Geophysical monitoring and reactive transportsimulations of bioclogging processes inducedby Leuconostoc mesenteroides

Yuxin Wu1, Vikranth Kumar Surasani2, Li Li3, and Susan Sharpless Hubbard1

ABSTRACT

Although bioclogging has been used for various applications,its performance has been unpredictable. We carried out a bio-clogging experiment and developed a reactive transport modelto understand and quantify geophysical responses to the produc-tion of a biopolymer (dextran) in a silica sand porous medium.The developed model was used to predict effectiveness of bio-clogging and the associated geophysical signature under differ-ent treatment conditions. The porosity reduction calculated fromthe reactive transport modeling matched the concurrent increasein electrical resistivity and confirmed the dominant contributionof pore fluid conductivity to the bulk electrical conductivity.Correlations between measured electrical phase signals and

predicted mineral surface area reduction indicated the control-ling effect of mineral surface area on polarization. The joint useof the two methods quantitatively estimated the extent of de-crease in porosity as well as effective mineral surface area, bothof which are challenging to measure nondestructively in biologi-cal systems. The joint use of the geophysical methods and re-active transport modeling provided a better understanding of thedominant processes that govern dextran-based bioclogging andthe associated geophysical responses. This opens new opportu-nities for quantifying changes associated with bioclogging proc-esses and can potentially lead to new conceptual models thatrelate hydraulic property changes to the porosity and mineralsurface area, which will enhance prediction, monitoring, andcontrol of applications that use bioclogging.

INTRODUCTION

Bioclogging is the reduction of the fluid-conducting properties ofporous media through the production of exopolymer, biomass/bio-film growth, and/or the generation of metabolic byproducts such asbiogenic gas and biomineralization. Bioclogging studies have beencarried out numerically and experimentally in both laboratory(Taylor et al., 1990; Cunningham et al., 1991; Vandevivere andBaveye, 1992a, 1992c; Wu et al., 1997; Baveye et al., 1998;Kim and Fogler, 2000; Brovelli et al., 2009) and field scales (Liet al., 2010). Although bioclogging is typically considered to havenegative effects on industrial and medical applications (Videla andCharacklis, 1992; Khardori and Yassien, 1995; Bott, 1998; Brown,2010), engineered/preferential bioclogging has been explored as a

viable technique for bioremediation of contaminated soils (Zhanget al., 1995), improvement of soil strength and hydraulic propertiesin geotechnical engineering (Ivanov and Chu, 2008), microbial-enhanced oil recovery (MEOR) (Abdel-Waly, 1999), and, poten-tially, CO2 sequestration (Mitchell et al., 2009). Understandingand controlling bioclogging processes are hindered by limited pre-dictive and monitoring capabilities. In the case of MEOR, althoughthere have been hundreds of field tests (Brown, 2010), the lack ofadvanced modeling and monitoring tools has contributed to subop-timal performance.Bioclogging studies at various spatial scales have primarily fo-

cused on examining biofilm growth and the associated evolutionof hydraulic conductivity. Experiments and models at the columnscale have been used to establish constitutive relationships between

Manuscript received by the Editor 21 March 2013; revised manuscript received 1 July 2013; published online 27 November 2013.1Lawrence Berkeley National Laboratory, Earth Sciences Division, Berkeley, California, USA. E-mail: ywu3@lbl.gov; sshubbard@lbl.gov.2The Pennsylvania State University, John andWillie Leone Family Department of Energy and Mineral Engineering, University Park, Pennsylvania, USA, and

Birla Institute of Science and Technology, Department of Chemical Engineering, Pilani-Hyderabad Campus, Hyderabad, India. E-mail: surasani@psu.edu.3The Pennsylvania State University, John and Willie Leone Family Department of Energy and Mineral Engineering, University Park, Pennsylvania, USA.

E-mail: lili@eme.psu.edu.© 2013 Society of Exploration Geophysicists. All rights reserved.

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GEOPHYSICS, VOL. 79, NO. 1 (JANUARY-FEBRUARY 2014); P. E61–E73, 8 FIGS., 2 TABLES.10.1190/GEO2013-0121.1

porosity and permeability (Thullner et al., 2002). Pore-scale modelshave been developed to understand the mechanisms of bioclogging(Baveye and Valocchi, 1989; Taylor and Jaffe, 1990; Tan et al.,1994; Clement et al., 1996; Kildsgaard and Engesgaard, 2001;Thullner et al., 2004). However, detailed evolution of processesand properties during bioclogging processes, including time-depen-dent porosity and mineral surface area changes that can be critical incontrolling the bioclogging processes, are typically challenging tomeasure nondestructively.Non- and minimally invasive geophysical monitoring techniques

have been proven to be very useful for the characterization of proc-esses in heterogeneous subsurface (Rubin and Hubbard, 2005;Snieder et al., 2007), especially for capturing dynamic changesdue to biogeochemical interactions in subsurface. Among the geo-physical techniques, time-lapse electrical geophysical methods holdpotential for providing quantitative information about subsurfacebiogeochemical changes (Daily, 1984; Parra, 1988; Ntarlagianniset al., 2005a, 2005b; Atekwana and Werkema, 2006; Davis et al.,2006; Personna et al., 2008). Such biogeochemical processesinclude microbial colonization and growth, changes in pore-fluidgeochemistry, mineral surface modification as well as mineral dis-solution/precipitation, gas production/exsolution, and changes in re-dox conditions (Abdel Aal et al., 2004; Ntarlagiannis et al., 2005a;Williams et al., 2005; Atekwana and Werkema, 2006; Personnaet al., 2008; Atekwana and Slater, 2009). All of these changescan result in electrical signals of varying magnitude. For instance,metal sulfide precipitation (Ntarlagiannis et al., 2005a; Slater et al.,2005; Personna et al., 2008), often observed during subsurfaceremediation, produces an electric polarization signal, the magnitudeof which is controlled by the surface area of the precipitated min-erals (Hubbard and Rubin, 2000; Thullner et al., 2004). Electricalpolarization has also been observed to be associated with calciteprecipitation (Wu et al., 2010, 2011). Changes in electrical resistiv-ity and polarization signals have also been documented to be asso-ciated with microbial cell and biomass growth, fluid chemistryalteration, and mineral surface modification (Abdel Aal et al.,2004, 2006; Ntarlagiannis et al., 2005b). Abdel Aal et al. (2010)studied the effects of bioclogging on the complex conductivity sig-natures of porous media and associated changes in hydrologicalproperties. They attributed the observed changes in the polarizationsignals to the different stages of surface attachment and biofilmgrowth. Another study also demonstrated the sensitivity of complexconductivity signals to artificial biofilms (Ntarlagiannis and Fergu-son, 2009). A review of current biogeophysical research is providedby Atekwana and Slater (2009). In spite of significant advances thathave been made over the years, the application of geophysical meth-ods to study microbial processes is still in its infancy, with mostbiogeophysical research focusing on establishing petrophysical cor-relations between geophysical attributes and microbial processes.Reactive transport modeling provides an integration tool to quan-

