Reassessment of the estimation of dissolved oxygen concentration profile and KLa in solid-state fermentation

Process Biochemistry 36 (2000) 9 – 18 www.elsevier.com/locate/procbio

Reassessment of the estimation of dissolved oxygen concentration profile and KLa in solid-state fermentation Jules Thibault a,*, Kathleen Pouliot b, Eduardo Agosin c, Ricardo Pe´rez-Correa c a

Department of Chemical Engineering, Uni6ersity of Ottawa, Ottawa, Ont., Canada K1N 6N5 Department of Chemical Engineering, La6al Uni6ersity, Sainte-Foy, Que., Canada G1K 7P4 c Department of Chemical and Bioprocess Engineering, Pontificia Uni6ersidad Cato´lica de Chile, Casilla 306, Santiago 22, Chile b

Received 18 November 1999; accepted 5 March 2000

Abstract Oxygen mass transfer in aerobic microbial growth systems is often a limiting factor for optimal growth and productivity. Oxygen mass transfer has been widely studied in submerged fermentations but has attracted as yet little attention for solid state fermentations. The parallel to submerged fermentation has led to the incorrect interpretation and use of the overall oxygen mass transfer coefficient (KLa) to assess the ability of a particular fermentation system to supply the oxygen to microorganisms. The use of KLa, as traditionally defined, should be used with caution in solid substrate fermentation systems because there is no convection on the liquid side of the medium, and oxygen is consumed in the biofilm. Hence, KLa must be redefined for solid state fermentation. In this paper, the use of oxygen mass transfer coefficients in solid state fermentations is clarified. Published literature data were analysed with a simple pseudo-steady-state model and used to discuss the influence of the biofilm thickness, the dissolved oxygen diffusion coefficient, the convective gas mass transfer coefficient, and the gas flow rate on the oxygen mass transfer coefficient in solid state fermentations. © 2000 Published by Elsevier Science Ltd. All rights reserved. Keywords: Oxygen mass transfer; Solid state fermentation; Biofilm; Diffusion coefficient; Dissolved oxygen coefficient

1. Introduction In aerobic fermentations, oxygen transfer to the microorganism is undoubtedly the most important phenomenon to sustain microbial activity. The rate of oxygen transfer to the cells is often the limiting factor that determines the rate of biological conversion. An insufficient oxygen transfer leads to a decrease of microbial growth and product formation. To quantify oxygen transfer to the fermentation medium, the overall oxygen mass transfer coefficient (KLa) is usually measured or estimated. In submerged fermentations (SMF), oxygen in gas bubbles diffuses toward the liquid film where it dissolves at the gas–liquid interface. The dissolved oxygen, then, diffuses through the liquid film that surrounds the gas bubble before entering the continu* Corresponding author. Tel.: +1-613-5625920; fax: + 1-6135625172. E-mail address: [email protected] (J. Thibault).

ous liquid bulk where it is made available to microorganisms. KLa accounts for the total surface area between the gas and the liquid phase (a), and the overall convective mass transfer coefficient (KL). The latter considers the mass transfer resistance on both sides of the gas–liquid interface. Outside the gas and the liquid films, the gaseous and dissolved oxygen concentrations are considered homogeneous. Several methods, such as sulphite oxidation, the dynamic method or overall gas balance are currently employed to measure or estimate KLa. Moreover, the dissolved oxygen concentration, required by most methods for KLa evaluation, can be easily measured in this culture system using a dissolved oxygen probe. In solid state fermentation (SSF), a packed bed of moist solid substrate particles is used for microbial growth. The microorganisms grow within or on the surface of solid particles, which are surrounded by thin liquid film. Because of the relatively little amount of liquid in the growth environment, microorganisms are in close contact with the gaseous oxygen that flows in

0032-9592/00/$ - see front matter © 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S0032-9592(00)00156-4

