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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 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 ), 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 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 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 . 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 ½al;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 ½CH3COOHð20Þ mediated redox reactions given in Eqs. (12)–(15). 1 Following the approach used by Wang and Van FeðIIIÞ ∂ðFeðOHÞ Þ=∂t ¼ −k ½CH COOHð21Þ 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 2þ½ 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 ¼ki;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

19 k ; n þ n 6 i bp ¼ 1 b p ð25Þ ki;0 n0 Table 2 Densities of precipitating minerals (CRC Press, 1998) Minerals Mineral density (g/cm3) nbp ¼ n0 nb þ np ð26Þ

Calcite (CaCO3) 2.71 where ki,bp is the biomass plus metal precipitation Dolomite (CaMg(CO3)2) 2.86 2 affected intrinsic permeability (L ), ki,0 is the initial Siderite (FeCO3) 3.90 2 Rhodochrosite (MnCO ) 3.70 intrinsic permeability (L ), n0 is the initial soil porosity, 3 Iron Sulphide (FeS) 4.70 nbp is the biomass plus precipitation affected porosity, 38 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 constant over most of the column, i.e., a constant capillary to solve the coupled transport model and biogeochemical pressure prevails over the entire column. Therefore, reaction equations. The mathematical formulation of the kinetic biodegradation reactions gives a system of ordinary differential equations, which is solved by the dp dp dp c ¼ g w ¼ 0 ð28Þ stiff ordinary differential equation system solver SFODE dx dx dx (Morris, 1993). where p is the capillary pressure (M/LT2). Thus, At each location in the modelled domain the redox c potential (pE) is estimated using the concentrations of l q the dominant terminal electron acceptor and its lwqw g g þ ¼ ð Þ ki;bpg qw qg 0 29 corresponding reduced species calculated from the krw krg transport and kinetic biodegradation model (Smith and The relative permeabilities to water and gas are given Jaffé, 1998). The estimated pE is used in the equilibrium as (Parker et al., 1987; Parker, 1989): speciation model to determine the speciation of trace metals and non-dominant redox species at that location, ðθ Þ¼θ1=2ð −ð −θ1=mÞmÞ2 ð Þ krw w e 1 1 e 30 and the equilibrium state towards which the system is driven. The rate expressions in Table 1 are then used to ðθ Þ¼ð −θ Þ1=2ð −θ1=mÞ2m ð Þ krg w 1 e 1 e 31 calculate the rates of the non-dominant redox reactions (not applicable to the present study) and precipitation or hwhwr where he ¼ is the normalised water content hws hwr dissolution of minerals. At locations where the chemi- (ignoring the effects of bioaccumulation and chemical cal equilibrium model predicts that the ion activity precipitation on θ and θ ), θ is the water content, θ w ws w wr product exceeds the solubility product (K ) precipita- is the residual water content, θ is the saturated water sp ws tion occurs, and where the converse applies dissolution content, m=1−1/n,andn is the van Genuchten equation occurs. Finally, the masses of all mineral phases are parameter. As the effect of bioaccumulation and chemical updated and the dissolved species re-equilibrated at each precipitation on θ and θ is ignored, a single value of w ws time step. water content is obtained for the entire column by A grid spacing (Δx) of 0.25 cm, giving a Peclet minimising the sum of squares of the residuals from number (Δx/α) of 2 using the measured dispersivity (α) (μ q / k − μ q / k )plusk g(ρ − ρ )usingthe w w rw a a ra i,bp w a of 0.12 cm, is used to meet the Peclet criterion, and a Levenberg–Marquardt algorithm (Morris, 1993). The time step (Δt) of 0.00625 days is chosen to satisfy the reduction in hydraulic conductivity is calculated as: Courant criterion (v Δt/Δx≤1). Model simulations are performed for 126 days to cover Phases 1 and 2 of k ; k Reduction in KðÞ¼k 1 i bp rw 100 ð32Þ column operation. The transport simulations involve ki;0 one organic compound (acetic acid) and 14 dissolved inorganic components (yielding 42 inorganic species in The above model is a simple, but approximate the MINTEQA2 chemical equilibrium speciation representation of the processes by which gas bubble model) and 7 solid mineral phases. The simulation form, coalesce, and then escape by forming a continuous parameters are summarised in Table 3 and the gas phase. Furthermore, the model neglects hysteretic biochemical parameters (i.e., growth rates, yield coeffi- effects of periodic gas accumulation and venting. As cients, and half saturation constants), obtained during such, the model represents an averaged effect of gas formation over the long-term; a more accurate repre- sentation of the short-term effect of gas formation on soil permeability can be developed by following Amos Table 3 Values of the model simulation parameters and Mayer (2006b). Parameter Value 4. Numerical solution and coupling of modules Column length, L 50 cm Column diameter 5 cm Δ – Time step, t 0.0125 day The one-dimensional advection dispersion equation is Space discretisation, Δx 0.5 cm solved using a finite difference scheme with central Darcy flux, q 16.9 cm/day weighting in space and time as discussed by Islam and Dispersivity, α 0.12 cm Singhal (2002). A two-step sequential operator splitting Initial porosity, n 0.41 − 3 method, similar to that used by Walter et al. (1994),isused Saturated hydraulic conductivity, Ks 8.8×10 cm/s N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 39

