Mass Transfer Limitation ofBiotransformation: QuantifyingBioavailabilityT O M N . P . B O S M A , * , †

P E T E R J . M . M I D D E L D O R P , ‡

G O S S E S C H R A A , ‡ A N DA L E X A N D E R J . B . Z E H N D E R §

Swiss Federal Institute for Environmental Science &Technology (EAWAG), Limnological Research Center,CH-6047 Kastanienbaum, Switzerland, Department ofMicrobiology, Agricultural University, Wageningen,The Netherlands, and Swiss Federal Institute forEnvironmental Science & Technology (EAWAG),CH-8600 Dubendorf, Switzerland

Biotransformation is controlled by the biochemical activityof microorganisms and the mass transfer of a chemical tothe microorganisms. A generic mathematical conceptfor bioavailability is presented taking both factors into account.The combined effect of mass transfer of a substance tothe cell and the intrinsic activity of the cell using the substanceas primary substrate, is quantified in a bioavailabilitynumber (Bn). The concept can easily be extended tosecondary substrates. The approach has been applied toexplain the observed kinetics of the biotransformation oforganic compounds in soil slurries and in percolation columns.The model allowed us to predict threshold concentrationsbelow which no biotransformation is possible. Dependingon the environmental system and the chemical involved,predicted threshold concentrations span a range of 11 ordersof magnitude from nanograms to grams per liter and matchwith published experimental data. Mass transfersand notthe intrinsic microbial activitysis in most cases the criticalfactor in bioremediation.

IntroductionThe rate at which microbial cells can convert chemicals duringbioremediation depends on two factors: (1) the rate of uptakeand metabolism (the intrinsic activity of the cell); (2) the rateof transfer to the cell (mass transfer). The so-called bio-availability of a chemical is determined by the rate of masstransfer relative to the intrinsic activity of the microbial cells.Much research effort in bioremediation has been spent onthe optimization of the microbes’ activity by the addition ofnutrients or bioaugmentation (1, 2). The lack of success ofmeasures to enhance the intrinsic microbial activities duringbioremediation is often attributed to the reduced bioavail-ability of the chemicals of concern without further investiga-tions. Evidently, increased microbial conversion capacitiesdo not lead to higher biotransformation rates when masstransfer is the limiting factor. This appears to be the rulerather than the exception in most contaminated soils andaquifers.

The bioavailability of a chemical is controlled by a numberof physical-chemical processes such as sorption and des-orption, diffusion, and dissolution (3-6). Particularly in oldpolluted sites, part of the contaminants appear to beinaccessible for biodegradation. For example, no degradationof chlorophenols was observed in a soil that was polluted forover 40 years while chlorophenol degradation proceededrapidly in freshly polluted soil. A freshly added amount ofpentachlorophenol in the old polluted soil, however, wasmineralized instantaneously, indicating that sufficient amountsof chlorophenol-degrading organisms were present (7).Similar results were reported for two soils contaminated withpolycyclic aromatic hydrocarbons (8) and for the reductivedechlorination of hexachlorobenzene in contaminated sedi-ment (9). R-Hexachlorocyclohexane (R-HCH) biotransfor-mation in lysimeters at concentrations below 150 mg/kg couldnot be stimulated by adding nutrients or oxygen, indicatingthat nutrient availability was not limiting. In contrast,treatments involving a rigorous mixing of the soil breakingup the larger soil particles stimulated biotransformationdrastically (10).

All these observations indicate a reduced availability ofpollutants in soils and sediments contaminated for a pro-longed period of time, pollutantsand not nutrientsavailabilitybeing the obvious cause. The decrease of the bioavailabilityin the course of time is often referred to as “ageing” or“weathering”. It may result from (i) chemical oxidationreactions incorporating them into natural organic matter (11-13), (ii) slow diffusion into very small pores and absorptioninto organic matter, or (iii) the formation of semi-rigid filmsaround non-aqueous-phase liquids (NAPL) with a highresistance toward NAPL-water mass transfer (6).

