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Biochemical Engineering Journal 31 (2006) 188–196

Gas–liquid mass transfer in an up-flow cocurrentpacked-bed biofilm reactor

Julio Perez a,b,∗, Jose Luis Montesinos a, Francesc Godia a,b

a Departament d’Enginyeria Quımica, Escola Tecnica Superior d’Enginyeria, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spainb Institut d’Estudis Espacials de Catalunya IEEC-UAB, Barcelona, Spain

Received 6 June 2005; received in revised form 24 January 2006; accepted 30 July 2006

bstract

Gas–liquid mass transfer was investigated in an up-flow cocurrent packed-bed biofilm reactor. In aerobic processes gas–liquid mass transfer cane considered as a key operational parameter as well as in reactor scale-up. The present paper investigates the influence of the liquid phase mixingn the determination of the volumetric gas–liquid mass transfer coefficient (kLa) coefficient. Residence time distribution (RTD) experiments wereerformed in the reactor to determine the flow pattern of the liquid phase and to model mathematically the liquid phase mixing. The mathematicalodel derived from RTD experiments was used to evaluate the influence of the liquid mixing on the experimental estimation of the (kLa) in this

eactor type. The methods used to estimate the kLa coefficient were: (i) dynamic gassing-out, (ii) sulphite method, and (iii) in-process estimationhrough biological conversion obtained in the reactor. The use of standard chemical engineering correlations to determine the kLa in this type of

ioreactors is assessed. Experimental and modelling results show how relevant can be to take into consideration the liquid phase mixing in thealculations of the most-used methods for the estimation of kLa coefficient. kLa coefficient was found to be strongly heterogeneous along theeactor vertical axis. The value of the kLa coefficient for the packed-bed section ranged 0.01–0.12 s−1. A preliminary correlation was establishedor up-flow cocurrent packed-bed biofilm reactors as a function of gas superficial velocity.

2006 Elsevier B.V. All rights reserved.

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eywords: Gas–liquid mass transfer; Biofilm reactor; Packed-bed bioreactors;

. Introduction

Mass transfer coefficients in chemical reactors are commonlystimated in chemical engineering using empirical or semi-mpirical correlations [1]. The range of application of theseorrelations is often related to the specific process, which iseing carried out in the reactor. In the biochemical reaction fieldset of correlations has been also developed for certain biore-

ctor types, such as stirred tanks or bubbling columns, amongthers [2].

For the case of packed-bed biofilm reactors only few worksave been published providing useful specific empirical corre-

ations for the determination of the volumetric mass transferoefficient between gas and liquid phases. In this reactor type,ommonly used for aerobic processes, the oxygen supply is one

∗ Corresponding author at: Departament d’Enginyeria Quımica, Escolaecnica Superior d’Enginyeria, Universitat Autonoma de Barcelona, 08193 Bel-

aterra, Barcelona, Spain. Tel.: +34 93 581 33 02; fax: +34 93 581 20 13.E-mail address: julio.perez@uab.es (J. Perez).

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369-703X/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.bej.2006.07.006

cation; Mathematical modelling; Flow model

f the key operating conditions for an appropriate reactor per-ormance and for its scale-up.

This coefficient is recently becoming widely used in researchn wastewater treatment processes due to the application ofespirometric techniques to study biological parameters such asffinity constants for particular biomass species or consortiums3–5].

The oxygen mass transfer depends on the individual massransfer coefficient (kLa) and the driving force Cint − C, where

is the dissolved oxygen concentration in the liquid phase andint is the oxygen concentration at the gas–liquid interface. For

ow soluble gases, as oxygen, the individual mass transfer coef-cient, kLa can be considered equal to the overall mass transferoefficient, KLa [6], as it is stated in Eq. (1):

La ≈ KLa (1)

.1. Why existing correlations are not useful for the case of

acked-bed biofilm reactors?

