factors affecting mass transfer limited biodegradation in saturated porous media

Ž .Journal of Contaminant Hydrology 50 2001 99–120www.elsevier.comrlocaterjconhyd

Factors affecting mass transfer limitedbiodegradation in saturated porous media

Stefano F. Simoni 1, Anke Schafer, Hauke Harms),¨Alexander J.B. Zehnder

( )Swiss Federal Institute for EnÕironmental Science and Technology EAWAG ,CH-8600 Dubendorf, Switzerland¨

( )Swiss Federal Institute of Technology Zurich ETHZ , CH-8000 Zurich, Switzerland¨

Received 18 February 2000; received in revised form 30 October 2000; accepted 24 January 2001

Abstract

Microbial degradation rates in the subsurface are not only limited by the physiological capacityof the organisms, but also by inefficient supply of nutrients to the microbes. Although masstransfer limitation of biodegradation in the subsurface has been postulated for years, experimentalevidence is still scarce. In the column experiments described here, diffusive transport of4-nitroanisole from the bulk solution to cells of Rhodococcus opacus strain AS2 immobilized onglass beads or sand appeared to be responsible for the slow transformation rates observed.

ŽAssuming steady state, we applied a coupled transformationrtransport equation to these data Best.equation and apparent bead-related mass transfer coefficients were found to increase in propor-

tion to the surface area covered with bacteria. This implies that mass transfer coefficients forindividual cells remained constant. In an idealized oligotrophic environment where cells are onlyloosely clustered and do not shield each other, we would therefore expect biodegradation rates tobe independent from the longitudinal distribution of the total biomass along a given flow path.Moreover, apparent mass transfer coefficients increased with the grain size of the column fillings,but did not change upon varying the flow rate. With a limiting external transport step, overalltransformation fluxes do not become saturated at concentrations as low as predicted forMichaelis–Menten-type kinetics. Mass transfer limitation thus offers a justification for the

) Ž .Corresponding author. Present address: Swiss Federal Institute of Technology Lausanne EPFL , IATE-Pedologie, GR Ecublens, CH-1015 Lausanne, Switzerland. Tel.: q41-21-693-3773; fax: q41-21-693-5670.´

Ž .E-mail address: [email protected] H. Harms .1 Present address: Swiss Re Insurance Company, Mythenquai 50r60, CH-8022 Zurich, Switzerland.¨

0169-7722r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-7722 01 00099-7

( )S.F. Simoni et al.rJournal of Contaminant Hydrology 50 2001 99–120100

common assumption that biodegradation rates in the subsurface follow first order kinetics in awide concentration range. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Bacteria; Biodegradation; Groundwater; Mass transfer; Pollutants; Solute transport

1. Introduction

Due to their omnipresence and their metabolic flexibility, microbes are widelyrecognized to be of great importance to the fate of chemicals in the subsurface. Besidesother factors like lacking nutrients or water, and inadequate temperature or pH, thelimited efficiency of substrate microscale transport is likely to keep biodegradation rates

Žbelow the intrinsic biological capacity Bosma et al., 1997; Harms, 1998; Harms and.Bosma, 1997 . This so-called mass transfer limitation is to be expected when rates of

substrate consumption exceed the rates of substrate supply. The concept of mass transferlimitation has been applied to experimental biodegradation data to discuss the influence

Žof sorption, desorption, and intrasorbent diffusion Mihelcic and Luthy, 1991; Rijnaarts.et al., 1990; Scow and Alexander, 1992 , substrate transport from the bulk solution to

Žthe surface of porous media Aksu and Bulbul, 1998; Chen et al., 1992; Harms and¨ ¨Zehnder, 1994; Namkung et al., 1983; Rittmann and McCarty, 1980; Schafer, 1997;¨

. ŽShreve and Vogel, 1993; Tros et al., 1998 , slow substrate dissolution Stucki and.Alexander, 1987; Volkering et al., 1992 , or combinations of several processes in

Ž .slurries Ramaswami and Luthy, 1997 .Mass transfer effects on biodegradation of attached bacteria in porous media have

been predicted with limited success so far. Good agreement was reported for columnsŽ . Žwhere substrates were degraded by a relatively thick biofilm f100 mm Namkung et

.al., 1983; Rittmann and McCarty, 1980 and by cells immobilized in alginate beadsŽ .Aksu and Bulbul, 1998 . In a study allowing biofilm growth at fairly low flow rates¨ ¨Ž y5 y1.average linear velocity Us1.5=10 m s , results were satisfactory only for

Ž .toluene but deviated from predictions for benzene Chen et al., 1992 . Furthermore,overestimation of the extent of biodegradation in columns based on batch kinetic datawas reported in several short term studies where mass transfer limitation was expected

Ž . Ž .to be absent Schafer, 1997; Tros et al., 1998 , or small Harms and Zehnder, 1994 . The¨observed discrepancies were found to depend on the amount of biomass in the columns,on the flow rates, or on both. These reports shared a common experimental setup insofaras growth was prevented by omission of essential nutrients, and the fractional coverageof the supporting beads or grains rarely exceeded a few percent. An overestimation ofbiodegradation based on batch-derived data was also reported for unsaturated columnswhere mass transfer was not included in the model, but was mentioned as a possible

Ž .explanation for the observations Langner et al., 1998 . Although it is difficult to ruleŽout changes in microbial physiology triggered by the proximity of a surface Fletcher,

.1985; van Loosdrecht et al., 1990 , these results and a recent theoretical study on theŽeffects of pore scale heterogeneity in reactive solute transport Dykaar and Kitanidis,

.1996 , led us to conclude that a further inspection of possible mass transfer processes isindispensable for a better understanding of biodegradation rates in porous media.

( )S.F. Simoni et al.rJournal of Contaminant Hydrology 50 2001 99–120 101

In the present study, we want to corroborate the effect of mass transfer from the bulkon biodegradation rates of attached bacteria in porous media, especially at low celldensities. In an introductory theoretical section, we give a short overview over thecurrent understanding of mass transfer in packed beds and present our approach basedon a quasi-steady state. In the experimental section, we show results from columnexperiments where 4-nitroanisole was degraded by Rhodococcus opacus strain AS2.Independent kinetic parameters obtained from simultaneous batch experiments allowedus to fit mass transfer coefficients to the column data. Apparent mass transfer to thebead surface was proportional to the number of immobilized cells, increased withincreasing size of the supporting beads, but was independent from flow velocity. Finally,we discuss the implications of these findings for biodegradation in the subsurface and inengineered packed beds.