A reduced bioavailability of pollutants in soil is caused bythe slow mass transfer to the degrading microorganisms.Pollutants become unavailable when the rate of mass transferis zero (e.g., in the case of bound residues). A unifying conceptto understand and quantify the limitation of biodegradationby mass transfer kinetics is presented on the basis of themicroscopic distribution of bacteria and contaminants innatural porous media and a simple quantitative expressionfor the threshold concentration resulting from the microbialmaintenance requirements is derived. The concept wasapplied to previously published data on R-HCH biotrans-formation in soil slurries (14) and 3-chlorodibenzofuran(3CDF) biotransformation in percolation columns (15).Estimates of the threshold concentrations show that bacteriamay have a famine existence at polluted sites despite thepresence of high amounts of pollutant.

TheoryMicroscopic Distribution of Microbes and Pollutants in Soil.Soils and aquifers are desolate environments from the pointof view of microbes (Figure 1A). The average distance betweencolonies containing up to 100 individual cells can be estimatedto be at least 100 µm based upon bacterial densities and theobservation that bacteria mainly live in pores with sizes of0.8-3 µm, where they are protected against predation (16-18). On the other hand, pollutants can be present in extremelysmall pores or in pure form, as a solid or liquid. Upon enteringa porous system, they first contaminate the macropores andthe particle surfaces containing relatively few bacteria. Then,they diffuse into smaller pores where biotransformation maytake place when the environmental conditions favor microbialactivity. Pollutants also slowly diffuse into extremely smallpores (, 1 µm) where microorganisms are absent. Afterexposure of a soil to contamination over periods of years ordecades, a considerable part of the organic pollutants will be

* Corresponding author present address: TNO Institute of Envi-ronmental Sciences, Energy Research and Process Innovation, P.O.Box 342, NL-7300 AH Apeldoorn, The Netherlands; phone:+31.55.5493493; fax +31.55.5493201; e-mail: t.bosma@mep.tno.nl.

† EAWAG, Kastanienbaum.‡ Agricultural University.§ EAWAG, Dubendorf.

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in these extremely small pores (19). Part of the pollutantsmay also be present in pure form, as a solid or as NAPL. Asa result, pollutants and bacteria have a different microscopicdistribution in contaminated soil, and pollutants must diffuseto the bacteria before they can be taken up and degraded(Figure 1A).

Kinetics of Mass Transfer Limited Biotransformation:the Best Equation. Pollutant uptake and biotransformationresult in a depletion of organic pollutants close to the bacteria,which in turn leads to a diffusion gradient between thepolluted pores and the surface of the cells (Figure 1B). Byapplying Michaelis-Menten kinetics, the quantity qc (M T-1)of pollutant that is converted by a cell is given as

qmax is the maximum conversion flux that can be achieved bya cell (M T-1), Km is the cell surface concentration yielding1/2qmax (M L-3), and Cc (M L-3) is the concentration at the cellsurface (M L-3). The Michaelis-Menten equation is the basicexpression for the microbial conversion of nutrients. At lowconcentrations (Cc , Km), the kinetics of biodegradation areessentially first order with the ratio qmax/Km as a first-orderconstant. For this reason, first-order expressions are oftenused to describe biodegradation of contaminants in soil,without the awareness however that the first-order kineticsmay be caused by mass transfer kinetics. In order to give ageneric framework, this work relies on the Michaelis-Mentenexpression. Order of magnitude estimates of Km are generallysufficient as input because of its relative insensitivity.

Resupply of pollutantsspossibly after dissolution of thepure solid or liquidstakes place via sorption retardeddiffusion. The quantity qd (M T-1) of pollutant that diffusesto one cell or microcolony is determined by the differencebetween the distant concentration Cd (M L-3) and theconcentration at the cell surface Cc (M L-3), acting as a drivingforce and an exchange constant k (L3 T-1):