In spite of the extensive studies in the chemical engineeringiterature, a high percentage of the existing correlations cannot

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J. Perez et al. / Biochemical Eng

e applied to packed-bed biofilm reactors. Indeed, most of theublished studies for fixed-bed reactors with two fluid phasesliquid and gas) correspond to countercurrent flow [7]. On thether hand, for cocurrent flow, few correlations can be found inhe open literature [7]. Moreover, the major part of the cocurrenttudies is focussed in down-flow reactors. Only some of thetudies presented specific correlations for the volumetric massransfer coefficient in the case of up-flow cocurrent reactors [8].he values obtained by the correlation proposed by Specchiat al. [8] are considered as wrong by Carra and Morbidelli [7],hile Charpentier [9] proposed as conservative value for the kLa

oefficient of 0.15 s−1, for reactions in packed-bed reactors witharallel up-flow.

Semi-empirical correlations for the estimation of the kLaoefficient in fixed-bed reactors can be divided into two groups:hose in which the evaluation of the coefficient is made using theressure drop and those based on the physical properties of gasnd liquid phases and on their superficial velocities. For the lat-er group, the main conclusions of the studies carried out showow the influence of the superficial velocity of the liquid phasen the volumetric mass transfer coefficient is relevant, usuallyt a similar level of contribution than the influence of the gashase [9]. As a general conclusion, it can be stated that contactimes for chemical reactors are lower than for bioreactors. Inhat way, superficial liquid velocity is playing a very importantole in gas–liquid mass transfer in chemical reactors, while inhe case of bioreactors is not, mainly due to relatively low liquiduperficial velocities (i.e. longer contact times are required iniological processes).

One of the main difficulties for the application of these corre-ations in bioreactors is mainly related to the range of superficialas velocities of gas and liquid phases. Usually, neither valuesf each gas and liquid superficial velocities are in the rangef applicability in which the correlation has been validated,or the ratio between these two velocities is the suitable oneo apply the correlation. When applying this type of correla-ions to bioreactors the values obtained for the kLa coefficientre underestimated, as already demonstrated by Deront et al.10].

In order to carry out an effective correlation between the dif-erent values of the kLa coefficient found in literature, a set ofifferent factors must be taken into account. Superficial veloc-ties of the two fluid phases, particle diameter and density andeometry of the solid particle [11] together with the physico-hemical properties of the liquid, are a priori the most relevantactors to be considered. However, the effect of temperature andhe specific configuration of each system could produce relevanthanges in the value of the volumetric mass transfer coefficient.he fact that kLa coefficient increases with temperature cane explained due to the increase of the diffusion coefficient,hich is directly proportional to the mass transfer coefficient

12]. For instance, when temperature is increased from 20 to5 ◦C, 20% increase of the kLa coefficient is observed [10].

he specific configuration of the system can modify the valuef the kLa coefficient in the bed: type of sparger used, type ofrids used to distribute the fluid phases and the system geometrytself.

tsfc

ing Journal 31 (2006) 188–196 189

The factors listed make very difficult to provide general cor-elations for the estimation of the volumetric oxygen transferoefficient in packed-bed biofilm reactors.

It is important to outline that in the study of Deront et al. [10],n which a bioreactor was used, the liquid flow pattern in theeactor was not experimentally verified. These authors assumeddeal plug flow in an up-flow cocurrent packed-bed reactor. Themportance of considering empirical residence time distributionor the liquid phase and its influence on the determination of theLa coefficient will be shown in this paper.

Two different techniques are used in this paper to character-ze gas–liquid mass transfer in up-flow cocurrent packed-bediofilm reactors. Residence time distribution experiments werearried out to evaluate the liquid flow pattern in the reactor.

mathematical flow model based on a tanks in series modelas modified with a backmixing flow to simulate the mixingroduced by the gas flow. This model was integrated in theethodology for the determination of the volumetric gas–liquidass transfer coefficient.

