Prediction of Complete Bio Remediation Periods for PAH Soil Pollutants in Different Physical States by Mechanistic Models

7/31/2019 Prediction of Complete Bio Remediation Periods for PAH Soil Pollutants in Different Physical States by Mechanistic

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Prediction of complete bioremediation periods for PAH soil

pollutants in dierent physical states by mechanistic models

H. Mulder a,b, A.M. Breure a,*, W.H. Rulkens b

a Laboratory for Ecotoxicology, National Institute for Public Health and the Environment, P.O. Box 1, Bilthoven 3720 BA,

The Netherlandsb Department for Environmental Technology, Wageningen Agricultural University, P.O. Box 8129, Wageningen 6700 EV,

The Netherlands

Received 17 July 1999; accepted 19 May 2000

Abstract

Mass-transfer models and biodegradation models were developed for three theoretical physical states of polycyclic

aromatic hydrocarbons (PAHs) in soil. These mechanistic models were used to calculate the treatment periods nec-

essary for complete removal of the PAH pollutants from the soil under batch conditions. Results indicate that the

bioremediation of PAHs in such systems is mainly mass-transfer limited. The potential for bioremediation as a

treatment technique for PAH contaminated soils is therefore mainly determined by the mass-transfer dynamics of

PAHs. Under mass-transfer limited conditions simplied mathematical models, based on the assumption of a zero

dissolved PAH concentrations, can be used to predict the period of time needed for complete bioremediation. 2001Elsevier Science Ltd. All rights reserved.

Keywords: Bioavailability; Biodegradation; Mass-transfer; PAH; Physical states; Modeling

1. Introduction

The physical states in which polycyclic aromatic

hydrocarbons (PAHs) are present in soil mainly

determine the potential of remediation techniques. It

must be analyzed whether the mobility requirements ofpossible remediation techniques can be met in and by

the physical state of the contaminant in the soil

matrix.

Bioremediation is a clean-up technology that was

initially presumed to have great potential, but it became

evident that just like the physical and chemical treatment

techniques for polluted soil, biological methods had

their disadvantages. Long treatment periods and high

residual concentrations were the main problems. This is

especially true for PAH-polluted soil. Because of their

hydrophobicity and low water solubilities, PAHs

strongly interact with the soil matrix and can even form

separate phases. Microorganisms can only degrade dis-

solved PAHs and so they have to be released from thesolid phase to an aqueous phase in which they are

available. As a result of low mass-transfer rates in the

soil matrix, this release is often limiting the eectiveness

of bioremediation and we speak of a reduced bioavail-

ability of the pollutants causing the reduced eective-

ness.

On a theoretical basis, several simplied states of

PAHs in soil have been suggested (Fig. 1) and mass-

transfer models are formulated to describe the release of

PAHs from these dierent states to obtain an estimated

time in which the PAHs concentration can be reduced

by leaching processes (Rulkens and Bruning, 1995). The

same procedure can be applied to bioremediation pro-

Chemosphere 43 (2001) 10851094

* Corresponding author. Tel.: +31-30-274-3068; fax: +31-30-

274-4413.E-mail address: [email protected] (A.M. Breure).

0045-6535/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 4 5 - 6 5 3 5 ( 0 0 ) 0 0 1 8 5 - 5


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cesses when microbial kinetics is incorporated into these

models. Mathematical simulations of the combined

mass transfer and microbiological conversion indicatethe time needed to reduce the concentrations of the

dierent PAHs to certain levels. Hereby, the potential of

bioremediation can be estimated and decisions can be

made whether or not bioremediation should be

attempted.

The aim of this paper is to translate the theoretical

considerations concerning the mass transfer of hydro-

phobic pollutants in dierent physical states in the soil

to the situation where microorganisms can degrade the

contaminants. The eect of several model parameters on

the availability of pollutants towards microbial popu-

lations is illustrated with the results of mathematical

simulations with model PAHs.

