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Reactive Transport Modeling of Induced SelectivePlugging by Leuconostoc Mesenteroides in CarbonateFormationsJavier Vilcáez a b , Li Li a b c , Dinghao Wu d & Susan S. Hubbard ea John and Willie Leone Family Department of Energy and Mineral Engineering , ThePennsylvania State University , University Park , Pennsylvania , USAb EMS Energy Institute , The Pennsylvania State University , University Park , Pennsylvania ,USAc Earth and Environmental System Institute (EESI) , The Pennsylvania State University ,University Park , Pennsylvania , USAd College of Information Sciences and Technology , The Pennsylvania State University ,University Park , Pennsylvania , USAe Earth Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California ,USAAccepted author version posted online: 21 Feb 2013.

To cite this article: Javier Vilcez , Li Li , Dinghao Wu & Susan S. Hubbard (2013) Reactive Transport Modeling of InducedSelective Plugging by Leuconostoc Mesenteroides in Carbonate Formations, Geomicrobiology Journal, 30:9, 813-828, DOI:10.1080/01490451.2013.774074

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Geomicrobiology Journal (2013) 30, 813–828Copyright C© Taylor & Francis Group, LLCISSN: 0149-0451 print / 1521-0529 onlineDOI: 10.1080/01490451.2013.774074

Reactive Transport Modeling of Induced Selective Pluggingby Leuconostoc Mesenteroides in Carbonate Formations

JAVIER VILCAEZ1,2∗, LI LI1,2,3, DINGHAO WU4, and SUSAN S. HUBBARD5

1John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania State University, UniversityPark, Pennsylvania, USA2EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania, USA3Earth and Environmental System Institute (EESI), The Pennsylvania State University, University Park, Pennsylvania, USA4College of Information Sciences and Technology, The Pennsylvania State University, University Park, Pennsylvania, USA5Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA

Received September 2012, Accepted January 2013

A process-based mechanistic reactive transport model was developed to understand how in-situ coupled processes and operationalfactors affect selective plugging of reactive carbonate formations by the fermenting bacteria Leuconostoc mesenteroides that producesa plugging polymer dextran. The growth and transport of L. mesenteroides and the associated (bio) geochemical reactions weresimulated explicitly with enzyme activity at the field scale over spatial extents of hundreds of meters. Simulations were performedto explore controls on selective bioplugging of high permeability zones in a representative carbonate reservoir, a process that can beused to improve oil sweep efficiency through lower permeability layers. Simulation results indicate that dextran production and theeffectiveness of plugging can be largely affected by sucrose and bacteria injection rates. Selective plugging of high permeability zonescan only be achieved when the injection rates are high compared to the rates of dextran production. Otherwise, plugging only occursat the vicinity of injection wells. Due to the dependence of enzyme activity on pH and the reactive nature of carbonate formations, thechemistry of the injection and the formation water is also important. The injection of sucrose and L. mesenteroides at the optimumpH for dextran production (5.2) leads to the dissolution of calcite and an increase in pH levels. However, the resulting pH doesnot suppress plugging with dextran. Lactic acid and CO2 formed during the growth of L. mesenteroides buffers the pH of water tolevels between 5.2 and 7.0 for continued dextran production. At neutral and basic pH levels, induced precipitation of calcite doesnot significantly modify the permeability profile at carbonate concentrations typically found in oilfield formation waters. This is thefirst work that examines the controlling parameters that affect selective plugging of carbonate formations at the field scale within thecontext of enhanced oil recovery. The demonstrated approach can be used to identify optimal operational conditions for enhancedoil recovery and other applications where selective plugging can be beneficial.

Keywords: enhanced oil recovery, modeling, permeability modification, reactive transport, selective plugging

Introduction

Microbial growth and the associated biogeochemical reactionproducts can lead to significant changes in porosity and per-meability of subsurface. Reduction in porosity and permeabil-ity can be caused by the growth of microbes and the deposi-tion of extra-polymeric substances (EPS) in the void space ofrocks (Davery et al. 1998), whereas an increase in porosityand permeability may occur due to the dissolution of rocksaccelerated by produced organic acids (e.g. acetic acid, lacticacid, etc.) during microbial growth (Adkins et al. 1992).

The process of reduction in permeability due to micro-bial processes is called bioclogging. Bioclogging has been ob-

∗Address correspondence to J. Vilcaez, Faculty of Engineering,The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-8656,Japan; Email: vilcaez@frcer.t.u-tokyo.ac.jp

served in various applications, including environmental biore-mediation (Englert et al. 2009; Li et al. 2009; Li et al. 2010;Zhang et al. 1995), microbial enhanced oil recovery (MEOR)(Abdel-Waly 1999), and potentially geological CO2 sequestra-tion (Mitchell et al. 2009). Bioclogging has also been observedin both laboratory studies (Baveye et al. 1998) and columnexperiments (Cunningham et al. 1991; Johnston 1997; Tay-lor et al. 1990; Thullner et al. 2002a; Thullner et al. 2002b;Thullner 2010; Vandevivere and Baveye 1992; Wu et al. 1997).

Although bioclogging is usually considered as having neg-ative effects on many processes (Bott 1998; Brown 2010;Khardori and Yassien 1995; Videla and Characklis 1992), pref-erential bioclogging, or selective plugging, has been consideredas a viable technique for the bioremediation of contaminatedsoils and water (Zhang et al. 1995). For example, selectiveplugging of aquifer flowpaths can lead to the formation ofbiobarriers, which inhibit contaminant mobility. In MEOR,selective plugging of high permeability zones has been

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observed to improve the sweep efficiency through low per-meability zones (Gullapalli et al. 2000; Kim and Fogler 2000;Thullner et al. 2002a).

In particular, with the continuous decline in light oil re-serves, the strategy of using microbes to selectively plug high-permeability zones to prevent premature breakthrough andto enhance the flooding efficacy of the injected water throughlower permeability zones has motivated a number of labora-tory experiments (e.g., Harish et al. 2009; Lappan and Fogler1994; MacLeod et al. 1988; Raiders et al. 1989) and field stud-ies (Knapp et al. 1992). In microbially enhanced oil recoverypractice, it may be simpler to reduce the permeability of highpermeability zones to enhance recovery from low permeabilityzones than to induce bio-products to change rock wettabilityand oil viscosity (Sen 2008).