Table 4 Calibrated values for kinetic microbial transformation parameters Biological parameters Calibrated parameters Literature values References − 5 Maximum microbial capacity for attachment (Xmax), mol-cell/g-sand 8×10 –– 3 Biomass density (ρs), g-protein/cm 35 –– − 1 Detachment coefficient (Kdet), day 0.02 0–5.36 7, 18, 21 − 1 Attachment coefficient (Katt), day 75 nb 7.4–410 7, 18, 21

Sulphate reducing bacteria: − 1 Maximum growth rate (μmax), day 0.034 0.001–30 2, 4, 5, 8, 9, 12, 14–16, 19, 20 − 1 − 6 Decay coefficient (Kdec), day 0.003 1×10 –0.4 2, 4, 5, 12, 14, 15, 17, 19, 20 − 4 − 4 Half-saturation constant for acetic acid (Ks), mol HAc/l 2×10 1×10 –4 4, 5, 8, 12, 15, 20 − 4 − 6 −3 Half-saturation constant for sulphate (Kea), mol SO4/l 1×10 1×10 –1×10 4, 14, 15 Yield coefficient for acetic acid (Y), mol-cell/mol-HAc 0.006 0.003–0.125a 5, 8, 9, 12, 15, 20

Methanogenic bacteria: − 1 − 4 Maximum growth rate (μmax), day 0.062 1×10 –1.69 1–5, 9–11, 13, 16–17, 20 − 1 − 6 Decay coefficient (Kdec), day 0.006 1×10 –0.05 2–5, 9–11, 13, 16–17, 20 −3 − 5 −2 Half-saturation constant for acetic acid (Ks), mol HAc/l 2.0×10 5×10 –4×10 1–5, 9–11, 13, 16–17, 20 −3 Inhibition constant for sulfate (IC), mol SO4/l 1.0×10 –– 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- sulphate and acetic acid concentrations, indicates that mental observations, are presented in Table 4. the initial concentration of sulphate reducers is small (5% of the measured initial total biomass concentration). As 5. Simulation results and discussion shown on Figs. 1 and 2 the agreement between the simulated and observed acetic acid and sulphate profiles 5.1. Biochemical reactions in both phases is good; however, the fits for Phase 2 are somewhat poorer than those for Phase 1. A comparison The initial biomass concentration of sulphate reducers of the simulated and observed concentrations of attached and methanogens, estimated by adjusting their relative and suspended biomass concentrations (Fig. 3) shows proportions to match the observed and simulated that the attached and suspended biomass profiles fit the

Fig. 1. Comparison of observed and simulated concentrations of (a) acetic acid and (b) sulphate during Phase 1. 40 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47