. Materials and methods

.1. Reactor description

An up-flow packed-bed cocurrent reactor is used for nitri-cation. The biofilm is integrated by Nitrosomonas europaeaATCC 19718) and Nitrobacter winogradskyi (ATTC 25391).his bench scale nitrifying reactor is used in a pilot plant for theevelopment of life support systems [13,14]. The main featuresf the biofilm reactor are shown in Fig. 1. Total reactor volumes 0.62 L and reactor height is approximately 43 cm. As it cane seen in Fig. 1, there are two main reactor diameters: 3.8 and.8 cm. The reactor has three main parts: (i) the bottom sectionn which there is a magnetic stirrer for liquid homogenization,ii) the bed, with the physical support for biofilm development,nd (iii) the top section for gas–liquid separation. The supportarticles are spherical expanded polystyrene beads (Biostyr®,.1 mm of mean diameter). External recirculation loop is used tomprove liquid mixing in the reactor. Temperature is controlledt 28.0 ± 0.1 ◦C using a thermostatic bath for the external jacketf the bed. The reactor was operating at atmospheric pressure.

The three different reactor parts described above have differ-nt geometries and the liquid and gas phases are flowing withifferent superficial velocities through them. This means that thexygen mass transfer rate could be different for each one of thehree parts.

.2. Liquid phase flow pattern

The analysis of the liquid mixing was carried out throughesidence time distribution (RTD) experiments. The tracer usedas blue dextran (SigmaTM Chemical Co.). This compound was

elected due to its high molecular weight (2 × 106 g/mol). Injec-

ion of tracer was performed in all experiments in the bottomection of the reactor (see Fig. 1). Samples were withdrawnrom the top section of the reactor (see Fig. 1). Blue dextranoncentration was determined by absorbance measurement at a

190 J. Perez et al. / Biochemical Engineering Journal 31 (2006) 188–196

Fig. 1. General schematic of the up-flow cocurrent packed-bed biofilm reactor: (1) packed-bed section, (2) bottom section for aeration and liquid distribution, (3)t , (7)p s.

wi

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op section for gas disengagement, (4) gas sparger, (5) gas exit, (6) liquid feedrobe, and (11) pH probe. Flow model assumptions for the liquid and gas phase

avelength of 618 nm. In Table 1 the different conditions usedn the experiments are presented.

.3. Determination of the kLa coefficient

.3.1. Gassing-out methodThe gassing-out method is a dynamic method which deter-

ines directly the volumetric mass transfer coefficient [15].his method is based on the dissolved oxygen concentration

n the culture broth. If the reactor gas supply is switched off, theissolved oxygen concentration measured will decrease follow-ng its consumption by the microorganisms. When the aerations switched on again the dissolved oxygen concentration willncrease to achieve the initial concentration. Mathematically,he kLa coefficient can be estimated from the increasing oxy-en concentration profile as a function of time of the last part inhe described experiment. This technique can be also applied toeactors without living microorganisms, in which the decrease of

he dissolved oxygen concentration can be reproduced by oxy-en stripping using a nitrogen gas flow through the reactor. Thatatter version of the method was the used for the experimentsescribed in this paper.

akls

able 1xperimental conditions for RTD experiments

xperiment no. Gas flow-rate(mL/min)

Liquid flow-rate(mL/min)

40 0.8540 0.85

500 0.80

liquid recirculation, (8) liquid outlet, (9) base addition, (10) dissolved oxygen

Oxygen concentration in the bulk liquid is determinedhrough a dissolved oxygen probe. Often, the dynamics of therobe is not fast enough to be neglected in the estimation ofLa coefficient. The following expression takes into account therobe dynamics [16]:

= C∗ + C∗ − C0

1 − τkLa

[τkLa exp

(− t

τ

)− exp(−kLat)

](2)

here C is the predicted dissolved oxygen concentration inhe bulk liquid, C* the oxygen solubility, C0 the initial dis-olved oxygen concentration and τ is the probe response timeonstant.

The probe response time constant can be determined using ahort experiment. For the assay the probe is located in a well-ixed tank in which no dissolved oxygen is present in the liquid

hase (this can be achieved through vigorous nitrogen bubbling).n the other hand, a second small vessel is saturated with oxygen

using air, and maintaining the vessel at atmospheric pressure

nd at the same working temperature that will be used for theLa determinations). Once the signal amplifier is showing veryow oxygen concentration, the probe is rapidly placed into theecond vessel. The recorded evolution of the dissolved oxygen

Stirring (rpm) Recirculation flow-rate(mL/min)

Recirculation ratio(inflow/rec.)