2. Theoretical framework

2.1. Steady state flux driÕen by biodegradation

When bacteria consume a dissolved substrate, they create a depletion zone in theirvicinity. The concentration C at the cell surface is thus lower than the concentrationcell

in the bulk solution C , and diffusive transport tends to equalize this concentrationbulk

gradient. A quasi steady state is reached when the degradation flux q equals thedeg

transport flux q . To facilitate quantification, the involved transport processes are oftent

lumped into a so-called mass transfer coefficient in the engineering literature. The masstransfer coefficient relates the transport flux q of a compound towards a surface to thet

w y3 xconcentration gradient between C and C moles mbulk cell

q skDCsk C yC . 1Ž . Ž .t bulk cell

The flux q may for example be expressed per unit area, per unit volume, or per unitt

biomass and the dimensions of the mass-transfer coefficient k change accordingly.Based on a Michaelis–Menten-type transformation kinetics, the degradation flux for a

single cell can be expressed as

Ccellq sq 2Ž .deg max K qC1r2 cell

w y1 y1 xwhere q moles s cell denotes the maximal specific degradation flux per cellmaxw y3 xand K moles m stands for the concentration at half-maximal transformation rate.1r2

Ž . Ž .Assuming steady state, C can be eliminated from Eq. 2 by substitution from Eq. 1 ,cell

and the flux can be expressed as a function of C only. This results in the so-calledbulkŽ .Best equation Best, 1955; Bosma et al., 1997; Koch, 1990 . As it is arbitrary to choose

a single cell as the reference for the formulation of the fluxes, the Best equation can bewritten in a general form for a dimensionless flux

y1 y1q C qK qq k 4C q kbulk 1r2 max bulk maxs 1y 1y . 3Ž .y1 2) y1q 2 q kmax max C qK qq kŽ .bulk 1r2 max


More general discussions of the properties of the Best equation can be found forŽ . Ž .example in Bosma et al. 1997 and van Leeuwen 1999 .

Ž .This approach is valid under two conditions: i in case of a sorbing substrate, localŽ . Ž .sorption equilibria must have been reached Angley et al., 1992 ; ii local concentration

gradients must have developed. For diffusion controlled transport, the time t needed toss

reach steady state can be approximated by

d 2 r 2dif bead

t s F 4Ž .ss D Ddif dif

w x w 2 y1 xwhere d m is a measure for the diffusion path length, D m s is the diffusiondif difw xcoefficient, and r m is the bead radius, which is an appropriate measure for thebead

Ž .upper limit of d . For the grain sizes used in this study Table 2 , this results indif

2.5-t -2250 s. The columns with the biggest beads have thus to be run for at leastss

38 min in order to reach local steady state.

2.2. Simplified one-dimensional coupled transport-degradation equation

For biodegradation in saturated columns without growth of the organisms, a coupledtransport-degradation equation can be written under the simplifying assumption of radialmixing and negligible dispersion

EC U EC m xŽ .bulk bulksy yq C . 5Ž . Ž .bulk

Et P Ex Ap

w x w xIn this equation, t is time s , x is the longitudinal coordinate in the column m , U isw y1 x Ž .the average linear velocity m s , p is the porosity of the column packing, q C isbulk

w y1 y1 xthe specific transformation rate per unit of biomass moles cell s in function ofŽ . w y1 xC , e.g. according to Eq. 3 , m is the biomass density per unit length cells m , andbulk

w 2 x Ž .A is the cross-section of the column m . For steady state, Eq. 5 equals zero and canbe rearranged to an integral form

EC 1 Mout LbulkCbulk sy m x Exsy 6Ž . Ž .H Hin q C Q QŽ .C 0bulkbulk

w 3 y1 x w xwhere Q is the volumetric flow rate m s , L is the column length m , and M is thew xtotal biomass in the column cells . If q is a function of C only and does not dependbulk

on biomass density, we find the integral with respect to C on the left-hand side ofbulkŽ .Eq. 6 to be independent of biomass density, too. The concentration in the column

outlet would therefore be independent from the exact distribution along the column axis,Ž .which is represented by the function m x . This conclusion is valid only for low cell

densities where it is unlikely that a considerable number of cells is shielded from thebulk solution, e.g. in the center of large aggregates or inside thick biofilms.

2.3. Mass transfer expressions

Ž .It is important to be aware of the fact that Eq. 1 relates macroscale parameters andŽthat neither the coefficient k nor DC have a precise microscopic meaning Dykaar and


.Kitanidis, 1996 . In consequence, values for k are hard to predict from theory. Inengineering literature, they are usually derived from empirical correlations. Althoughdifferent scales of mass transfer might be involved, it is common practice to assumemass transfer in porous media to depend on diffusion across a stagnant layer ddifŽ .Namkung et al., 1983; Rittmann and McCarty, 1980 , the magnitude of which depends

Ž .on geometry and flow velocity Levich, 1962 .ŽFollowing a reasoning derived for diffusion to an isolated sphere Berg and Purcell,

.1977 , mass transfer to active cells immobilized on a collector bead can be most easilyŽ .understood for two limiting cases. i With a lot of bacteria on each bead, the whole

bead surface becomes a sink. Adding or removing single bacteria will then hardly0 w 3 y1change the flux to the bead and the mass transfer coefficient for the bead k m sbead

y1 xcell is independent from the exact number of bacteria on the collector. Individualcells will have to share the flux to the bead, and a cell-based coefficient k is obtainedcell

0 Ž . Žby dividing k by the number of cells per bead n Harms and Zehnder, 1994 Fig.bead.1A

k sk 0 rn with k 0 sconst. 7Ž .cell bead bead

Ž .ii A single cell or very few cells are immobilized on a bead and the flux to the beadis the sum of the fluxes to these single cells. Here, the introduction of a constant

0 w 3 y1 y1 x Ž .cell-related mass transfer coefficient k m s cell is more convenient Fig. 1Bcell

k snk 0 with k 0 sconst. 8Ž .bead cell cell

The bead related coefficient k has to be interpreted with caution, however. As notbead

the whole bead surface is a sink, k relates the flux to the bead to the concentrationbead

gradient between the bulk solution and the surface of the active cells and not to thatbetween the bulk solution and the average concentration at the bead surface. Withincreasing n, k becomes more and more saturated and approaches k 0 .bead bead

A first step to understand mass transfer would consist in the discrimination betweenŽ . Ž . 0 0the two domains represented by Eqs. 7 and 8 , where either k or k is constantbead cell

with respect to biomass density. In the following, we will point out how independentestimates for k 0 and k 0 could be obtained.bead cell

Mass transfer coefficients for diffusive film transport to a particle in porous media areŽoften obtained from correlations of the form Dykaar and Kitanidis, 1996; Karabelas et

.al., 1971; Kunii and Suzuki, 1967; Levich, 1962

Ddif ck s aqbPe 9Ž . Ž .area 2 rbead

w y1 xwhere k is a mass transfer coefficient per unit area m s , Pe is the Peclet number´areaŽ .Table 1 , and a, b and c are constants for specified solvent, solute and geometry. Thepower of Pe varies between 1r3-c-1. Independent estimates for k are especiallyarea

Ž . Ždifficult to derive for low flow velocities Pe-100 Kunii and Suzuki, 1967; Satter-. Ž . Žfield, 1980 . However, it follows from Eq. 9 and experimental evidence Kunii and.Suzuki, 1967 that the expression obtained for diffusion to a single sphere from infinity

Ž .as2 and bs0 gives at least an order of magnitude for k and 1-Pe-100.area


Fig. 1. Exemplifying mass transfer situations for cells immobilized on a collector bead and consuming asubstrate, which diffuses in from the pore space. Solid lines and dashed lines apply to bead-based andcell-based coefficients, respectively, and arrows indicate the direction of the substrate flux to the cells.