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. The the reported slow rate of FeCO3 precipitation (Wajon model did not fully capture the decrease in suspended et al., 1985; Greenberg and Tomson, 1992). biomass concentrations at later times, which is likely The observed and simulated concentration profiles for caused by a lowering in detachment rates under slow dissolved and total solid calcium are shown in Fig. 5,and microbial growth conditions (Hornberger et al., 1992; for dissolved carbonate and solution pH in Fig. 6.The Tan et al., 1994). dissolved Ca(II) simulations show a gradual decrease The observed and simulated changes in Fe (II) and along the column, instead of the observed quick decrease Mn(II) concentrations resulting from the reduction of in the 0–5 cm section followed by a relatively constant Mn(IV) and Fe(III) oxides in sand due to redox reactions concentration in the remainder of the column — apattern with dissolved sulphide ions and the microbial oxidation similar to that observed for Mg(II) concentrations (data of organic carbon are shown on Fig. 4. The rate not presented here). The observed rapid decrease in constants obtained by fitting the data are presented in dissolved calcium occurs in the inlet region, where a large Table 1. Model simulations indicate that Mn(IV) oxide attached biomass concentration is present. This rapid reduction by Fe(II) oxidation is a minor abiotic decrease in dissolved calcium may have resulted from reduction pathway. The Fe(II) concentrations decrease enhanced precipitation of calcium via nucleation on the at the column inlet due to precipitation as FeS, but then reactive sites of bacterial cell surfaces (Brune et al., 1994; increase further into the column due to the microbial Fortin et al., 1997; Fortin and Ferris, 1998). The reduction of Fe(III) oxide in sand. The precipitation rate simulations for total calcium match the observations at of Fe(II) as FeCO3 is found to be small, consistent with day 58, but significantly overpredict those at day 126.

Fig. 3. Comparison of observed and simulated concentrations of (a) attached and (b) suspended biomass. N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 41

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

5.2. Porosity and permeability reduction limited to the 0–1.5 cm section of the column. With time there was an increase in the amount as as the length The soils were initially saturated, but gradually be- of column-zone affected by porosity reduction. By came unsaturated due to gas production in the columns. 126 days the porosity was predicted to reduce by 70% in The piezometric head measurements were affected by the 0–5 cm section of the column. gas formation and flow in the columns, especially Fig. 7 also shows the observed and simulated during Phase 2 when the gas production rates were hydraulic conductivity (with and without the consider- larger. Awater content of 0.373 and 0.370 at days 80 and ation of gas phase) values. The simulations presented for 86, respectively, was estimated using Eq. (29) with a days 56, 73 and 126 consider only the effect of residual water content (θwr) of 0.045, van Genuchten bioaccumulation on hydraulic conductivity and show parameter n of 2.68 for sand (Carsel and Parrish, 1988), similar trends as porosity. The simulated hydraulic soil porosity of 0.41, saturated hydraulic conductivity of conductivities are larger than those observed, and while 8.8×10− 3 cm/s, and observed gas flow rates of 1080 the simulations better approximate the observations at and 1440 ml/day and a water flow rate of 331 ml/day. larger times, an observable difference between these The above estimates give a gas saturation of approxi- values remains. After 126 days of operation a reduction mately 10%, which corresponds to a reduction in hy- in hydraulic conductivity of 99.6% (decrease from − 3 − 5 draulic conductivity of 60% (i.e., krw =0.4). 8.8×10 cm/s to 3.5×10 cm/s) was observed in the The simulated porosity values are shown on Fig. 7, 2–6 cm section of the column. The model simulations which suggest that the most significant changes in show that hydraulic conductivity reduction due to metal porosity over a short distance from the inlet. Over precipitation is under 1% and can be ignored. Also, 58 days the predicted decrease in porosity was 32% and when only bioaccumulation is considered (i.e., the gas

Fig. 5. Comparison of observed and simulated concentrations of (a) dissolved and (b) precipitated calcium. 42 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47