300 0 –300 4.5 1/6300 4.5 1/6

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3Three sections were considered to model the liquid flow in the

reactor, corresponding to the reactor configuration, as describedin Fig. 1. Each one of these parts was modelled as an ideallymixed tank. A dead volume was associated to the top part of the

J. Perez et al. / Biochemical Eng

oncentration is then used to determine the response time con-tant, assuming simple first order dynamics.

To determine the kLa coefficient with this method a univari-ble optimisation has been carried out using least squares toinimise sum of squares of the differences between the exper-

mental data recorded for dissolved oxygen concentration andq. (2).

.3.2. Sulphite methodThe classical chemical method for the determination of the

as–liquid oxygen transfer coefficient is the sulphite method.he principle consists on the measurement of the oxygen con-umption rate in the reactor once this is filled with a sodiumulphite solution and the aeration is switched on. The dissolvedxygen reacts with sulphite ions to produce sulphate and theecreasing sulphite concentration is followed by titration withodium thiosulphite. The oxygen consumption rate can be calcu-ated from the stoichiometry of the reaction. The full descriptionf the methodology for a well-mixed tank can be found else-here [6]. The reaction between oxygen and sulphite is assumed

o be instantaneous because it is a fast reaction catalysed byobalt ions and because the low solubility of oxygen in the liquidhase. This assumption allows to determine easily the kLa coeffi-ient as the ratio of the oxygen consumption rate and the oxygenolubility. The mass balances required to apply this methodol-gy are usually developed for stirred tanks. Here, the equationsave been adapted to the up-flow cocurrent packed-bed biofilmeactor using the corresponding flow model.

Determination of oxygen solubility in aqueous solution wasrst estimated using Henry’s law. Then, Henry’s constant wasorrected with the ionic strength of the aqueous solution and withemperature following the methodology proposed by Schumpet al. [17].

Samples as well as feed stock solutions were kept under inerttmosphere (nitrogen) during the experiments. In the experimentresented in this paper, samples were withdrawn from three dif-erent heights in the reactor (1–3 in Fig. 1).

.3.3. In-process estimationWhen the nitrifying biofilm reactor is in operation a direct

etermination of the kLa coefficient can be carried out throughhe methodology described by Kargi and Moo-Young [18] forxygen limiting conditions using the following equation:

La = YNO2−rNO2

− + YNO3−rNO3

−

C∗ − C(3)

here Yi are the stoichiometric parameters for the ammoniumxidation into nitrite (1.5 mol O2/mol NO2

−) and ammoniumxidation into nitrate (2 mol O2/mol NO3

−). ri is the nitrite anditrate production rates obtained in the packed-bed.

.4. Numerical methods: resolution of ODEs andptimisation. Determination of confident contours

The software used to carry out the different simulationsnd optimisations was MATLABTM 6.5 (R13). For the inte-ration of ordinary differential equations (ODEs) the standard

Fi4rr

ing Journal 31 (2006) 188–196 191

ATLABTM function ode15s was used, since this routine isainly using numerical differentiation formulas and Gear’sethods. When interpolation is required a polynomial interpo-

ation with three points (splines method, MATLABTM functionnterp1) was used. Parameters identification was made using

constrained optimisation methodology (MATLABTM func-ion fmincon), and least squares was used as goal function. Forhe estimation of confident contours in non-linear least squares

ethods the technique described by Draper and Smith [19] wassed.

. Results and discussion

.1. Modelling RTD experiments

Results of the RTD experiments are presented in Fig. 2.imensionless tracer concentration was obtained by multiply-

ng tracer concentration times the ratio: liquid volume/mass ofracer. Dimensionless time was obtained using the number of res-dence times (residence time was determined as liquid volumeivided by liquid flow-rate). As can be observed, RTD was closeo a well-mixed tank for experiments 2 and 3. In these exper-ments, vigorous aeration is used (experiment 3), or at least aigh external recirculation ratio is applied (experiment 2). Onhe contrary, no external recirculation is applied in experiment, where a relatively important deviation from an ideally mixedank can be observed in Fig. 2.