Ž . Ž Ž ..Situations shown correspond to beads entirely covered by cells A Eq. 7 , or to beads which are onlyŽ . Ž Ž ..covered by few cells B Eq. 8 .

Ž . 0 0Eq. 9 allows now to obtain expressions for k and k by multiplication with thebead cell

reactive surface area

k 0 sk 4p r 2 s2pD ar qbDycU cr Ž1qc. 10Ž .Ž .bead area bead dif bead dif bead

and

pD r 2dif cell0 2 y1 yc c Žcy1.k sk p r s ar qbD U r . 11Ž .Ž .cell area cell bead dif bead2

Ž . Ž .According to Eqs. 10 and 11 , mass transfer is likely to increase with r forbead

entire collectors whereas a decrease with r is to be expected for single cells. A trendbead

with respect to variation in U is less evident as the ratio of the constants a and b playsan important role.

The above area-based approach predicts a linear increase of k with the areabeadŽ . Ž .covered by active cells analogous to Eq. 8 Fig. 1B

k snk p r 2 12Ž .bead area cell


Table 1Definition and meaning of microscale dimensionless groups

Group Definition Meaning

Pe 2 r UrD Peclet number, ratio of time-scales needed for diffusive and´bead dif

convective transport, respectively, over a characteristic length2Da k r rD s Damkohler number, ratio of time-scales needed for diffusive¨deg bead dif

2Ž . Ž . Ž .q rK MrV r rD transport over a characteristic length r , and a pseudo-max 1r2 pore bead dif beadafirst-order reaction, respectively

aM is the total biomass in the column and V is the pore-volume. This choice yields a maximum for Dapore

as the first order reaction rate is based on the maximal transformation rate according to Michaelis–Mentenkinetics and on a maximal diffusion path length r .bead

Žand has been applied to model substrate transport to microcolonies of bacteria Chen et. 0al., 1992; Molz et al., 1986 . But in fact, it yields a lower limit for k because itcell

neglects diffusion parallel to the bead surface towards the sink spots. Including thisŽ .additional flux, k is expected to increase faster with n than predicted by Eq. 12 andbead

Ž 0 . Ž .saturation k is reached at lower cell numbers as shown by Berg and Purcell, 1977bead

k 0 s4D r 13Ž .cell dif cell

nrcell0k sk 14Ž .bead bead nr qp rcell bead

0 Ž Ž .where k again corresponds to the case for radial diffusion from infinity Eq. 10bead.with as2, bs0 . For dimensions representative for bacteria and a sandy aquifer

Ž y6 y3 . 0r ;10 m, r ;10 m , 90% of k is reached if only 0.7% of the surfacecell bead bead

are covered by bacteria. This holds only for evenly distributed cells that do not formŽ .clusters, however Berg and Purcell, 1977 .

3. Materials and methods

3.1. Organisms and culture conditions

R. opacus strain AS2 has been isolated from soil samples and is able to useŽ .4-nitroanisole as a sole source of carbon and energy Schafer et al., 1996 . We grew the¨

Ž . y1 Žbacteria in a mineral medium Harms and Zehnder, 1994 containing 100 mg l 654. y1

mM 4-nitroanisole and supplemented with 200 mg l yeast extract in order to increasethe biomass. 4-Nitroanisole was added aseptically when the media had cooled to 808Cafter autoclaving. After harvest by centrifugation during exponential growth, cells were

Ž .washed twice with phosphate buffered saline PBS, ionic strength Is100 mM, pHs7.2containing 4.93 g NaCl, 0.19 g KH PO , and 1.18 g K HPO per liter of deionized2 4 2 4

water. We kept cell suspensions on ice until experiments were started.

3.2. Column transformation experiments

We studied the transformation of 4-nitroanisole by strain AS2 in glass columnsŽ .Ls8.5 cm, rs0.5 cm, Omnifit, Cambridge, UK with porous polyethylene frits and


one adjustable endpiece. The columns were wet-packed with glass beads of various sizesŽ Ž .r s50 mm, Merck, Dietikon, Switzerland; r s200 mm 125–280 mm , Roth,bead bead

.Karlsruhe, Germany; r s1500 mm, Huber, Reinach, Switzerland or purified silicabeadŽ .sand FLUKA, Buchs, Switzerland . Prior to use, column packings had been soaked in

chromosulphuric acid, thoroughly washed with PBS and deionized water, and dried at1058C. We operated up to eight columns per experiment in a down flow mode with a

w Ž .peristatic pump and Tygon tubings Ismatec, Glattbrugg, Switzerland . The buffer-saturated columns were percolated with 100 mM PBS for at least 24 h at 258C before

Žcells were loaded by replacing the influent with a cell suspension in PBS 0.3-OD546. y1-1.0 . The flow rate was 0.4 or 0.6 ml min during cell loading. Loading time was up

to 1 h and was followed by 15 min of rinsing with PBS. We collected the effluent duringloading, and determined the biomass attached to the collector beads by subtraction of thebiomass in the effluent from the biomass in the influent. After initial washout of looselyattached cells, the remaining cells were found to adhere well. Immediately after loading,we determined q of 4-nitroanisole degradation in batch experiments with themax

suspensions used for loading the columns. We then started the column degradationexperiments by changing influent solutions to PBS containing approximately 20 mM of4-nitroanisole. In order to minimize substrate losses due to sorption or degradation bycells adhered to tubing, we replaced the tubings used for cell loading by Teflonw tubingsŽ . wOmnifit, Cambridge, UK , except for about 10 cm of Tygon tubing necessary forperistaltic pumping. Moreover, these compound tubings were presaturated by flushingwith a 60 mM 4-nitroanisole solution for 15 min, which was then replaced by a solutionof approximately 20 mM for another 45 min. After this pretreatment, the effluent of thetubings was found to remain within 95–100% of the concentration in the feed vessel.We varied the flow rates between 0.08 and 1.5 ml miny1 during the biodegradationexperiments. The loaded biomass was between 27 and 1145 mg dry-weight per column,corresponding to a fractional surface coverage between 0.1% and 21%. The reduction ofthe column pore volume remained well below one per mille. Effluents were sampledregularly with fraction collectors, the sampling vials of which contained 10 N phospho-

Ž .ric acid in volumes of up to 3% vrv of the final sampling volume in order to stopbiodegradation. The obtained fractions were analyzed by RP-HPLC after centrifugationfor 5 min at 10,000=g. Degradation activity was followed between 1 and 3 h untilconcentrations in the outflow remained fairly constant. Cells were found not to grow inthe PBS-substrate solutions without macronutrients and trace elements. Control experi-ments without immobilized cells showed complete breakthrough. We concluded thatsorption equilibria were reached in the columns and that substrate losses due to sorptionto the column fillings were negligible.