Various types of microbes are capable of enhancingthe oil recovery through selective plugging, including Leu-conostoc mesenteroides (Lappan and Fogler 1994), Bacilluslicheniformis (Harish et al. 2009), and Klebsiella pneumonia(MacLeod et al. 1988). Among these, L. mesenteroides pos-sesses excellent plugging capabilities. This fermenting microbeproduces an extracellular enzyme called dextransucrase whenit grows in sucrose rich media. The enzyme dextransucrasethen uses sucrose as the raw material to produce dextran, ahigh molecular weight D-glucose polymer that can effectivelyplug the porous space. At the laboratory scale, L. mesen-teroides completely plugged a ceramic core with an initialporosity of 55% within one day (Lappan and Fogler 1992;Lappan and Fogler 1994). In addition, available informationabout the mechanism and growth kinetics of L. mesenteroidesmakes this microbe an excellent model organism for under-standing and predicting selective plugging in subsurface. De-tailed description of L. mesenteroides and the formation ofplugging EPS (dextran) can be found in various publications(Naessens et al. 2005).

Although carbonate rocks constitute approximately halfof the hydrocarbon reservoirs worldwide, limited informationabout the key controls over microbially induced permeabil-ity modification is available for carbonate rocks. One of themost important factors that control the effectiveness of selec-tive plugging is the response of microbes to in-situ conditionswhere solution composition changes because of the interac-tions among water, rock, and microbes. For example, one im-portant characteristic of L. mesenteroides is that it producesan enzyme called dextransucrase that is most effective whenthe pH values are between 5.0 and 5.5 (Lazic et al. 1993). Con-sequently, controlling the solution pH has been proposed asa method to achieve selective plugging of high permeabilityzones and to avoid plugging the low-permeability zone in theimmediate vicinity of the injection points (Wolf and Fogler2005).

However, carbonate rocks are highly reactive. Low pH in-jection solutions can accelerate the dissolution of carbonateminerals, which may further increase the permeability of highpermeability zones. On the other hand, the produced calciumspecies can lead to high pH conditions which may cause theprecipitation of carbonate minerals. As such, the effectivenessof the selective plugging with L. mesenteroides is ultimately de-termined by the complex interplay among microbial growth,

reactions between microbial reaction products and the sur-rounding rocks, and the flow and transport processes.

Various modeling and experimental studies have describedcoupled microbial and geochemical processes that lead to bio-clogging porous media for various applications. Experimen-tal studies have demonstrated the potential of bioclogging forcontaminant remediation (e.g., Wu et al. 2011) and for soil sta-bility (DeJong et al. 2006). However, pore-scale mechanisticstudies of plugging by microbe-produced dextran in carbonateformations have yet to be carried out. Models have been de-veloped to represent components that contribute to microbialselective plugging, such as water chemistry evolution, trans-port of microbes, attachment/detachment of microbes to thesurface of rocks, and minerals dissolution and precipitationreactions (Ginn et al. 2002; Murphy and Ginn 2000).

Although much attention has been devoted to using thesemodels to understand the fate of contaminants and microbesin groundwater, only a few studies have focused on mineralprecipitation and biogeochemical reaction products and theireffect on transport processes (Knutson et al. 2005; Li et al.2010). The majority of modeling studies does not take into ac-count the dependence of microbial activity on water chemistryand typically assume that the initial permeability distributionremains constant. In addition, microbial activities are gener-ally assumed to depend only on the substrate and nutrientconcentrations, yet it is known that the microbial activitiesof microbes such as L. mesenteroides can be very sensitive topH conditions and are a result of combined biological andgeochemical reactions. As such, it is necessary to develop a re-active transport model capable of taking into account relevantphysical, geochemical, and microbiological processes.

The objective of this study is to develop a reactive transportmodel to mechanistically understand the complex interplaybetween microbial growth, dextran production, and the in-teractions between the microbial byproducts and the reactivecarbonate rocks. This mechanistic understanding is then usedin synthetic numerical studies to identify the controlling fac-tors that govern selective plugging of carbonate rocks with L.mesenteroides and help predict the effectiveness of microbialselective plugging under an array of injection conditions. Inthis work, we focus on the water phase without consideringthe presence of oil, because most reactions that are relevant tobioclogging occur either within the aqueous phase, or at thewater-rock interphase. We developed a new multi-componentreaction network for the microbiological and geochemical re-actions of L. mesenteroides and carbonate rocks, a permeabil-ity profile modification procedure corresponding to the poros-ity change, and a kinetic equation for dextran production as afunction of pH.

With the established framework, we explored the effect ofcarbonate reactivity and injection conditions (flow rate, mi-crobe and sucrose concentrations) on water chemistry and onpermeability modification as a result of dextran production.As far as we know, this is the first model that can be usedto quantify and predict the coupled physical, geochemical,and microbiological processes in the context selective plug-ging with L. mesenteroides at the scale of hundreds of meters.Although some of the specific characteristics are particular toL. mesenteroides, the general framework can be extended for

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Modeling of Induced Selective Plugging by Leuconostoc Mesenteroides 815

other types of microbes and a range of applications. Insightsgained from this work will be useful for guiding the operationof selective plugging schemes at the field scale.

Reactive Transport Modeling

Reactive transport modeling aims at a comprehensive, quan-titative, and ultimately predictive understanding of chemicaltransformation and mass transfer within earth systems (Reg-nier et al. 2003). Various reactive transport codes are availablefor coupling microbial and geochemical reactive transport inporous media [e.g., Geochemist’s Workbench (GWB), Hydro-geochem, Bioslurp, CrunchFlow, etc]. Because of its flexibilityand capability of dealing with multicomponent geochemicaland microbially mediated reactions in heterogeneous systems,in this study CrunchFlow (Steefel 2009) has been used as aframework for modeling and simulating the selective pluggingprocesses. The major capabilities of CrunchFlow code includethe simulation of coupled advective, dispersive and diffusivetransport, and reaction processes in up to three dimensions.