titatively estimate and predict biogeochemical processes (Atekwanaand Slater, 2009; Li et al., 2011; Vilcáez et al., 2013). Such modelscan be used to predict changes in aqueous chemistry, solid phasecomposition, dynamic porosity and permeability, and other subsur-face properties. With proper constraints from experimental or fielddata, reactive transport modeling can provide a powerful tool formechanistic understanding of processes and quantitative predictionof property evolution in subsurface (Schafer et al., 1998; Islam andSinghal, 2002; Mayer et al., 2002; Prommer et al., 2003; Li et al.,

2009, 2010, 2011; Centler et al., 2010; Wissmeier and Barry, 2010).However, the use of reactive transport modeling is often limited bythe available data and sufficient constraints to reduce the degree offreedom (Baveye and Valocchi, 1989; Taylor and Jaffe, 1990; Tanet al., 1994; Clement et al., 1996; Kildsgaard and Engesgaard, 2001;Thullner et al., 2002, 2004; Chen et al., 2009; Singha et al., 2011).The joint use of geophysical data and reactive transport modelinghas the potential to improve both methods in process understandingand quantification. Given the uncertain and nonunique nature ofgeophysical data (i.e., signals can respond to a variety of changesthat occur during a subsurface perturbation), modeling can help todistinguish the geophysical signature associated with particularprocesses or end products. In turn, geophysical monitoring can pro-vide constraints for modeling on processes that are difficult to mea-sure using conventional approaches, such as the evolution of solidphase properties and the accumulation of biomass. A few recentstudies have demonstrated the value of combining geophysicalmonitoring and reactive transport modeling for improved under-standing of various processes (Scheibe et al., 2006; Singha et al.,2011; Wu et al., 2011; Sassen et al., 2012). However, to the best ofour knowledge, there have been no studies that focus on combiningsuch methods to understand, quantify, and monitor biocloggingprocesses as is needed to improve the various bioclogging appli-cations that are of interest to the energy and environmentalcommunity.The objectives of this study are to identify the electrical signa-

tures of the bioclogging process, develop a reactive transport modelthat can accurately simulate biopolymer-induced clogging ofporous media, and explore the joint use of reactive transport mod-eling and geophysical monitoring in gaining insights about bioclog-ging processes that would have been challenging to identify using asingle approach alone. We studied the fermentation of sucrose me-dia and production of a biopolymer called dextran using the bacteriaLeuconostoc mesenteroides. We chose to explore clogging throughdextran production because its production mechanism has been wellunderstood (Naessens et al., 2005) and its clogging capabilities havebeen demonstrated (Lappan and Fogler, 1994, 1996). Our approachis to perform geophysical and aqueous geochemical monitoring to-gether with reactive transport modeling studies of a column experi-ment. The developed model is then used to numerically explore theinjection conditions under which bioclogging are effective and toquantify the evolution of petrophysical and geophysical properties.This is a first attempt to jointly use geophysical observations andreactive transport modeling results to study bioclogging. This willlay the petrophysical and modeling foundation for large field-scalebioclogging simulation and predictions.

MATERIALS AND METHODS

Experimental section

Microbial selection

L. mesenteroides was chosen as the model bacteria for this study.It is a facultative microbe widespread in natural environments(Reiter and Oram, 1962). Most strains of L. mesenteroides appearas cocci in liquid culture, and their ability to produce viscous poly-saccharides (presumably dextran) was observed in the early days ofmodern microbiology (Pasteur, 1861). For potential application inMEOR and other treatments where the need to minimize clogging

E62 Wu et al.

near the wellbore is desired, L. mesenteroides has the advantage ofselectively producing dextran based on the supplied growth media.That is, L. mesenteroides can produce dextran with sucrose, but notwith glucose (Lappan and Fogler, 1994; Padmanabhan and Kim,2002). This functionality potentially allows one to optimize injec-tion strategy for targeted clogging at desired locations.Dextran production by L. mesenteroides is an enzymatic reaction

that starts with the expression of the enzyme dextransucrase.Detailed descriptions of L. mesenteroides and the formation of dex-tran can be found in literature (Naessens et al., 2005). The reactionkinetics will also be discussed in the following reactive transportmodeling subsection.The microbe stock solution was acquired from American Type

Culture Collection (ATCC) (8293) and was incubated in a growthmedia containing sucrose (15 g∕L), sodium acetate (1 g∕L), ammo-nium citrate (0.6 g∕L), KH2PO4 (100 mM), K2HPO4 (100 mM),trace minerals (0.0592 mMMn2þ; 0.984 mMMg2þ), Thauer’svitamins (a few μM for most vitamins contained), and yeast extract(0.5 g∕L). The microbes were incubated for ∼20 h at 30° C in thegrowth media (pH ¼ 6.8).

Column setup

A schematic of the experimental column setup is shown inFigure 1. The middle section of the column had a dimension of

2.54 cm inner diameter by 8.4 cm length, and it was packed withOttawa sand (∼600‐μm diameter). The parameters of the packedcolumn are shown in Table 1. The porosity was calculated throughcomparing the weight difference between a dry and a water-saturated column. Two ports were installed on the middle sectionof the column for microbe and sucrose media injection as well asfluid sampling. The two end pieces of the column were fitted withports for Ag∕AgCl electrode housing for electrical measurements.A 0.2‐μm filter was installed on each end piece for confinement ofthe sand in the middle as well as to minimize microbial migrationout of the sand pack in the middle compartment; thus, microbialactivities and dextran production occur only in the sand pack. Thisensured that the total mass of produced dextran was captured withinthe measurement channel allowing for dextran quantificationthrough mass balance from up- to downgradient of the sand pack.After assembly, the column was packed with the sand used in theexperiment and saturated with a NaCl solution with matching fluidconductivity of the growth media (1.3 S∕m) to acquire a baselineelectrical data set for system testing and reference.

