þ R ¼ Rd þ f Ra þ f Rc ð16Þ ð Þ ð Þþ þ ⇒ 2 þ o þ e s 2Fe OH 3 s H2S 4H 2Fe S 6H20 where Rd, Ra,andRc are the half-reactions for the electron ð17Þ donor, acceptor, and bacterial cell synthesis respectively, fs ð Þþ þ þ⇒ 2þ þ o þ ð Þ is the fraction of electrons diverted for synthesis, fe is the MnO2 s H2S 2H Mn S 2H20 18 fraction of electrons used for energy generation, and the MnO ðsÞþ2Fe2þ þ 4H O⇒Mn2þ þ 2FeðOHÞ ðsÞþ2Hþ sum of fs and fe equals 1. The values for fs are 0.40, 0.07, 2 2 3 2− 0.06, and 0.05 with Fe(III), Mn(IV), SO4 ,andCO2, ð19Þ respectively, as electron acceptors (Criddle et al., 1991). The changes in concentrations of the electron acceptors, Rate expressions: pH, and inorganic carbon due to biodegradation reactions are computed from the stoichiometry of the microbial MnðIVÞ ∂ðMnO2Þ=∂t ¼ −k ½CH3COOH ð20Þ mediated redox reactions given in Eqs. (12)–(15). 1 Following the approach used by Wang and Van FeðIIIÞ ∂ðFeðOHÞ Þ=∂t ¼ −k ½CH COOH ð21Þ Cappellen (1996) primary reactions, i.e., reactions involv- 3 1 3 ing biodegradation of acetate using Fe(III) and Mn(IV) as ∂ð ð Þ Þ=∂ ¼ − FeðIIIÞ½ ½ ð Þ ðÞ electron acceptors, are represented as first-order kinetic Fe OH 3 t k2 TS Fe OH 3 22 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 37
∂ð Þ=∂ ¼ − MnðIVÞ½ ½ ðÞ MnO2 t k2 TS MnO2 23 np is the volume fraction of the precipitated minerals 3 3 ð Þ (L /L ), nb is the volume fraction of the soil-attached ∂ð Þ=∂ ¼ − Mn IV ½ 2þ ½ ðÞ 3 3 MnO2 t k3 Fe MnO2 24 biomass (=Xsρs /ρb)(L biomass/L total), and ρb is the attached biomass density (M/L3). Assuming 50% of where So is sulphide in solid state and TS is the sum of − − cellular carbon is protein (Luria, 1960) and solid phase [H S], [HS ], and [S2 ]. 2 biomass density is 70 mg-volatile solids/cm3 (Cooke et al., 1999), the attached biomass density (ρb)is 3.2. Permeability reduction model estimated as 35 mg-protein/cm3. The densities of the various precipitating minerals modelled in this study are This model consists of two modules — one for listed in Table 2. The large difference in biomass and predicting the effect of bioaccumulation and chemical mineral densities can have a significant influence on the precipitation–dissolution, and the other for the effect of relative contribution of biomass growth and mineral gas formation, on the soil's porosity and permeability. The precipitation to permeability reduction. combined effect of bioaccumulation, metal precipitation, and gas formation on hydraulic conductivity is modelled 3.2.2. Gas formation module as a multiple of the amended intrinsic permeability The rate degradation of acetate to gaseous products, (reduced by solids formation via bioaccumulation and methane and carbon dioxide is described by Eqs. (5), metal precipitation) and the relative permeability to water (14) and (15). Acetate degradation in the column is (to account for the presence of a gaseous phase). quick and results in vigorous production of methane, which being poorly soluble in water, forms separate 3.2.1. Biomass production and chemical precipitation phase gas bubbles. Carbon dioxide has high solubility in module water and its contribution to the gaseous phase is The models for estimating changes in soil properties ignored. It is assumed that the bubbles coalesce over a (such as, porosity, permeability and surface area) due to sufficiently short interval (estimated from methane biomass accumulation (e.g., Taylor et al., 1990; Sarkar production rates to be less than 10 cm) of the column et al., 1994; Clement et al., 1996a)) have not been so that a separate gas phase can be assumed to prevail in extensively tested in the laboratory or the field. The the entire column. The effect of gas flow on soil models make different assumptions and incorporate permeability is modelled using the generalised Darcy's varying levels of complexity to estimate the permeabil- Law (modified after Huyakorn and Pinder, 1983). ity by relating biomass to the reduction in pore space ∂ available for flow. As stated previously, no single ¼ ki;bpkra pa þ ̂; ¼ ; ð Þ qa ∂ qa g a w g 27 bioclogging model has been shown to better represent la x the underlying processes or more accurately predict the changes in permeability reduction. In this study, given where μα is the dynamic viscosity of fluid (M/LT), ρα is the need to adopt a permeability reduction model that the density of fluid (M/L3), ĝ is the acceleration due to 2 could be readily interfaced with the geochemical gravity (L/T ), krα is the relative permeability that speciation module, the model proposed by Clement accounts for the reduction in the permeability to water et al. (1996a) was adopted. To estimate the permeability due to the presence of a second phase (i.e., gas), pα is the 2 and porosity reduction by bioaccumulation and chem- pressure (M/LT ), and qα is the Darcy flux (L/T) for the ical precipitation the Clement model was modified by water (α=w) and gaseous (α=g) phases. including the reduction in pore volume from precipita- To parallel the assumption of gas coalescence over short tion as follows: distances, it is assumed that water saturation is relatively