3.3. Batch transformation experiments with cell suspensions

In order to assess the intrinsic kinetic parameters of the cells used for the biodegrada-tion experiments in the columns, we added 4-nitroanisole to 10 ml of the cellsuspensions used for column loading to concentrations of approximately 20 mM. Thesesuspensions were incubated at 258C in stirred Erlenmayer flasks. Samples were removedat time intervals of 1–3 min, acidified, and analyzed by RP-HPLC after centrifugation


Ž .for 5 min at 10,000=g. As reported earlier Schafer, 1997 , substrate decrease was¨linear with time in these experiments so that q could be determined from the slopemaxŽ y1 Ž .y1 y1 Žq ;20 nmoles min mg dry-weight , range 13-q -28 nmoles min mgmax max

.y1 .dry-weight . In independent experiments, transformation rates were measured atinitial substrate concentrations between 0.06 and 1 mM and accordingly less biomass.Although these experiments were subject to experimental and analytical uncertainties,

Ž . Ž .we found K s0.047 mM rses15% by least-squares fitting to Eq. 2 .1r2

3.4. Verification of cell distribution in biotransformation columns

We qualitatively verified the longitudinal distribution of bacteria after two columnŽ .experiments small glass beads, r s50 mm . For this purpose, columns werebead

drained, disassembled, and the cores were cut to slices of about 1 cm. Each slice wasŽ .mixed and approximately 1.5 g portions wet-weight were filled in 2.2 ml polypropy-

lene test-tubes. Then 1 ml 100 mM PBS containing 20 mM 4-nitroanisole was addedand the test tubes were placed on an end-over-end mixer at 2 rpm and 258C. A total of150-ml samples were removed at time intervals of 5 or 10 min, acidified, and analyzedby RP-HPLC after centrifugation for 5 min at 10,000=g. Degradation rates determinedwere normalized to the dry-weight of column-material in individual batches in order toobtain a measure for the active biomass present at each depth.

3.5. Analytical techniques

We determined cell density in suspension by measuring optical density at 546 nm.Ž y1 y1 .The correlation of OD with cell dry weight 230 mg dry-weight l OD was546 546

established by filtering cell suspensions of a known OD through 0.2 mm Nucleoporew

546Ž .polycarbonate filters ds47 mm, Costar, Cambridge, MA . We washed the filters with

deionized water and dried them to constant weight at 1058C. The dry weight wascalculated from the net weight of the dried filters after subtracting blank values obtained

Ž 8by filtration of buffer only. The correlation of dry weight with cell numbers 8=10Ž .y1 .cells mg dry-weight was then obtained by counting cell suspensions of known

Ž .OD in a Thoma counting chamber. The effective radius r 0.96 mm was546 cell

determined microscopically from the geometric mean of the average cell length andŽ .width of 50 cells Schafer, 1997 . 4-Nitroanisole was measured by RP-HPLC as¨Ž .described previously Schafer et al., 1996 . Oxygen saturation in the column effluent¨

Žwas measured polarographically with an oxygen electrode Rank Brothers, Cambridge,. Ž .UK , the measuring chamber of which was modified to a flow-through cell Vf0.5 ml .

3.6. Estimation of mass transfer coefficients from biodegradation columns

We modeled steady state biodegradation of 4-nitroanisole with a standard spreadsheetŽ .program adapted from Harms and Zehnder, 1994 . In this spreadsheet, biodegradation

was determined sequentially for 1000 longitudinal column sections. These sections wereassumed to be radially well mixed, and the output of each section was used as an input


for the following one. This approach corresponds to the finite differences form of Eq.Ž .5 assuming a quasi steady state

q C DMŽ .iC sC y . 15Ž .iq1 i Q

Ž .The specific transformation rate q was calculated according to Eq. 3 , C is the bulki

concentration in section i, DM is the average-biomass per column section, and Q is thevolumetric flow-rate. The kinetic parameters q and K obtained from batchmax 1r2

experiments, the concentration at the column inlet, the loaded biomass, and the flow ratewere used as input parameters.

Given the low fractional surface coverages in our experiments, we assumed q to beŽ .independent from the local biomass density m x as a working hypothesis. This

Ž . 0corresponds to the situation of Eq. 8 and Fig. 1B where k remains constant. Ascell

shown in Section 4, this assumption is reasonable. Under this assumption, the outputconcentration of a column does not depend on the longitudinal distribution of the

Ž .biomass. This consequence of Eq. 6 was verified with modified spreadsheets, whereoutput concentrations were found to remain identical when the biomass distribution wasvaried.

Mass transfer coefficients were fitted to experimental steady-state concentrations inthe column outlets with a routine provided by the spreadsheet solution. Bead-based and

Žcell-based mass transfer coefficients k and k are mutually convertible cp. Eqs.bead cellŽ . Ž ..7 and 8 . This allowed to obtain k by multiplicating k by the number of cellsbead cell

Ž .per bead n according to Eq. 8 .

4. Results and discussion

4.1. Biodegradation rates in the columns remain below qm a x

We followed 4-nitroanisole concentrations in the outflow of columns with immobi-lized cells of R. opacus strain AS2 until a steady state was reached, which usually was

Ž .the case after several pore volumes Fig. 2 . Transformation rates in the columnsremained well below the maximal specific transformation rate q to be expected frommax

Ž . Ž Ž ..batch kinetic data Fig. 3 . According to Michaelis–Menten kinetics Eq. 3 , degrada-tion should have proceeded at relative transformation rates qrq close to unity in allmax

Žexperiments, because even the lowest concentration measured in a column effluent 3.mM was much higher than K .1r2

In batch experiments with fillings previously used in transformation columns, weŽ .found the degradation activity to be well distributed along the column axis Fig. 4 . The

reduced transformation rates are therefore unlikely to be the consequence of heteroge-neous biomass distribution, e.g. the accumulation of biomass close to the column inlet.Furthermore, external limitations due to insufficient supply with other nutrients seems


Fig. 2. Relative 4-nitroanisole concentrations in two representative transformation experiments with R. opacusŽ .strain AS2 immobilized in columns filled with glass beads r s200 mm . Experiments were run untilbead

Ž .concentrations in samples averaged over 10 min intervals indicated steady state dashed lines in the outflow.C was 19.9 mM. For circles with dots, average linear velocity was Us9.7=10y5 m sy1 , one pore volumein

corresponded to 5.5 min, total biomass was 80 mg dry weight, the average number of cells per bead wasestimated to be ns507. For circles with crosshairs, average linear velocity was Us8.8=10y5 m sy1 , onepore volume corresponded to 6.1 min, total biomass was 610 mg dry weight, the average number of cells perbead was estimated to ns4119. The experiments shown include the transition from a first steady state with alower C rC due to a slower percolation rate.out in

unlikely as cells were not growing in our experiments. This assumption was verified foroxygen: in an experiment with rather high biomass, we found the oxygen saturation inthe column outlet to be still 70%. Oxygen diffuses about twice as fast as 4-nitroanisolein water. If oxygen was to become limiting, its consumption should be more than 20times faster than the consumption of 4-nitroanisole. This seems unlikely to occur.