J. Thibault et al. / Process Biochemistry 36 (2000) 9–18

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the void space of the packed bed. Therefore, oxygen mass transfer coefficient and rates might be even more critical in SSF than in SMF, as recently proposed by Oostra et al. [1] and in contradiction with previous reports [2]. In SSF, the oxygen mass transfer to the microorganism is similar to SMF as far as the gas phase and gas film are concerned. Indeed, oxygen from the flowing gas diffuses toward the liquid film where it dissolves at the gas–liquid interface. However, a uniformly mixed bulk liquid phase beyond the liquid film does not exist in SSF and there is no convection on the liquid side. The dissolved oxygen simply diffuses within the stagnant liquid film under a concentration gradient resulting from the utilisation of dissolved oxygen by the microorganisms. Therefore, KLa reported for SSF cannot be interpreted in an identical manner as in SMF. A few attempts have been made to evaluate KLa in SSF. Durand et al. [3] proposed an interesting adaptation of the sulphite oxidation method to determine KLa in a packed bed fermentation system. Gowthaman et al. [4,5] have used the overall gas balance method for estimating KLa in the course of SSF. The latter method uses the difference of oxygen gas concentration between inlet and outlet gas streams. In both papers, the volumetric rate of oxygen mass transfer is expressed using an equation similar to the following: NO2 = KLa(CL,R 2 −CL,R 1)

(1)

where NO2 represents the number of moles of oxygen consumed per cubic meters of fermenter per s. R1 is the radius of the solid particle alone and R2, the radius of the solid particle with the surrounding liquid film. This equation assumes quasi-steady state fermenter operation, resistance to mass transfer only due to the liquid film, and microorganisms grow only in the liquid film surrounding the particle. Based on these assumptions, CL,R 2 is in thermodynamic equilibrium with the gas phase outside the particle and the concentration of dissolved oxygen within the solid particle is uniform and equal to CL,R 1. However, since there is no convection on the liquid side, the use of KLa does not meet the strict definition of the overall oxygen mass transfer coefficient. Indeed, on the assumption that there is no oxygen consumption in the liquid film but only oxygen diffusion across the film, as normally it is assumed in SMF, the overall convective mass transfer coefficient (KL) could only be interpreted as the ratio of the dissolved oxygen diffusion coefficient in the liquid film to the thickness of the liquid film (d), as given by the Fick’s first law of diffusion: NO 2 =

 

DO2,L a(CL,R 2 −CL,R 1) d

(2)

Since in SSF, oxygen is consumed in the liquid film due to the presence of the microorganism, the dissolved

oxygen concentration profile results from both diffusion and consumption. Hence, to determine the dissolved oxygen concentration profile the mass balance equation must be solved, as it will be seen later in this paper. Even though the mass flux density as given by Fick’s law of diffusion, will vary across the liquid film due to oxygen consumption, Eqs. (1) and (2) account for the average behaviour of the oxygen transfer across the film. In summary, the use of KLa to describe the oxygen mass transfer in SSF is inappropriate in two accounts, the absence of convection on the liquid side and the oxygen consumption in the liquid film. Despite these shortcomings, the use of Eq. (1) can still provide some assessment of the influence of operating conditions on the oxygen mass transfer. However, the determination of this KLa value is not trivial since the dissolved oxygen concentration in the liquid film cannot be measured. Most methods developed for the determination of KLa require this measurement. The objective of the present paper was to clarify the oxygen mass transfer phenomena in SSF. In particular, a model to determine the oxygen concentration profile within the biofilm and to estimate the KLa value has been developed and tested with the experimental data of Gowthaman et al. [4,5]. The paper is divided as follows — after a brief description of the experiments that were used to generate the data, the mass transfer model and some results are presented and discussed.

2. Materials and methods The experimental data used in this investigation to assess the oxygen mass transfer in a SSF, were taken from Gowthaman et al. [4]. The same data were used by Gowthaman et al. [5] to estimate KLa during SSF. The fermenter used in their work was a stainless-steel packed column bioreactor, 345-mm high and 150 mm in diameter. The production of amyloglucosidase on moistened commercial wheat bran by Aspergillus niger was used as a SSF model. In addition to the stainless steel column, the experimental unit consisted of a humidifier, an air-flow meter, wet and dry bulb thermometers, temperature data logger, and oxygen and carbon dioxide analysers. The biological reactor was aerated from the bottom. In their experiments, gas sampling ports were located taken at five axial positions (33, 80, 120, 170, and 280 mm) and the oxygen concentration of the inlet air was 20.8% (v/v). The bioreactor outlet oxygen concentration was not reported. The model presented in the next section has, therefore, been developed for a 280-mm high packed-column bioreactor instead of the actual height of 345 mm. The results of Gowthaman et al. (1993) were presented in graphical form. Therefore, the UN-SCAN-IT software (Silk Sci-