The exchange constant k, referred to as the permeability factorin the literature about transport in biological membranes,can often be calculated as the product of a surface area (L2)and a mass transfer coefficient (L T-1), which itself is the ratioof the effective diffusion coefficient Deff (L2 T-1) of the chemical

in the matrix and the diffusion distance δ (L). Table 1 listssome expressions to calculate k for various specific masstransfer mechanisms that may be useful to obtain indepen-dent estimates of k in well-defined systems. In reality, theuptake pathway of pollutants in a soil involves a combinationof various mass transfer mechanisms, e.g., dissolution froma non-aqueous phase followed by sorption retarded diffusionor the mass transfer from a flowing liquid into soil aggregateswhere sorption retarded diffusion takes place. It has beenshown mathematically that the mass transfer from a flowingliquid into structures of variable geometry is best ap-proximated by first-order kinetics as given by eq 1 (20). It isworthwhile to note that the mass transfer coefficient is a scale-dependent property with a tendency to decrease withincreasing scale (21). In situations with complex pathwaysof mass transfer, k can only be inferred from experimentalor field data.

Under conditions of steady state, i.e., qd ) qc, eqs 1 and2 can be combined to yield an expression for the quantity q(M T-1) of pollutant that is transformed by the combinedaction of mass transfer and microbial conversion:

FIGURE 1. (A) Schematic drawing showing the different locations of pollutants and bacteria in a porous system. (B) Graphic representationof the concentration gradient between the bacteria and the pollutants. Concentrations at the cell surface are lower due to biodegradation.Resupply of pollutants requires mass transfer via pathways including dissolution, (sorption retarded) diffusion, and/or mass transfer fromflowing to immobile water.

qc ) qmax

Cc

Km + Cc(1)

qd ) k(Cd - Cc) (2)

TABLE 1. Expressions Used To Calculate the ExchangeConstant k

mass transfer mechanism expressiona

linear diffusion (23) DeffA/δradial diffusion, no advective flow (43) Deff4πR(R + δ)/δradial diffusion, δ . R (43) Deff4πRdissolution kinetics (26, 44) kdAswadvective flow, monolayer of cells on

particles with diffusion layeraround them (15)

ηApU/n

aSymbols that are not explained in the text: R, cell radius (L); kd,dissolution rate constant (L T-1); Asw solid/water contact surface area(L2); η, collector efficiency (-) (45); Ap cross-sectional surface area ofparticles in porous media (L2); U, flow velocity in porous media (L T-1);n, number of bacterial cells per particle in porous media.

q ) qmax

Cd + Km + qmaxk-1

2qmaxk-1 {1 -

[1 -4Cdqmaxk-1

(Cd + Km + qmaxk-1)2]1/2} (3)

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This equation is known as the Best equation (22, 23). Althoughthe steady-state assumption has been used to derive theequation, it is not necessary to impose a condition as stringentas the steady state. Cd and Cc may both change. It is onlynecessary that they maintain the relationship Cc ) Cd - qc/k,which is referred to as quasi-steady-state (22). The Bestequation can be scaled up to the macroscopic level of alaboratory batch or column experiment to describe theaverage biotransformation rate, assuming homogeneity withrespect to physical-chemical and microbial parameters. Thisis done by multiplying the left- and right-hand sides of eq 3by the number of cells per unit of volume. q and qmax arethen expressed in units of mass per volume per unit of time(M L-3 T-1), k is a first-order exchange constant (T-1), and Cd

is the bulk aqueous concentration (M L-3).The Best equation can be rewritten as

with

When C* ) 1, the conversion rate is at its maximum (Q*) 1), i.e., the pollutant is fully available for biodegradation.Lower values of C* indicate less bioavailability (Figure 2). Theimportance of mass transfer relative to the intrinsic activityof the cell is quantified in the bioavailability number Bn, whichis the ratio of the mass transfer rate constant to the microbialspecific affinity qmax/Km. The specific affinity acts as first-order constant of biodegradation when C , Km and deter-mines the ability of microorganisms to reduce the concen-tration of a substrate at the cell surface (24). Calculationswith the Best equation indicate that substrate bioavailabilityreduces faster for cells with a high specific affinity, i.e., lowvalue of qmax/Km, than for cells with a low specific affinity ata given distant concentration (25). Bn expresses control bymass transfer at values less than unity and control by microbialdegradation at values greater than unity. When mass transferis fast compared to biodegradation (e.g., Bn ) 100), Q*exponentially approaches 1 until C* ) 0.5; Q* is always closeto 1 for 0.5 < C* e 1; such a curve represents the behaviorof the Michaelis-Menten equation. In contrast, a linearrelationship exists between C* and Q* at small values (e.g.,Bn ) 0.01). This curve represents the behavior of eq 2.