2. Physicochemical properties of PAHs

PAHs are extremely hydrophobic compounds due to

the absence of polar groups on the molecules. This re-

sults in very low water-solubilities and high octanol

water partitioning coecients (Table 1). Besides the

solubility C and the octanolwater partitioning coef-cient Kow, there is little dierence in the values of theother physicochemical properties of the PAH listed in

Table 1. Because diusion coecients depend mainly on

the molar volume of the diusing solute (Bird et al.,

1960), the decrease of the diusion coecient with an

increased number of aromatic rings is relatively small.

Due to their hydrophobic nature, PAH have high solu-

bilities in hydrophobic organic solvents. Because emis-

sions of PAHs are often accompanied by spills of non-

aqueous-phase-liquids, this is of importance for thephysical state in which PAHs are present in the soil

(Ghoshal and Luthy, 1998).

3. Physical states of pollutants

In an earlier study on the eect of physical states of

soil pollutants on the remediation potential of physical

separation processes (Rulkens and Bruning, 1995), six

simplied physical states for soil contaminants were

proposed on a theoretical basis. In this work, three of

these states (Fig. 1) are further analyzed as far as the

C dissolved PAH concentration in the pores

(kg m3)C mean contaminant concentration (kg m3)

C solubility of the PAH (kg m3)

Cb dissolved PAH concentration in the bulk liq-uid phase (kg m3)

Ci initial dissolved PAH concentration (kg m3)

CR0 dissolved PAH concentration at the surface of

the particle (kg m3)

DAB diusion coecient of the PAH in water

(m2 s1)

Deff eective diusion coecient (m2 s1)

D0eff overall eective diusion coecient (m2 s1)

foc fraction organic carbon in the soil matrix ()

Fo Fourier number ()

k mass-transfer coecient (m s1)

K sorption coecient (m3 kg1)

Koc organic carbon partition coecient (L kg1)

Kow octanolwater partition coecient ()

Ks Monod constant (kg m3)

N ux of the dissolved PAH over a stagnant

uid layer at the solidliquid interface

(kg m2 s1)

Ns mass ux from the particle (kg m2 s1)

NT total mass ux (kg s1)

Q concentration in the solid phase (kg kg1)

r coordinate in the direction of transport (m)

R radius of PAH particle (m)Rcf radial location of the contaminant front (m)

Ri initial particle radius (m)

R0 particle radius (m)

t time (s)

V volume per particle (m3)

X biomass concentration in the bulk liquid (kg

m3)

Xi initial biomass concentration (kg m3)

Y yield coecient (kg kg1)

Greeks

e particle porosity (m3 m3)

l growth rate (s1)lmax maximum growth rate (s

1)

q density of PAH particle (kg m3)

qs solid matrix density (kg m3)

s period to achieve a 99% reduction of PAH

pollution (s)

Fig. 1. Schematic presentation of three proposed physical

states of PAHs in soil particles and mathematical parameters.

Solid-phase PAH as: pure particle (I), pure solid in a pore (II)

and sorbed into a soil aggregate (III).

1086 H. Mulder et al. / Chemosphere 43 (2001) 10851094


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inuence on the bioavailability and bioremediation po-

tential is concerned.For simplicity sake, only one-component PAH

contamination is considered. The presence of non-

aqueous-phase-liquids, which were mentioned before is

neglected. However, with the methodology followed in

this study, such systems can also be described by in-

corporating for instance the partitioning of PAHs into

an organic phase. The considered physical states are:

solid PAH particles, PAHs which have formed pure

solid phases in the pores of porous soil aggregates and

PAHs that are intrapartically sorbed to soil organic

matter. The rst two states are likely to be found in

heavily contaminated situations (hot spots), whereasthe latter state is probable when diusive emissions

occurred. At hot spots, PAHs are often transported in

high concentrations into the soil by lighter hydrocar-

bons like, for instance, gasoline (Wilson and Jones,

1993). The lighter compounds disappear faster than the

PAHs, which can lead to over-saturation and the for-

mation of separate phase PAHs.