J. Thibault et al. / Process Biochemistry 36 (2000) 9–18

entific) has been used to digitise each experimental data point of zoomed graphical plots in order to provide tables of gaseous oxygen concentration as a function of fermentation time. It is estimated that the resolution of the experimental points obtained by this discretisation scheme is very good. 3. Development of the oxygen mass transfer model The model developed in this investigation considers the oxygen mass transfer mechanisms in a packed bed of spherical particles during the growth of a filamentous fungus. The microorganism is assumed to grow uniformly on the surface of each spherical particle. Fig. 1 presents a schematic view of the oxygen transfer mechanisms that take place in the vicinity and in a hypothetical spherical particle surrounded by a thin liquid film in which the mycelium grows. In any section of the packed bed, oxygen diffuses from the gas phase to the gas–liquid interface, where it dissolves to enter the liquid phase. The dissolved oxygen, then, migrates in the liquid film and in the solid particles under the action of a concentration gradient that results from the consumption by microorganisms of the oxygen in the liquid film. Oxygen material balances will be restricted to the four sections of the packed bed for which experimental data are available, i.e. 0 – 33, 33 – 80, 80– 170, and 170–280 mm. To develop the model the following simplifying assumptions were made. 1. In view of the relative slow dynamics of cellular growth in the biofilm compared to transport dynamics, the hypothesis of pseudo-steady-state condition is justified [6]. This implies that the concentration profiles in the gas and liquid phases can be considered constant and result oxygen consumption. The activity of microorganisms is such that the oxygen consumption is equal to the deficit of oxygen in the gas phase in given section of the packed bed. 2. The fungus is unable to penetrate into the matrix of the solid particles and grows strictly in the surrounding liquid film. The oxygen is, thereby, only consumed in the biofilm, and no oxygen consumption inside the solid particles occurs.

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3. The thickness of the biofilm is constant; that is the film does not expand in time. This assumption is not restrictive in view of the pseudo-steady-state assumption since the influence of the biofilm thickness can easily be investigated. 4. The density of biomass in the biofilm and the oxygen consumption rate are uniform. Thus, the profile of oxygen in the biofilm will only vary with the radial position. 5. The oxygen diffusivity is identical both in the particle and in the liquid film. However, the model can accommodate two distinct diffusivities. 6. The oxygen concentrations in the gas and the liquid phases at the gas–liquid interface are in equilibrium (C iG, C iL). The equilibrium oxygen solubility can be calculated with Henry’s law. 7. All particles are spherical and have the same diameter. 8. The volumetric gas flow rate is constant throughout the bioreactor. With these assumptions, the oxygen mass equation and the boundary conditions for each individual bed particle can be written as follows: Mass balance:



1 ( 2 (Co2 r − DO2,L 2 r (r (r



= − DO2,L



( 2Co2 2 (Co2 + r (r (r 2

= Ro2

(3)

Boundary conditions: At r= 0;

(CL =0 (r

At r= R1;

D FO2,L

(C FL (C SL S =D O ,L 2 (r (r

(5)

At r=R2;

D FO2,L

(C FL =kG(CG − C iG) (r

(6)

(4)

The values of the parameters used in the simulation were chosen as close as possible to the experimental parameters of Gowthaman et al. [5]. The values of these parameters are given in Table 1. To solve the oxygen mass balance, the gas-phase mass transfer coefficient (kG) was calculated with correlations found in the literature (see Appendix A). Having estimated kG by one of the equations of Appendix A, it is now possible to calculate the oxygen concentration at the gas–liquid interface (C iG) using the following equation: QG(CG,In − CG,Out)= kGAPnP(C( G − C iG)

Fig. 1. Schematic representation of mass transfer mechanisms.



(7)

This equation simply states that the oxygen content lost in a section of the packed column must equal the total amount of oxygen transferred by convection to the nP particles. C( G is taken as the mean between CG,In and CG,Out of a section of the packed column. C iG can, therefore, be calculated explicitly from Eq. (7). As a

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12 Table 1 Nominal values of simulation parameters Parameter Biofilm thickness (d) DO2,G DO2,L Diameter of packed column P QG R R1 T o rG rL mG

Value 25mm 2.08×10−5 m2/s 2.50×10−9 m2/s 0.150 m 101 300 Pa 5, 20 l/min 8.313 Pa m3/gmol K 2 mm 30°C 0.4 1.177 kg/m3 1000 kg/m3 1.846×10−5

Reference

through the section of the column. This stationary oxygen mass balance allows calculating the average rate of oxygen consumption in the liquid film as expressed by the following equation:

Assumed

Ro2 = Gowthaman et al. [4] – Gowthaman et al. [4] – Gowthaman et al. [4] Assumed Assumed