Intermediate bioavailability numbers result in sigmoidal Q*vs C* plots (as for Bn ) 5).

Ghoshal et al. (26) successfully applied a Damkohlernumber Da to assess the mass transfer control of naphthalenebiodegradation in coal tar. This Damkohler number is theinverse of our bioavailability number for the case of dissolutioncontrolled biodegradation. Bn values for the biodegradationof naphthalene from small coal tar globules appeared to varybetween 0.05 and 0.14, depending on the origin of the coaltar and the specific surface area.

Threshold Concentration for Growth. The biotransfor-mation of a variety of organic pollutants results from theactivity of microorganisms that use them as source of carbonand energy for growth (27-31). Since the growth of suchorganisms in soil and groundwater is directly coupled to therate of biotransformation of the pollutants, it is also limitedby the mass transfer of the pollutants to the cells. Theexpression describing growth under conditions of masstransfer limitation is equivalent to eq 3. Maintenancerequirements can be included analogous to the way it is donein the standard Monod expression (32). Since µ ) qY andµmax ) qmaxY, the specific growth rate can be written as

µ and µmax are the specific and maximum specific growthrates (T-1), and b is the maintenance rate (T-1).

The quantity q of pollutant that is transformed per unitof time is partly diverted to a constant base level maintenanceflux qm (M T-1) while the rest (qg) is used for growth (33):

When the total flux (q) decreases, the maintenance require-ments significantly reduce the flux directed to growth untilq is just enough to meet the maintenance requirements. Cellswill either die or enter a dormant state when the supply rateof substrate cannot meet the maintenance requirementsanymore (34). Hence, a threshold concentration will beobserved as soon as the supply rate, which is given by thediffusive flux, becomes equal to the maintenance require-ments (qd ) k(Ct - Cc) ) qm). When Cc , Ct, Ct (M L-3) isgiven by

Thus, the threshold concentration for growth is inverselyproportional to k and proportional to qm.

Calculations. We applied the Best equation to thebiotransformation of R-HCH in soil slurries (14) and to thesteady state biotransformation of 3-chlorodibenzofuran(3CDF) by Sphingomonas sp. strain HH19k attached to glassbeads in percolation columns (15). The time progress curvesof R-HCH biotransformation were calculated using a com-mercially available spreadsheet program. Equation 3 wasused to calculate the biotransformation rate in 0.1-h intervals,and the R-HCH-concentration was updated accordingly. Inthe calculations of 3CDF biotransformation in columns withSphingomonas sp. strain HH19k, the columns were dividedin 1000 sections. Homogeneous conditions were assumedfor each. Equation 3 was used to calculate the degradationin each column section on the basis of the qmax [19.6 nmolmin-1 mg of protein)-1] and Km (265 nmol/L) of the cells, thek value for the particular experiment, the influent concentra-tion, the protein content of the section, and the flow rate.Relevant values were taken from the original study. The kvalue for each experiment was calculated by applying the last

FIGURE 2. Plot of the dimensionless conversion rate Q* vs thedimensionless concentration C* at Bn values of 0.01, 5, and 100. Q*expresses the conversion rate normalized to qmax while C* can beviewed as the bioavailable concentration. When C* ) 1, theconversion rate is at its maximum (Q* ) 1), i.e., the pollutant is fullyavailable for biodegradation. Lower values of C* indicate lessbioavailability.

Q* ) 1 + Bn-1

2(1 - C*){1 - [1 - 4C*1 - C*

1 + Bn-1]1/2} (4)

Q* ) q/qmax

C* ) Cd(Cd + Km + qmaxk-1)-1 (5)

Bn ) k/qmaxKm-1

µ ) µmax

Cd + Km + qmaxk-1

2qmaxk-1 {1 -

[1 -4Cdqmaxk-1

(Cd + Km + qmaxk-1)2]1/2} - b (6)

q ) qg + qm (7)

Ct ) qm/k (8)

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expression of Table 1. The effluent concentration of onespecific column section was used as the influent concentrationof the next.