Reactions that can be simulated include, for example, ther-modynamically controlled aqueous complexation and surfacecomplexation reactions, sorption and desorption, kinetically-controlled mineral precipitation and dissolution, microbe-mediated reactions with Monod kinetics. The code uses thestandard EQ3/EQ6 thermodynamic database (Wolery et al.1990). The code has been used to model many reactive trans-port processes in various applications (Giambalvo et al. 2002;Knauss et al. 2005; Maher et al. 2006; Navarre-Sitchler et al.2009; Singha et al. 2011; Steefel et al. 2003), including thosethat involve microbe-mediated reactions in porous media withspatially variable properties (Li et al. 2009; Li et al. 2010;Li et al. 2011). Because microbial selective plugging with L.mesenteroides involves transport of microbes in the aqueousphase, we have added source codes for the simulation of micro-bial processes in the aqueous phase to complement its originalcapability of modeling microbial reactions with immobile mi-crobes attached to porous media.

General Mass Conservation Equations

Classical formulation of reactive transport equations can befound in (Lichtner 1985) and (Steefel and Lasaga 1994). InCrunchFlow, the mass conservation equation of an aqueousprimary species J in a single phase system is written in termsof a total concentration (Uj):

∂

∂t

(ϕρfMH2OUj

) + ∇ · (uρfMH2OUj − D∇ · (

ρfMH2OUj))

= Rj (j = 1,....., Nc) (1)

where MH2O is the mass fraction of water, ρf is the densityof fluid in units of kg per unit volume, ϕ is porosity, u is theDarcian flux in units of length per unit time, D is the combineddispersion-diffusion coefficient in square unit length per unit

time, Rj is the total rate of reactions:

Rj = Rminj + Raq

j (2)

in units of moles per kg-H2O per unit time that involve thejth primary species J that can react in the mineral or aqueousphase. Nc is the total number of primary species.

The total concentration term (Uj) in units of moles perkg-H2O is defined as:

Uj = Cj +Nx∑i=1

vijXi (3)

where Nx is the number of secondary species I , Xi is the con-centration of secondary species I in units of moles per kg-H2O,ν ij is the stoichiometric coefficient between primary j and sec-ondary species i, and Cj is the concentration of primary speciesj in units of moles per kg-H2O. The secondary species can bewritten in terms of primary species through the following re-action:

Ii ⇔Nc∑j=1

vijJj (4)

where vij is the stoichiometric coefficient of the reaction. Thesereactions are at equilibrium, the concentration of J (Cj) canbe calculated using the laws of mass action for each reaction[4] as:

Xi = K−1i γ −1

i

Nc∏j=1

(γjCj

)vij (5)

where γ i and Ki are the activity coefficient and equilibriumconstant, respectively. These equations apply equally to bi-otic and abiotic reactions. The total rates of heterogeneousreactions for primary species j that occur at the mineral-waterinterface (Rj

min) is written as the sum of all individual mineral-water reactions that species j is involved in:

Rminj = −

Nm∑m=1

vjmrm (6)

where Nm is the number of kinetic-controlled reactions, rm isthe rates of kinetically controlled mineral reactions, includingmineral dissolution and precipitation reactions, vjm is the sto-ichiometric coefficient in the reaction m that involves primaryspecies j. The rates of the kinetic-controlled reactions in theaqueous phase (Rj

aq) are given by:

Raqj = −

Nx∑i=1

vijri (7)

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Table 1. Half reactions

Donor Fd (Sucrose) 148 C12H22O11 + 13

48 H2 → 14 CO2 + H+ + e−

Acceptor Fa (Lactate) 16 CO2 + 1

12 HCO−3 + H+ + e− → 1

12 CH3CHOHCOO− + 13 H2O

Acceptor Fa (Acetate) 18 CO2 + 1

8 HCO−3 + H+ + e− → 1

8 CH3COO− + 38 H2O

Acceptor Fa (Mannitol) 313 CO2 + H+ + e− → 1

26 C6H14O6 + 313 H2O

Acceptor Fa (Ethanol) 16 CO2 + H+ + e− → 1

12 CH3CH2OH + 14 H2O

Acceptor Fa (Fructose) 14 CO2 + H+ + e− → 1

24 C6H12O6 + 14 H2O

Acceptor Fc (Cell) 15 CO2 + 1

20 NH+4 + HCO−

3 → 120 C5H7O2N + 9

20 H2O

where Nx is the number of kinetic-controlled reactions inthe aqueous phase, including microbe-mediated reactions(biomass growth and dextran production).

Reaction Network and Kinetics

The reaction network considered for microbial selective plug-ging includes biogeochemical reactions that involve L. mesen-teroides, mineral dissolution and precipitation reactions, andaqueous speciation reactions. L. mesenteroides growth reac-tion is formulated following the method outlined by Rittmannand McCarty (2001) based on bacteria energetics and availableexperimental information (Dols et al. 1997; Dols et al. 1998;Santos et al. 2000). Table 1 lists the half reactions involvedin sucrose fermentation by L. mesenteroides. In fermentationreactions where more than a single product is formed (suchas sucrose fermentation by L. mesenteroidesa), informationregarding the relative proportion of electron equivalents rep-resented by each of the reduced end products is critical. Inthis research, that information is obtained from the followingstoichiometric equation, which has been determined experi-mentally by Dols et al. (1997):

1 Sucrose → 1 Fructose + 0.5 Lactate + 0.5 Acetate+ 0.1 Mannitol + 0.5 Ethanol + 1 CO2 (8)

Table 2 shows the resulting proportion of electrons equiva-lents required for the calculation of the energy reaction (Fe):

Fe =p∑

i=1

eiFa,i − Fd (9)

Table 2. Electron equivalents

Electron moles × ei = (moles ×acceptors moles e- eq/mol e-eq/mol e-eq/mol)/sum

Lactate 0.5 12 6 0.141Acetate 0.5 8 4 0.094Mannitol 0.1 26 2.6 0.0610Ethanol 0.5 12 6 0.141Fructose 1 24 24 0.563

Sum = 42.6

where p is the number of electron accepting products. The cellsynthesis reaction (Fs) is given by:

Fs = Fc − Fd (10)

The overall reaction is obtained through inserting equa-tions 9 and 10 into the following expression:

F = feFe − fsFs (11)

where fe and fs are the electron fraction used for energy andcell synthesis respectively. This gives the following L. mesen-teroides growth reaction:

0.2083C12H22O11 + 0.2NH+4 + 0.341HCO−

3 →0.2C5H7O2N + 0.14076C6H12O6 + 0.0705CH3CHOHCOO− +0.0705CH3COO− + 0.01408C6H14O6 + 0.0705CH3CH2OH +0.4184CO2 + 0.7259H2O

(12)

C12H22O11: SucroseC5H7O2N: L. mesenteroidesC6H12O6: FructoseCH3CHOHCOO-: LactateCH3CH2OH: EthanolC6H14O6: Mannitol

This global microbiological reaction represents all possiblereaction products, including the growth of bacterial cells. Theelectron fraction from sucrose used for L. mesenteroides syn-thesis (fs) is assumed to be 0.4, a typical value for fermentingbacteria (Rittmann and McCarty 2001).