QG(CG,In − CG,Out) nP(4/3)p(R 32 − R 31)

(8)

RO2 and NO2 both express the volumetric rate of oxygen consumption, RO2 is evaluated on the basis of the total volume of biofilms in a section of the packed column whereas NO2 is defined using the total volume of a particular section of the packed column. The oxygen mass balance in the liquid film and the solid particle can easily be solved in order to calculate the dissolved oxygen profile using an implicit finite difference method which allows to modify easily any assumption such as having values of DO2,L and RO2 that vary with position. However, if all the above assumptions are strictly adhered to, the following analytical solution can be used:





CL(r) 1 RO2R2 = 1+ 6 DO2,LC iL C iL

      r R2

2

−1 +2

R1 R2

3

R2 −1 r

n

(9)

4. Results

Fig. 2. Dissolved oxygen radial concentration profiles for various axial positions at 20 h of fermentation.

result, C iL, the equilibrium concentration at the gas–liquid interface on the liquid side, can simply be calculated from Henry’s law and used directly as the boundary instead of solving Eq. (6). Similarly, given the above assumptions, it is possible to simplify the calculation by setting the derivatives at the particle – film boundary equal to zero. Finally, the average oxygen consumption rate in the biofilm for a specific section of the packed column must be equal to the deficit in oxygen of the gas passing

The pseudo-steady-state model was used to determine dissolved oxygen concentration profiles in the biofilm and in the solid particle that corresponded to the experimental gaseous oxygen concentration drop in a given section of the packed column. Profiles were obtained for various sections of the packed column, various fermentation times, and two gas flow rates (5 and 20 l/min). The nominal thickness of the biofilm was assumed to be 25 mm. This biofilm thickness is undoubtedly conservative for the majority of biochemical systems at a later stage of fermentation but will not affect the discussion of this paper. To make a parallel with previous studies, the overall oxygen transfer coefficient (KLa), as defined by Eq. (1) was calculated in each case. The influence of the dissolved oxygen diffusivity, the gas-phase mass transfer coefficient (kG), and the biofilm thickness were also investigated.

4.1. Oxygen concentration profiles and KLa estimation The dissolved oxygen concentration profiles in the solid particle with its biofilm have been calculated at various fermentation times (12, 20, 24, 42, 48 h) and for different sections of the packed column. All results are similar so that only few profiles are presented. Fig. 2 presents dissolved oxygen concentration profiles, corresponding to a fermentation time of 20 h, for the four

J. Thibault et al. / Process Biochemistry 36 (2000) 9–18

sections of the packed column and for the two gas flow rates. In this investigation, it was assumed that microorganisms surrounded the solid spherical particles to form a thin biofilm and no growth occurred inside the particles. As a result, oxygen consumption occurred only in the biofilm. Therefore, within the particle (r[0, 1] mm), a flat concentration profile prevails under pseudo-steady state conditions which is the reason for showing only a portion of the plot. Within the biofilm, the drop in the dissolved oxygen concentration varied from 14% (170–280 mm) to 27% (0 – 33mm) for a gas flow rate of 5 l/min and from 10% (80 – 170 mm) to 53% (0 – 33 mm) for an air flow rate of 20 l/min. Fig. 2 also shows the influence of the gas flow rate on the equilibrium dissolved oxygen concentration at the

Fig. 3. Dissolved oxygen concentration profiles for various fermentation times for the section of the packed column between 33 and 80 mm.

Table 2 Difference in dissolved oxygen concentration (DC) across the biofilm for various fermentation times for a specific section of the packed column (33–80 mm) Fermentation time (h)

12 20 25 42 48

Air flow rate= 5 l/min

Air flow rate= 20 l/min

DC (%)

DC (%)

