Modeling NAPL dissolution and biodegradation intera tions: e e t of
toxi ity and biomass growth limitations
C. Gallo a b
and S.M. Hassanizadeh a
a
Dept. ofCivil Engineering and Geos ien es, TUDelft, The Netherlands
b
CRS4, VI Strada Ovest, Z.I. Ma hiareddu, UTA (CA), Italy
Thisworkfo usesonsomeaspe tsoftheintera tionsbetweenNAPLdissolution,mole -
ular di usionandbiodegradationpro esses. Startingfromatest problembasedonareal
eld s enario, a one-dimensional modelis set up. A numberof simulations are run using
di erent biomass distributions, varying di usion oeÆ ients and biologi al kineti rates.
Results indi ate that under ideal onditions biomass distribution along the olumn does
not make a real di eren e in terms of total amount of dissolved oil degraded. Results
hange dramati ally when introdu ing limitations in the growth of biomass and the ef-
fe ts of toxi ity into the model. Both of these are modelled as fun tions for whi h some
threshold orboundinglevelsare spe i ed. Inparti ular, toxi ity fun tionis derived from
some phenomenogi al onsiderations, sin e, atleast tothe author's knowledge,no do u-
mentation in the literature is available in this regard. Constrained biomass growth and
ontaminanttoxi ityhavebeenfoundtoyieldresults onsistentwith elddataon ontam-
inant distribution. This would support our presumption that biomassgrowth onstraint
and toxi ityplay amajorrole inredu ing natural attenuation eÆ ien y.
1. INTRODUCTION
Inthiswork,wehavestudiedthe ombinationofbiodegradationanddissolution. There
are a number of studies on NAPL dissolution me hanisms and properties of two-phase
ow([5,7,4,6℄). Similarly,mu h workhas been arriedoutonbiodegradationof dissolved
ontaminants and di erent mathemati al/numeri al approa hes have been presented in
the literature(see[2℄and referen es listedtherein). However, thereare onlyafewstudies
that have dealt with the oupling between the two pro esses. This situation typi ally
o urs in near-to-sour e ontamination s enarios in whi h both NAPL phase and a tive
biomassarepresent. Near-to-sour edoesnotimplyapre isemeasure intermsofdistan e
from the spill lo ation. However, it should be intended as \suÆ iently lose" to the
ontaminantspillsothatthe on urren eofpro essessu hasNAPLdissolution,transport
ofdissolvedoilinthe aqueousphase,biodegradation,biomassgrowth,andtoxi itye e ts
shouldbea ountedfor. Therelativeweightofea hpro essmayplayaroleontheoverall
degradation.
This work is a ontinuation of the resear h presented in our previous paper [3℄. The
solution and biodegradation. This isdis ussed in lightof the presen e of \nonidealities"
in the system. The word \nonidealities" stands for those pro esses whi h may dimin-
ish, inhibit, or de nitetely stop the biodegradation pro ess. Two degradation-limiting
pro esses are onsidered, that is, biomassgrowth limitationsand toxi ity of the ontam-
inant for ba terial population. These fa tors may have a strong impa t on ontaminant
biodegradation,but, toourknowledge, noextensive study hasbeenpresented inorder to
quantify these e e ts. In this paper, preliminaryresults are presented on the topi s.
2. GOVERNING EQUATIONS
NAPL dissolution, dissolved-oil transport and biodegradation are pro esses that are
in luded in the model. Dissolved-oil di usive transport in the aqueous phase ismodeled
as follows:
S
l
C S
t +D
2
C S
x 2
=E
l n
S
l B
S
: (1)
whereC S
is on entrationof dissolvedNAPL, tistime, is porosity,S
l
isaqueousphase
saturation,v
l
isaqueousphasevelo ityand Dismole ulardi usion oeÆ ient. Theterm
E
l n
is linearly proportional to the di eren e between the solubility limit of NAPL, C S
eq ,
and its a tual on entration, C S
, i.e.
