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Modelling of multispecies biofilm population dynamics in a trickle-bed bioreactor used for waste gas treatment

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Modelling of multispecies bioﬁlm population dynamics in atrickle-bed bioreactor used for waste gas treatment
Dariusch Hekmat*, Markus Stephan, Ru¨diger Bauer, Annette Feuchtinger, Dieter Vortmeyer
Institute of Chemical Engineering, Munich University of Technology, Boltzmannstrasse 15, 85747 Garching, Germany
Received 19 September 2005; received in revised form 30 January 2006; accepted 7 February 2006
Abstract
The dynamics of a multispecies bioﬁlm population in a laboratory-scale trickle-bed bioreactor for the treatment of waste gas is described.Calculations using a simpliﬁed multispecies–multisubstrate model were compared to existing experimental data. The bioreactor was operatedunder transient conditions by applying pollutant concentration shifts and a prolonged starvation period. A non-pollutant degrading population waspredominantly existing in the bioﬁlm. These so-called saprophytes utilized a secondary carbon source consisting of intermediates and lysisproducts. The modelled microbial interactions were proto-cooperation and competition. According to experimental evidence, the bioﬁlm wasconsidered as a heterogeneous structurewith strong backmixing. A satisfactory agreement of model calculations and measured time courses of thepopulation fractions was achieved. According to the calculations, the pollutant degraders reacted about 4–10 times faster after a shift-up of thepollutant supply rate than the inactive cells and the saprophytes. Hence, the bioreactor performance adapted relatively fast to abrupt changes of thepollutant supply rate. Even after the prolonged starvation period, the culture was able to recover within a few hours indicating that the biologicalsystem was robust.
#
2006 Elsevier Ltd. All rights reserved.
Keywords:
Bioﬁlm; Mathematical modelling; Multispecies; Population dynamics; Trickle-bed bioreactor; Waste gas treatment
1. Introduction
Waste gas can be treated effectively in trickle-bedbioreactors, especially when the pollutant concentration levelsare relatively low at around 1 g m
3
. The biodegradation of theorganic pollutants takes place mainly via aerobic oxidation. Amixed population of microorganisms is immobilized in abioﬁlm which covers the surface of a suitable packing materialof the trickle-bed column. Previous studies have examinedtrickle-bed bioreactors for the treatment of volatile organiccompounds (VOC’s) such as dichloromethane [1], toluene [2–
4], polyalkylated benzenes [5], mono-chlorobenzene [6],
styrene [7,8], and benzene [9]. Further work was performed
with regard to the biodegradation dynamics, since thewaste gastreatment under real conditions is usually unsteady [10–14].This is due to the facts that the pollutant sourcevaries with timeand that the bacterial culture exhibits an internal dynamicbehavior. For simpliﬁcation, however, the bioﬁlms wereregarded as a homogeneous mass consisting of one type of species in most studies. Thus, the properties of distinct specieswere ignored [15]. However, in any open environmentbiological system, multispecies bioﬁlms exist. The variouspopulations in these bioﬁlms interact with each other. Theseinteractions inﬂuence the structure and the physiology of thebioﬁlm as it develops [16]. An example of metabolicinteractions between community members was reported byMøller et al. [17] in a binary population bioﬁlm of
Pseudomonasputida
and
Acinetobacter
sp.degradingtoluene.In continuation of this work, Christensen et al. [18] studied theinteractionsofthisbinarypopulationdegradingbenzylalcoholin a surface-attached culture and in a suspended chemostatculture. It was observed that the two organisms exhibitedcompetition and/or commensal interactions. It was shown thatmultispecies bioﬁlms represent quite complex dynamicsystems [19]. Due to this complexity, current understandingofbioﬁlmsystemsforwastegastreatmentislimited.Onlylittlework exists on the description of the microbial compositionand structure of a multispecies bioﬁlm for the treatment of waste gas [3,20]. Furthermore, few examinations of themicrobial population dynamics during long-term operationunder transient conditions of such systems have been carriedout [21].
www.elsevier.com/locate/procbioProcess Biochemistry 41 (2006) 1409–1416* Corresponding author. Tel.: +49 89 289 15770; fax: +49 89 289 15714.