4. Mathematical models

In this section, three mass-transfer models arepresented to describe the uxes of the contaminant

from polluted particles to the bulk aqueous phase in

which biodegradation is possible. These models are

based on a mathematical description of microbial de-

gradation kinetics and of mechanistic processes, using

data on the physicochemical properties of the con-

taminant and the porous soil matrix (e.g., situations II

and III, Fig. 1). The models describe the ux of

contaminant from the spherical polluted particles to

the bulk liquid and the loss of pollutant from these

particles and the biodegradation. The decrease in de-

gree of contamination can therefore be calculated as a

function of time.

4.1. Microbial growth and degradation kinetics

The growth of biomass on the contaminant dissolved

in the bulk liquid phase can be described according to

Monod kinetics. The growth rate is then expressed as a

function of the maximal growth rate, the Monod con-

stant and the dissolved PAH concentration in the bulk

liquid phase

l lmaxCb

Cb Ks; 1

where l is the growth rate (s1), lmax the maximum

growth rate (s1), Ks the Monod constant (kg m3), and

Cb is the dissolved PAH concentration in the bulk liquidphase. The development of the specic organisms

growing on the dissolved PAH in time can be described

by

dX

dt lX 2

with

X Xi at t 0 I:C:; 3

where t is the time (s), X the biomass concentration inthe bulk liquid (kg m3), and Xi is the initial biomass

concentration (kg m3). When the dissolved PAH con-

centration is high compared to the anity constant, the

biomass concentration increases exponentially in time

due to zero order kinetics. When the PAH concentration

is low compared to Ks (Eq. (1)), rst order kinetics are

observed. The degradation of dissolved PAHs is coupled

to biomass growth by the yield coecient. In the case

that there is no supply of PAHs from the soil to the

liquid this gives

dCb

dt

1

Y

dX

dt

lX

Y ; 4

Table 1

Physicochemical properties (at 30C) of some PAHs

MWa

(g mol)

Densitya

(103 kg m3)

DABb

(1010 m2 s1)

C c

(kg m3)

log Kowc ()

Naphthalene 128 1.03 9.31 0.0317 3.37

Acenaphtylene 152 0.899 8.35 0.00393 4.07Fluorene 166 1.20 7.88 0.00198 4.18

Phenanthrene 178 0.980 7.70 0.00129 4.46

Anthracene 178 1.28 7.70 0.000073 4.45

Pyrene 202 1.27 7.05 0.000135 5.32

Fluoranthene 202 1.25 6.90 0.00026 5.33

Chrysene 228 1.27 6.44 0.000002 5.61

a Adapted from Weast (1974).b Calculated values (Bird et al., 1960).c Adapted from Sims and Overcash (1983).

H. Mulder et al. / Chemosphere 43 (2001) 10851094 1087


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where Y is the yield coecient (kg kg1). When there is

a supply of dissolved PAHs to the bulk liquid by dis-

solution or desorption, an additional term describing

this mass transfer must be incorporated in Eq. (4). In

this model for biodegradation of contaminants by

specic populations, the growth of the microorganismson other carbon sources is neglected for the sake of

simplicity.

4.2. Dissolution of solid PAH particles and subsequent

biodegradation

The dissolution of PAHs particles in a well-mixed

bulk liquid phase can be described by simple mass-

transfer equations. The ux of a PAH to the bulk liquid

phase is described by

N

k

C

C

b; 5

where Nis the ux of the dissolved PAH over a stagnant

uid layer at the solidliquid interface (kg m2 s1), k

the mass-transfer coecient (m s1), and C is the sol-

ubility of the PAH (kg m3). The mass-transfer coe-

cient k depends on hydrodynamic conditions and for

small particles or large particles at low relative velocities,

the value of this parameter can be approximated by

k DAB

R; 6

where DAB is the diusion coecient of the PAH in

water (m2 s1), and R is the radius of the PAH particle

(m). The decrease in the particle radius in time can be

expressed by

dR

dt

DAB

qRC Cb 7

with

R Ri at t 0 I:C:; 8

where q is the density of the PAH particle (kg m3) and

Ri is the initial radius of the particle (m). A mass balance

for one dissolving PAH particle with subsequent bio-degradation in a space element with a volume of V (m3)