A plausible explanation remaining to explain these findings is that effective concen-trations at the cell surface C were below C as a result of slow mass transfer. In thecell bulk

following, we use this approach to interpret our experimental data.

4.2. Application of the Best equation to biotransformation columns

Following our approach to investigate whether mass transfer limitation could offer anŽ Ž ..explanation for these findings, we verified how application of the Best equation Eq. 3

Ž Ž ..instead of Michaelis–Menten kinetics Eq. 2 would alter expected biodegradationŽ . Ž . Ž .rates Fig. 5 . We found that for input 20 mM and lowest output 3 mM concentra-

tions in our columns, k must be smaller than 2 or 15=10y17 m3 sy1 celly1 in ordercell


Fig. 3. Relative biotransformation rates qrq vs. average cell number per collector bead n. Data weremax

obtained from transformation of 4-nitroanisole by cells of R. opacus strain AS2 immobilized in columns filledŽ . y4 y1 Ž .with glass beads r s200 mm . Average linear velocity was Us0.9=10 m s "15% . Everybead

symbol stands for a single column and different symbols represent independent series of experiments. DataŽ .points from Schafer 1997 are indicated by filled symbols. The two circles with a dot or a crosshair are data¨

from the transformation experiments shown in Fig. 2. The maximum on the abscissa corresponds to afractional surface coverage of 4.5%.

to obtain qrq below unity, respectively. In this case, qrq depends almost linearlymax max

on k at a given concentration.bead

4.3. Collector-based mass transfer coefficients show linear dependence on number ofcells per collector

We deduced apparent mass transfer coefficients k and k by fitting eachbead cell

parameter to experimental data obtained with cells of R. opacus strain AS2 immobilizedŽ .on glass beads r s200 mm . Whereas bead-based k show a linear relation withbead bead

Ž .the mean number of cells per collector bead n Fig. 6A , cell-based k seem to becellŽ .unaffected by n Fig. 6B . This corresponds to the situation where the initial slope of

k vs. n can be interpreted as a measure for the average mass transfer coefficient of abead0 Ž Ž . .single cell k Eq. 8 , Fig. 1B . An important consequence of this finding is that q incell

Ž .Eq. 3 is independent of the biomass density and that the outflow of an idealizedŽcolumn should be the same for different biomass distributions along the column Eq.

Ž ..6 . Moreover, k is an appropriate parameter to evaluate the influence of othercell

factors like hydrodynamics or geometry on biodegradation. Our findings suggest that theapproach proposed earlier to share the total flux to a collector among the number of cells


Ž .Fig. 4. Longitudinal distribution of transformation activity after two column-experiments r s50 mm .bead

Activities were determined in batch experiments from sliced column-fillings. They are given relative to thetotal activity found per column.

Ž .per collector Harms and Zehnder, 1994 is not appropriate for the low cell densities inour experiments.

4.4. Cell-based mass transfer coefficients seem to be independent of flow Õelocity

Ž .For medium-sized glass beads r s200 mm , a variation of the flow velocity Ubead

did not result in a clear-cut change of the apparent mass-transfer coefficient on a cellŽ .basis k Fig. 7 . According to diffusive film theory, the influence of U is predicted tocell

Ž Ž ..vanish for low Pe Eq. 11 , but this prediction is often not supported by experimentalŽ .evidence from chemical engineering applications Kunii and Suzuki, 1967 . As far as

biodegradation studies are concerned, a higher U has been reported to increaseŽ .biodegradation rates in saturated columns Aksu and Bulbul, 1998 whereas there are¨ ¨

Žindications for a contrary effect in unsaturated columns Kelsey and Alexander, 1995;.Langner et al., 1998 .

We might argue that the average diffusion path length d seems to be insensitive todif

the flow velocity. d is not a well-defined length, but can be understood as thedifŽ .distance, over which the important concentration changes occur Levich, 1962, p. 60 .

For the range of Pe in our study, d can be assumed to be of the same order ofdifŽ .magnitude as the average pore-width d Table 2 . This means that the boundary layerpore

concept cannot be applied any more because concentration gradients extend over thewhole pore space. The importance of pore-scale heterogeneity in concentrations for mass


Ž Ž ..Fig. 5. Relative biotransformation rates qrq according to the Best equation Eq. 3 in function of bulkmax

concentration C and cell-based mass transfer coefficient k , which was arbitrarily chosen as a measurebulk cell

for the degree of mass transfer limitation. Kinetic parameters of R. opacus strain AS2 transformingŽ y1 Ž4-nitroanisole were used as input parameters to calculate the curves q s20 nmoles min mg dry-max

.y1 .weight , K s0.047 mM . Two limiting cases can be distinguished: For high values of k , the1r2 cell

transsects for qrq vs. C approach classical Michaelis–Menten behavior. For low k , qrqmax bulk cell max

decreases linearly with C . The slope corresponds to a first order reaction rate constant, which is not onlybulk

determined by the intrinsic biological degradation kinetics, but by mass transfer as well.

transfer has been illustrated recently in a study presenting a numerical solution forŽ .reactive transport in a simplified porous medium Dykaar and Kitanidis, 1996 .

4.5. Cell-based mass transfer coefficients increase with collector size

We found a linear correlation between apparent k and n for various sizes of glassbeadŽ .beads and for sand Fig. 8A–C . This corresponds to the situation depicted in the left

Ž .part of Fig. 1B. It is therefore not surprising that apparent k Figs. 6A and 8A–Cbead

was mostly smaller than independent estimates of k 0 based on diffusive transport tobeadŽ .an isolated sphere Table 3 . The only exceptions were found with the biggest beads,

Ž .where the highest fractional surface coverage could be reached Table 2 . This indicatesŽ .that Eq. 10 with bs0 underestimates mass transfer at least for the biggest grain size.


Fig. 6. Influence of average cell number per collector bead n on apparent mass transfer coefficients inŽ .biotransformation columns r s200 mm . Symbols are used as in Fig. 3. Bead-based coefficients kbead bead

Ž .show a linear increase with n A , whereas cell-based coefficients k seem to scatter randomly within abeadŽ . y4 y1 Ž .factor of 2 B . Average linear velocity was Us0.9=10 m s "15% .