E-mail address:
hekmat@lrz.tum.de (D. Hekmat).1359-5113/$ – see front matter
#
2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.procbio.2006.02.003
In order to understand the complex behavior of microbialbioﬁlms, the tool of mathematical modelling has been used formore than three decades as pointed out by Noguera et al. [22].These models have been used in order to identify the governingparameters of the bioﬁlm processes and to simulate themicrobial systems. Most of the models in the literature dealwith aquatic systems or waste water treatment processes, suchas the fundamental dynamic multisubstrate–multispeciesmodel of Wanner and Gujer [23]. However,as to the knowledgeof the authors, few studies have been presented so far dealingwith the mathematical modelling of the multisubstrate–multi-species bioﬁlm population dynamics in a trickle-bed bioreactorused for waste gas treatment [24]. Therefore, the aim of thepresent study is to develop such a mathematical model and tocompare the modelling results with existing data from transientbiodegradation experiments using a VOC-mixture of poly-alkylated benzenes as the pollutant.
2. Modelling
2.1. Two-species-two-substrates (2S2S) kinetic model
The biodegradation of mixtures of VOC’s by mixedpopulations is usually accompanied by an accumulation of intermediate products [25]. These intermediates are formed asbyproducts of the biodegradation itself and, in addition, arederived from lysis processes. Therefore, non-pollutant-degrading heterotrophs (so-called saprophytes) are oftenobserved which utilize these intermediates and in factdominate the bioﬁlm community [24]. Thus, a multisub-strate–multispeciessystemexists.Duetoreasonsofsimplicity,it is assumed in the present model that (i) two distinct viablespecies are encountered, the pollutant degraders (
X
A
) and thesaprophytes (
X
B
) and (ii) two distinct substrates exist, i.e. thepollutant as the primary carbon source (
S
1
) and the pool of intermediates asthe secondarycarbonsource(
S
2
)
.
As afurthersimpliﬁcation, it is assumed that the pollutant degraders areable to utilize both types of substrates while the saprophytesare only able to mineralize the secondary carbon source. Bothviable populations are subjected to endogeneous decay andinactivation. The latter process leads to an inactive population(
X
P
)
.
All three populations are subject to lysis. The schematicdescription of the 2-species–2-substrates (2S2S)-model isgiven in Fig. 1. The resulting microbial interactions are (i)proto-cooperation, i.e. population
X
B
proﬁts in an obligatemannerfrompopulation
X
A
and(ii)competitionwithregardtothe utilization of
S
2
.The formulation of microbial kinetics is usually performedassuming ‘‘balanced growth’’ [26]. In these cases, simpleunstructured quasi-stationary overall kinetics can be appliedsuch as the Monod kinetics. The rates of endogeneous decay aswell as cell inactivation/lysis are formulated as being linearlyproportional to the cell concentration [27]. Thus, the reactionrates of species A, B, and P are given as follows
r
A
¼
m
m
;
A1
S
1
X
A
K
M
;
A1
þ
S
1
þ
m
m
;
A2
S
2
X
A
K
M
;
A2
þ
S
2
k
eA
X
A
I
A
X
A
;
(1)
r
B
¼
m
m
;
B2
S
2
X
B
K
M
;
B2
þ
S
2
k
eB
X
B
I
B
X
B
;
(2)
r
P
¼
I
A
X
A
þ
I
B
X
B
I
P
X
P
:
(3)The consumption rates for both substrates are formulatedusing yield coefﬁcients
r
1
¼
1
Y
A1
m
m
;
A1
S
1
X
A
K
M
;
A1
þ
S
1
1
Y
PS
k
P
m
m
;
A1
S
1
X
A
K
M
;
A1
þ
S
1
;
(4)
r
2
¼
1
Y
A2
m
m
;
A2
S
2
X
A
K
M
;
A2
þ
S
2
1
Y
B2
m
m
;
B2
S
2
X
B
K
M
;
B2
þ
S
2
þ
k
P
m
m
;
A1
S
1
X
A
K
M
;
A1
þ
S
1
þ
1
Y
P
I
P
X
P
:
(5)
2.2. Bioﬁlm model