In addition, in all three experiments, the maximum dimen-ionless tracer concentration is found to be higher than unity.his fact, together with the shape of the RTD curve, suggests aead volume in the reactor [20].

.1.1. Flow model

ig. 2. Experimental results for residence time distribution (RTD) experimentsn the up-flow cocurrent packed-bed biofilm reactor (experiment 1: gas flow-rate0 mL/min, no external recirculation; experiment 2: gas flow-rate 40 mL/min,ecirculation ratio 1/6; experiment 3: gas flow-rate 500 mL/min, recirculationatio 1/6, for more details about experimental conditions, see Table 1).

1 ineering Journal 31 (2006) 188–196

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Table 3Experiment conditions and kLa determination using the gassing-out method

Gas flow-rate(mL/min)

Stirring(rpm)

Recirculationflow-rate(qr, mL/min)

vvm(min−1)

kLa (s−1)(top section)

40 300 4.5 0.08 0.001340 300 9 0.08 0.001640 500 4.5 0.08 0.0014

100 300 4.5 0.2 0.0032250 300 4.5 0.5 0.00725

3

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92 J. Perez et al. / Biochemical Eng

eactor, since an important change in the nominal diameter inhe top part of the reactor exits (see Fig. 1), which can easilyead to poor mixing in this reactor section. The mass balancequations for the tracer in each defined tank in which the reactoras divided, can be written as,

dCA

dt= 1

VA[qrCC + f (q + qr)CB − (1 + f )(q + qr)CA] (4)

dCB

dt= 1

VB[(1 + f )(q + qr)CA + f (q + qr)CC

− (1 + 2f )(q + qr)CB] (5)

dCC

dt= 1

VC − Vd[(1 + f )(q + qr)CB − (1 + f )(q + qr)CC]

(6)

here CA, CB and CC are the tracer concentrations for each tank, B and C defined in Fig. 1. The liquid volumes of each tank

re VA = 0.0683 L, VB = 0.1705 L and VC = (0.2332 − Vd) L. Vds the dead volume assumed to be associated to the top section.

is the liquid flow-rate and qr is the recirculation flow-rate.he following expression defines the target function used for

he calibration of the model:

obj =n∑

i=1

(ythei − y

expi

)2

(7)

here n is the number of experimental points for each RTDxperiment and ythe

i is the theoretical concentration of tank C atime t, calculated after solving the differential equation systemefined in Eqs. (4)–(6). y

expi is the experimental value of tracer

oncentration at the same time instant t. Interpolation at that timenstant is required for ythe

i , once the integration is performed.The optimisation variables are the backmixing coefficient (f)

nd the dead volume defined for the top section (Vd). In addition,he following constraints were added to the multivariable optimi-ation problem: (i) f ≥ 0 and (ii) 0 ≤ Vd ≤ 0.233. For experimenta univariable optimisation was carried out. The variations in

ead volume are assumed to be related to the recirculation flow-ate applied. For this reason the dead volume was fixed as the oneetermined in experiment 2. The confidence contour is in this

xperiment a single interval. Results after optimisation estima-ion of backmixing coefficient and dead volume are summarisedn Table 2. Fitting results for each experiment are presented inig. 3.

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able 2esults of the optimized parameters for the liquid flow model

xperiment no. Backmixingcoefficient (f)

Backmixing flow-rate(qr, mL/min)

Dead volum(Vd, mL)

0.7515 0.6 93.12.027 0.14 52.42.0 ± 0.8 10.6 52.4

onsistency of the RTD experiments was verified comparing measured and calculatedTD curve. Confidence contour for experiments 1 and 2 are presented in Fig. 3 B1 an

00 300 4.5 1.0 0.012

.2. kLa determination applying the gassing-out method

The experiment carried out to determine the probe responseime constant is shown in Fig. 4A. The estimated value forhe response time constant of the dissolved oxygen probe usedInPro 3000/120, Mettler Toledo) is 27.5 ± 0.4 s.