ŽFurthermore, we could not find an indication for saturation of k to occur Figs. 6Abead. 0and 8A–C . Finally, the initial slopes, corresponding to experimental k , increasedcell

Ž .with the size of the supporting beads Table 3 .This latter finding would not be expected from theory if unhindered diffusion to

Ž Ž . Ž ..spheres was considered Eqs. 11 and 13 . However, it becomes understandable uponconsidering all three dimensions in space: For a given surface cell-density, the cell-to-cellseparation in the pore-space is biggest for the largest beads. Indeed, calculated cell-to-cell


Fig. 7. Apparent mass transfer coefficients for single cells k in biotransformation columns plotted againstcellŽ .average linear velocity U r s200 mm . Different symbols represent independent series of experiments,beadŽ .and datapoints from Schafer 1997 are indicated by filled symbols.¨

separations increase with the size of the glass beads even for the maximal cell densitiesŽ .reached with each bead-size Table 2 . The larger the beads, the less likely the cells

therefore are to compete for the substrate in their vicinity.

Table 2Comparison of different column packings

aPacking Derived parametersb c d e e f gr p d d Pe Da u rbead dif pore max cell – cell

w x w x w x w xmm mm mm mm

Glass beads 1500 0.40 268 485 240–480 460–4690 0.25 12200 0.38 70 61 15–160 3–156 0.045 1150 0.23 28 6 9–15 3–16 0.011 7

hSand 125 0.45 51 48 13–38 1–27 0.015 15

a y10 2 y1 Ž .Calculated with D s8.5=10 m s Schafer, 1997 .¨difb Porosity was determined gravimetrically.c y1r3 Ž . y4 y1Average thickness d f r Pe Levich, 1962, p. 85 with Us10 m s .dif beadd Ž . ŽBased on an interpolation between different types of packings, d s 1.1969 py0.1557 r Johnsonpore bead

.and Elimelech, 1995 .eAs defined in Table 1.f Ž .Maximal fractional surface coverage in experiments Figs. 5 and 7 .g Half the cell-to-cell separation for u and assuming a hemisphere with the average pore-volume per cellmax

around each cell.h Ž .Number based mean Simoni et al., 1998 .


Ž . 0Two irregularities deserve a brief discussion. i The experimental k for sandcell

grains does not follow the size-dependence found for glass beads. It is smallest althoughr is bigger than that of the smallest glass beads. As size and shape of the sand grainsbead

are much less uniform than those for the glass beads, the reduced k 0 could be ancellŽ .indication for preferential flow paths in the columns Kunii and Suzuki, 1967 , or for

increased heterogeneity in the cell distribution. Whereas the first hypothesis is notŽconfirmed by non-reactive tracer data obtained with sand-filled columns Simoni et al.,

. Ž .1998 , we can hardly rule out the second hypothesis. ii The increase in experimentalk 0 for the glass beads is more pronounced between the smallest and the medium sizecell

than between the medium and the biggest size. A comparison of the respectiveŽ .microscale Damkohler numbers Da Tables 1 and 2 offers a rationalization for these¨

findings: simulations obtained for sine-shaped pores showed that an increase in Daresults in bigger pore scale heterogeneity of concentration and increased transport

Ž .limitation of a surface reaction Dykaar and Kitanidis, 1996 . This effect is morepronounced for Da)100 and might thus bias the dependence of k 0 on r .cell bead

Furthermore, artifacts due to wall effects might be more important for the biggest beadsize. Indeed, a control experiment with a thicker column hinted at an increase in k beadŽ .asterisk in Fig. 8A , although the effect was not very pronounced.

Experimental k 0 were in the same order of magnitude as independent estimatescell

based on multiplication of the area specific fluxes with the cross section of a single cellŽ Ž . .Eq. 11 , Table 3, Fig. 1B . In contrast, they were clearly smaller than predictions

Ž Ž .taking into account the effect of lateral diffusion to a small sink patch Eq. 13 ,y15 3 y1 y1.3.2=10 m s cell . This again supports the idea that radial concentration

gradients are dominant. This conclusion was confirmed qualitatively by simulations ofŽ .concentration isoplethes in biofilms with irregular biomass distribution Wanner, 1989 .

Ž .Moreover, it can be deduced from Eq. 14 that clustering of cells significantly decreases0 Ž .apparent k as derived from the slope of k vs. n Berg and Purcell, 1977 . Incell bead

fluorescent micrographs of DAPI-stained cells on glass beads taken from a transforma-Ž .tion column not shown , we indeed found that bacteria were immobilized as single cells

but often loosely clustered. Although this might be due to artifacts, similar observationsŽ .were made for natural environments as well Gray, 1967; Harvey et al., 1984 .

4.6. SensitiÕity of apparent mass transfer coefficients to experimental parameters

Column degradation studies are subject to numerous sources of artifacts resulting inŽ .scattering of the data obtained Figs. 6–8 . These include imprecise quantification of the

biomass on the columns, physiological changes of the organisms, clogging of pores inthe porous bed or in the connecting tubing, as well as analytical errors. These factors arein general difficult to control and unfortunately, it is impossible to exactly reproduce asingle experiment in order to apply conventional statistics to a specific setup. Thismakes it necessary to consider a large number of column experiments, which all slightlydiffer from each other. This is the reason why we used linear regressions to theexperimental parameters covering the largest range of values in a given set of experi-ments to interpret the data. Together with the regression lines, this approach yields someinformation about the reliability of the data.


Table 3Mass transfer characteristics of different column packings

0a bPacking Experimental k Calculated coefficientscell2 0c 0dw xr mmbead Slope rse No. r k kbead cell

3 y1 y1 3 y1 y1 3 y1 y1w x w x w x w xm s cell % m s bead m s celly1 7 y12 y17Glass beads 1500 1.7=10 16 16 0.74 16.0=10 0.2=10y1 7 y12 y17200 1.5=10 6 17 0.94 2.2=10 1.2=10y1 7 y12 y1750 0.7=10 23 16 0.57 0.5=10 4.9=10y1 7 y12 y17Sand 125 0.5=10 15 8 0.89 1.3=10 2.0=10

a Ž . Ž .Initial slopes by linear regression of k vs. n Figs. 5A and 7A–C with relative standard errors rse ;bead

number of independent column experiments and coefficient of regression are given as well.b y10 2 y1 Ž .Calculated with D s8.5=10 m s Schafer, 1997 .¨difc Ž .From Eq. 10 with as2, bs0.d Ž .From Eq. 11 , with as2, bs0.

