Modeling and scale up of airlift bioreactor

Computers and Chemical Engineering 28 (2004) 2765–2777

Modeling and scale up of airlift bioreactor H. Znada,∗ , V. B´aleˇsa , Y. Kawaseb a

Department of Chemical and Biochemical Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinsk´eho 9, 81237 Bratislava, Slovakia b Department of Applied Chemistry, Toyo University, Japan Received 10 March 2004; received in revised form 20 August 2004; accepted 20 August 2004 Available online 6 October 2004

Abstract A previously presented mathematical model based on a tanks-in-series model with back flow for an airlift bioreactor is extended by considering the variations of the oxygen in the gas phase and the hydrostatic pressure along the bioreactor. The kinetic model used considers the effect of two substrates (glucose and dissolved oxygen) on the growth rate. A set of first order differential equations for the material balances of the micro-organism, glucose, product, dissolved oxygen, and oxygen in the gas phase around the hypothetical well mixed stages in the riser and the downcomer were solved simultaneously using Athena software package. The model has been validated with experimental data of gluconic acid fermentation in two different scales of internal loop airlift bioreactor, 10.5 dm3 and 35 dm3 . The scale up effects on the performance, kinetic parameters and model predictions of gluconic acid fermentation in airlift bioreactors were studied. The model is simple enough to be used in design and scale up studies and it can be adapted to other airlift system configurations and fermentation systems other than gluconic acid fermentation. © 2004 Elsevier Ltd. All rights reserved. Keywords: Airlift bioreactor; Gluconic acid; Dissolved oxygen; Modeling; Bioreactors

1. Introduction Many fermentor designs have been proposed for increasing the oxygen transfer rate and for minimizing the power consumption, one of the most promising was found to be the airlift bioreactor which was first patented by (Lefrancois, Mariller, & Mejane, 1955). Airlift bioreactors are comprised of four distinct zones, each with its own distinct flow pattern. The first zone, in which the gas is sparged, is denoted the riser, as the gas–liquid dispersion travels upward in cocurrent. This section has the higher fractional gas hold up and where most of the gas–liquid mass transfer takes place. The liquid leaving the top of the riser enters a gas disengagement zone, the gas–liquid separator, where, depending on its specific design, some or most of the dispersed gas is removed. The gas free liquid (or a dispersion of lesser gas hold up) then ∗

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flows into the downcomer and travels to the base of the device, through the bottom, where it re-enters the riser. Thus, the liquid phase circulate continuously around the loop. Airlift bioreactor commonly used in aerobic fermentation processes because of their simple structure, low shear stress, and easy of maintenance in comparison to the conventional stirred tank bioreactor. An accurate description of the performance of airlift bioreactors is still difficult (Merchuk, 1993; Onken & Weiland, 1983). Mixing in airlift bioreactors is usually imperfect and mathematical models for airlift bioreactors cannot be described by neither the perfect mixing (continuous stirred tank reactors: CSTR) nor the plug flow (plug flow reactors: PFR) (Luttman, Thoma, Buchholz, & Schugerl, 1983a,b). Little work has been done on the mathematical modeling of real fermentation systems involving imperfect mixing and their optimal design in airlift bioreactors. The mixing models used in most of the previous investigations dealing with airlift bioreactors are an axial dispersion model (ADM) and

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Nomenclature Ad Ab Ar b Cl Cl∗ DO Dax Dr g hb hD hL hr KB kl a K0 Ks M mO mS N P PG Pe Ql QG S t Ugr Ulr Vb Vd VL Vld Vlr Vr Vt X YPO YPS YXO YXS

β (m2 )

cross sectional area of the downcomer cross sectional area under the baffle (m2 ) cross sectional area of the riser (m2 ) back flow dissolved oxygen concentration (g dm−3 ) equilibrium dissolved oxygen concentration (g dm−3 ) dissolved oxygen axial dispersion coefficient (m2 s−1 ) riser diameter (m) gravitational acceleration (m s−1 ) height of bottom section of the bioreactor (m) height of dispersion (m) height of gas-free liquid (m) height of riser (m) form friction loss coefficient for the bottom section overall oxygen mass transfer coefficient (h−1 ) Contois oxygen limitation constant Contois saturation constant number of stages in the riser oxygen maintenance coefficient: g oxygen·(g cells h)−1 glucose maintenance coefficient: g glucose·(g cells h)−1 number of stages in the bioreactor product concentration (g dm−3 ) power input due to gas (W) Peclet number liquid flow rate (dm3 min−1 ) gas flow rate (dm3 min−1 ) substrate concentration (g dm−3 ) time (h) superficial liquid velocity in the downcomer (m s−1 ) superficial liquid velocity in the riser (m s−1 ) volume of the bottom section (dm3 ) volume of the downcomer section (dm3 ) working volume of the reactor (dm3 ) linear liquid velocity in the downcomer (m s−1 ) linear liquid velocity in the riser (m s−1 ) volume of the riser section (dm3 ) volume of the top section (dm3 ) biomass concentration (g dm−3 ) yield constant g product/g oxygen yield constant g product/g glucose yield constant g biomass/g oxygen yield constant g biomass/g glucose