Results and DiscussionThe biotransformation of sorbed R-HCH in soil slurries wasshown to be limited by desorption kinetics (14). The kineticsof mass transfer were varied by applying two different mixingprocedures. Mass transfer was slowest when the slurries weregently mixed in an end-over-end mixer. In contrast, masstransfer was facilitated when the slurries were vigorouslystirred on a magnetic stirrer. We applied eq 3 to simulate theR-HCH data and compared the results with calculations thatignore mass transfer (Figure 3). The first-order estimates ofthe desorption rates (k) were 0.010 h-1 for the end-over-endmixed and 0.018 h-1 for the stirred incubations, respectively(14). The microbial parameters of the system were takenfrom independent studies: qmax ) 3.04 mg L-1 h-1; Km ) 8.5mg/L (35). Based on these parameter values, the values ofBn were 0.016 and 0.030, respectively, indicative of masstransfer limitation. At the start of the experiments the valuesof C* were 0.56 and 0.70, respectively, which indicates thatR-HCH availability was limited throughout the experiments.The calculations with the Best equation describe the datavery well, clearly demonstrating its validity for the descriptionof desorption limited biodegradation.

Harms and Zehnder studied the biotransformation of3CDF by Sphingomonas sp. strain HH19k attached to glassbeads in percolation columns (15). They did experiments atseveral flow rates and cell densities resulting in various valuesof the mass transfer coefficient. Furthermore, they variedthe 3CDF concentration in the column influents. Biodeg-radation was quantified by comparing influent and effluentconcentrations. We analyzed these results with the Bestequation. The observed overall activities in the columnexperiments were overestimated when k was estimatedcompletely independently with the last expression of Table1 (Figure 4). We therefore used the data from one of theexperiments (indicated by the open circle in Figure 4) toestimate the collision efficiency η. The fitted value was 0.0045while the independent estimates for the various experimentswere in the range 0.2-0.8. The k values for the otherexperiments were extrapolated by applying the fitted valueof η in the last expression of Table 1. Thus, the overall activitiesobserved in the other column experiments were correctlypredicted (Figure 4). The values of Bn were in the range0.08-0.7 depending on the flow rate and the cell densities.The independent estimates of k would have resulted in 2orders of magnitude higher values, indicating that no masstransfer limitation would have been expected on the basis ofthe application of state of the art expressions for mass transferin percolation columns. We found similar discrepanciesbetween predicted and actual mass transfer limitations during

3-chlorobenzoate degradation in percolation columns withPseudomonas sp. strain B13 (Tros, M. E.; et al., unpublisheddata). The reasons for these discrepancies remain to beclarified.

Figure 5 graphs the calculated threshold concentration asa function of the mass transfer coefficient in the range from10-8 to 10-16 cm3 s-1. The extremes represent the diffusionof hydrophilic organic compounds in water (10-8 cm3 s-1)and of hydrophobic compounds in structured soil (10-16 cm3

s-1). A variation of 8 orders of magnitude of the residualconcentration may be expected based on published valuesof the effective diffusion coefficient Deff that were used toestimate k (14, 19, 36). The difference between the upperand lower line stands for the variation of threshold concen-trations that are the result of differences in metabolicefficiency between bacterial species. qm ≈ 10-11 µg/s forcopiotrophic bacteria adapted to high nutrient concentrationswhereas qm ≈ 10-14 µg/s for oligotrophic bacteria, which areadapted to extremely low nutrient concentrations and whichare very efficient in their metabolism (37-39). The resultingvariation in residual concentration is 3 orders of magnitude.The overall variation of the estimated residual concentrationsis as large as 11 orders of magnitude, with a lower limit ofabout 1 ng L-1 and an upper limit of 100 g L-1.