A sensitivity analysis showed fitted mass transfer coefficients k and k to becell beadŽ .sensitive to changes of the input parameters Table 4 , which is a basic condition for our

Ž .approach. Two findings might seem surprising and therefore need some explanation. iLack of sensitivity to the kinetic input parameters K and q : for K , this1r2 max 1r2

Ž .outcome can be easily understood from Eq. 3 by considering that K appears in a1r2

sum, to which its contribution is very small. As far as maximal biomass specifictransformation rates q are concerned, a higher q increases the overall degradationmax max

capacity. In response to the increasing substrate demand, mass transfer limitationŽ Ž ..becomes more severe and the normalized transformation rate qrq Eq. 3 de-max

creases. In consequence, mass transfer coefficients need not change for the flux q toŽ .remain constant. This is typical for mass transfer limited biodegradation. ii Differences

between k and k : these result because column length and total biomass both affectcell bead

the number of cells per bead n, which is the proportionality factor between the two masstransfer coefficients. An increase in column length increases the column residence time,its pore volume, as well as the number of beads per column. For a given C , theout

overall degradation rate in the column does not change. This degradation activity isdistributed on the same number of cells, and therefore k remains unaffected. Incell

contrast, the degradation acitivity per bead decreases, which is reflected in a sinkingapparent k . On the other hand, an increase in total biomass has no influence on thebead

degradation activity per bead, which is needed, but leads to an increase in the maximalpossible degradation rate per bead. In a bead-based view, this situation is identical tothat discussed above for an increase in biomass specific degradation rate q ; therefore,max

k is expected to remain unaffected. We expect a decrease in k , however, becausebead cell

Ž . Ž . Ž .Fig. 8. A–C Plots of apparent k vs. n for different sizes of glass beads AqB and quartz sand C .bead

Every symbol stands for a single column, different symbols represent independent series of experiments. TheŽ .asterisk in panel A represents a datapoint obtained with a thicker glass column rs1.25 cm . The maxima on

the abscissa correspond to a fractional surface coverage of 25%, 1.1%, and 1.5% in panels A, B, and C,respectively.


Table 4Sensitivity of apparent mass transfer coefficients to column parameters

a bParameter Base value Change of apparent k in %cell

upon changing parameter

q20% y20%y5Average linear velocity 8.6=10 q20 y20

y1w xU m sy2w x Ž . Ž .Column length m 8.5=10 0r y17 0r q25

w x Ž . Ž .Biomass mg dry weight 0.61 y17r y-1 q25r q-1y1wq nmoles min 21.4 y-1 q-1max

y1Ž . xmg dry weightw xK nM 47 q-1 y-11r2

w xInput concentration mM 19.3 q17 y21w xOutput concentration mM 6.5 y17 q21

a Ž .Taken from a representative experiment with medium beads r s200 mm , intermediate biomassbead

load, and k s6.13=10y14 m3 sy1 beady1, k s1.51=10y17 m3 sy1 celly1.bead cellb Values for k are identical except for numbers in brackets; see text for explanation.bead

the increase in total biomass needs to be compensated by a lower degradation activityper cell.

5. Conclusions

5.1. Implications for biodegradation in the subsurface and in engineered systems

Although film mass transfer has been considered to be a possible bottleneck forbiodegradation and microbial growth in the subsurface for more than two decadesŽ .Rittmann and McCarty, 1980 , direct evidence for its importance is scarce. In thisstudy, we show that mass transfer limitation might in fact be responsible for the reducedbiodegradation rates observed in porous media. Apparent mass transfer coefficients werefound to be constant with respect to biomass or cell numbers, and they are in the sameorder of magnitude as theoretical predictions. Moreover, they depended on the geometryof the porous medium, which indicates that a direct surface impact on microbialphysiology is unlikely for our conditions. Finally, we could not find a clear influence ofthe flow velocity on biodegradation in the velocity range tested.

In addition to the resulting hindrance to biodegradation, mass transfer limitation leadsŽ .to first order degradation rates with respect to concentration Fig. 5 , an assumption

quite popular in modeling of biodegradation. As cell-based mass transfer coefficients areconstant for low surface coverages, varying biomass concentrations along the flow pathdo not alter the degree of mass transfer limitation. In principle, this also applies to

Žoligotrophic aquifers, where reported cell densities Harvey et al., 1984; Webster et al.,.1985; Wilson et al., 1983 are similar to those in our experiments and the formation of

thick biofilms is not to be expected. However, our flow rates were at the upper end ofthe range typically found in natural aquifers and it remains to be verified whether thisconclusion can be extrapolated to lower flow rates.


The situation is quite different for biofilms on porous media in engineering applica-tions, e.g. in biofilters. As the biofilm approaches a monolayer, mass transfer per unitbiomass will no longer remain constant but will decrease upon a further increase of thebiomass. Thus an increase in transformation capacity might be balanced by a moresevere mass transfer limitation.

Acknowledgements

We thank Herman van Leeuwen, Agricultural University of Wageningen, TheNetherlands, for his stimulating interest and constructive remarks. We further appreci-ated helpful discussions with Tom N.P. Bosma, TNO Institute of EnvironmentalSciences, Apeldoorn, The Netherlands, and Oskar Wanner, EAWAG.

References

Aksu, Z., Bulbul, G., 1998. Investigation of the combined effects of external mass transfer and biodegradation¨ ¨rates on phenol removal using immobilized P. Putida in a packed-bed column reactor. Enzyme Microb.Technol. 22, 397–403.

Angley, J.T., Brusseau, M.L., Miller, W.L., Delfino, J.J., 1992. Nonequilibrium sorption and aerobicbiodegradation of dissolved alkylbenzenes during transport in aquifer material: column experiments and

Ž .evaluation of a coupled-process model. Environ. Sci. Technol. 26 7 , 1404–1410.Berg, H.C., Purcell, E.M., 1977. Physics of chemoreception. Biophys. J. 20, 193–215.Best, J.B., 1955. The inference of intracellular enzymatic properties from kinetic data obtained on living cells:

I. Some kinetic considerations regarding an enzyme enclosed by a diffusion barrier. J. Cell. Comp. Physiol.Ž .46 1 , 1–27.

Bosma, T.N.P., Middeldorp, P.J.M., Schraa, G., Zehnder, A.J.B., 1997. Mass transfer limitation of biotrans-Ž .formation: quantifying bioavailability. Environ. Sci. Technol. 31 1 , 248–252.

Chen, Y.M., Abriola, L.M., Alvarez, P.J.J., Anid, P.J., Vogel, T.M., 1992. Modeling transport and biodegrada-tion of benzene and toluene in sandy aquifer material: comparisons with experimental measurements.

Ž .Water Resour. Res. 28 7 , 1833–1847.Dykaar, B.B., Kitanidis, P.K., 1996. Macrotransport of a biologically reacting solute through porous media.

Ž .Water Resour. Res. 32 2 , 307–320.Fletcher, M., 1985. Effect of solid surfaces on the activity of attached bacteria. In: Savage, D.C., Fletcher, M.