5 15 15 11 8

KLa (per s) 0.344 0.344 0.344 0.344 0.344

12 20 40 20 8

KLa (per s) 0.344 0.344 0.344 0.344 0.344

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gas–liquid interface (C iL). The maximum variation of the equilibrium concentration is 7.5% when the gas flow rate was 5 l/min, whereas it was negligible for the higher gas flow rate of 20 l/min. The maximum variation of the dissolved oxygen concentration at the interface was observed in the higher section of the packed column because of the slight depletion of the oxygen in the gas stream. Increasing the gas flow rate from 5 to 20 l/min only produces a 6% increase in the equilibrium dissolved oxygen concentration in the higher portion of the bed and a negligible one in the first section. Hence, in SSF, an increase in the gas flow rate would not improve significantly the oxygen mass transfer. Dissolved oxygen concentration profiles being known, it is possible to evaluate KLa, using Eq. (1). For each section of the packed column, for a fermentation time of 20 h, and for both gas flow rates, KLa values were identical and equal to 0.344/s. This simply indicated that the ratio of the average rate of consumption to the average concentration gradient in the biofilm was a constant. The dissolved oxygen mass flux density was maxima at the surface of the biofilm and became zero at the particle–biofilm interface. The various dissolved oxygen concentration profiles for the second section of the packed column (33–80 mm) as a function of the fermentation time are presented in Fig. 3. The percentages of the variation of the oxygen concentration as a function to time are presented in Table 2 along with the calculated values of KLa determined for each experimental data point. The dissolved oxygen concentration differences (DC) across the biofilm varied from 5 to 15% for an air flow rate of 5 l/min and in the range of 8–40% at 20 l/min depending on the current estimated biological activity within the biofilm. Results of Table 2 also indicated that at the fermentation time for which the maximum metabolic activity occurred (20–25 h) [4] the highest oxygen concentration variations were reached. The value of KLa, as defined by Eq. (1) was still equal to 0.344/s for all cases. The inverse value of KLa of the order of 3 s, can be viewed as a mass transfer time constant. Since this value was is significantly smaller than the biological reaction rate, the hypothesis of pseudo-steady-state conditions was justified.

4.2. Diffusion coefficient As showed in Fig. 1, oxygen was transferred by convection from the gas phase to the biofilm and then diffused through the biofilm and the solid particle. It is clear that the main resistance to mass transfer was due to the biofilm and the dissolved oxygen diffusivity was the most appropriate parameter to characterise the oxygen mass transfer in SSF. The influence of the dissolved oxygen diffusivity has been tested under identical experimental conditions,

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An increase in the dissolved oxygen diffusivity leads to a small decrease of the concentration difference across the biofilm, resulting in a flatter concentration profile. A decrease in the diffusivity has a profound impact on the oxygen concentration profile. If the dissolved oxygen diffusivity is too small, the oxygen availability to the microorganisms located at the solid–liquid interface could be critical. Anaerobic conditions could, therefore, exist in a portion of the biofilm.

4.3. Gas-phase mass transfer coefficient Three different literature correlations (Eqs. (10)– (12), Appendix A) were used to calculate the gas phase convective mass transfer coefficient (kG). Dissolved oxygen concentration profiles obtained with each correlation under identical operating conditions, for a fermentation time of 20 h and the section of the packed column corresponding to 33–80 mm, are presented in Fig. 5. Values of the convective mass transfer coefficients for each of these correlations and for the two air flow rates are given in Table 3. Fig. 4. Influence of the dissolved oxygen diffusivity on concentration profiles.

4.4. Biofilm thickness The thickness of the biofilm used in all previous simulations was 25 mm and was chosen somewhat arbitrarily. In practice, this film would change throughout the fermentation as well as being influenced by other operating conditions. Fig. 6 presents the dissolved

Fig. 5. Dissolved oxygen concentration profiles for three estimations of kG at 20 h and for the section of the packed column between 33 and 80 mm. Table 3 Gas-phase mass transfer coefficient (kG) for a fermentation time of 20 h and an axial position of 33–80 mm Air flow rate (l/min)

kG (m/s) Eq. (5)

5 20

Eq. (6)

Eq. (7)

1.05×10−3 7.90×10−3 2.03×10−2 7.29×10−3 1.79×10−2 2.03×10−2

that is a fermentation time of 20 h and for the section of the packed column corresponding to 33 – 80 mm. The nominal value of the dissolved oxygen diffusivity was 2.5 ×10 − 9 m2/s (Table 1). Dissolved oxygen profiles for five different values of DO2,L are presented in Fig. 4.

Fig. 6. Influence of the biofilm thickness on the dissolved oxygen concentration profiles.

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oxygen concentration profiles calculated for a biofilm thickness of 10, 25, and 35 mm for the same experimental conditions as used in the two previous sections. Results indicate that the dissolved oxygen concentration drop across the biofilm was strongly influenced by the thickness of the biofilm. A thinner film implies a higher volumetric oxygen consumption rate in the liquid film (RO2) because the identical oxygen deficit measured in the gas phase has to be consumed in a smaller liquid volume. The volumetric oxygen consumption rate (NO2) of Eq. (2) was constant for each experimental point so that a decrease in the biofilm thickness has to be compensated by a decrease in dissolved oxygen concentration difference, as evidenced by the results of Fig. 6. Indeed, the ratio of the concentration difference to the biofilm thickness was nearly constant for a particular experimental point so that KLa should be higher for thinner biofilms. This increase in KLa is the result of a reduction in the film diffusive resistance. Hence, if the biofilm grows with time, the value of KLa should decrease as fermentation proceeds.