is used to describe the evolution of the dissolved bulk

PAH concentration in time

dCb

dt

4pRDAB

VC Cb

lX

Y9

with

Cb 0 at t 0 I:C: 10

When the dissolved PAH concentration Cb is zero, thefollowing expression can be obtained from Eq. (7) for

the period s that is necessary to achieve a 99% re-

duction (dened as complete removal) of the original

PAH volume (Rulkens and Bruning, 1995):

s 0:95qR2i2DABC

: 11

4.3. Dissolution of PAH from lled pores and subsequent

biodegradation

In the case of pure solid-phase contaminant located

in the pores of a soil particle (Fig. 1; state II), the dis-

solution of PAHs from these pores to the bulk liquid

phase can be described with the `shrinking-core model'.

In this model, the contaminant front located at Rcfmoves inward as a result of the compound ux to the

bulk. The interactions of the dissolved PAHs in the

pores are neglected. Assuming pseudo-steady-stateconditions, the total mass ux of pollutant through the

pores between Rcf and R0 to the solidliquid interface

can be described by

NT 4pr2Deff

dC

drRcf6 r6R0; 12

where r is the coordinate in the direction of transport

(m), NT the total mass ux (kg s1), Deff the eective

diusion coecient through the water lled section of

the pores (m2 s1), Rcf the location of the contaminant

front (m), R0 the radius of the particle (m), and C is the

dissolved PAH concentration in the pores (kg m3).

Several empirical, semi-empirical, and theoretical rela-

tions that describe the inuence of pore geometry (pore

tortuosity and constrictivity) on eective diusion coef-

cients have been reported in literature (Van Brakel and

Heertjes, 1974; Wu and Gschwend, 1986). In this work,

the eective diusion coecient is expressed as a func-

tion of the aggregate porosity e and the diusion co-ecient of the PAH in water DAB (Van Brakel andHeertjes, 1974)

Deff 0:66eDAB; 13

where e is the particle porosity (m3 m3). Eq. (12) can be

integrated between Rcf and R0 assuming that NT is

constant due to the pseudo-steady-state conditions. The

total mass ux from the particle solidliquid interface to

the bulk liquid can also be described by

NT 4peR20kCR0 Cb; 14

where k is dened in Eq. (6) and CR0 is the dissolved

PAH concentration at the surface of the particle (kg

m3). Elimination of CR0 , by using the integrated Eqs.

(12) and (14), yields the following expression for the

total mass ux to the bulk liquid:



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NT 4pR20eDeffk

Deff 1

Rcf 1

R0

R20ek

C Cb: 15

The change of the location of the contaminant front as a

function of time can be formulated by

dRcf

dt

R20Deffk

qR2cf Deff 1

Rcf 1

R0

R20ek

h i C Cb 16

with

Rcf R0 at t 0 I:C: 17

The concentration in the bulk liquid phase is described

by an equation that follows from a mass balance:

dCb

dt

4peR20Deffk

V Deff 1

Rcf 1

R0

R2

0ekh i C

Cb lX

Y18

with

Cb 0 at t 0 I:C: 19

The period s necessary to degrade 99% of the pollutantfrom relatively large particles (k ) Deff=R0) at a zerodissolved bulk-liquid PAH concentration can be de-

duced from Eq. (16)

s 0:98qeR206DeffC

: 20

4.4. Desorption from porous particles and subsequent

biodegradation

Concentration proles in porous particles, of radius

R0, with intrapartically sorbed PAHs can be described

with the following partial dierential equation (Wu and

Gschwend, 1986; Mulder et al., 1997):

oC

ot

Deff

e 1 eqsK

o2C

or2

2

r

oC

or

06 r6R0; 21

with

oC

or 0 at r 0 B:C:; 22

C Cb at r R0 B:C:; 23

C Ci for 06 r< R0; and Cb 0 at t 0 I:C:;

24

where qs is the solid matrix density. The eective diu-

sion coecient is dened by Eq. (13). The sorption co-

ecient K describes the linear partitioning of the

pollutant over the solid and liquid phase

Q KC; 25

where Q is the concentration of the sorbed pollutant in

the solid phase which is in local equilibrium with the

dissolved concentration. The sorption coecient of hy-

drophobic compounds like PAHs can be related to thefraction organic carbon foc in the soil matrix and theorganic carbon partition coecient Koc, by Karickhoet al. (1979)

K focKoc

1000; 26

where foc is the organic carbon fraction in the soil and

Koc is the organic carbon partition coecient (L kg1).