Ž .Eds. , Bacterial Adhesion: Mechanisms and Physiological Significance. Plenum, New York, pp. 339–362.Gray, T.R.G., 1967. Stereoscan electron microscopy of soil microorganisms. Science 155, 1668–1670.

Ž .Harms, H., 1998. Bioavailability of dioxin-like compounds for microbial degradation. In: Wittich, R.-M. Ed. ,Biodegradation of Dioxins and Furans. Landes Bioscience, Austin, TX, pp. 135–163.

Harms, H., Bosma, T.N.P., 1997. Mass transfer limitation of microbial growth and pollutant degradation. J.Ind. Microbiol. Biotechnol. 18, 97–105.

Harms, H., Zehnder, A.J.B., 1994. Influence of substrate diffusion on degradation of dibenzofuran andŽ .3-chlorodibenzofuran by attached and suspended bacteria. Appl. Environ. Microbiol. 60 8 , 2736–2745.

Harvey, R.W., Smith, R.L., George, L., 1984. Effect of organic contamination upon microbial distributionsŽ .and heterotrophic uptake in a Cape Cod, Mass. aquifer. Appl. Environ. Microbiol. 48 6 , 1197–1202.

Johnson, P.R., Elimelech, M., 1995. Dynamics of coloid deposition in porous media: blocking based onŽ .random sequential adsorption. Langmuir 11 3 , 801–812.

Karabelas, A.J., Wegner, T.H., Hanaratty, T.J., 1971. Use of asymptotic relations to correlate mass transferdata in packed beds. Chem. Eng. Sci. 26, 1581–1589.

Kelsey, J.W., Alexander, M., 1995. Effect of flow rate and path length on p-nitrophenol biodegradation duringtransport in soil. Soil Sci. Soc. Am. J. 59, 113–117.


Koch, A.L., 1990. Diffusion-the crucial process in many aspects of the biology of bacteria. Adv. Microb. Ecol.11, 37–69.

Kunii, D., Suzuki, M., 1967. Particle-to-fluid heat and mass transfer in packed beds of fine particles. Int. J.Heat Mass Transfer 10, 845–852.

Langner, H.W., Inskeep, W.P., Gaber, H.M., Jones, W.L., Das, B.S., Wraith, J.M., 1998. Pore water velocityŽ .and residence time effects on the degradation of 2,4-D during transport. Environ. Sci. Technol. 32 9 ,

1308–1315.Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs, NJ.Mihelcic, J.R., Luthy, R.G., 1991. Sorption and microbial degradation of naphthalene in soil water suspensions

Ž .under denitrification conditions. Environ. Sci. Technol. 25 169 , 169–177.Molz, F.J., Widdowson, M.A., Benefield, L.D., 1986. Simulation of microbial growth dynamics coupled to

Ž .nutrient and oxygen transport in porous media. Water Resour. Res. 22 8 , 1207–1216.Namkung, E., Stratton, R.G., Rittmann, B.E., 1983. Predicting removal of trace organic compounds by

Ž .biofilms. J. Water Pollut. Control Fed. 24 9 , 1533–1565.Ramaswami, A., Luthy, R.G., 1997. Mass transfer limitation and bioavailability of PAH compounds in coal tar

Ž .NAPL-slurry systems: 2. Experimental evaluations. Environ. Sci. Technol. 31 8 , 2268–2276.Rijnaarts, H.H.M., Bachmann, A., Jumelet, J.C., Zehnder, A.J.B., 1990. Effect of desorption and intraparticle

mass transfer on the aerobic biomineralization of a-hexachlorocyclohexane in a contaminated calcareousŽ .soil. Environ. Sci. Technol. 24 1349 , 1349–1354.

Rittmann, B.E., McCarty, P.L., 1980. Evaluation of steady-state biofilm kinetics. Biotechnol. Bioeng. 222359–2373.

Satterfield, C.N., 1980. Heterogeneous Catalysis in Practice. McGraw-Hill, New York.Schafer, A., 1997. Bacterial transport and pollutant degradation: influences of air–water interfaces and solid¨

surfaces. PhD Dissertation, Eidgenossisch Technische Hochschule ETH, Zurich.¨ ¨Schafer, A., Harms, H., Zehnder, A.J.B., 1996. Biodegradation of 4-nitroanisole by two Rhodococcus sp.¨

Biodegradation 7, 249–255.Scow, K.M., Alexander, M., 1992. Effect of diffusion on the kinetics of biodegradation: experimental results

Ž .with synthetic aggregates. Soil Sci. Soc. Am. J. 56 128 , 128–134.Shreve, G.S., Vogel, T.M., 1993. Comparison of substrate utilization and growth kinetics between immobi-

lized and suspended Pseudomonas cells. Biotechnol. Bioeng. 41, 370–379.Simoni, S.F., Bosma, T.N.P., Harms, H., Zehnder, A.J.B., 1998. Population heterogeneity affects transport of

Ž .bacteria through sand columns at low flow rates. Environ. Sci. Technol. 32 14 , 2100–2105.Stucki, G., Alexander, M., 1987. Role of dissolution rate and solubility in biodegradation of aromatic

Ž .compounds. Appl. Environ. Microbiol. 53 2 , 292–297.Tros, M.E., Schraa, G., Zehnder, A.J.B., Bosma, T.N.P., 1998. Anomalies in the transformation of 3-chloro-

Ž .benzoate in percolation columns with Pseudomonas sp. strain B13. Water Sci. Technol. 37 8 , 89–96.van Leeuwen, H.P., 1999. Metal speciation dynamics and bioavailability: inert and labile complexes. Environ.

Ž .Sci. Technol. 33 21 , 3743–3748.van Loosdrecht, M.C.M., Lyklema, J., Norde, W., Zehnder, A.J.B., 1990. Influence of interfaces on microbial

Ž .activity. Microbiol. Rev. 54 1 , 75–87.Volkering, F., Breure, A.M., Sterkenburg, A., Van Andel, J.G., 1992. Microbial degradation of polycyclic

aromatic hydrocarbons-effect of substrate availability on bacterial growth kinetics. Appl. Microbiol.Ž .Biotechnol. 36 548 , 548–552.

Ž .Wanner, O., 1989. Modeling population dynamics. In: Characklis, W.G., Wilderer, P.A. Eds. , Structure andFunction of Biofilms. Wiley, Chichester, UK, pp. 91–110.

Webster, J.J., Hampton, G.J., Wilson, J.T., Ghiorse, W.C., Leach, F.R., 1985. Determination of microbial cellnumbers in subsurface samples. Ground Water 23, 17–25.

Wilson, J.T., McNabb, J.F., Balkwill, D.L., Ghiorse, W.C., 1983. Enumeration and characterization of bacteriaindigenous to a shallow water-table aquifer. Ground Water 21, 134–142.

factors affecting mass transfer limited biodegradation in saturated porous media

Documents