For the formulation of the stoichiometric reactionfor dextran production, the Michaelis-Menten reactionmodel was employed: Sucrose + Dextransucrase →Sucrose·Dextransucrase → Dextransucrase + Dextran +Fructose. Here, Dextransucrase is the catalysis. This equationessentially assumes that there is an enzyme in bacteria cells tofacilitate the dextran production. The stoichiometric equationof this reaction is usually written in the following way (Santoset al. 2000):

xC12H12O11 → (C6H12O5)x + xC6H12O6xSucrose → Dextran + xFructose (13)

where the value of x determines the molecular weight of thedextran produced. The degree of polymerization of dextran

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Modeling of Induced Selective Plugging by Leuconostoc Mesenteroides 817

Table 3. Aqueous speciation reactions

Aqueous species reactions pKeq (25◦C)

NaHSiO3(aq) + H+ ↔ Na+ + SiO2(aq) + H2O 8.3040HSiO−

3 + H+ ↔ SiO2(aq) + H2O 9.9525H6(H2SiO4)2−

4 + 2H+ ↔ 4SiO2(aq) + 8H2O 13.6400H4(H2SiO4)4−

4 + 4H+ ↔ 4SiO2(aq) + 8H2O 35.9400H2SiO2−

4 + 2H+ ↔ SiO2(aq) + 2H2O 22.9600CaCl2(aq) ↔ Ca2+ + 2Cl− 0.6436CaCl+ ↔ Ca2+ + Cl− 0.6729CaSO4(aq) ↔ Ca2+ + SO2−

4 −2.1111H2SO4(aq) ↔ SO2−

4 + 2H+ 1.0209HSO−

4 ↔ H+ + SO2−4 −7.2054

NaSO−4 ↔ Na+ + SO2−

4 −0.8200CaCO3(aq) + H+ ↔ Ca2+ + HCO−

3 7.0017CO2−

3 + H+ ↔ HCO−3 10.3288

CaHCO+3 ↔ Ca2+ + HCO−

3 −1.4000NaCO−

3 + H+ ↔ Na+ + HCO−3 9.8144

NaOH(aq) ↔ Na+ + OH− 14.7948CO2(aq) + H2O ↔ H+ + HCO−

3 −6.5804

Equilibrium constants are from EQ3/EQ6 database (Wolery et al. 1990).

depends on various factors including sucrose concentration,temperature and strain of L. mesenteroides employed (Ilievand Vasileva 2012; Kim et al. 2003). Typical molecular weightsof dextran produced by L. mesenteroides are within 1 × 103−1 × 106 g/mol (Kim and Rbyt 1996). In this work, a molecularweight of 1.62 × 103 g/mol is used, which corresponds to anx value of 10 in Equation 13.

L. mesenteroides growth and dextran production reactionsare kinetically controlled reactions; these biogeochemical re-actions are the driving force of the system. The dextran isproduced by the enzyme in the bacteria L. mesenteroides. It isassumed that one L. mesenteroides cell produces one unit of en-zyme (dextransucrase) per mole of sucrose metabolized. Thisvalue gives similar maximum consumption rates of sucrose(VMax) to those reported in experimental studies on dextranproduction by L. mesenteroides (Hehre 1946; Neely 1958). Thebiomass was assumed to be able to precipitate on solid phaseonce the aqueous phase concentration exceeds the concentra-tion of 1.13 g/L. This is similar to the sorption or attachmentprocess that leads to the formation of biofilm (Vandevivereand Baveye 1992a).

Similar to other studies (Lappan and Fogler 1994; Wolfand Fogler 2001), the kinetic equation for the growth of L.mesenteroides is represented by Monod’s equation (Table 5).Monod’s equation is empirical and only applies to bacterialpopulations made of large numbers of microbial cells. In the

Table 4. Mineral dissolution or precipitation reactions (Brant-ley 2008; Chou et al. 1989)

kl pKeq

Minerals reactions (mol/ m2/s) (25◦C)

SiO2(s) ↔ SiO2(aq) 1.58 E − 12 −3.1240CaCO3(s) + H+ ↔ Ca2+ + HCO−

3 6.45 E − 7 2.2257

Table 5. Kinetic equation for dextran formation

L. mesenteroides (X) dXdt = μmax

SKs+S X

Sucrose (S) − dSdt = σ1

dXdt + α1

dDdt

Fructose (S) dFdt = σ2

dSdt + α2

dDdt

Lactate (L) dLdt = σ3

dSdt

Dextransucrase (E) dEdt = β dX

dt

Dextran (D)

dDdt = Vmax

SKD+S

Vmax = k·E1+ H+

KaES+ KbES

H+

pores of a porous medium, the number of microbial cellsmay be significantly smaller. However, because the relativelyhigh concentrations of L. mesenteroides injected in this work,Monod’s equation is assumed to be valid. The kinetic equationfor dextran formation is based on Michaelis-Menten reactionmechanism with a bell-shape activity curve (Figure 1) result-ing from the ionization of functional groups in the enzyme(Nelly 1958).

Because the ionization of functional groups depends on theconcentration of protons, the enzyme activity depends on pH.Values of pH in the system are the microbe-mediated reactionsand the associated geochemical reactions given in Table 3 andTable 4. The coefficients α1, α2, σ1, σ2, σ3, and β in thekinetic equations of Table 5 correspond to the stoichiometriccoefficients of Equations 11 and 12.