E
l n
= S
n k
do
C S
eq C
S
: (2)
k
do
isthedissolutionrate oeÆ ientandS
n
isNAPL saturation. The termB S
designates
the biodegradation rate and takes the form
B S
=C X
Y
0
"
C S
K
1=2 +C
S
#
; (3)
where
0
is the maximum degradation rate, K
1=2
is the half-saturation onstant, C X
is
biomass on entration, and Y is a yield oeÆ ient.
Finally, the rate of mi robialgrowth/de ay reads asfollows:
1
C X
C X
t
=
0
C S
K
1=2 +C
S
!
F k
d
: (4)
k
d
is the de ay rate oeÆ ient, while F in orporates nonidealities in the system. F =1
unless expli itlyspe i ed (see below).
3. SIMULATION RESULTS AND DISCUSSION
3.1. Test ase des ription
The test problemstudied here is based on the fra tured eld site at Ringe, Denmark.
We onsider a porous medium in whi h two zones an be identi ed: fra tures/high-
permeabilityandmatrix/low-permeabilityzones. Flowof uidsisassumedtoo urwithin
the fra tures only. Thus, the bulk uid ow withinthe matrix isassumed negligibleand
the migration of the ontaminant in the soil matrix is only due to di usion. Biodegra-
ontain free NAPL and this may prohibit biomass growth due to toxi ity e e ts. More-
over, thevolumefra tionofhigh-permeabilitysoilisgenerallysmallerthanthefra tionof
low-permeability soil matrix and, thus, its ontribution to the biodegradation pro ess is
negligible. So, wefo usoursimulationsonthedi usionintoanddissolutionandbiodegra-
dation within the matrix. We simulate the matrix zone as a 1-D olumn of 10 m long.
lled witha porousmedium. The olumnis dis retizedinto50elementsof 0.002mlong.
The olumnis assumed tobe fully saturated with water ex ept forthe rst one entime-
ter (next to the fra ture) where we have a residual NAPL saturation of 0.20. (S
n
=0:2,
S
l
= 0:8 for 0 x <1 m, S
l
= 1 elsewhere). The total simulation time is 40 days and
a time step of 34 s (0.0004 days). Initial ontaminant on entration is assumed to be
zero. The initialbiomass on entration is 3.53 x 10 3 kg/m 3
. Starting with this initial
ondition, the olumn is assumed to be sealed. Zero-di usion boundary ondition is set
for the transport. Under these onditions, NAPL dissolution, dissolved-NAPL di usion
and biodegradation are the only pro esses taking pla e in the system. Other data used
inthe simulationare reported in table1.
Table 1
Biologi alparameters.
Parameter value parameter value
K S
(kg/m 3
) 0.120 Y
S
(-) 3.56
k
d
(1/s) 2.3E-07
0
(1/s) 5.E-05
C S;eq
(kg/m 3
) 5.E-03 k
do (m
2
/s) 6.9E-11
3.2. E e t of Di usion
The rst set of simulationswere run onsidering di usion varying within two ordersof
magnitude,thatis,D=[1:410 10
;1:410 8
℄m 2
/s. Assimulationstarts,NAPLdissolves
and invades the olumnatarate thatis afun tionof the di usion oeÆ ient: thehigher
the di usion, the higher the on entration within the olumn. Figure 1 (left) shows the
mass present in the olumn as a fun tion of time for di erent values of the di usion
oeÆ ient. The dissolved-NAPL mass present in the olumn in reases proportionally to
di usion oeÆ ient, but for the largest D the urve shows a knee. This orresponds to
the momentthat C S
=C S
eq
and that the olumnis saturated with dissolved NAPL. The
dissolved-oil mass present in the olumn is lower when biodegradation is a tive, but the
total dissolved NAPL equals the sum of the a tual mass present in the olumn and the
mass degraded by ba teria. Thus, as shown inFigure1-right,the total mass of dissolved
NAPL (i.e. the organi substrate in ow) is mu h higher than in the previous ase. This
indi atesthat biodegradation an reallyenhan e free-phasedissolution, both interms of
rate of dissolution and in terms of amountof mass dissolved.