Fig. 6. Comparison of observed and simulated concentrations of (a) total dissolved carbonate and (b) pH. phase is ignored), the simulations show decreases in models for permeability reduction by bioaccumulation hydraulic conductivity in the 0–2 cm and 2–6cm and gas formation. Also of significance is the assump- sections of the column of 97% and 67%, respectively. tion of continuous gas flow in the simulations; in the Simulations accounting for the effects of gas production experiments gas flow is seen to occur intermittently, on hydraulic conductivity show a smaller difference suggesting that during the intervening period gas between the observations and predictions in the inlet buildup occurs within the column until the gas-pressure section of the column, but a consistently lower predicted increases to force gas escape from the column. A similar hydraulic conductivity than observed in the remainder situation is encountered during water in of the column. When bioaccumulation and gas forma- unsaturated soil where gas saturation builds up before tion are both considered, the simulated decreases in air can escape (Wang et al., 1997). The model does not hydraulic conductivity are 99% and 87% in the 0–2cm include the above phenomena and ignores permeability and 2–6 cm sections, respectively. The combination of reduction due to bubble formation and entrapment due bioaccumulation and continuous gas flow predicts a to organic biodegradation in soil. Additionally, the use 62% decrease in hydraulic conductivity in the 10–50 cm of discontinuous gas flow in the simulations will lessen section of the column, instead of the 80% and 11% the predicted decrease in hydraulic conductivity in the observed at 22 cm and 37 cm, respectively. As tail section of the column. Despite the underestimation bioaccumulation accounts for only 6% of the simulated of hydraulic conductivity reduction in the inlet region hydraulic conductivity decrease, the predicted conduc- and overestimation in the tail section of the column, the tivity decrease is largely due to gas flow in the column. model's performance is deemed acceptable for its The differences between the observed and simulated simple formulation. The permeability reduction model values are attributed to the use of simple uncalibrated can be further improved by calibrating the exponent in

Fig. 7. (a) Simulated porosity and (b) observed and simulated hydraulic conductivity. N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 43

Fig. 8. Simulated (a) porosity and (b) hydraulic conductivity for different substrate loadings. the bioaccumulation module and including gas bubble media at the small scale by decreasing the effective size formation and entrapment in the gas formation module. of larger pores available for water flow. However, at While the findings of the study may not be directly larger scales there may be an increase in heterogeneity applicable to the field due to the small scale of the due to formation of preferential flow paths as the flow physical model, one-dimensional vertical flow, and circumvents regions with reduced permeability. large acetic acid concentration, it does however provide clues on the effects of interactions occurring in selective 5.3. Case studies portions of a leachate contaminated aquifer. Of the processes considered, bioclogging would appear to have The rate of clogging under a landfill is a function of the most significant effect on permeability reduction. the flow rate, soil grain size, temperature and leachate Under anaerobic conditions gas formation would also composition (e.g., organic content, suspended solids, contribute to permeability reduction by decreasing the and calcium content) (Rowe, 1998). A sensitivity analy- amount of pore space available to flow. Furthermore, sis was performed using the model developed in this chemical precipitation is unlikely to contribute signif- study to assess the effects of substrate loading, leachate icantly to permeability reduction. It must be noted that flow rate, particle size, and mineral precipitation on the permeability reduction will occur in selective regions as clogging of soils underlying landfills. A one-dimension- excessive bioaccumulation and gas formation only al vertical flow of leachate is assumed beneath the land- occur significantly in areas containing large concentra- fill. Unless stated otherwise, simulations are done using tions of organic matter. Although the issue of soil the calibrated parameter values for the controls listed in heterogeneity is not considered in this paper, bacterial Table 3. Five test cases were simulated: Cases 1, 2 and 3 and gas accumulation are likely to homogenise the assess the effect of influent acetic acid at concentrations

Fig. 9. Simulated concentration profiles of (a) attached biomass and (b) acetic acid for different substrate loadings. 44 N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47