Table 3 shows all aqueous speciation reactions that involvequartz and calcite as mineral constituents. Table 4 shows disso-lution and precipitation reactions of quartz and calcite. Thesereactions are readily available from literature (Brantley 2008;Lasaga 1998; Li et al. 2008). Quartz is included in the reac-tion network to take into account its possible formation fromreactions among aqueous species. For simplicity it is assumedthat the carbonate rock is composed of only calcite. Over ge-ological time scales, it is a common practice to assume calcitedissolution/precipitation reactions to be sufficiently large toreach local equilibrium conditions (Xu et al. 2004). However,

Fig. 1. Maximum consumption rate of sucrose (VMax) as a func-tion of pH. Optimum pH for enzyme (dextransucrase) activity isat pH of 5.2 (Neely 1958) (color figure available online).

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because the time scale of enhanced oil recovery operations isrelatively short, we assume that both quartz and calcite disso-lution/ precipitation reactions are kinetically controlled reac-tions (Table 4). All other aqueous abiotic reactions are instan-taneous reactions that occur at the time scale of seconds andtherefore are thermodynamically controlled (Table 3) (Moreland Hering 1993).

The rate laws for mineral precipitation and dissolution inCrunchFlow are based on the transition state theory (Lasaga1984) where the resulting kinetic equation (Equation 14) is afunction of saturation state of the solution and it is generallyapplicable for all minerals (Lasaga 1998).

rm = −Askl

Nc+Nx∏i=1

ai

[1 − Qs

Keq

](14)

Here Qs represents the ion activity products, Keq is the equilib-rium constant, As is the surface area of individual minerals, aiis the activity of component i, and kl is the reaction rate con-stant. The value of Qs/Keq in equation 14 determines whethera mineral precipitates or dissolves.

Porosity Permeability Relationships

Various mathematical models have been developed to describemicrobial clogging processes (Thullner and Baveye 2008; Van-devivere et al. 1995). These models assume that biofilm for-mation is responsible for porosity and permeability reduction.They are not suitable for describing clogging processes in thiswork because dextran contributes mostly to the clogging pro-cesses while the volume occupied by microbes in the pore spaceis negligible, as will be shown later. The following permeabilitymodification equation is used in this work:

K = K0

(ϕ − ϕc

ϕ0 − ϕc

)n

(15)

where K0 and ϕ0 are the initial permeability and porosity,respectively.

This equation includes a non-zero critical porosity (ϕc)at which permeability is reduced to zero (Verma and Pruess1988). This equation assumes the porosity value is non-zerowhen permeability is reduced to zero, which has been observedby many studies (Bernabe et al. 2003; Navarre-Sitchler et al.2009; Noiriel et al. 2005; Saripalli et al. 2000). The criticalporosity value (ϕc) is different for different types of porous me-dia. In literature, various combinations of critical porosity (ϕc)and exponent values (n) have been used to calibrate porosity-permeability relationships. For instance, combinations of nvalues of 2 − 9 and ϕc values of 0.095 − 0.9, have been usedfor sandstone reservoirs (Verma and Pruess 1988; Xu et al.2004). Relationship between permeability and porosity in re-active carbonate rocks during the growth of L. mesenteroidesis unknown. Here we choose to use values of n and ϕc to be2 and 0.1, respectively. These values are within the reportedrange and we use them for the sake of an example.

During the bioclogging process, the mineral fractions ϕminand precipitated dextran ϕdex evolved over time. As a result,

porosity evolved according to the following equation:

ϕ = 1 −Nm∑k=1

ϕmin − ϕdex (16)

The volume fraction of minerals (ϕmin) was calculated everytime step from the kinetically controlled reactions (rm):

ϕmin(t + t) = ϕmin(t) + Vminrm(t + t)t (17)

Similarly, ϕdex was updated based on the amount of precip-itated dextran mass and its molar volume of dextran (Vdex).The volume of the dextran was calculated from its molecularweight and molar volume assuming that the density of theproduced dextran is equal to that of water.

Scenario Setup

A vertical cross-section, shown in Figure 2, was designed torepresent a carbonate reservoir region targeted for selectiveplugging of the high permeability zones. The 2D domain ex-tends 100 meters by 100 meters domain and is discretized into10,000 cells with a resolution of 1 meter. The left and rightboundaries of the hypothetical field are open to flow while thetop and the bottom boundaries are no flow boundaries.

The initial porosity and permeability values shown in Fig-ure 2 are consistent with the characteristic data for typical car-bonate petroleum reservoirs (Ehrenberg and Nadeau 2005);the contrasting values in different layers present favorable con-ditions for selective plugging of the high permeability zones,as is desired to enhance sweep through the lower permeabilityzones. The relationship between the initial permeability andporosity distribution is given by the Kozeny–Carman equa-tion:

K = cd2ϕ3

(1 − ϕ)2 (18)

This equation gives the dependence of permeability on theeffective porosity (ϕ) and grain size (d). Here we use a d valueof of 65.5 μm, and a constant c of 2.46 (Ehrenberg and Nadeau2005; Oelkers 1996).

Initial biogeochemical conditions and injection geometrieswere also defined for the synthetic domain (Figure 2). Sucroseand L. mesenteroides were assumed to be initially absent in thecarbonate formation and were injected at a constant volumet-ric flow rate through four ports installed on an injection wellalong the left side (updgradient) of the 2D cross-section. Theinfluence of gravity on the injectates was assumed to be neg-ligible. The initial aqueous concentrations in the carbonateformation were assumed to be initially uniform throughoutthe entire domain. To produce sufficient dextran to plug theporous space, sucrose concentration levels used for simulationswere calculated using the reaction (13), the molecular weightand the molar volume of dextran. Since the volumetric flow

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Fig. 2. Initial porosity (A) and permeability (B) distributions within a hypothetical 2D vertical carbonate reservoir. The wellboredrilled through the target zone located at depths up to thousands of meters has four injection ports.

rate of injection water was constant, the seepage flow velocityat each cell in the mesh changed if the porosity changes.