The organic carbon partition coecient can be corre-

lated to the octanolwater partition coecient by em-

pirical relations similar to the following (Karickho

et al., 1979; Chiou et al., 1998):

log Koc log Kow 0:21; 27

where Kow is the octanolwater partition coecient.

Often, an overall eective diusion coecient is dened

(Wu and Gschwend, 1986; Ball and Roberts, 1991),

which includes the sorption term in Eq. (21)

D0eff Deff

e 1 eqsK; 28

where D0eff is the overall eective diusion coecient (m2

s1). The ux of the dissolved PAH at the surface of theporous particle to the liquid phase can be described by

the following expression:

Ns DeffoC

or

rR0

; 29

where Ns is the mass ux from the particle (kg m2 s1).

It is assumed that external mass-transfer resistances are

negligible. Analogous to the two earlier models, the

evolution of the dissolved bulk PAH concentration can

be described by a mass balance incorporating the ux of

the pollutant to the bulk liquid (of volume V per parti-

cle) and the degradation by microorganisms:

dCb

dt

4pR20Ns

VlX

Y30

with

Cb 0 at t 0 I:C: 31

At high values for the Fourier number Fo > 0:02 and aconstant zero bulk-liquid PAH concentration, the ratio

between the mean contaminant concentration C andthe initial concentration Ci can be calculated by(Crank, 1975)



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C

Ci

6

p2

XIn1

1

n2en

2p

2Fo 32

with

Fo D0

efftR20

: 33

The period that is necessary to remove 99% of the pol-

lutant from a relatively large porous particle can then be

evaluated from

s 0:42R20

D0eff: 34

4.5. Numerical approximation

The models described in the previous sections cannotbe solved analytically due to the non-linearity of the

coupled (partial) dierential equations (Eqs. (2), (7), (9),

(16), (18), (21) and (30)). However, these equations can

be numerically integrated to calculate the development

of the variables R;Rcf;Cb;X in time on the basis of theinitial conditions. For the rst two models, a fourth-

order RungeKutta routine was programmed in FOR-

TRAN to calculate the values of the model variables as a

function of time (Press et al., 1992). The third model was

solved numerically with the appropriate boundary con-

ditions, using a CrankNicholson scheme (Press et al.,

1992) programmed in a FORTRAN routine.

5. Results and discussion

5.1. Biodegradation of PAH particles

When PAH pollutants have formed separate solid

particles in the soil, the radius of the PAH particle and

the solubility of the PAHs determine the time needed for

the nearly complete dissolution (99%) of the particle at a

maximum driving force for dissolution (Rulkens and

Bruning, 1995). It was expected that these factors also

determine the potential of bioremediation and severalmathematical simulations were performed to study this

eect (Fig. 2). In these simulations, PAH concentrations

of 1000 mg kg1 dry weight of soil and slurry concen-

trations of 1:10 (m3 soil) (m3 aqueous phase)1 were

assumed. The microbiological parameters were opti-

mized so mass-transfer limited biodegradation was as-

sured. Values of maximum growth rates varied between

1:3 104 s1 for naphtalene and 1:0 105 s1 forphenanthrene degradation, respectively, which are fea-

sible values (Keuth and Rehm, 1991; Boldrin et al.,

1993; Volkering, 1996; Mulder et al., 1998). Due to the

lack of literature data, the value for the Monod constant

is assumed to be a factor hundred less than the solubility

of the PAH under consideration. The yield was assumed

to be 0.5 kg kg1 which is a common value for micro-

organisms that can use the PAH as sole source of energy

and carbon (Volkering, 1996). The values in Table 1 are

used for the physical properties of the PAHs (density,

solubility, and diusion coecient).

Results (Fig. 2) show that, indeed, the particle radius

of the PAHs is of great eect on the period s that isrequired for 99% biodegradation of the contaminant.