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; Simulation results for the Cases 1 to 3 showing the Case 4 simulates permeability reduction in soils for an effects of substrate loading on porosity and hydraulic influent acetic acid concentration of 6000 mg/L (same as conductivity are presented in Fig. 8 and for attached Case 2) and a flow rate of 0.11 ml/min (corresponding to biomass and acetic acid in Fig. 9. Increasing substrate half the flow rate for Cases 1, 2 and 3); and, Case 5 loading results in further lowering of porosity and simulates permeability reduction in soils with a particle hydraulic conductivity by only 4%; however, the zone size of 0.2 mm, half the size of particles used in the affected by these reductions is increased by approxi- previous cases, for an influent acetic acid concentration mately 4 cm for every 3000 mg/L increase in the of 6000 mg/L. The attachment coefficients (Katt) were influent acetic acid concentration. The simulated calculated using the theory (Tien et al., 1979). attached biomass profiles show that permeability Accordingly, in Case 4 the attachment was decreased by reduction is due to biomass growth and retention in 50% and in Case 5 it was increased by 217%. The soil, and that the higher influent acetic acid concentra- detachment coefficient (Kdet) value was kept the same for tion increases the length of the zone over which acetic all the cases. Model simulations were run for a total acid is available to bacteria. Figs. 10 and 11 compare the simulation time of 180 days. In addition, two simulations effects of reducing the flow rate (Case 4) and sand size were done to examine the effect of calcium and mag- (Case 5) with Case 1, noting that mass influx of acetate nesium precipitation with influent calcium and magne- in Cases 1 and 4 is the same. Case 4 gives very similar sium concentrations of 400 and 240 mg/L, and 1200 and results to Case 1 for porosity and permeability reduction 730 mg/L, respectively, at pH 8. The simulated maxi- (Fig. 10) as well as the attached biomass (Fig. 11) in soil. mum reduction in permeability due to mineral precipi- Reducing the particle size increases the attachment tation was only 8% and the results are not presented coefficient. In Case 5 the increase in the attachment here. coefficient and a larger biomass buildup for an influent

Fig. 11. Simulated (a) attached biomass and (b) acetic acid showing the effects of flow rate (Case 4) and particle size (Case 5). N. Singhal, J. Islam / Journal of Contaminant Hydrology 96 (2008) 32–47 45 acetate concentration of 6000 mg/L lead to greater to solutions is slow, successful adoption of such models reductions in porosity and hydraulic conductivity. Case would require the development of efficient numerical 5 results suggest that hydraulic conductivity reductions schemes coupled with rigorous testing and validation of of more than three orders of magnitude can result in soils the integrated approaches. under specific conditions. Acknowledgements 6. Conclusions We would like to acknowledge the comments and The biogeochemical model developed in this study suggestions from the journal editor, E.O. Frind, and one shows satisfactory agreement with experimental data for anonymous reviewer. acetic acid, sulphate, suspended and attached biomass, Fe(II), Mn(II), dissolved and total calcium, carbonate References ions, pH, and the soil's hydraulic conductivity. The model for permeability reduction by gas formation is Aguilar, A., Casas, C., Lema, J.M., 1995. Degradation of volatile fatty acids by differently enriched methanogenic cultures: kinetics and simplistic and can be improved by incorporating a gas inhibition. Water Res. 29 (2), 505–509. bubble formation and entrapment mechanism. While the Allison, J.D., Brown, D.S., Nova-Gradac, K.J., 1991. MINTEQA2/ fitted parameters are within the range of values reported PRODEFA2, A Geochemical Assessment Model for Environ- in literature, the diversity range of values reported in the mental Systems: Version 3.0 User's Manual, Environ. Res. Lab, literature and the large number of calibrated parameters Off. Of Res. and Dev., U.S. Environ. Prot. Agency, Athens, GA. suggests that issues of non-uniqueness may remain and Amos, R.T., Mayer, K.U., 2006a. Investigating ebullition in a sand will need addressing via on-going research. The column using dissolved gas analysis and reactive transport simulations show that bioaccumulation causes the modeling. Environ. Sci. Technol. 40, 5361–5367. largest reduction in permeability. Gas formation can Amos, R.T., Mayer, K.U., 2006b. Investigating the role of gas bubble also be a significant contributor to permeability formation and entrapment in contaminated aquifers: reactive transport modeling. J. Contam. Hydrol. 87, 123–154. reduction, but metal precipitation in comparison has a Angelidaki, I., Ellegaard, L., Ahring, B.K., 1999. A comprehensive negligible effect. Simulations also show that higher model of anaerobic bioconversion of complex substrates to biogas. substrate concentrations may increase the length of the Biotechnol. 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