Experimental procedure

The materials and parts used for the column experiment weresterilized with an autoclave or an ethanol rinse (whichever wasapplicable) before assemblage. The Ottawa sand used in the col-umns was pretreated with a 10-mM hydrochloric acid solutionfor 24 h to remove oxides. After oxide removal, the sand waswashed with deionized water for a few times and then autoclavedbefore being wet packed into the column with the sucrose growthmedia solution as the wetting phase. After packing, about three porevolumes of the growth media were pumped into the column at0.1 ml∕min before effluent fluid conductivity reached the influentvalue (1.3 S∕m) indicating a steady state condition. One pore vol-ume of the microbial suspension (∼27 ml with a cell density of∼2E8 cells∕ml) was then injected into the column, and the columnwas left for 24 h for cell growth and colonization. Following inoc-ulation, baseline geophysical and geochemical parameters weresampled before starting the experiment. We used an “inject-then-pause” method to increase fluid residence time for enhanced dex-tran production. For each inject-then-pause cycle, a 30-ml freshsucrose media was injected into the column over a 60-minuteperiod, and then the ports were shut off and the column was leftfor 24 h for the dextran production to occur. This process was re-peated 10 times. Electrical geophysical measurements were col-lected after each fresh sucrose media injection to ensure that the

Figure 1. Schematic setup of the column for the experiment. Thesediment packed into the column was Ottawa sand with ∼600‐μmaverage diameter.

Table 1. Column and sediment parameters.

Length 8.43 cm

Diameter 2.54 cm

Minerals Quartz (Ottawa sand)

Porosity 0.6383

Particle size 600 μmSpore4 3617 m2∕m3

4The term Spore means the surface area per unit pore volume

Bioclogging monitoring and simulation E63

pore water chemistry was the same for each measurement andthe changes in response could be exclusively related to dextranproduction.

Geochemical and microbial analysis

Before each fresh media injection, 1 ml of pore fluid was ex-tracted with a syringe from the sampling port in the middle ofthe column (Figure 1) and preserved with 10 μl of 70% formalde-hyde for microbial cell counts and total organic carbon (TOC)analysis in the pore fluid. For microbial analysis, the cells werestained with acridine orange, fixed on glass slides, and counted us-ing a Zeiss Axioskop fluorescence microscope. Samples for TOCanalysis were filtered with 0.2‐μm filters to remove small dextranfibers and microbes and analyzed with a Shimazu TOC analyzer.The mass balance of the TOC was used to estimate dextran produc-tion in the column over time. We note that TOC consumption in thecolumn was a sum of the usage for dextran production, cell growth,and enzyme production. The utility of TOC for dextran quantifica-tion is based on the assumption that organic carbon used for cellgrowth is minor, which was verified with cell counts as discussedin a later section. Fluid conductivity and pH were measuredevery other day with standard probes and meters from ThermoScientific.

Destructive sampling

After the experiment, the column was drained and the sand in thecolumn was carefully collected to measure insoluble dextrantrapped in the sand pack. The collected sand was washed three timeswith 50-ml deionized water (>18 MΩ) to remove the dextran in thepore spaces or those loosely affiliated with the sand grains. Thewash fluid was then forced through preweighted 0.2‐μm filtersto collect insoluble dextran. Deionized water was forced throughthe filters after dextran collection to rinse off residual growth media.The filters were then dried at 60° C overnight and weighed to cal-culate the amount of dextran they collected. The washed sand wasdried and weighed as well. The dry weight difference of the sandbefore and after the experiment was the amount of dextran still af-filiated with the sand surface after washes, i.e., those strongly as-sociated with the sand surface. The dried sand was subsequentlyheated at 550° C for 1 h, and the weight loss during the thermog-ravimetric analysis was also used to confirm the amount of dextranstill attached on the sand grains after washes. The sum of the dex-tran in the wash fluid collected on the filters and those on the sandgrains is the total insoluble dextran produced in the column at theend point of the experiment and was compared with TOC results.Note that efforts were not taken to separate cells from biopolymerbecause of their close affiliation, and the contribution of the micro-bial cells to the total biomass was considered negligible.

Geophysical methods

Measurements of complex resistivity ρ� (or conductivity σ�) wereused in this study to monitor geophysical signatures of bioclogging.A detailed discussion of the method can be found in Kemna (2000).Briefly, complex resistivity signals measure the charge conductingproperty of a porous medium and are normally frequency dependentfor geologic samples. For fully saturated porous media, the real (orin-phase) component (σ 0) of the complex term measures charge

conduction electrolytically (σf) through interconnected fluid filledpores and along the mineral surfaces (σ 0

S). These two pathwaysare conventionally considered parallel at low frequencies (Reviland Florsch, 2010). For porous media with no clay content (i.e.,lack of narrow pore throats), the imaginary (or quadrature) compo-nent (σ 0 0) of the complex conductivity at low frequencies measurescharge storage through the electrical double layer (EDL) polariza-tion at mineral/fluid interface. When complex conductivity is mea-sured in a frequency domain, the magnitude jσj and the phase φvalues are normally recorded and converted to the real and imagi-nary components of the complex term. The correlations betweenthese different terms can be expressed as

σ� ¼ 1

ρ�¼ jσj expðiφÞ ¼ σ 0 þ iσ 0 0; (1)

σ 0 ¼ σf þ σ 0S ¼

1

Fσw þ σ 0

S; (2)

jσj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσ 02 þ σ 0 02

p; (3)

φ ¼ arctan

�σ 0 0

σ 0

�≈σ 0 0

σ 0 ðwhen φ is smallÞ; (4)

where F is the formation factor of the porous media (F ¼ ∼10 at thestart of this experiment) and σw is the pore fluid conductivity.Complex conductivity measurements were collected with a

National Instruments dynamic signal analyzer (DSA, NI 4461) us-ing Ag∕AgCl electrodes installed along the length of the column(Figure 1). The measurements were recorded relative to a precisionreference resistor over 40 frequencies spaced at equal logarithmicintervals from 0.1 to 1000 Hz. The accuracy of the conductivitymagnitude measurement is better than 0.5%, and the accuracy ofthe phase measurement is better than 0.2 mrad and 0.4 mrad at< 400 Hz and between 400 and 1000 Hz, respectively.We expect to observe changes in electrical resistivity and polari-

zation from dextran production based on the assumption that dex-tran is a nonconductive and nonelectrically polarizable molecule.This assumption is reasonable because dextran is a complex glucanand the molecule is nonpolar (or weakly polar at the best). Longchain and branched dextran is largely insoluble and can exist inthe pores and on grain surfaces, both of which could change theresistivity and phase signals through pore blocking or surfacepassivation.