Because the microbiological kinetics were optimized,dissolved aqueous-phase concentrations were very low

during degradation of the particles. Therefore, the times

calculated for complete degradation of the pollutants by

bacteria are the same to the dissolution times calculated

in earlier work (Rulkens and Bruning, 1995) (Eq. (11)).

However, to assure mass-transfer limited growth

conditions, certain microbiological conditions must be

met. This is illustrated with Fig. 3, where the eect of the

maximal growth rate and the initial biomass concen-

tration was determined in calculations on the biodeg-

radation of a naphthalene particle. Here, a value for the

Monod constant (4:0 105

kg m3

) was used fromliterature (Volkering et al., 1992) and the yield was as-

sumed to be 0.5 kg kg1. The upper value for the max-

imum growth rate (1:3 104 s1) was experimentallydetermined (Mulder et al., 1998) and the upper value of

the inoculum size (1:0 101 kg m3) is a feasible bac-terial density. The plateau in the value of s (Fig. 3)

shows that an increase of microbiological capacity

(maximal growth rate, initial biomass concentration),

does not necessarily result in a shorter treatment period.

In fact, this plateau indicates that the removal of PAH

was mainly mass-transfer limited instead of microbio-

logically limited. From the development of the biomass

in time (data not shown), it could be seen that the period

Fig. 2. Inuence of initial particle radius Ri and compound

identity on the period needed for complete biodegradation sof pure PAH particles.



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necessary to build up sucient biodegradation capacity

increased with a decreasing inoculum size and a de-

creasing maximum growth rate.

5.2. Biodegradation of PAH dissolving from lled pores

Simulations in which microbial conditions were op-

timized, similar to those described in the previous sec-

tion, were performed with the shrinking-core model,where justied, values for the model parameters (degree

of contamination, maximum growth rate, yield, Monod

constant) were identical to those used to construct Fig.

2. In contrast to the rst model, external mass-transfer

limitations are negligible in the calculation with the

shrinking-core model. The results indicate that treat-

ment periods for both physical states are similarly af-

fected by particle radius and compound properties. This

agrees with calculations performed on the mass-transfer

dynamics in these two dierent systems (Rulkens and

Bruning, 1995) (Eqs. (11) and (20)). Only the eect of the

pore geometry on the eective diusion coecient (Eq.(13)) results in longer treatment periods for PAH located

in the pores of porous particles compared to particulate

PAHs.

Experimental work on the inuence of mass transfer

on the biodegradation and bioavailability of PAHs has

been done earlier for solid state PAHs (Volkering et al.,

1992; Volkering, 1996; Mulder et al., 1998) and sorbed

PAHs in porous matrices (Volkering, 1996; Mulder et

al., 1997). In these studies, the eect of the physical

states of PAHs on the development of dissolved PAH

and biomass concentrations were measured and mod-

eled. It was shown that the models could predict the

biodegradation and mass-transfer processes in well-

dened experimental systems that were designed to

mimic the physical states of PAH pollutants in the two

situations. However, such experiments have not been

performed on the system in which pores of porous

particles are lled with solid-phase PAH. Therefore, we

have now calculated the evolution in time of the con-taminant front, the biomass and dissolved PAH con-

centration for the batch degradation of solid-phase

naphthalene located in the pores e 0:05 of a 250 or500 lm soil particle at a high external mass-transfer

coecient k ) Deff=R0 (Fig. 4). Here, a solid to liquidratio of 1:100 (m3 soil) (m3 aqueous phase)1 was as-

sumed and, initially, the pores of the soil aggregate were

completely lled with the pollutant.