3.3. Biomass distribution e e ts
Initial biomass distribution an be important when dealing with fra tured soils. As
reportedin[1℄, a tivebiomassislo ated inasmallregionofsoiladja enttofra tures. In
Figure1. NAPLdissolvedinthe olumnwithoutbiodegradation(left)andwithbiodegra-
dation (right) (M
p
: mass present inthe aqueous phase; M
d
: mass degraded).
tobelo ated losetofra turesand/orzonesofhighpermeability,areabletohostba terial
growth. The rest of the soil is inert with respe t to biodegration. Two initial biomass
distributions are onsidered: BioF (full; that is, C X
(t = 0) = 0:0 for 0 x < 1 m,
C X
(t = 0) = 0:0353 kg/m 3
otherwise); BioP (partial; that is, C X
(t = 0) = 0:0 for
0x<1 m, C X
(t=0)=0:0353kg/m 3
, for1 x<2 m, C X
(t=0)=0:0otherwise).
Simulations similar to those des ribed in the previous se tion (for varying D) are now
arried out here with two di erent spatial biomass distributionsBioP and BioF.Results
indi ated that on entrationdistribution of dissolved oilin the BioFand BioP ases are
almost identi al. This an beexplained when examiningbiomass distributionat the end
of the simulation. C X
pro les for di erent values of the di usion oeÆ ient and various
biodegradation kineti s are almost identi al, ex ept for low
0
in whi hsome di eren es
are present at early times. Plots of biomass on entration vs spa e and time are shown
in Figure2. It is apparent that for long simulationtimes, on entrations of dissolved oil
for both ases approa h pseudo steady-state onditions are rea hed.
4. INTRODUCING NON-IDEALITIES IN THE SYSTEM
Toooftennon-idealitiesarenegle tedinsimulationsofbiodegradationpro esses. Inreal
eld appli ations, many fa tors may play a role in the degradation pro ess and some of
themare riti alforin reasingorde reasingthedegradationrate. Forexample,negle ting
biomass growth limitationsimplies that aslong asdissolved oilis available,biomass an
grow on and on, regardless of the volume available for a ommodating biomass. This
is a strong simpli ation and may lead to ex essively optimisti predi tions. Also, high
on entration of dissolved ontaminants may be toxi to ba teria and an inhibit either
temporarilyor de nitely the biodegradation pro ess. In the following paragraphs, these
Figure2. Biomass on entrationpro lesatt =400daysand
0
=1:e 51/sfor aseBioP
(left)and BioF(right).
4.1. The e e t of biomass growth limitations
From the mathemati al point of view, biomass growth limitation an be introdu ed
de ningF =F
bg
=(1 C X
=C X
max
)inequation(4). WhenC X
!C X
max
,ba terialgrowth
rate redu es to zero and only biomass de ay (k
d C
X
in equation 4) may o ur. In the
simulations reported here, C X
max
is set to 10 1
kg/m 3
. For low values of D, dissolved-
oil on entration is low in the olumn ex ept lose to the fra ture zone where NAPL
is trapped. Dissolved-oil migration is also slow and biomass an degrade the in oming
ontaminantrate inboth BioPand BioF ases. However, forlarge D, NAPL dissolution
ratein reasesalsoandba teriaareprovidedwithalargeamountofoiltodegradeperunit
time. Withbiomassgrowth limited, largepeaksof biomass on entration are suppressed
and BioP and BioF biomass initial distributions yield di erent results. As shown in
Figure 3,an a umulation of dissolved oil o urs in the olumn. In this ase, biomassis
able to degrade almost all dissolved oil for BioF distribution, while the same annot be
said in the BioP ase whose degradation apa ity islimited.