Reactive transport and petrophysical modeling

Reaction network and kinetics

We formulated the reaction network associated with dextran bio-clogging based on published findings (Dols et al., 1997, 1998; San-tos et al., 2000). The overall reaction network can be classified intotwo stages: (1) cell growth and enzyme production and (2) enzymecatalyzed dextran production. The stoichiometric representation ofthe overall cell growth can be written as

E64 Wu et al.

sucroseþ 0:2NHþ4 þ 0:341HCO−

3

→ 0:2C5H7O2Nþ 0:14076 fructoseþ 0:0705 lactate

þ 0:0705 acetateþ 0:01408 mannitol þ 0:0705 ethanol

þ 0:4184CO2 þ 0:7259H2Oþ 0:2 dextransucrase;

(5)

where C5H7O2N is a representative chemical formula of the bacte-rial cell (L. mesenteroides) (Rittmann and McCarty, 2001). Cellgrowth reaction in equation 5 is derived using the bacterial energeticmethod given by Rittmann and McCarty (2001). According to thismethod, some fraction of the energy produced by the reaction isused for cell maintenance and the remaining fraction is used forcell growth. Note that detachment and decay processes were notconsidered in our model due to the short duration of the experimentas well as the insufficient data availability and models. In derivingthe reaction network, we assumed a fraction of 0.4 for cell growthand 0.6 for cell maintenance (VanBriesen, 2002). The produced en-zyme dextransucrase catalyzes the conversion of sucrose into dex-tran and fructose as

5:3 sucroseþ dextransucrase ⇔ sucrose:dextransucrase

⇔ 2.9 dextranþ 4.5 fructoseþ dextransucrase: (6)

The reaction can potentially lead to dextran accumulation inporous media. The rates of the two microbe-mediated reactions fol-low the Monod rate law (Monod, 1949; Rittmann and McCarty,2001), which can be represented as

Rr ¼ kmax;rXr

Csucrose

Csucrose þ KM;sucrose; (7)

where Csucrose is the sucrose concentration in mol∕L. The cellgrowth rate and the dextran production rates, expressed as Rr, de-pend on the rate constant kmax;r (mol∕L∕cells∕s) and also on theamount of biomass Xr (cells). For example, in equation 6, the en-zyme-mediated dextran production rate R2 depends on kmax;2 andthe amount of enzyme X2, which depends mainly on the amount ofbiomass given by Michaelis-Menten reaction kinetics. The rate con-stants kmax for cell growth reaction in equation 5 and enzyme cata-lyzed reaction in equation 6 are 2.0656E-17 and 3.598E-12(mol∕L∕cells∕s), respectively. These values were obtained by fit-ting the experimental data of dextran production over time. Thehalf-saturations KM;sucrose in equation 7 for reactions in equations 5and 6 are 7.3E-3 and 7.3E-4 (mol∕l), respectively, which are amongthe typical values in literature (Jung et al., 1999; Liu et al., 2001).The molar volume of the biomass was assumed to be 336 cm3∕mol,a number in the middle range of those reported in the literature(Loferer-Krossbacher et al., 1998). In addition to these kinetic-controlled reactions, a series of aqueous speciation reactions occurin the aqueous phase and are typically considered instantaneous re-actions. These reactions are listed in Table 2 and described inthe next section (Lichtner, 1985; Morel and Hering, 1993; Liet al., 2006) with their equilibrium constants Keq obtained fromthermodynamic database that has been extensively used (Woleryet al., 1990).

Reactive transport modeling

Modeling of the representative processes in dextran productionwas carried out using CrunchFlow (Lichtner, 1985, 1996; Steefelet al., 2005; Li et al., 2008; Steefel, 2008; Salehikhoo et al.,2013). Reactive species were grouped into primary and secondaryspecies (Table 2) (Reed, 1982; Lichtner, 1985; Kirkner and Reeves,1988). The model solves the mass conservation equations for theprimary species, and concentrations of the secondary species wereobtained from thermodynamic equilibrium relations using primaryspecies. Mass conservation of the primary species in the aqueousphase can be represented as

∂ðϕCiÞ∂t

¼∇ · ðϕDi∇CiÞ−∇ðϕuCiÞ−XNr

r¼1

νirRr −XNm

m¼1

νimRm:

(8)

Equation 8 is the conservation equation for an aqueous primaryspecies i in a control volume with fractional pore volume (porosity)φ and concentration Ci (mol∕L). Di (m2∕s) is the dispersion/diffusion coefficient of the species, and u (m2∕s) is the superficialvelocity. The symbols νir and νim are stoichiometric coefficients ofspecies i in microbe-mediated reactions with rate Rm (mol∕L∕s) andmineral precipitation/dissolution reaction with rate Rm (mol∕L∕s).The mineral dissolution/precipitation rates Rm are represented withtransition state theory (Lasaga, 1998). Subsequent variation of the

Table 2. Primary species and their initial conditions, andsecondary species, aqueous speciation reactions, gases andminerals, and their respective thermodynamic parameters.

Primary species Initial concentration (mmol∕kg)

Sucrose 43.0

NHþ4 8.7

HCO−3 3.1623

Fructose 0.0

Lactate 0.0

Acetate 12.2

Mannitol 0.0

Ethanol 0.0

CO2 (aq) 0.0

SiO2 (aq) 0.0

Secondary species Instantaneous aqueous reaction logKeq

CO2−3 CO2−

3 þ Hþ ↔ HCO−3 10.3288

HCO−3 CO2 ðaqÞ þ H2O ↔ Hþ þ HCO−

3 −6.5804Acetic acid (aq) CH3COO

−ðacetateÞ þ Hþ ↔CH3COOHðacetic acidÞ

4.7572

NH3 (aq) Hþ þ NH3 ðaqÞ ↔ NHþ4 −9.2410

OH− Hþ þ OH− ↔ H2O 14.0

Gases

CO2ðgÞ CO2 ðaqÞ þ H2O ↔ Hþ þ HCO−3 −7.8136

Minerals species Reaction logKeq

Quartz Quartz ↔ SiO2 ðaqÞ −3.1240

Bioclogging monitoring and simulation E65

solid phase in terms of volumetric porosity can be estimated usingthe differential equation