Only few data are available relating mass transfer toresidual concentrations that remain after biotransformation.An estimation of the residual concentration depends on theavailability of estimates of the numbers of pollutant-degradingbacteria in the system considered. We included some datafrom the HCH study (10, 14) in Figure 5 to illustrate the validity

FIGURE 3. Simulation of the biodegradation of r-HCH in stirred (2)and end-over-end mixed (b) soil slurries using the Best equation(solid lines) and the Michaelis-Menten equation without masstransfer (dashed lines).

FIGURE 4. Prediction of 3CDF biodegradation by cells of Sphin-gomonas sp. strain HH19k attached to glass beads in percolationcolumns using the Best equation: (2) completely independentpredictions; (b) extrapolations using the collision efficiency η fromthe fit of one column experiment (indicated by O). The graph comparespredicted and measured effluent concentrations. The solid linerepresents a correct prediction of the measured data.

FIGURE 5. Threshold for growth as a function of the mass transfercoefficient. The extremes represent the diffusion of hydrophilicorganic compounds in water (10-8 cm3 s-1) and of hydrophobiccompounds in structured soil (10-16 cm3 s-1). (2) data from ref 14;(b) data from ref 10.

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of the estimates of Ct. The exchange constants k wereestimated by dividing the first-order estimates of the HCHdesorption rates by the number of HCH-degradating cells asreported in the publications. The rate of HCH desorption inthe experiments by Doelman et al. (10) was estimated as 10-5

h-1, assuming that the rate constant is inversely proportionalto the particle size. All data are within the range of estimatedvalues of Ct. More evidence for the validity of the derivedexpression for residual or threshold concentrations is providedby the observation that biotransformation of chlorobenzenesin columns packed with sediment from a dune infiltrationarea resulted in residual concentrations that were positivelycorrelated with the hydrophobicity of the compound (40).Residual concentrations varied from 0.03 µg L-1 for chlo-robenzene to 0.05-0.4 µg L-1 for dichlorobenzenes and 2.6µg L-1 for 1,2,4-trichlorobenzene. These differences may beexplained by the decreased mass transfer efficiencies of thestronger sorbing compounds.

Understanding the principles of bioavailability is ofconsiderable advantage for assessing the suitability of bio-logical remedial measures for the cleanup of polluted soilsand aquifers. The mathematical concept presented hereallows the estimation of (i) to what extent such measuresmay be hampered by either the intrinsic microbial activityor the mass transfer and (ii) whether the contaminantconcentrations are already below a site-specific thresholdconcentration (Figure 5). Microbial limitations can beovercome by either improving environmental conditions (e.g.,with nutrients or electron acceptors) orsin some instancessthe augmentation of the microbial population with desiredmicrobes (1, 2). However, a critical analysis of bioremediationdata reveals that the intrinsic microbial activities limitbioremediation only in a few cases. In most cases masstransfer limitation prevented the full exploitation of themicrobial degradative potential. Technical measures areneeded to change the physical structure of the contaminatedmaterial, which enhances the bioavailability and lowers thethreshold concentrations of pollutants. This can be done insitu, but costly ex situ operations are generally required (10).Another possibility would be the addition of surfactants. Thisis the topic of an ongoing discussion that goes beyond thescope of this paper. The addition of surfactants seems tostimulate biodegradation in some cases while having aninhibitory effect in others (41). It is also conceivable to turnthe problem around and to stimulate the immobilization ofpollutants by bound-residue formation instead (42).

A reduced bioavailability causes bacteria to live a famineexistence at polluted sites, even at high pollutant concentra-tions. Our concept of bioavailability provides a tool to helpevaluate the potential risk of soil and groundwater pollution.The decision to remediate should also be based on theconsideration that pollutants that are hardly available arealso less toxic (42), while the cost of their removal is veryhigh.

AcknowledgmentsP.J.M.M. was supported by the Netherlands Integrated SoilResearch Programme. We thank Hauke Harms for criticaldiscussions and providing raw data. We thank D. Imboden,A. Sinke, M. Tros, and O. Wanner for critical review and J.Davis for editing the manuscript.

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Received for review May 1, 1996. Revised manuscript receivedAugust 28, 1996. Accepted August 28, 1996.X

ES960383U

X Abstract published in Advance ACS Abstracts, November 1, 1996.

252 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 31, NO. 1, 1997