5. Discussion Using the identical experimental data, Gowthaman et al. [5] have also used the overall gas balance method for estimating KLa in the course of SSF. The difference of oxygen gas concentration between inlet and outlet gas streams was used to evaluate the overall oxygen transfer rate (NO2) that is subsequently used with Eq. (1) to determine the value of KLa. The value of the dissolved oxygen concentration (CL,R 2but commonly expressed in SMF as C *) L that would be in equilibrium with the gas phase can be estimated fairly accurately using Henry’s law so that Eq. (1) remains with two unknowns, the dissolved oxygen concentration in the bulk of the liquid phase (CL,R 1) and the overall mass transfer coefficient (KLa). As the dissolved oxygen concentration in the bulk of the liquid phase (CL,R 1) could not be experimentally measured in the liquid film, Gowthaman et al. [5] overcame this lack of measurement by assuming that the concentration difference (CL,R 2 −CL,R 1) was always equal to 10% of the saturation concentration. This assumption was based on an investigation in a trickleflow fermenter performed by Briffaud and Engasser [6]. This assumption leads to a significant variation of KLa during the course of the fermentation even if the air flow rate and all the other experimental conditions remained constant. It seems logical to believe that KLa should remain constant but the concentration difference across the liquid film should vary with the intensity of biochemical activity. Results presented in this paper clearly indicate that the assumption used by Gowthaman et al. [5] is not appropriate for SSF. Based

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on Eq. (1), it is clear that a variation of the oxygen utilisation rate (NO2) with an assumed constant concentration difference of 10% across the liquid film, is immediately reflected into a variation in KLa. For the particular assumptions made in this investigation, KLa is constant and equal to 0.344/s under all experimental conditions tested, and as shown in Fig. 3, the higher biological activity is expressed as a more or less pronounced concentration profile. With their calculation, Gowthaman et al. [5] have obtained KLa values varying between 0.30 and 1.70/s for an air flow rate of 5 l/min and between 0.28 and 1.97/s at 20 l/min. KLa is a constant of the system and it is normally assumed independent of the concentration difference. As suggested by Eq. (2), it is proportional to the ratio of the oxygen diffusivity and the thickness of the biofilm. It is, therefore, expected that KLa will vary during the course of fermentation as the biofilm grows and small changes in diffusivity occur, but never to the extent reported by Gowthaman et al. [5]. As the limiting step to oxygen mass transfer mechanism in SSF is the diffusion of dissolved oxygen in the biofilm, the estimation of the diffusion coefficient is important to predict the correct dissolved oxygen profile within the biofilm. One should expect the value of the effective diffusion coefficient to be lower than the value of pure water due to the presence of microorganisms and dissolved nutrients. However, Horn and Hempel [7] observed that the oxygen diffusion coefficient in the biofilm was higher than in pure water and Siegrest and Grujer [8] reported an increased average diffusion coefficient with increasing biofilm thickness. The probable causes of such discrepancies were attributed to the irregularities of biofilms. Most observations were made for biofilms in contact with a liquid phase and may not be necessarily representative of biofilms in contact with a gas phase as in SSF. Contradictory observations of the current literature are certainly an indication of the complexity of biofilm architecture and its impact on mass transport mechanism [9]. Po¨rtner and Koop [10] suggested a value of approximately 80% of the one for pure water which is believed to be a good approximation. The three curves of Fig. 5, associated to the three drastically different correlations of Appendix A, are superposed for each flow rate. It is clear from these results that the gas convective mass transfer coefficient has no influence on the oxygen transfer rate in SSF. One could assume the dissolved oxygen concentration at the gas–liquid interface to be in equilibrium with the local gaseous oxygen concentration without affecting mass transfer calculations. The main influence of the air flow rate, as far as the oxygen mass transfer is concerned, is to maintain a high local gaseous oxygen concentration throughout the packed column. In SSF the choice of the proper air flow rate is dictated more