Bioﬁlms are multiple-phase systems where a liquid phaseﬁlls the pores and cavities of a sponge-type structure of a solidphase. The latter consists of cell agglomerates which areembedded in a coherent porous structure of extracellularpolymeric substances (EPS). It was shown experimentally thatthe formationof EPSisdirectly coupled tocellgrowth [28].Forsimpliﬁcation, it is therefore assumed that the ratio of EPS tocells is constant. The solid phase is assumed to have a constantdensity and to be incompressible. Furthermore, it is assumedthatthereisnoactivebiomasssuspendedintheliquidphaseandthat no attachment or detachment of biomass from the solidphasetakesplace.Thevolumefractionofliquidinthebioﬁlmisgiven by the liquid porosity
f
‘
which is assumed to be constant.The remaining volume fraction (1
f
‘
) is assigned to the solidphase. With
X
i
(
i
= A, B, P) being the dry biomassconcentrations of the cells and the constant and equal celldry biomass densities
r
i
, it follows for the sum of the volumefractions of all bioﬁlm compartments
X
A
r
A
þ
X
B
r
B
þ
X
P
r
P
þ
f
‘
¼
1
:
(6)Growth of cells results in an increase of the bioﬁlmthickness, i.e. an advective ﬂow of cells perpendicular to the
D. Hekmat et al./Process Biochemistry 41 (2006) 1409–1416
1410Fig. 1. Schematic description of the 2-species–2-substrates (2S2S)-model withtwo active populations (
X
A
, degraders;
X
B
, saprophytes), one inactive popula-tion (
X
P
), and two substrates (
S
1
, pollutant;
S
2
, secondary substrate pool).
bioﬁlm surface exists. For the compensation of the volume of the growing porous solid structure, liquid ﬂows in the oppositedirection. With the assumption that the wet biomass consistsmainly of water, it follows
f
‘
u
‘
ð
1
f
‘
Þ
u
f
;
(7)where
u
f
is the advection velocity of the solid matrix and
u
‘
isthe advection velocity of the liquid phase. The bioﬁlm systemscan be described using complex transient reaction-diffusionmodels incorporating partial differential equations[6,11,14,23,29–31]. Thus, in case of a stratiﬁed ﬂat and evenlydistributed bioﬁlm, the transient one-dimensional mass balanceof species
X
i
is
@
X
i
@
t
¼
@
ð
u
f
X
i
Þ
@
X
@
J
i
@
X
þ
r
i
;
(8)where
J
i
are area-speciﬁc diffusive mass ﬂow rates and
r
i
arevolumetric reaction rates of the components
i
, respectively. Thecorresponding mass balance for the substrates is taking intoaccount that the substrates solely exist in the liquid phase
@
ð
f
‘
S
i
Þ
@
t
¼
@
ð
u
‘
f
‘
S
i
Þ
@
X
@
J
i
@
X
þ
r
i
:
(9)According to previous work, there is experimental evidencethat convective ﬂow occurs in heterogeneous bioﬁlms [32] andthat pores and channels exist extending all along the bioﬁlmdepth[3,20].Infact,anevendistributionofpollutant-degradingbacteria and saprophytes through the bioﬁlm depth wasobserved [20]. Hence, it can be assumed that there is strongbackmixing within the bioﬁlm. Thus, it follows
@
X
i
@
X
¼
@
S
i
@
X
¼
@
J
i
@
X
¼
0
:
(10)From above equations, the mass balances of the threepopulations are obtainedd
X
A
d
t
¼
X
A
1
f
‘
r
k
r
k
þ
r
A
;
t
¼
0
:
X
A
¼
X
A
ð
0
Þ
;
(11)d
X
B
d
t
¼
X
B
1
f
‘
r
k
r
k
þ
r
B
;
t
¼
0
:
X
B
¼
X
B
ð
0
Þ
;
(12)d
X
P
d
t
¼
X
P
1
f
‘
r
k
r
k
þ
r
P
;
t
¼
0
:
X
P
¼
X
P
ð
0
Þ
;
(13)where the reaction rate
r
k
represents the sum of all reactiveterms and is given by
r
k
¼
r
A
þ
r
B
þ
r
P
:
(14)The ﬁrst terms on the right hand side of Eqs. (11)–(13)represent the dilution effect by growth of the bioﬁlm. Thecorresponding mass balances for the two substrates areobtained assuming that both substrates solely exist in theliquid phased
S
1
d
t
¼
S
1
f
‘
r
k
r
k
þ
1
f
‘
r
1
þ
J
LS
L
f
;
t
¼
0
:
S
1
¼
S
1
ð
0
Þ
;
(15)d
S
2
d
t
¼
S
2
f
‘
r
k
r
k
þ
1
f
‘
r
2
;
t
¼
0
:
S
2
¼
S
2
ð
0
Þ
:
(16)The ﬁrst terms on the right hand side of Eqs. (15) and (16)
represent source terms according to the advection of liquid intothe pores and channels of the bioﬁlm structure due to growth of the solid matrix.