dϕ

dt¼

�−XNr

r¼1

νirRr

~Mi

ζiþXNm

m¼1

νimRm

~Mi

ζi

�; (9)

where ~M is the molar weight (kg∕mol) of the solid phases and ζ isthe mass density (kg∕m3) of the solid phases.These equations were discretized in a 1-D grid with 100 blocks

and solved computationally. The parameters of the column areshown in Table 1. According to the experimental procedure, thepore space was replaced with fresh sucrose media every 24 h.The injection of the fresh media took place in 1 h, and the columnwas allowed for dextran production for the next 23 h. Geophysicaldata and geochemical samples were taken at the end of the 23-hperiod. In the simulation, flow and reactions were considered forthe first 1-h injection period. Reactions continued under no-flowconditions for the next 23 h. This procedure was repeated for 10cycles to be consistent with the experimental procedure. The endtime point solid phase composition (of minerals, cells, and dextran)and aqueous concentrations of each cycle are the initial conditionsof the subsequent one. Reactive transport modeling was used tomatch the dextran data and the electrical geophysical data by adjust-ing several key parameters, which will be elaborated in the nextsubsection. The obtained parameters were then used to predictthe evolution of petrophysical and geophysical properties under in-jection conditions in flow through bioclogging column experimentsdocumented in the literature (Lappan and Fogler, 1994, 1996).

Petrophysical model for resistivity and phase prediction

The solutions to equations 8 and 9 give spatial and temporal evo-lution of the aqueous geochemistry and mineral and biomass com-positions during the bioclogging process. The ionic strength (I) ofaqueous solution can then be estimated using

I ¼ 1

2

XNaq

i¼1

z2i Ci; (10)

where zi is the charge of species i and Naq is the number of aqueousspecies. Several empirical correlations exist to estimate the electri-cal conductivity of the aqueous fluid (σw) using the ionic strength.Lind’s relation (Lind, 1970) is one example, which is given as

σw ¼ 1

ρw¼

�I − 0.00015

0:4 × 10−5

�× 10−4 ; (11)

where ρw is aqueous resistivity (ohm-m). The aqueous electricalresistivity was related to the properties of the porous media usingArchie’s law (Archie, 1942). For the single-phase saturated porousmedia used in this work, the resistivity of the bulk media (ρ) is afunction of formation factor (F ¼ ϕ−b) and fluid resistivity (ρw).The relationship is typically given as

ρ ¼ φ−bρw ¼ Fρw; (12)

where the cementation exponent bwas used as a fitting parameter tomatch the resistivity data. According to Lesmes and Friedman(2005), values of b range from 1.2 to 4.4, depending on conditions

such as the states of consolidation and geometrical arrangement ofgrains. In this work, the value of 1.5 gives the best fit to the elec-trical resistivity data, which fall in the range for unconsolidatedmaterials. Equation 12 calculates effective resistivity of the porousmedium filled with ionic fluid and is used to predict the resistivity ofthe column during the bioclogging process.It has been observed in the literature (Knight and Nur, 1987;

Slater and Glaser, 2003; Slater et al., 2006; Weller et al., 2010) thatthe power law relationship exists between the imaginary conduc-tivity (σ 0 0) and the surface area per unit pore volume (Spore). In thiswork, we applied similar relations to predict imaginary conductivity(σ 0 0) as

σ 0 0 ¼ d S0:8pore; (13)

where d is the constant of proportionality, the value of which is de-termined to be 7.0E-5 to best fit the phase data. Note that althoughequation 13 was developed for porous media without a biologicalcomponent, it yields reasonable results as shown in later sections,indicating that such correlations can be applied similarly in biologi-cal systems. Equation 13 was used to predict the imaginary conduc-tivity from Spore, which varies with porosity through the followingfunction:

Spore ¼ Spore;0

�ϕ − ϕc

ϕ0 − ϕc

�23

: (14)

In this equation, ϕ0 and ϕc are the initial and critical porosity andSpore;0 is the initial surface area per unit pore volume (Table 1). Thevalue of Spore;0 was determined using column packing conditions,i.e., packing dimensions, porosity, and grain size of packingmaterial. The critical porosity ϕc is the porosity at which the porousmedia become fully clogged. It was determined to be 0.15 in ourcase by fitting the phase data. The phase of the complex conduc-tivity can be obtained using equation 4. Note that the exponents inequations 13 and 14 are based on other researches because evalu-ations based on biopolymer studies are not available.The procedure of the coupled reactive transport modeling and

predictive geophysical modeling is presented in the flowchartin Figure 2. Reactive transport model was formulated for bioclog-ging column experiment by passing initial conditions, i.e., poros-ity, permeability of the bioclogging column, and the inoculatedmicrobe mass. The numerical simulations were carried out forexperimental operating conditions with sucrose concentrationand injection conditions. Aqueous species concentrations weresolved using equation 8, and the subsequent biomass species (dex-tran þ L. mesenteroides) immobilization was calculated usingequation 9. The modeling output at the corresponding times ofexperimental monitoring and sampling includes dextran mass,ionic strength, and porosity and permeability. These values wereused in the petrophysical models (equations 10–14) to predict geo-physical variables. The model prediction dextran mass, resistivity,and phase were compared with the bioclogging experimentalmonitoring data. Several parameters, including cell growth anddextran production rates in equation 7, b in equation 12, d in equa-tion 13, and critical porosity in equation 14, are adjusted to matchthe data.

E66 Wu et al.

Model prediction of bioclogging under variable injectionconditions

With the model parameters obtained by matching the experimen-tal data as discussed above, the reactive transport model was used toexplore the effects of flow rates and sucrose injection concentrationson the efficiency of bioclogging and on the associated geophysicalsignals. Numerical experiments were carried out according to theflow sheet presented in Figure 2. Sensitivity of the biocloggingunder the conditions of continuous sucrose media injection intothe column is tested for 50 days. Here, we simulated four bioclog-ging scenarios by using two different sucrose concentrations 1.5and 15 g∕l in the injection media with two differ-ent flow rates of 0.1 and 1.0 ml∕min. The flowrates and sucrose concentrations were chosen tobe the same as those used for the Damkohler ex-periments by Lappan and Fogler (1994, 1996).The column in these numerical simulations hassimilar dimensions and morphology as that ofthe bioclogging experiment in this work. Theparameters obtained by matching the experimen-tal work in this study were used in the reactivetransport modeling and petrophysical modelingfor the flow through column experiments.