Results: Effects of Controlling Factorson Selective Plugging

We used the developed model to explore the impacts of var-ious factors on selective plugging with L. mesenteroides, in-cluding injection rate, pH, and sucrose and L. mesenteroidesconcentrations. Table 6 summarizes parameters used for dex-tran production with L. mesenteroides. Table 7 shows typ-ical concentrations of primary species (Wright et al. 1977)used as input data to represent the reservoir formation waters.The concentrations of the secondary species listed in Table 3were calculated based on the given concentrations of primaryspecies. Table 8 shows all scenarios considered for simulatingthe plugging of zones with different permeability levels (45,120, 267, and 529 mD, where 1 mD corresponds to 9.87 ×10−16 m2). The eight scenarios given in Table 8 reflect howinjection flow, ratio of L. mesentroides to sucrose, and pH fac-tors were changed in the numerical case studies to explore keycontrols on selective plugging. Injection flow rates are given inbarrels per day (bbl/day) as this is the most frequent unit used

Table 6. Kinetic parameters

Parameter Value Reference

μmax (h-1) 0.90 Lappan and Fogler (1993)Ks (mg/L) 2500 Lappan and Fogler (1993)KaES 1 × 105 Neely (1958)KbES 3.98 × 105 Neely (1958)KD (mg/L) 30 Neely (1958)Log Kps −15 AssumedMWdex (g/mole) 1620 AssumedCritical porosity, φc 0.1 AssumedExponent value, n 2.0 Assumed

Table 7. Injection and initial concentration of primary species

Formula Concentration (mg/L)

H2S(aq) 5.0CO2(aq) 2.0Ca2+ 9.1NH4+ 300.0Na+ 43000.0HCO3

− 130.0Cl− 87600.0SO4

2− 430.0HS− 10.0SiO2(aq) 100.0Acetate 430.0Sucrose Variable∗C5H7O2N Variable∗H+ Variable∗Dextran 0.0Fructose 0.0Lactate 0.0

∗Except for sucrose, C5H7O2N and H+, the concentration of all otherspecies at the injection points are the same to the concentrations at begin-ning in the carbonate formation.

Table 8. Scenarios

Injection flow Injection C5H7O2N(g/L)/ Initial Injection(bbl/day) Sucrose (g/L) pH pH

1 50 1/25 7.0 7.02 100 1/25 7.0 7.03 100 2/10 7.0 7.04 100 2/20 7.0 7.05 100 1/5 5.2 5.26 100 1/5 8.0 8.07 100 1/5 7.0 5.28 100 1/5 7.0 4.2

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Fig. 3. Permeability profile modification after 250 days of flooding in a carbonate formation with an injection water containing 1 g/Lof L. mesenteroides and 25 g/L of sucrose under two different injection rates. (A) 50 bbl/day. (B) 100 bbl/day. The color scale indicatesthe ratio of modified permeability over initial permeability K0. The initial pH in the formation water and in the injection water is 7.0(color figure available online).

Fig. 4. Spatial distribution of produced dextran after 250 days of flooding in a carbonate formation with water containing 1 g/L ofL. mesenteroides and 25 g/L of sucrose under two different injection rates: (A) 50 bbl/day and (B) 100 bbl/day. The units of dextranare the volume percentage occupying the pore space. The initial pH in the formation water and the injection water is 7.0 (color figureavailable online).

Fig. 5. Spatial distribution of L. mesenteroides assuming complete precipitation as solid phase after 250 days of flooding a carbonateformation with water containing 1 g/L of L. mesenteroides and 25 g/L of sucrose under two different injections rates: (A) 50 bbl/day,and (B) 100 bbl/day. The initial pH in the formation water and the injection water is 7.0 (color figure available online).

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in enhanced oil recovery operations. One barrel is equivalentto 159 liters.

Effect of Injection Rates (Scenarios 1 and 2)

Figures 3, 4, and 5 illustrate the spatial distribution of per-meability modification (defined as K/K0, the ratio of currentpermeability over initial permeability), dextran accumulation,and biomass accumulation on solid phases after 250 days offlooding in a carbonate formation with 1 g/L of L. mesen-teroides and 25 g/L of sucrose at injection rates of 50 and100 bbl/day, respectively. The initial and injection pH was 7.0in both cases. Comparison between Figures 4 and 5 indicatesthat even if all biomass precipitated, the volume fraction of thebiomass on the solid phase is 2–3 orders of magnitude lowerthan that of the dextran and therefore has a negligible impacton modifying permeability profile.

After 250 days permeability was reduced by 2–3 ordersof magnitude in certain areas in both cases. This is reflectedby permeability ratio values close to zero in Figure 3. Theconcomitant occurrence of large volumes of dextran and per-meability reduction indicates that plugging was caused by thegrowth of L. mesenteroides and the production of dextran.With the injection flow rate of 100 bbl/day, the higher per-meability zone (529 mD) was preferentially plugged with amuch larger permeability reduction area than in the case of 50bbl/day, as shown in Figure 3. This is because a high injectionrate led to a low residence time, which allowed the injectedsucrose and microbe to travel a longer distance at the sametime duration. In all other low permeability zones (45, 120,and 267 md), the injection rate of 100 bbl/day also resulted inlarger areas of plugging than in the case of 50 bbl/day.

However, permeability reduction was limited to areas closeto the injection point. This is because the low permeabilityleads to low flow rates and longer residence time for bacteriaand dextran production close to the injection point. The sig-nificant growth of bacteria consumed all of the sucrose closeto the injection point, which inhibited permeability reductiondeeper into the reservoir. These results indicate that the in-jection rates have a significant effect on permeability profilemodification by L. mesenteroides, with higher injection ratesleading to deeper dextran emplacement and more extensiveplugging.

Effect of L. mesenteroides and Sucrose InjectionConcentrations (Scenarios 3 and 4)

Increasing L. mesenteroides and sucrose concentrations shouldresult in higher rates of dextran formation. To evaluate theeffect of L. mesenteroides and sucrose concentrations on theeffectiveness of selective plugging, concentrations of L. mesen-teroides were increased to 2 g/L, and concentrations of sucrosewere decreased to 10 g/L and 20 g/L, respectively. An injectionflow rate of 100 bbl/day was used to facilitate deep dextranemplacement.

Although the concentration of L. mesenteroides was dou-bled, lower concentrations of sucrose resulted in the reductionof dextran production, as shown in Figure 6. This is reflected

by a decrease in the plugging of the 529 mD permeabilityzone relative to the plugging that occurred under conditionsshown in Figure 3 (Scenario 2). Doubling the concentrationof L. mesenteroides did not compensate for the reduction insucrose concentration. This suggests that selective plugging ofhigh permeability zones can be obtained only at certain com-binations of L. mesenteroides and sucrose concentrations atinjection rates below and above threshold values that can beestimated by performing optimization calculations.