A set of experiments was performed using the reactor con-itions as shown in Table 3. Using the probe response timereviously determined, the kLa coefficient could be obtained.he estimated values for the kLa coefficient are presented

n Table 3. An example of the model output is given inig. 4B.

Using the flow model results, the effect of the liquid mix-ng in the determination of kLa was investigated. A simulationas performed to reproduce the gassing-out method applied

xperimentally. The following term corresponding to the oxy-en transferred to the liquid phase in each one of Eqs. (4)–(6)as included,

kLa)i(C∗ − Ci) (8)

here C* is the oxygen solubility already defined for Eq. (2)nd Ci is the dissolved oxygen concentration of the bulk liquid.ubscripts i denotes the corresponding reactor sections, A, Bnd C for Eqs. (4)–(6), respectively. Results of this simulationre presented in Fig. 5. The (kLa)i values were fixed as stronglyeterogeneous along reactor vertical axis (i.e. in the reactor sec-ions A, B and C).

To determine the influence of the liquid mixing in the deter-

ination of the kLa coefficient through the method gassing-out,second type of simulation was performed. This method was

pplied independently for each section, considering each onef the three sections as stirred tanks not connected through the

e Measured mass oftracer (g)

Calculated massof tracer (g)

Deviation in massof tracer (%)

0.1839 0.1825 10.1825 0.1726 60.1869 0.1763 6

mass of tracer. Calculated mass of tracer was found integrating the experimentald 2.

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efraction can be calculated using the following equations:

FBi

J. Perez et al. / Biochemical Eng

iquid phase. In that way, it is possible to evaluate the effect ofhe liquid mixing in the dynamic variation of dissolved oxygenn the bulk liquid.

As can be observed in Fig. 5 there are important differencesn the dissolved oxygen concentration between both simulationserformed. Clearly, the influence of the dissolved oxygen sup-lied to one of the sections from the contiguous ones throughhe liquid phase is not negligible. It is clearly demonstrated thato determine the kLa coefficient with this method it is necessaryo take into account the flow model.

Since the dissolved oxygen probe is placed in the top sec-ion of the reactor, the kLa could be associated to this sec-

ion. Nevertheless, given that it is shown that liquid mixingan hide the real value of the kLa coefficient other method-logy could be required for the correct estimation of the kLaoefficient.

ig. 3. Results of the model after optimisation of parameters for RTD experiments. A2 the confidence contour of the parameters optimised for experiments 1 and 2, respe

s a single interval, detailed in Table 2. Experimental conditions are detailed in Table

ing Journal 31 (2006) 188–196 193

.3. kLa determination applying the sulphite method

Taking into account the flow model already validated the oxy-en mass balance in the reactor can be expressed as (see Fig. 1):

inyin − Goutyout = (rO2 )AVA + (rO2 )BVB + (rO2 )CVC (9)

here G is the molar gas flow-rate, y the oxygen molar fraction,ubscripts in and out denote reactor inlet and outlet, respectively,O2 the oxygen consumption rate and V is the volume, both forach reactor sections A, B and C. The outflow oxygen molar

yout = A1

1 + A1; where A1 = yB − (rO2 )C(VC/GB)

1 − yB;

with GB = GA − (rO2 )BVB (10)

1, A2, A3 are the model results for experiments 1–3, respectively, and B1, arectively. The confidence contour in experiment 3 for the backmixing coefficient1.

194 J. Perez et al. / Biochemical Engineering Journal 31 (2006) 188–196

F const4

y

Wr

(

(

(

w

Fgotl(

sr

ig. 4. Dynamic gassing-out method. Determination of the probe response time0 mL/min, recirculation flow-rate: 4.5 mL/min, stirring 300 rpm.

yB = A2

1 + A2; where A2 = yA − (rO2 )B(VB/GA)

1 − yA;

with GA = Gin − (rO2 )AVA (11)

A = A3

1 + A3; where A3 = yin − (rO2 )A(VA/Gin)