RESULTS AND DISCUSSION

Microbial and geochemical results

Total microbial cell counts (Figure 3) revealeda twofold increase in cell density from approxi-mately 2.0Eþ 8 to 4.6Eþ 8 cells∕ml in the porefluid during the first three days of the experi-ment. After day three, the cell counts decreasedto below 3.0Eþ 8 cell∕ml. Overall, the increasein cell counts was not considered significant.Therefore, the consumption of organic carbonby cell growth was assumed to be minor com-pared to those used for dextran production. Thissuggests that the calculation of dextran produc-tion based on the mass balance of TOC was rea-sonable. Note that the cell counts were measured based on extractpore fluids and therefore did not take into account the microbialcells attached to the sand grains. However, the total contributionto TOC consumption from cell growth was still negligible evenif the amount of cells attached to the sand grains is an order of mag-nitude higher than those in the pore fluids based on an estimatedweight of a single microbial cell at 10−12 g. Figure 3 also showsthe morphology of the dextran produced at nine days after the ini-tiation of the experiment. The produced dextran is fiberlike withlengths varying from millimeters to centimeters. Many of the micro-bial cells are affiliated with the dextran consistent with researchshowing close association between exopolymer material and cellsurfaces (Vandevivere and Baveye, 1992b)The TOC content of the fluids collected from the column was

measured to quantify dextran production over time. By comparingTOC concentrations in the injected fresh media and those collectedat the end of each step, TOC consumption for each injection wascalculated to range from 80 to 140 mg per injection (∼3–5.2 mg∕ml

of injectate). Assuming most of the TOC was used to produce

dextran, which has an organic carbon at ∼45% based on its typicalmolecular structure ðHðC6H10O5ÞxOHÞ, daily dextran productionranged from 180 to 310 mg per injection (∼6.7–11.5 mg∕ml of in-jectate), and the total accumulated dextran during the experimentwas approximately 2.1 g. The recovered dextran from postexperi-mental destructive analysis was approximately 1.5 g total, withabout 1.2 g from the wash fluids and 0.3 g from the dried sandgrains. Although difficult to confirm, the discrepancy of the totaldextran between destructive analysis and fluid TOC analysismay be related to the incomplete recovery of the dextran duringdestructive analysis or from the loss of water during the dryingprocess because dextran is highly hydrated. In addition, dextran

Figure 2. Flowchart representation of coupled reactive transport modeling and predic-tive geophysical modeling.

Figure 3. Microbial cell counts from pore fluid collected in themiddle of the column during the experiments at different times.The small orange dots (or short chains) in the inserted imagesare L. mesenteroides microbes, and the fiberlike substance revealedat nine days after the initiation of the experiment is dextran. Thescale bars on the images represent 100 μm.

Bioclogging monitoring and simulation E67

production calculated based on the mass balance of TOC tends tooverestimate because the amount of TOC consumed for cell growth,enzyme production, and the release of CO2 was not accounted for,although these contributions were relatively small.The fluid conductivity of the initial fresh growth media was

1.3 S∕m and was increased to 1.5 S∕m after 24 h of fermentation.The pH of the fresh sucrose media was ∼6.8� 0.2, and it was re-duced to 5.6� 0.2 at the end of fermentation. The variations of fluidconductivity and pH at the end of each injection were within 5% and�0.2 pH units, respectively. The conductivity increase and pHdecrease can be attributed to organic acid production as well asCO2 production and dissolution during sucrose fermentation(equation 5).

Geophysical data

Figure 4 shows spectral electrical data collected during the ex-periment. Data from day zero are the baseline data measured aftermicrobial inoculation and are identical to the baseline acquired be-fore microbial inoculation, indicating minimal effects from micro-

bial cells, which could be related to the high fluid conductivity ofthe pore fluid. A continuous increase of resistivity from 7.7 to8.6 ohm-m was observed during the experiment. Because each re-sistivity data set was collected after fresh sucrose injection, there-fore the pore fluid chemistry is identical to the baseline, the changeof the resistivity can be linked exclusively to dextran production.Note that the dextran formed in the column was small in total vol-ume; thus, the amount of residual fluid trapped within its structureshould be minor and should not have a significant effect on the geo-physical signals. In addition, the change in the pore fluid conduc-tivity between freshly injected growth media and those in thecolumn after 24-h incubation was relatively small, further support-ing minor effects of any trapped fluid within the dextran on the geo-physical signals. The phase and imaginary conductivity showedsmall but consistent changes over time (Figure 4). The baselinephase (0.7 mrad at peak frequency) and imaginary conductivity(8.9E-5 S/m at peak frequency) signals at day 0 were presumablyassociated with the electrochemical polarization at the EDL of thesilica sand used in the experiment. We note that a clear critical fre-quency with maximum phase value was observed for each spec-trum, but at higher frequencies (∼300 Hz) when compared withother studies where the peak frequency was observed at much lowervalues (< 0.1 Hz) (Lesmes and Frye, 2001; Weller et al., 2010;Revil, 2012). This critical frequency was consistently observedthroughout the experiment and was also observed in a preliminarytest run. The preliminary experiment was conducted for geophysicaldata assessments without microbial and geochemical analysis andthus is not presented here. This high critical frequency could berelated to the high fluid conductivity as well as the complex com-ponents of the sucrose growth media, which can potentially modifythe EDL property and its polarization characteristics through sur-face complexation between functional groups and mineral surfacesites. Also shown in Figure 4 is the system test data with the NaClsolution having the same fluid conductivity with the growth media.This data set shows that when saturated with the NaCl solution, apolarization signal over the same frequency range was not observed,indicating the likelihood of the contribution of the sucrose growthmedia to the observed polarization signals. However, further inves-tigation of this observation is warranted. Figure 4 shows that smallbut consistent decreases of phase and imaginary conductivity wereobserved, which suggests that there is a systematic electrical re-sponse to the production of dextran because the pore fluid chemistrywas the same for all the measurements. It is worth noting that im-aging the small amount of electrical signal changes observed in thisexperiment will be difficult in the field. However, the amount ofdextran produced in this experiment and the baseline polarizationsignal are very small. In a field setting where the baseline polari-zation signatures are normally much higher, the changes in electri-cal signals could be much enhanced, thus becoming a reasonabletarget to monitor. It is also noteworthy that previous studies onthe effects of biofilms on electrical signals generally observed in-creases of the polarization signals (Ntarlagiannis and Ferguson,2009; Abdel Aal et al., 2010), contrary to our observations in thisexperiment. Although not confirmed, this may be related to thedifferences in electrical properties between the biopolymer pro-duced in this experiment and the biofilms generated in those studies.Correlations between resistivity, phase, and the accumulated dex-

tran in the column were observed during the experiment, as shownin Figure 5. The amount of produced dextran is positively correlated

Figure 4. Spectral electrical responses during the experiment: (a) re-sistivity, (b) phase magnitude, and (c) imaginary conductivity. Notethat baseline data with the NaCl solution (fluid conductivity at1.3 S∕m) is also presented.