Effect of pH (Scenarios 5 and 6)

It has been reported that the pH range for formation wa-ters in oil reservoirs in North America is between 3.0 and9.9 (Jenneman 1989). In order to evaluate the permeabilityprofile modification of carbonate formations flooded with L.mesenteroides and sucrose under acid and alkaline pH levelconditions, simulations were carried out with injection andformation waters having pH values of 5.2 and 8.0. As shownin Figure 1, a pH of 5.2 is optimum while a pH of 8.0 isunfavorable for dextran production.

Figure 7 shows the effects of pH on the effectiveness ofselective plugging. In contrast with the case of pH 8.0 whereall zones remain practically unplugged (Figure 7B), pluggingoccurs around the injection wells when the formation waterhas a pH of 5.2 (Figure 7A). A faster production of dextranat pH 5.2 than at pH 8.0 shortens the length of residence timerequired for L. mesenteroides to produce sufficient amountsof dextran to plug zones at the vicinity of the injection wells(Figure 8).

Comparison of the simulation results with those of Sce-nario 1 (Figure 3A) suggests that the plugging efficiency anddeep dextran emplacement at pH 5.2 can be improved by in-creasing the injection rate and decreasing the concentrationof sucrose. It is interesting to note that lower rates of dextranproduction at pH 8.0 can potentially facilitate deeper dextranemplacement, as shown in Figure 7. Therefore, selective plug-ging of high-permeability zones is affected by three main vari-ables, the injection rates, concentrations of L. mesenteroidesand sucrose, and resulting pH.

Because calcite is susceptible to pH modifications, we an-alyzed the impact of dissolution and precipitation as a func-tion of pH. As expected, with the formation water of pH5.2, calcite dissolution occurs, as indicated by negative sat-uration index values (Figure 9A). The dissolution of calcitedoes not result in alkaline pH as one might expect (Figure10A). This is because the pH increase during the dissolutionof carbonate is compensated by the generation of CO2 andlactic acid during the growth of L. mesenteroides (Figure 11).Consequently, zones of lowest pH levels are concomitant withzones of highest dextran emplacement, whereas zones of high-est pH levels are concomitant with zones of lowest microbialactivity and no dextran emplacement. On the other hand, inthe case of formation water pH of 8.0, precipitation of cal-cite occurs, as reflected by positive saturation index values(Figure 9B).

Zones of highest dextran concentration (Figure 8B) areconcomitant with the zones of lowest amounts of calcite pre-cipitation (Figure 9B) and lowest pH levels (Figure 10B),

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Fig. 6. Permeability profile modification after 83.3 days of flooding in a carbonate reservoir. (A) Injection water contains 2 g/L of L.mesenteroides and 10 g/L of sucrose. (B) Injection water contains 2 g/L of L. mesenteroides and 20 g/L of sucrose. The initial pH inthe formation and the injection water is 7.0. Injection flow rate is 100 bbl/day (color figure available online).

Fig. 7. Effects of pH on permeability profile modification in a carbonate formation after 250 days of flooding with water containing1 g/L of L. mesenteroides and 5 g/L of sucrose. (A) Initial pH of injection and formation water is 5.2. B) Initial pH of injection andformation water is 8.0. Injection flow rate is 100 bbl/day (color figure available online).

Fig. 8. Volume percentage of dextran precipitated after 250 days of flooding a carbonate formation with water containing 1 g/L of L.mesenteroides and 5 g/L of sucrose. (A) Initial pH of injection and formation water is 5.2. (B) Initial pH of injection and formationwater is 8.0. Injection flow rate is 100 bbl/day. The units of dextran are the volume percentage occupying the pore space (color figureavailable online).

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Fig. 9. Saturation index (Log(Q/Keq)) after 250 days of flooding in a carbonate formation with water containing 1 g/L of L.mesenteroides and 5 g/L of sucrose. (A) Initial pH of injection and formation water is 5.2. Calcite dissolves in this case, as indicatedby the negative saturation index values. (B) Initial pH of injection and formation water is 8.0. Calcite precipitates in this case, asindicated by the positive saturation index values. Injection flow rate is 100 bbl/day (color figure available online).

Fig. 10. pH in a carbonate formation after 250 days of flooding, with water containing 1 g/L of L. mesenteroides and 5 g/L of sucrose.Injection flow rate is 100 bbl/day. (A) Initial pH of injection and formation water is 5.2. (B) Initial pH of injection and formationwater is 8.0 (color figure available online).

Fig. 11. (A) CO2 (aq) and (B) lactate distribution after 250 days of flooding a carbonate formation with water containing 1 g/L of L.mesenteroides and 5 g/L of sucrose. Initial pH of injection and formation water is 5.2. Injection flow rate is 100 bbl/day (color figureavailable online).

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Fig. 12. Permeability profile modification after 250 days of flooding a carbonate rich formation with water containing 1 g/L of L.mesenteroides and 5 g/L of sucrose. The injection water pH is (A) 5.2, and (B) 4.2. The initial pH of the formation water is 7.0.Injection flow rate is 100 bbl/day (color figure available online).

Fig. 13. pH profiles of a carbonate formation after 250 days of flooding with water containing 1 and 5 g/L of L. mesenteroides andsucrose respectively. The injection water pH is (A) 5.2, and (B) 4.2. The initial pH of the formation water is 7.0. Injection flow rate is100 bbl/day (color figure available online).

Fig. 14. Saturation index (Log(Q/Keq)) after 250 days of flooding with water containing 1 g/L of L. mesenteroides and 5 g/L ofsucrose. Initial pH in the carbonate formation is 7.0. (A) pH of injection water is 5.2. (B) pH of injection water is 8.0. Calciteprecipitates and dissolves as indicated by the positive and negative saturation index values, respectively. Injection flow rate is 100bbl/day (color figure available online).

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indicating that the growth of L. mesenteroides can reduce theextent of mineral precipitation. The production of CO2 andlactic acid, in the case of formation water pH of 8.0, is reflectedby a general reduction of pH throughout the whole formation.