4.2. The e e t of ontaminant toxi ity
In many ases, a ontaminant that is normaly degraded at low on entration, may
be ome toxi for ba teriaat high on entration. This has an impa ton the e e tiveness
of overal degradation pro ess. Consider trapped NAPL that dissolves and di uses along
the olumn. If any a tive biomass is present, biodegradation begins. Depending on the
relativeweightsof dissolution rate and mole ulardi usion oeÆ ient, ifdi usion pro ess
isnot suÆ iently fast,dissolved oil maya umulate. Thus, if C S
approa hes the toxi ity
level,indi atedwith C S
tox
,biodegradationratede reasesand thebiomassbe omeina tive
forC S
C S
tox
. Basedonthisreasoning,wepropose tomodelthetoxi ity e e tbysetting
F =F
tox
=1 (C S
=C S
tox )
2
for C S
C S
tox
, and F
tox
=0 for C S
>C S
tox . If C
S
fallsbelow
C S
, biodegradation resumes and biomass an ontinue to grow. For the simulations
Figure 3. Dissolved-oil on entration pro le in time and spa e with
0
=2.5E-5 1/s for
ases BioP (left)and BioF(right)with biomass growth limitation.
reported here, C S
tox
is set to 5x10 3
kg/m 3
and D = 1.4x10 9
m 2
/s. Simulation results
obtained for a wide range of values of k
do
and
0
, are shown in Figure 4-left. These
results indi ate that there is a riti al value of the maximum degradation onstant
0
below whi h biodegradation de reases sharply. This riti al value depends on the value
of the mass dissolution rate oeÆ ient,k
do
, and di usion oeÆ ient, D. This result does
not give any real insight in terms of pra ti alappli ations, given the arti ialand sharp
transitionbetween the two zoneswhi hseems mainlyamathemati alout ome. It would
beprobablypossibleto ndafun tionalrelationshipbetweenk
do
,D,and
0
forestimating
a-priorithe riti alrangeof onditionsforbiodegradationtoo ursu essfully. However,
it is not in the purpose of this work to ome up with a mathemati al orrelation of this
dependen y. We believethat this orrelation would bestrongly test- ase dependent.
4.3. Combination of biomass-growth onstraint and toxi ity e e ts
The ombination of the two nonidealities introdu ed here, an be in luded in equa-
tion (4)by de ning F =F
bg
F
tox
. The numeri alinvestigationis ondu ted onsidering
a olumnof100 mand simulationtimeof 400days. Inthe simulations,variationsofthe
three most importantparameters of the model, that is, NAPL dissolution rate onstant
k
do
, mole ulardi usion oeÆ ient D, and the degradation kineti rate onstant
0 have
been onsidered. Figure4-rightis anexample ofhow the totaldissolved-oilmass isin u-
en edby thedegradationrateand thedissolution rate oeÆ ient. Otherparameters su h
as mole ular di usion and yield oeÆ ient are, of ourse, also important. These e e ts
Figure4. C S
pro lesasafun tionof
0
(left-onlytoxi itya tive). Dissolved-oildegraded
as afun tion of
0 and k
do
(right).
5. CONCLUSIONS
Severalpro esseso urring inaNAPLdissolutions enarioandtheirimpa tonnatural
biodegradation have been investigated. Preliminary results indi ated that when nonide-
alities, su h as biomass growth limitation and toxi ity, are negle ted, spatial biomass
distribution is not really riti al for the overall ontaminant degradation, and mole ular
di usion simply dominates the equilibrium between NAPL dissolution and biodegrada-
tion. Di erent results are obtained when nonidealities are in luded in the simulations.
For example, we found that initialbiomass distribution is riti alunder biomass growth
limitations. When toxi ity is in luded, biodegradation seems to be ontrolled by a rit-
i al value of the maximum biodegradation rate below whi h biodegradation slows down
signi antly. More pronoun ed e e ts are obtained when biomass growth limitationand
toxi ityare both in luded. Simulationresults showthat toxi ity plays animportantrole
indetermining the su ess or failureof biodegration.
AknowledgmentsThisresear hhasbeenpartly arriedoutintheframeworkoftheTRIAS
proje t "Multiphase ow and enhan ed biodegradation of non-aqueous phase liquids"
(Delft Cluster Proje t 5.1.6). The work of C. Gallo was partly supported by Sardinian
RegionalAuthoritiesandbytheItalianMinistryofthe University (proje tISR8-C11/B).
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