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by process considerations in order to maintain, close to optimal, the temperature and moisture content of the packed bed rather than for the modulation of the convective oxygen mass transfer coefficient. The higher biological activity observed in the results of Gowthaman et al. [5] at higher gas flow rates is undoubtedly due to favourable local operating conditions resulting from the suitable gas flow rate rather than a higher mass transfer coefficient. Durand et al. [3], using a model fermentation system, found that KLa increases with an increase in air flow rate and a decrease in the solid moisture content. Their findings, should, however be interpreted with caution because of few problems detected with their proposed methods, that is an adaptation of the sulphite oxidation method for a packed bed. In their study, a packed column of leached sugar beet pulp was moistened with a sodium sulphite solution and air was passed through the column where oxygen, transferred from the gas phase to the liquid, converts sulphite into sulphate simulating an hypothetical biological reaction. Pulp samples were taken periodically and the oxidation rate of sulphite determined by the usual iodiometric method [11]. The first difficulty of their method is to measure the remaining amount of sulphite in the solid material. It is claimed that approximately 70% of the remaining sulphite was accessible after 20 min of titration. However, it is probable that less of the remaining sulphite would be accessible with time, as the non-reacted sulphite would increasingly be localised at the centre of the solid particle. A second problem is the assumption of a uniform sulphite concentration inside the solid particle and a zero concentration of the dissolved throughout the experiment. Since the liquid phase is not mixed, diffusion will predominate creating concentration gradients within the particle, thereby leading to a time-varying mass transfer at the surface of the particles. A third and more obvious problem is the variation of KLa with the concentration of the cobalt catalyst under identical operating conditions (flow rate and solid moisture content). The value of KLa under identical operating conditions should have been identical and the increase of KLa detected with an increase of concentration of cobalt chloride is due to the chemical oxidation rate enhancement in the liquid film [12]. If the concentration of cobalt catalyst is greater than 10 − 6 kmol/m3, it was clearly shown that the physical absorption is enhanced by the chemical reaction [13]. Values of KLa presented by Durand et al. [3] were obtained with a cobalt catalyst concentration of 1.22 kmol/m3. This concentration of catalyst simultates a given biochemical reaction whereby in the liquid film there are two simultaneous phenomena, dissolved oxygen diffusion, and chemical disappearance of oxygen. Nevertheless, the approach of Durand et al. [3] is interesting because it is aimed at measuring the phenomena that

take place in the liquid phase that is, the phase that offers most resistance to mass transfer. On the other hand, the sulphite oxidation method can only be used for model systems and not in real fermentations. Varing the thickness of the biofilm has a profound impact on the oxygen concentration profile as it changes the length of the diffusion path. The calculation of the thickness of the biofilm is not trivial. Laukevics et al. [14] have shown that fungi usually reach low packing density in SSF due to steric hindrance that includes the contribution of geometric growth limitation as well as other limitations such as mass transfer and substrate availability. In this investigation, a nominal value of 25 mm was assumed. This biofilm thickness is undoubtedly conservative for the majority of biochemical systems at a later stage of fermentation but does not affect the point made in this paper. Results of Fig. 5 have shown how the thickness can impact the dissolved oxygen concentration profile within the biofilm. Further increasing the thickness of the biofilm would lead to anaerobic conditions. Indeed, for the identical conditions of Fig. 5, anaerobic conditions would be achieved for a biofilm thickness in the vicinity of 145 and 110 mm for the flow rates of 5 and 20 l/min, respectively. These thickness values are common values reported in the literature. Oostra et al. [1], using microelectrode measurements to confirm oxygen depletion in the biofilm, have shown that anaerobic conditions were achieved during the period of higher biological activity over a film thickness of 100 mm with the fast growing fungus Rhizopus oligosporus, and over a film thickness of 200 mm with the slow growing fungus Coniothyrium minitans. Rajapolan and Modak [15], in a simulation study of solid state fermentation, reported a biofilm as thick as 350 mm. All the above results clearly show that describing the oxygen mass transfer in solid state fermentation in terms of KLa and Eq. (1) is not the most appropriate way since it has no real physical meaning as it does for submerged fermentation. The authors believe that Eq. (2) is a much better equation to use because the parameters DO2,L,d and a are truly the physical parameters that dictate the rate of oxygen mass transfers in SSF. Realistic assumptions can be made about the values of these parameters in order to estimate the dissolved oxygen profile within the biofilm. These three parameters have a profound influence on the estimation of the oxygen transfer in SSF. These three parameters could be regrouped, as in Eq. (2) to have a unique parameter. However, to eliminate the ambiguity with KLa, it is suggested to use a new term such as the average biofilm conductance (KFa), where KF is the ratio of the dissolved oxygen diffusivity and the biofilm thickness. Because of possible anaerobic conditions in the lower parts of the biofilm, the value of d used to evaluate KFa, should be the smallest value between the

J. Thibault et al. / Process Biochemistry 36 (2000) 9–18

estimated or measured thickness of the biofilm and the thickness at which oxygen depletion occurs.