E68 Wu et al.

with resistivity increase and negatively correlated with phase valuesexcept the last two data points where a slight increase of phase isobserved, which could be related to dissociation of the biofilm fromthe mineral surface. As mentioned earlier, dextran was assumed tobe a nonconductive and nonpolarizable substance based on its pol-ymeric and nonpolar nature. The distribution and geometric ar-rangement of dextran within the pore space of the sand matrixare important for understanding the electrical signals. However, thiswas difficult to evaluate because of the elastic (and potentiallymobile) nature of the dextran in the sand matrix; thus, its originalstructural arrangement could not be preserved during destructivesampling. Nevertheless, based on the postexperimental analysisdextran was found on sand grains and in fluids, indicating thatdextran existed in the pore space as well as affiliated with the sandsurface. As such, it is reasonable to assume that dextran acted as apore-filling and surface-passivating reagent, although a quantitativeestimation of the relative contribution of each is difficult based onavailable data. The observed increase of resistivity and decrease ofpolarization signals are thus interpreted to be associated with thedecrease of porosity and sand grain surface masking effects thatreduce the available mineral surface area for charge polarizationon the sand surface.

Reactive transport and petrophysical modeling

Figure 6a compares the reactive transport modeling output ofdextran over time with the measurement data. The fit was obtainedby adjusting the cell growth rate and the dextran production rate inequations 5 and 6. The predicted porosity evolu-tion of the column is plotted in Figure 6b. Theporosity of the column decreased from its initialporosity of 0.638 to 0.591. The approximate 5%change in total pore volume is attributed tothe dextran production during the experiment.Note that the porosity of the column at theend of the experiment could not be measured be-cause the samples were destroyed to estimate themass of produced dextran. In addition, it is verydifficult to preserve the original volume of thedextran in the hydrated form during the porositymeasurement steps that involve drying. Mea-sured electrical resistivity and phase changesduring the experiments were compared with out-put from reactive transport modeling in Figure 7.Aqueous species concentrations from reactivetransport modeling were used to calculate theionic strength of the pore fluid in the column us-ing equation 10. The effective resistivity of thecolumn was estimated using petrophysical corre-lations in equations 11 and 12 and by adjustingthe cementation factor b. The mineral surfacearea and imaginary conductivity were computedusing equations 13 and 14, respectively, and thephase of the complex conductivity measurementswas calculated using equation 4.Figure 7a shows the evolution of resistivity for

experimental and modeling results. The pre-dicted resistivity change has the same trend aswas observed in the experiments. As mentionedbefore, the change in the ionic strength of the

aqueous phase was not significant due to the fresh replacementsof sucrose media every 24 h. As a result, the effective resistivityis closely related to the evolution of the porosity (through the for-mation factor) of the column, as described by equation 12 andFigure 6b. Figure 7b shows the evolution of the phase from geo-physical measurements and that from predictive petrophysical mod-eling and the predicted evolution of Spore. In the petrophysicalmodel, the effect of dextran production on Spore was based onequation 14 and the calculated Spore was then used to estimate ex-pected changes in imaginary conductivity (equation 13) and phase

Figure 5. Correlation between accumulated dextran, resistivity, andphase (at ∼100 Hz) during the experiment.

Figure 6. (a) Comparison of dextran evolution data and prediction and (b) prediction ofporosity evolution from reactive transport modeling.

Figure 7. Comparison of geophysical measurement data with predicted values frommodeling: (a) resistivity and (b) phase and Spore.

Bioclogging monitoring and simulation E69

(equation 4). Immobilized dextran in the column was assumed to beuniform throughout the column; therefore, there was uniform varia-tion of Spore throughout the column. After day one, model predic-tion of phase and Spore decreases almost linearly as dextranproduction increases (Figure 7b). The models overpredict the de-crease of phase during most of the experiment, likely due to theoverestimation of the initial surface area value Spore;0 that was cal-culated based on the column dimension, porosity, and grain size.Surface area is known to be critical in determining the physicaland chemical properties of solids; however, it is challenging toquantify accurately (Helgeson et al., 1984; Petersen et al., 1996).Nonetheless, the experimental data and the model output are ingood agreement in general, which indicates the dominant influenceof Spore in determining phase values. The concurrent quantificationof porosity and mineral surface area evolution during the experi-ments shows the promise of the joint use of reactive transportmodeling and geophysical monitoring to obtain mechanisticunderstanding and quantification of physical changes associatedwith bioclogging processes. Time-dependent data on porosityand surface area are typically challenging to measure nondestruc-tively. The joint use of the two methods can lead to time-dependent

estimation of these two parameters and will be very useful in relat-ing the extent of clogging to property changes of the porous media.