J
LS
of Eq. (15) is the overall area-speciﬁcpollutant stream being transferred from the recirculating liquidinto the bioﬁlm. The balance for the bioﬁlm thickness isd
L
f
d
t
¼
L
f
1
f
‘
r
k
r
k
;
t
¼
0
:
L
f
¼
L
f
ð
0
Þ
:
(17)
2.3. Column model
The overall area-speciﬁc pollutant stream into the bioﬁlm
J
LS
is derived from a simple stationary model of the trickle-bedcolumn. Here, the validity of stationarity can be assumed sincethe characteristic times of the microbial processes inside thebioﬁlm are signiﬁcantly larger than the mass transfer processesby convection and/or diffusion as well as mass transfer ratesacross phases in the trickle-bed column (see Table 1). Thus,compared to the microbial processes, the abiotic physicalmechanisms are in equilibrium at all times. The column israndomly packed with hydrophilized polypropylene Ralu
1
rings (Raschig AG, Ludwigshafen, Germany). The surface of this carrier material is evenly covered with a bioﬁlm [13]. Theliquidconcentrationisassumedtobeconstantalongthecolumnheight according to the uniform concentration model of Diksand Ottengraf [1].
J
LS
is obtained from a simple mass balancealong the column height for the stationary case where the massof pollutant being removed from the gas phase is equal to theamount of pollutant entering the bioﬁlm
J
LS
¼ð
c
g
;
in
c
g
;
out
Þ
w
g
Ha
:
(18)The exit gas concentration
c
g,out
is derived from thedifferential equation for the pollutant gas concentration
c
g
forco-current operation assuming plug ﬂow for the gas phase
w
g
d
c
g
d
z
¼
k
gl
a
ð
c
g
m
H
c
l
Þ
;
(19)
D. Hekmat et al./Process Biochemistry 41 (2006) 1409–1416
1411Table 1Estimated characteristic times of various processes taking place in the trickle-bed bioreactorDiffusion of pollutant in the gas phase (h) 0.00005Diffusion of pollutant in the bioﬁlm (h) 0.0001–0.3Mean residence time of gas (h) 0.005–0.01Mean residence time of liquid (h) 0.08Microbial growth (h) 1–100Decay, inactivation, lysis (h) 10–10000
with the boundary conditions
c
g
(
z
= 0) =
c
g,in
and
c
g
(
z
=
H
) =
c
g,out
.
Integration of Eq. (19) assuming that the liquidconcentration is constant along the column height yields
c
g
;
out
¼ð
c
g
;
in
m
H
c
l
Þ
e
k
gl
a
t
þ
m
H
c
l
;
(20)with the average gas residence time
t
¼
V ˙V
g
¼
H w
g
:
(21)Thus, it follows
J
LS
¼
c
g
;
in
m
H
c
l
t
a
ð
1
e
k
gl
a
t
Þ
:
(22)The column model is coupled to the bioﬁlm model via thepollutant stream
J
LS
with
c
l
=
f
‘
S
1
. The mixed population of thebioﬁlm grown on the carrier material of the packed column wasquantiﬁed inthe experiments as the number ofcellsper piece of carrier
N
i
. Since the mathematical model is formulated usingbiomass concentrations
X
i
, the following correlation is used inorder to be able to compare model results with the experimentaldata
N
calc
:
i
¼
X
i
L
f
Van
Fk
m
MO
;
(23)withthe total numberofcarrier piecesinthe column
n
Fk
andtheaverage dry mass per cell
m
MO
.