1 − yin(12)

hen the mass balance is applied, the (kLa)i coefficient for eacheactor section can be estimated as:

kLa)A = (rO2 )A

C∗A

; where C∗A = yinPin − yAPA

H ln(yinPin/yCPC)(13)

kLa)B = (rO2 )B

C∗B

; where C∗B = yAPA − yBPB

H ln(yAPA/yBPB)(14)

kLa)C = (rO2 )C

C∗C

; where C∗C = yBPB − yCPC

H ln(yBPB/yCPC)(15)

here P is the total pressure and H is the Henry’s constant.

ig. 5. Simulations to determine the influence of the liquid mixing on theas–liquid oxygen transfer dynamics. Simulation 1: flow model coupled toxygen gas–liquid transfer, and simulation 2: gas–liquid mass transfer for thehree sections considering them as separated reactors (without any physicalink). Values used for both simulations: (kLa)A = 0.0028 s−1, (kLa)B = 0.02 s−1,kLa)C = 0.0014 s−1, recirculation flow-rate = 4.5 mL/min.

w

w

tC

ibttCia

Ia4(tprft

ant determination (A) and example of kLa determination (B) aeration flow-rate:

To calculate the oxygen consumption rates in the three reactorections A, B and C, the sulphite mass balance equations in theeactor have to be considered, as follows:

dCA

dt= 1

VA[qrCC + f (q + qr)CB − (1 + f )(q + qr)CA]

− 2(rO2 )A (16)

dCB

dt= 1

VB[(1 + f )(q + qr)CA + f (q + qr)CC

− (1 + 2f )(q + qr)CB] − 2(rO2 )B (17)

dCC

dt= 1

VC[(1 + f )(q + qr)CB − (1 + f )(q + qr)CC]

− 2(rO2 )C (18)

ith (rSO32− )

i= 2(rO2 )i; i = A, B and C (19)

here (rSO32− )

iis the thiosulphate consumption rate.

Eqs. (16)–(19) show how the flow model is combined withhe oxygen consumption rate (rO2 )i for each section i = A, B and.

The sulphite concentration was determined experimentallyn the three sections defined in the reactor: packed-bed, top andottom sections. These experimental values are used as y

expi in a

arget function defined in Eq. (7). Whereas, in this case, yexpi are

he values obtained from the integration of Eqs. (16)–(18) forA, CB and CC at the different sampling times. When required

nterpolation at the particular sampling time has been used (aslready explained in Section 2.4).

The results after optimisation are presented in Fig. 6A.n this experiment the following conditions were fixed: aer-tion flow-rate at 40 mL/min and recirculation flow-rate at.5 mL/min. kLa values found were for the bottom sectionkLa)A = 0.024 s−1, packed-bed section (kLa)B = 0.077 s−1 andop section (kLa)C = 0.002 s−1. The confidence contours for the

arameters obtained determined for a confidence level of 95%,esults are shown in Fig. 6B. The highest accuracy was foundor (kLa)B, the volumetric mass transfer coefficient associatedo the packed-bed section. The highest oxygenation capacity is

J. Perez et al. / Biochemical Engineering Journal 31 (2006) 188–196 195

Table 4kLa determination in the bed section using the in-process estimation

Aeration flow-rate (mL/min) Inflow ammonium load(kg N m−3 day−1)

Removed ammoniumload (%)

Total removedload (%)

kLa range (s−1)

9 0.42 85.3 82.7 0.017 ± 0.0031 91.6

85.34 83.3

ata

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borihfio

FttBtE4

i[c(ccst[

C

5 0.429 0.550 1.11

lso associated to the packed-bed, where the gas–liquid massransfer is enhanced by improving the contact between phasest a higher gas superficial velocity.