6. Conclusion A simple pseudo-steady-state model was developed to study the oxygen mass transfer during a solid-state fermentaion. The dissolved oxygen concentration profiles in the biofilm and in the particles were calculated for several sections of a packed-column fermenter and for various fermentation times using previously published experimental data. Confusion arising from the use of KLa was discussed. Although, strictly speaking, KLa cannot be used to describe the oxygen mass transfer in solid state fermentation. A similar parameter can be of some use for comparing the influence of various operating variables on the oxygen mass transfer for a particular system. On the other hand, it can hardly be used to compare different solid state fermentation systems, and can certainly not be interpreted in the same manner as commonly used in submerged fermentations. To determine the dissolved oxygen concentration profiles in the solid particle and its surrounding liquid film from the gaseous oxygen concentration difference, the dissolved oxygen diffusivity, the biofilm thickness, and the volumetric interfacial area must be estimated. For the series of simplifying assumptions made in this paper, an analytical model for calculating the dissolved oxygen profile was developed. However, any of these assumptions can be relaxed and the system of equations solved numerically without any difficulty. Results have shown that the assumption of Gowthaman et al. (1995), who assumed a constant 10% dissolved oxygen concentration drop in the biofilm, is not valid. This concentration drop depends on the axial position within the fermenter, the biological activity, the thickness of the biofilm, the dissolved oxygen diffusivity, and the air flow rate. Instead of using KLa along with Eq. (1), it is proposed to use Eq. (2) with the three physical parameters DO2,L,d and a to describe the oxygen mass transfer in solid state fermentation. To avoid confusion with KLa used in submerged fermentation, it is proposed to use a conductive biofilm coefficient, KFa to regroup these three parameters and to estimate the dissolved concentration drop across the thin film.

7. Nomenclature

C( G CG CL DO2,G DO2,L dP kG KFa KLa NO2 nP P QG R r R1 R2 RO2 T UO Greek d r m o

a AP

3

gas–liquid volumetric surface area (m /m ) gas–liquid interfacial area of a particle (= 4pR 22) (m2)

average gas phase oxygen concentration in a bed section (mol/m3) gas phase oxygen concentration (mol/m3) dissolved oxygen concentration (mol/m3) oxygen diffusivity in the gas phase (m2/s) oxygen diffusivity in the liquid phase (m2/s) particle diameter with biofilm (=2R2) (m) gas–phase convective mass transfer coefficient (m/s) biofilm mass transfer overall conductance (1/ s) overall oxygen mass transfer coefficient (1/s) volumetric oxygen mass transfer rate on the basis of the total volume of the packed column (mol/m3 s) number of solid particles in a specific bed section pressure (Pa) gas flow rate (l/min) gas constant (Pa m3/gmol K) radial position coordinate (m) particle radius (m) radius of the particle with its biofilm (m) volumetric oxygen consumption rate on the basis of the volume of the biofilm (mol/m3) temperature (K) superficial gas velocity (m/s) letters biofilm thickness (m) density (kg/m3) gas viscosity (Pa.s) packed column void fraction

Subscripts and superscripts F film G gas phase L liquid phase S solid phase I interface

Appendix A Three correlations available in the literature to evaluate the gas mass transfer coefficient kG were tested in this investigation and their influence is discussed above. The first correlation was fitted from a graph contained in Brodkey and Hershey [16], in the range of gas flow rates encountered in this investigation, Sh=

2

17

 



kGdP 0.1 dPU0rG = DO2,G (1− o)1.4 mG



1.4

=

0.1 Re 1.4 (1−o)1.4 (10)

The second was proposed by Geankopolis [17]:



18

Sh= =

0.4548 dPU0rG o mG

  0.59

0.4548 Re 0.59Sc 0.33 o



mG rGDO2,G

J. Thibault et al. / Process Biochemistry 36 (2000) 9–18 0.33

(11)

The third was proposed by Wakao and Kaguei [18]: Sh = 2+ 1.1Re 0.6Sc 0.33

(12)

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