3. Experiment
The experiments were performed in a laboratory-scaletrickle-bed bioreactor under non-sterile conditions [13,21]. Thebioreactor geometry and the transient operating conditions aregiven in Table 2. The performance of the trickle-bed bioreactorundertransientconditionswasexaminedforaperiodofapprox.285 days. During this time period, several pollutant gas inletconcentration shift experiments were performed and aprolonged starvation period followed by a peak loading wereapplied. The experimental results were described in detail byHekmat et al. [21]. The speciﬁc pollutant load is deﬁned asPL =
c
g
,
in
/
t
, the speciﬁc elimination capacity is deﬁned asEC
=
(
c
g,in
c
g,out
)/
t
, and the degree of conversion is deﬁnedas DC = (
c
g,in
c
g,out
)/
c
g,in
.The concentrations ofthe pollutantand the secondary carbon source (pool of intermediates andlysis products) inside the bioﬁlm were not measured. Themixed population of the bioﬁlm was measured using the theﬂuorescenceinsituhybridization(FISH)method. Inthepresentsystem, two
Burkholderia
sp. and two
Pseudomonas
sp. wereidentiﬁed as pollutant degrading cells [21]. The sum of thesefour strains was deﬁned as pollutant degraders. For simplicity,all other active cells were assumed to be saprophytes. The sumof all active bacteria was measured using an eubacteria FISH-probe. The inactive cells were calculated from the difference of all cells (active and inactive) measured via the DAPI stainingmethod and all active cells.
4. Results and discussion
The described mathematical model represented a non-linearinitial value problem of ﬁrst order with time-dependentcoefﬁcients. The solution was obtained numerically usingcommercially available MATLAB routines. The determinationof the model parameters ofthe presented model was not an easytask since many parameters could not be derived frommeasurements directly. However, four of the parameters of the mathematical model were obtained from independent ownexperiments. Only one difﬁcult to determine parameter (thevolume fraction of liquid in the bioﬁlm
f
‘
) was taken fromliterature. These parameters are given in Table 3. Seventeen of the model parameters, however, were obtained from a ﬁt to theexperimental data using the common method of least squares.The initial values and the ﬁtted model parameters of the 2S2S-model are given in Table 4. A simple sensitivity analysisrevealed that only four of the seventeen ﬁtted model parameterswere sensitive as depicted in Table 4. The comparison of calculated and measured population time courses of degradercells, saprophytes, and inactive cells during the long-termtransient experiment is given in Fig. 2. As can be seen, themathematical model was able to describe the experimentallyobserved responses of the different species contained in theheterogeneous bioﬁlm towards externally imposed substrateshifts in a satisfactory manner. Compared to already publisheddata [24], such a description of the dynamics of a biologicalwaste gas treatment process was performed for the ﬁrst time.However, it should be mentioned that due to the lack of additional experimental data, the ﬁtted model parameters couldnot be validated independently. The time course of themeasured biomass dry weight per carrier (DW) and acomparison of calculated and measured time courses of the
D. Hekmat et al./Process Biochemistry 41 (2006) 1409–1416
1412Table 2Bioreactor geometry and operating conditions for the transient experiment withpollutant concentration shifts and a long-term starvation periodHeight of packed bed,
H
(m) 0.65Inner diameter of column,
D
(m) 0.14Total number of carriers,
n
Fk
1580Speciﬁc surface area of carriers,
a
(m
2
m
3
) 300Gas ﬂow rate,
˙V
g
(l min
1
) 35Average gas residence time,
t
(s) 17.2Gas inlet concentration,
c
g,in
(g m
3
) 1.44 (peak value);0.6; 0.2; 0Speciﬁc pollutant load, PL (g m
3
h
1
) 280 (peak value);120; 40; 0Recirculating liquid ﬂow rate,
˙V
l
(l h
1
) 120Trickling density (m
3
m
2
h
1
) 7.8Temperature (
8
C) 30pH 7Table 3Parameters determined from own independent experiments and from literatureGas-to-liquid mass transfer coefﬁcient,
k
gl
(m h
1
) 0.72Pollutant partition coefﬁcient,
m
H
0.4Dry biomass density,
r
i
(g m
3
) 1
10
5
Average dry mass per cell,
m
MOa
(g) 5.14
10
13
Volume fraction of liquid in bioﬁlm,
f
‘
0.93 [34]
a
Estimated from cell size and dry mass measurements.