Model prediction of bioclogging under variableinjection conditions

To understand the conditions under which the maximum bioclog-ging and petrophysical alteration can be achieved, the developedreactive transport and geophysical model were used to predictthe evolution of these key properties under a series of injection con-ditions. Here we vary two key operational variables, the sucroseinjection concentration and the injection flow rate. The specific val-ues of these variables were chosen from Lappan and Fogler (1994,1996), where the experiments were carried out using the same bac-teria species and sucrose concentration level in sand columns of thesame length. Figure 8 shows the predicted evolution of geochemi-cal, petrophysical, and electrical geophysical properties averagedover the entire length of the column under variable injection con-ditions. Figure 8a and 8b shows the accumulative dextran formationand average porosity as a function of time for all four cases. Withthe low influent flow rates of 0.1 ml∕min, approximately 4 and19 g of dextran was formed, respectively, within a period of 50 days(blue curves). In contrast, with a high flow rate of 1.0 ml∕min (redcurves), dextran formation is negligible. Corresponding to the dex-tran formation, average porosity decreased from 0.65 to 0.2 in thecase with the largest amount of dextran formation, while the amountof porosity decrease is much lower in the other three cases. This isbecause lower flow rates lead to longer residence times, which al-lows sufficient time for the microbe-mediated reactions to occur.Among the cases with the same flow rate of 0.1 ml∕min, 19 gof dextran was produced with the sucrose concentration of15 g∕l compared to 4 g of dextran with the inlet sucrose concen-tration of 1.5 g∕l. This is because higher sucrose concentrations re-sult in higher dextran production rates. Although a negligibleamount of dextran was formed at high flow rates in the columns,this does not mean dextran will not form at all under these flowrates. Residence time can be increased with longer columns, whichcan potentially lead to dextran formation that is deeper into the flowpath in longer columns.Dextran formation alters petrophysical parameters such as per-

meability and specific surface area. The estimation of these petro-physical parameters is typically challenging. Here, we estimate theevolution of permeability and other properties in the flow throughcolumn experiments using the model and parameters validatedthrough the experimental data obtained in this work. The evolutionof average permeability at different times over its original per-meability value (k0) is shown in Figure 8c. The average permeabil-ity value was calculated based on the sequential distribution of localpermeability values in each grid block. In the case with the highestdextran formation (0.1 ml∕min and 15 g∕L sucrose injection),there is more than three orders of magnitude decrease in averagepermeability of the column, essentially meaning that the columnis fully clogged. The second largest change was approximately a0.3 order of magnitude decrease in the case with 0.1 ml∕min

and 1.5 g∕L sucrose injection. In general, the results here qualita-tively agree with Lappan and Fogler’s observation that lower flowrates and higher sucrose concentration lead to a much larger amountof dextran formation and a permeability decrease. Quantitatively,the dextran production and the bioclogging rates in this work aresignificantly lower than those reported by Lappan and Fogler

Figure 8. Numerical bioclogging experiment under different flowrates and initial sucrose concentration condition. Evolution of geo-chemical parameters (a) dextran, (b) porosity, (c) logarithm of ef-fective permeability over original permeability ratio, (d) logarithmof specific surface area, (e) resistivity, and (f) phase.

E70 Wu et al.

(1994, 1996). In their experiment, in the case with 0.1 ml∕min and15 g∕L sucrose injection , the permeability decreased by three or-ders of magnitude in five days. For other cases, there were alsoapproximately two orders of magnitude decreases in permeability.This is likely due to different strains used, with ATCC 8293 in thiswork and ATCC 14935 used in Lappan’s work. Lappan and Fogleralso used a combination of glucose-fructose and yeast extract as thegrowing media, while we used the yeast extract with some additionsof salts and trace metals. This difference in growing media canpotentially contribute to the rate differences because bacteriaare known for being sensitive to the chemistry of their growingenvironment.The corresponding logarithm of specific surface area (surface

area per unit solid volume) of the column, resistivity, and phaseis shown in Figure 8d–8f. As the bioclogging progresses, the per-meability and specific surface area decrease in proportion to theamount of dextran formed. Likewise, the resistivity increases inproportion to the formation of dextran. The phase of the columndecreases consistently with the reduction in conductive mineral sur-face area in the pore space. These geophysical signatures can beused to nondestructively infer changes induced by the biocloggingprocesses.

CONCLUSION

In this study, we conducted an experiment to improve under-standing of the bioclogging process as well as the ability to monitorand model critical processes using complex resistivity and reactivetransport modeling approaches, respectively. During the experi-ment, small but consistent changes of electrical resistivity and phaseresponses were observed. A reactive transport model was developedto successfully capture the growth curve of dextran. In addition, thepetrophysical models based on the output of the reactive transportsimulations successfully reproduced the observed evolution of elec-trical resistivity and phase. The agreement between simulation re-sults and measured data confirmed that the parameterization of thereactive transport model was realistic and the increasing electricalresistivity signal is controlled by the decreasing available pore spacedue to dextran production, while the decreases in phase signal cor-respond to the decrease in available mineral surface area due to thesurface attachment effect by the dextran formation. With the devel-oped model and parameters that were constrained by the experimen-tal data, four numerical experiments were then carried out tounderstand the role of the sucrose injection condition, namely,the injection rate and concentrations, in controlling the biocloggingprocess and the corresponding extent of geophysical changes. Theinjection condition plays a pivotal role in determining the bioclog-ging processes and can be manipulated to control where and howmuch certain zones can be clogged. Slower injection rates can leadto bioclogging close to the injection point, while possible cloggingdeeper into the flow path is expected to occur with faster injec-tion rates.The fact that the joint use of the two methods can quantitatively

capture the extent of decrease in porosity and mineral surface areawill open new opportunities for understanding and quantifying bio-clogging processes. The porosity and surface are challenging tomeasure nondestructively. Traditional bioclogging experiments typ-ically measure the temporal evolution of hydraulic conductivitywithout explicitly measuring changes in porosity and surface areaof solid phases. The joint use of the modeling and monitoring tools

provides evidence of the concurrent change of these two parametersduring bioclogging processes. The capability to provide quantitativeconcurrent estimate of porosity and mineral surface area couldpotentially lead to new conceptual models for estimating andunderstanding hydraulic conductivity change during biocloggingprocesses.This study is a first step toward the development of a novel

monitoring and modeling technology for bioclogging. Closecorrespondence between the experimental data, geophysical mon-itoring measurements, and the reactive transport model providesconfidence that we have gained an improved understanding of bio-polymer clogging in porous media and the improved quantificationof changes in physical properties of porous media during the bio-clogging process, which is a prerequisite for optimal management.The joint use of geophysical monitoring and reactive transportmodel would eventually enhance monitoring, modeling, and con-trolling of subsurface bioclogging processes.

ACKNOWLEDGMENTS

Funding for this research is provided by Energy Bioscience In-stitute. The authors wish to thank T.-H. Kwon (Washington StateUniversity) for the preparation of the microbes and growth mediaand R. Chakraborty (Lawrence Berkeley National Laboratory) formicrobial cell counts and imaging. We thank the associate editor J.Carcione and three reviewers (D. Ntarlagiannis at Rutgers Univer-sity and two anonymous reviewers) for their helpful comments.

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