Effect of Water Mixing (Scenario 7 and 8)

Because of the common pH differences in injection and for-mation waters, they can potentially affect the metabolic pro-cesses and the rates of dextran production. In this section theeffect of water mixing is evaluated in terms of the resultingpermeability modification and pH. In practice, the pH of theinjection water can be modified by adding acid or base com-pounds to enhance the activity of the enzyme (dextransucrase)that is responsible for dextran production. Figure 12 shows thepermeability modification when a carbonate formation con-taining formation water of pH 7.0 is flooded with injectionwaters of pH of 5.2 and 4.2. Permeability reduction of thezone with highest permeability (529 mD) was achieved withan injection water of pH 5.2 as well as with an injection waterof pH 4.2. In these two cases, the resulting pH in the initialhigh permeability zone is between 4.5 and 6.0, which is closerto the optimum pH value of 5.2 for dextran production, asshown in Figure 13.

However, calcite dissolution rates are higher with an in-jection water of pH 4.2 than in the case with an injectionwater of pH 5.2, as shown in Figure 14. This is reflectedby an increase of permeability in zones where L. mesen-teroides does not reach. In zones reached by L. mesenteroides,permeability decreases due the production of dextran (Fig-ure 12B). As a result, although the resulting pH is closerto the optimum pH value of 5.2 in the case with an injec-tion water pH of 4.2, higher levels of calcite dissolution at-tenuates the degree of plugging with dextran produced byL. mesenteroides.

Conclusions

In this study, we developed a process-based mechanistic modelto explore the impact of operational processes on selectiveplugging. Here we focus on single fluid phase (water) systemsas bioclogging-relevant reactions occur only in the water phaseor at the water-rock interface. The investigated variables in-clude pH conditions, injection rate, concentrations of injectedmicrobes and substrates, and mixing of injection and forma-tion waters. A vertical, 2D synthetic modeling domain rep-resenting a carbonate formation having zones of contrastinginitial permeability values was used for the simulations. Theformulation of reaction network, permeability modification,and kinetic model equations pertinent to plugging with L.mesenteroides microbe were based on laboratory experimentaldata available in literature.

Simulations of dextran emplacement and the correspond-ing flow paths shows that preferential plugging of high-permeability zones is not only a function of the preferentialflow of the injected water throughout high-permeability zonesbut also a function of the residence time of L. mesenteroides.

These numerical findings are consistent with laboratory ex-periment results (Kowalewski et al. 2006; Lappan and Fogler1994; Raiders et al. 1989). Although L. mesenteroides is trans-ported preferentially through high-permeability zones, if theflow velocity is above some threshold value, the residence timeof L. mesenteroides in the formation will be too short to pro-duce sufficient dextran to plug high-permeability zones. Con-versely, if the seepage flow velocity is below a threshold value,the residence time will be too long and only zones close tothe injection points will be plugged instead of the high per-meability zones. Therefore, microbial plugging should not beassumed to be intrinsically selective.

In addition, preferential plugging depended on the localgeochemical conditions such as pH. Our simulations sug-gested that the use of the optimum pH of 5.2 for the enzyme ac-tivity resulted in enhanced production of dextran and a largerextent of permeability reduction than under neutral and al-kaline pH conditions, due to the dependence of the enzymeactivity on pH. Therefore, in addition to increasing L. mesen-teroides and sucrose concentrations in the injection water, pHof the injection water can be used as an operational variable toencourage deep and fast plugging of high-permeability zones.Doubling the concentration of sucrose had more effect on per-meability modification than doubling the concentration of L.mesenteroides. Thus, the design of an injection method shouldrely on changing the concentration of sucrose rather than onthe concentration of L. mesenteroides.

One might expect that the dissolution of carbonate at pH5.2 in combination with an increment of pH due to calcitedissolution will inhibit the production of dextran and increasethe permeability rather than reducing it. In contrast, we findthat although the pH does increase due to the dissolution ofcalcite, the resulting pH levels do not inhibit the productionof sufficient dextran to plug the high-permeability zone incarbonate formations. Lactic acid and carbonic acid formedduring the growth of L. mesenteroides help to maintain the pHaround 5.2 and 7.0 where the production rate of dextran is stillhigh. It is important to mention that the reactivity of carbon-ate formations may not be the same as the reactivity of ourhypothetical carbonate formation which was assumed to becomposed of pure calcite. In natural systems, the mineralogyof individual oil reservoirs varies depending on its origin andcomposition (Macaulay et al. 1993). Therefore, the effect ofmineralogy can be different depending on specific conditions.

The predictions of the model in this work are limited tothe assumptions made in its development. For example, L.mesenteroides is represented as solute and as part of the reac-tion products. Although we allow a certain level of depositionto represent the sorption and biofilm formation, this is over-simplifies the microbe transport and other related processes.In reality, chemotactic movement can occur and bacteria canonly move into pores that are sufficiently large. At the porescale, factors such as surface charge density of carbonate min-erals and dextran, molecular weight variation of produceddextran, colloidal transport behavior of dextran and microbesmay come into play. The model we formulate here only encap-sulates what we currently know from macro-scale core flowexperiments. In addition, L. mesenteroides would have to com-pete for sucrose with various types of indigenous microbes and

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contend with various types of predators in natural subsurfaceenvironments.

Although there is limited evidence suggesting that proto-zoan predators can have a significant influence on biocloggingrate and extent (DeLeo and Baveye 1997), this is yet to beverified for L. mesenteroides microbes. Also, other microbessuch as methanogens and denitrifiers present may producegases (Amos and Mayer 2006), which could also affect per-meability. Therefore, care should be taken in the applicationof the presented results to field applications. Simulations thatconsider multiphase flow (e.g., oil and water) and sensitiv-ity analysis warrant future research, as they are expected toimprove understanding of key controls and treatment design.

Nevertheless, the developed model is expected to be usefulfor understanding controlling parameters that affect microbe-induced selective plugging of carbonate formations at the fieldscale. For example, in oil fields, an important consideration isto avoid large reductions in permeability at injection locations,which could shut off flow into the formation. The developedmodel can be used to identify conditions under which well-bore plugging occurs to avoid such situation. With the explicitsimulation of the bacteria growth and transport and the as-sociated biogeochemical reactions and the implementation ofenzyme activity, the developed model can also be used to guildfield operations that would maximize the effectiveness of se-lective plugging. Although L. mesenteroides and dextran areconsidered in this study, the approach developed is generallytransferable to other microbe-mediated applications.

Acknowledgments

This work was supported by the University of California atBerkeley, Energy Biosciences Institute to Pennsylvania StateUniversity. The Energy Biosciences Institute is funded by BP.

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