total number of cells per carrier (TNC) during the long-termtransient experiment are given in Fig. 3. Again, a satisfactoryagreement of model and experiment was obtained.During the measurements of the populations after shift-experiments, it was observed for the ﬁrst time that the differentcell types reacted with different velocities to the suddenchanges of the environmental conditions. Thus, the pollutantdegraders were identiﬁed to exhibit the fastest response time,while the saprophytes were the slowest among the mixedpopulation [21]. As a matter of fact, the experimentallyobservedspeciﬁc change ofthe cellfraction oftheinactivecellswas somewhat higher compared to the saprophytes. Calcula-tions using the presented transient mathematical modelconﬁrmed these observations. This is demonstrated inTable 5 where exemplary calculated and measured relativespeciﬁc changes of cell fractions as deﬁned by Hekmat et al.[21] are compared. Thevalues were normalized to the degreeof change of the cell fraction of the degrader cells. The data aregiven for the ﬁrst shift-down on the 38th day and the secondshift-up on the 258th day after the prolonged starvation period.As can be seen, there was a qualitative agreement betweenmodel and experiment. In Fig. 4, exemplary calculated courses
D. Hekmat et al./Process Biochemistry 41 (2006) 1409–1416
1413Table 4Initial values and ﬁtted model parameters of the 2-species-2-substrates (2S2S)-modelInitial number of cells per carrier
N
i
(0),
i
= A, B, P (cells/carrier)1
10
7
Initial substrate concentrations
S
i
(0),
i
= 1, 2 (g m
3
)0Initial bioﬁlm thickness,
L
f
(0) (m) 1
10
6
Maximum speciﬁc growth rate of degraders on pollutant(primary substrate),
m
m,A1
(h
1
)0.08Maximum speciﬁc growth rate of degraders on secondary substrate,
m
m,A2
(h
1
)0.1Maximum speciﬁc growth rate of saprophytes on secondarysubstrate,
m
m,B2a
(h
1
)1.164Half saturation constant for growth of degraders on pollutant,
K
M,A1
(g m
3
)0.05Half saturation constant for growth of degraders on secondarysubstrate,
K
M,A2a
(g m
3
)0.816Half saturation constant for growth of saprophytes on secondarysubstrate,
K
M,B2
(g m
3
)20Endogeneous decay constant of degraders,
k
e,Aa
(h
1
)0.0153Endogeneous decay constant of saprophytes,
k
e,B
(h
1
)1
10
3
Formation rate constant of intermediates,
k
P
26Inactivation rate constant of degraders,
I
A
(h
1
)4
10
4
Inactivation rate constant of saprophytes,
I
Ba
(h
1
)7.02
10
3
Lysis rate constant of inactive cells,
I
P
(h
1
)0.013Yield coefﬁcient of degraderson pollutant,
Y
A1
5
10
3
Yield coefﬁcient of degraderson secondary substrate,
Y
A2
1.9Yield coefﬁcient of saprophyteson secondary substrate,
Y
B2
1.9Yield coefﬁcient of formationof secondary substrate by lysisof inactive cells,
Y
P
2Yield coefﬁcient of formation of secondary substrate from pollutantby degraders,
Y
PS
0.25
a
Sensitive model parameters.Fig. 2. Comparison of calculated and measured population time courses of degrader cells, saprophytes, and inactive cells during the long-term transientexperiment. First shift-down on the 38th day, ﬁrst shift-up on the 55th day,second shift-down on the 112th day (start of starvation period), second shift-upon the 258th day (peak load) as indicated by the arrow lines.Fig. 3. Time course of the measured biomass dry weight per carrier (DW) andcomparisonofcalculatedandmeasuredtimecoursesofthetotalnumberofcellsper carrier (TNC) during the long-term transient experiment. The shift experi-ments are indicated by the arrow lines.Table 5Comparison of calculated and measured relative speciﬁc changes of cellfractions as deﬁned by Hekmat et al. [21] exemplary for the ﬁrst shift-downon the 38th day and the second shift-up on the 258th dayFraction of cells Percentage of speciﬁc change of cell fractions [%]1st shift-down (38th day) 2nd shift-up (258th day)Calculated Measured Calculated MeasuredDegraders
100
100 +100 +100Saprophytes
19
12.5 +8.5 +13.5Inactive cells +74 +48
24.5
10.5

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