To illustrate the phenomena that occur when the

biodegradation is subsequently microbiologically limited

and mass-transfer limited, a maximum growth rate of

1:3 105

s

1

was used in combination with a low initialbiomass concentration (1:0 104 kg m3). The yieldwas again 0.5 kg kg1 and the Monod constant was a

factor of hundred less than the naphthalene solubility

(3:17 104 kg m3). The results in Fig. 4 are verysimilar to experimental ndings with respect to the

biodegradation of pure solid-phase PAHs (Volkering,

1996; Mulder et al., 1998). In such batch experiments an

initial microbiologically limited degradation phase was

observed with relatively high dissolved PAH concen-

trations. Thereafter, the biodegradation capacity ex-

ceeds the mass-transfer rate due to the increased

biomass concentration. At the transition point between

reaction and mass-transfer limited biodegradation, thedissolved PAH concentration becomes very low and the

driving force for mass transfer from the particle to the

bulk liquid is maximized. Although the dissolved PAH

concentration is very low during the mass-transfer

Fig. 4. Eect of particle radius (250 lm, closed symbols or 500

lm, open symbols) on the batch biodegradation of naphtha-

lene, dissolving from the pores of a soil particle: development of

bulk biomass (X; circles) and dissolved naphthalene (Cb; dia-

monds) concentrations and the contaminant front (Rcf

; trian-

gles) in time.

Fig. 3. Eect of maximal growth rate lmax and initial biomassconcentration Xi on the period needed for complete biodeg-radation s of a 100 lm naphthalene particle.



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limited degradation phase, the biomass concentration

still increases due to the partial conversion of contami-

nant to biomass. The maximization of the driving force

for mass transfer by reducing the dissolved PAH con-

centration to a very low value from the transition point

onwards results in great similarity between treatmentperiods calculated on the basis of mass-transfer models

solely (Rulkens and Bruning, 1995).

5.3. Biodegradation of PAH desorbed from porous

particles

When PAHs are sorbed into porous particles, the

description of the ux of the desorbed contaminant to

the bulk liquid becomes somewhat more complicated

compared to the other two systems with solid-phase

PAHs. To investigate whether the simple mass-transfer

models in a earlier study (Rulkens and Bruning, 1995)(Eq. (34)) are also valid to indicate the period needed for

complete bioremediation of such contaminated soils,

simulations were performed with the biodegradation-

desorption model presented. Sorption coecients Kwere calculated on the basis of an organic carbon con-

tent of 5% foc 0:05 and by application of Eqs. (26)and (27). A solid-phase density of 2:0 103 kg m3 wasused. The initial sorbed PAH concentration was calcu-

lated from the sorption coecient and the maximum

solubility. Thus, the initial level of contamination was

maximum for sorbed PAH. Overall eective diusion

coecients were calculated on the basis of Eq. (13) and

external mass transfer was neglected k ) Deff=R0. As aresult of the sorption term in Eq. (28), overall eective

diusion coecients were signicantly lower than the

eective diusion coecients and varied from

1:6 1013 to 1:6 1014 m2 s1. These values are inagreement with literature data on overall eective dif-

fusion coecients of hydrophobic compounds in soil

aggregates (Wu and Gschwend, 1986; Rijnaarts et al.,

1990; Chung et al., 1993). Again, the maximum growth

rate of the naphthalene degrading organisms was as-

sumed to be 1:33 104 s1 and Monod constant was4:0 106 kg m3 (Volkering et al., 1992). The initial

biomass concentration was 1:0 104

kg m3

and ayield of 0.5 kg kg1 was assumed. A solid to liquid ratio

of 1:100 (m3 soil) (m3 aqueous phase)1 was assumed

with a soil solid density of 2:0 103 kg m3. Resultsshow (Fig. 5) that simple mass-transfer models (Eq. (34))

can adequately predict the period of time needed to

lower the total PAH concentration in the particle to a

level of 1% of the initial amount.

Under mass-transfer limited biodegradation condi-

tions, an increase of PAH sorption K or the particleradius R0 signicantly increases the period needed forcomplete removal of the PAHs. Because the sorption to

hydrophobic material increases signicantly with in-

creasing PAH molecular weight (Table 1), relatively

longer bioremediation periods are needed for removal of

the high-molecular weight PAHs (Fig. 6). The overall

eective diusion coecients e 0:05;foc 0:05 werecalculated with Eqs. (13), (26)(28) and were:

2:24 1013, 4:00 1014, 2:93 1014, and1:50 1014 m2 s1 for naphthalene, acenaphtylene,uorene, and phenanthrene, respectively. Again, a solid

to liquid ratio of 1:100 (m3 soil) (m3 aqueous phase)1

was assumed with a soil solid density of 2:0 103 kg

Fig. 5. Period s needed for 99% naphthalene removal fromporous particles of dierent radii R0 R0 50 lm, circles;

R0 100 lm, squares; R0 250 lm, diamonds; R0 500 lm,triangles) and sorption coecients K. Drawn lines are calcu-lations with simple mass-transfer relations (Eq. (34)) and rep-

resent the shortest periods needed for 99% removal with a

maximum driving force for mass transfer. Overall eective

diusion coecients (crosses) are plotted on the right y-axis.

Fig. 6. Model calculations predicting the batch biodegradation

of four PAHs sorbed to porous soil particles

e 0:05;R0 200 lm with optimized microbial conditions.Overall diusion coecients were calculated according to the

data in Table 1 and Eqs. (13), (26)(28), assuming an organic

carbon content of 5%.



9/10

m3. The initial sorbed PAH concentration was calcu-

lated from the sorption coecient and the maximum

solubility. Yield coecients were 0.5 kg kg1, maximum

growth rates were 1:33 105 s1, the initial biomassconcentration was 1:0 104 kg m3 and the Monod

constants were assumed to be a factor hundred less thanthe solubility of the PAH under consideration.

6. General conclusions

It is shown that in this theoretical study that mass-

transfer models can be used to predict the period needed

to achieve a certain degree of PAH removal from soil by

bioremediation. However, the biological degradation

capacity must be sucient to obtain mass-transfer lim-

ited degradation of the contaminant. When this is the

case, removal rates of PAHs are dictated by mass-transfer processes. In model calculations on three dif-

ferent physical states of PAHs in soil matrices, the in-

uence of key mass-transfer parameters on the period

needed for 99% PAH removal by bioremediation was

investigated. During the simulation of the degradation

of the high-molecular weight PAHs, low values were

required for the microbiological parameters

Y; lmax;Ks. Since these calculations have been made onmodel systems with one component and one set of mi-

crobiological parameters, it might be an interesting ex-

ercise to study the eect of co-metabolism and multi-

component PAH mixtures on system stability. In

agreement with dissolution models it was found thatmass-transfer parameters, such as particle radius, water-

solubility and sorption coecients, indeed determine the

eciency of bioremediation under mass-transfer limited

conditions. However, these were model calculations on a

theoretical basis. In order to give these considerations a

practical use, more work is needed on the characteriza-

tion of the physical states of PAHs in soil matrices and

validation of the proposed transfer models in real soil

systems. Also the eect of aging and the presence of

dissolved organic carbon (DOC) on the dynamic release

of PAHs from soil matrices should be quantied and the

mechanisms should be incorporated in future mass-transfer models. At the moment, the mechanisms of

these processes are not fully understood and can there-

fore not be modeled mechanistically yet. For the mo-

ment, however, these considerations can be very useful

to roughly calculate, for instance, the (relative) eects of

soil sanitation measures like temperature elevation or

the introduction of bacterial biomass. Because of the

mechanistic nature of the models, these measures can be

implemented in the models by altering the model pa-

rameters. The eect of temperature on, for instance,

PAH solubility, diusion coecients, sorption coe-

cients, and growth rate are often known. By altering the

mass-transfer parameters on the one hand and the de-

gradation parameters on the other hand, one can cal-

culate whether the system will be mass-transfer limited.

When that is the case, the bioremediation time can be

calculated by the simple relations with the new param-

eter value at higher temperatures. Another use of these

models could be the prediction of `best-case' bioreme-diation periods of high-molecular weight PAHs based

on degradation kinetics of low-molecular weight PAHs

under mass-transfer limited conditions. Because the

mass-transfer processes are dominated by the physical

and chemical properties of the compounds, extrapola-

tion of this kinetic information on relatively mobile

pollutants can provide information on the release rate of

more persistent hydrophobic substances from soils.

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Prediction of Complete Bio Remediation Periods for PAH Soil Pollutants in Different Physical States by Mechanistic Models