.4. kLa determination through the in-process estimationethod

After several months of continuous operation of the nitrifyingiofilm reactor four different steady states were found in whichxygen limitation was governing the conversion obtained in theeactor. Load, conversion and aeration flow-rate for these exper-

ments are described in Table 4. Partial nitrification to nitriteas been reported by several authors [14,21–23]. Partial nitri-cation to nitrite is produced in biofilm reactors for dissolvedxygen concentrations lower than 2.5 mg L−1 [22,24]. Assum-

ig. 6. Determination of kLa coefficient using the sulphite method coupled withhe liquid flow model. (A) Experimental determination of the sulphite concen-ration (through titration) and model results for each reactor section: A, bottom,, packed-bed, C, top section. (B) Confidence contour of the optimised parame-

ers (kLa values for the three sections A, B and C) for a confidence level of 95%.xperimental conditions: aeration flow-rate: 40 mL/min, recirculation flow-rate:.5 mL/min.

wat

4wcfdw

wv

k

w

Ffld

89.9 0.018 ± 0.00377.7 0.022 ± 0.00468.2 0.026 ± 0.005

ng this dissolved oxygen concentration range in the bulk liquid0–2.5] mg L−1, a direct determination of the kLa coefficientan be carried out through the in-process estimation methoddescribed in Section 2.3.3). Oxygen solubility has been cal-ulated based on Henry’s law, correcting the value of Henry’sonstant taking into account the ionic strength of the feedingolution. For this calculation a second correction has been usedo include the effect of the pressure with the following expression25]:

∗corrected = C∗

[1 + ρg

Patm

1 − εg

1 − εp(h − l)

](20)

here ρ is the liquid density, g the gravity acceleration, Patm thetmospheric pressure, εg the gas hold up, εp the solid hold up, hhe sparger depth and l is the distance from the sparger.

The kLa value obtained with an aeration flow-rate of0 mL/min is 0.026 s−1, which is lower than the value estimatedith the sulphite method (0.077 s−1). The decrease in the kLa

oefficient when a mature biofilm is developed was also foundor a biofilm reactor by Fujie et al. [11]. They showed a 50%ecrease in the kLa value when this coefficient was comparedith the estimation prior inoculation of the reactor.With the results presented in Table 4 the following correlation

as established for kLa coefficient as a function of gas superficial

elocity (uG),

La = 0.082u0.35G (21)

ith uG in cm/s and kLa in s−1.

ig. 7. Correlation of kLa coefficient with gas superficial velocity (uG) and gasow-rate. Goodness of fitting for a confidence level of 95% is shown by theashed line. Experimental conditions are described in Table 4.

1 ineer

fi

4

bdftmtdobecet

ae

sspov0

A

tMNdC

R

[

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[[

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[

[

[

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96 J. Perez et al. / Biochemical Eng

In Fig. 7 the kLa values obtained are plotted versus gas super-cial velocity and gas flow rate.

. Conclusions

The gas–liquid mass transfer in an up-flow cocurrent packed-ed biofilm reactor was studied focussing the research in theetermination of the volumetric mass transfer coefficient (kLa)or oxygen. Residence time distribution experiments were usedo determine the liquid phase mixing in the reactor and a flow

odel has been calibrated and used for the final determination ofhe kLa coefficient. Three different methods for kLa coefficientetermination were used and assessed: (i) dynamic gassing-ut, (ii) sulphite method, and (iii) in-process estimation throughiological conversion obtained in the reactor. The flow modelxperimentally obtained using residence time distribution wasoupled to these methods. Simulation was used to stress the rel-vant effect of the liquid phase mixing in the determination ofhe kLa coefficient.

The kLa coefficient was found to be strongly heterogeneouslong reactor height. A value of the coefficient was estimatedxperimentally for each reactor section (bottom, bed and top).

kLa coefficient ranged between 0.01 and 0.12 s−1 in the bedection, where the biotransformation is taking place when theulphite method was coupled to the experimental liquid flowattern. An in-process estimation of the kLa value was used tobtain a preliminary correlation as a function of gas superficialelocity (i.e. gas flow-rate). The correlation found was: kLa =.082u0.35

G .

cknowledgements

This work has been carried out in the framework ofhe development and operation of the Pilot Plant of the

ELISSA project, European Space Agency (ESTEC/Contracto. 13292/98/NL/MV), with co-funding from Plan Nacionalel Espacio (ESP2004-20347-E) and DURSI (Generalitat deatalunya).

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