Greek letters α growth-associated product formation coefficient

γ δ λ µ µm εgd εgr ρL φ Ψ

non-growth-associated product formation coefficient (h−1 ) growth-associated parameter in the Luedeking–Pirt-like equation for substrate uptake g substrate/g biomass parameter in the Luedeking–Pirt-like equation for oxygen uptake g oxygen/g biomass non-growth associated parameter in the Luedeking–Pirt-like equation for substrate uptake g substrate/g biomass h (h−1 ) specific growth rate (h−1 ) maximum specific growth rate (h−1 ) gas hold up in the downcomer gas hold up in the riser liquid density (g dm−3 ) parameter in the Luedeking–Pirt-like equation for g oxygen/g biomass h oxygen uptake (h−1 ) parameter in Eq. (30)

tanks-in–series model (TSM) (Adler, Deckwer, & Schugerl, 1982; Luttman et al., 1983a,b; Merchuk, Stein, & Mateles, 1980). In Table 1 given a simple comparison between these two models. The relationship between these two models, can be represented by (Todt, Lucke, Schugerl, & Renken, 1977): 1 b + (1/2) = (1) Pe N If backflow is absent, i.e., b = 0, Eq. (1) changes to the wellknown relationship between the tanks-in-series model and the ADM where the equivalent number of tanks is given by Pe/2. Eq. (1) has another interesting feature; it shows that the overall back mixing process is the addition of the perfect mixing within each stage and the finite back mixing between each stage. An axial dispersion model and a tanks-in-series model have been applied to describe mixing in bioreactors, Table 2. In spite of the applicability and flexibility of the tanks-inseries model, only few investigations on the modeling for simulation of fermentation systems including imperfect mixing in an airlift bioreactor using the tanks-in-series model have been published. Turner and Mills (1990) pointed out that the tanks-inseries or mixing cell model is more realistic and advantageous compared with the ADM. Prokop, Erickson, Fernandez, and Humphrey (1969) and Erickson, Lee, and Fan (1972) examined the performance of a multistage tower fermentor using a tanks-in-series model with backflow. In their studies, bubble column bioreactors were considered rather than airlift bioreactors and furthermore no oxygen mass transfer was taken account of. Ho, Erickson, and Fan (1977), Andre, Robinson, and Moo-Young (1983) and Pigache, Trystram, and Dhoms (1992) applied tank-in-series models to simulate oxygen transfer in airlift bioreactors. However, they discussed

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Table 1 Comparison between the ADM and the TSM Axial dispersion model (ADM)

Tanks-in-series model (TSM)

Describe satisfactory only mixing which deviate slightly from the plug flow

Applicable to the whole mixing extents including perfect mixing and plug flow mixing Provides a set of first order differential equations, which can be solved using rather simple numerical techniques Extension of the model causes no difficulties in solving the equations Contain two parameters, the number of tanks in series N and the backflow b

Provide a set of differential equations and boundary conditions, has to be solved by rather complicated numerical techniques Extension of the ADM to more complicated mixing is very difficult Contain only one parameter, the axial dispersion coefficient, Dax , which characterize the deviation from the ideal flow

Table 2 Simulation of tower type bioreactors Authors

Reactor

Kinetic model

Operation

Mixing model

Prokop et al. (1969) Erickson et al. (1972) Ho et al. (1977) Merchuk and Stein (1981) Adler et al. (1982) Luttman et al. (1983a,b) Andre et al. (1983) Lavric and Muntean (1987) Pigache et al. (1992) Znad, B´aleˇs et al. (2004)

Airlift Bubble column Airlift Airlift Airlift Airlift Airlift Airlift Airlift Airlift

Oxygen transfer Monod Oxygen transfer Monod Monod Monod Oxygen transfer Monod Oxygen transfer Contois type model

Continuous Continuous Continuous and batch Continuous Continuous Batch Continuous and batch Continuous Continuous Batch

Tanks-in-series with back flow Tanks-in-series with back flow Tanks-in-series with back flow Axial dispersion Axial dispersion Axial dispersion Tanks-in-series Axial dispersion Tanks-in-series Tanks-in-series with back flow

no cultivation of micro-organisms in the bioreactors. Kanai, Uzumaki, and Kawase (1996) applied tanks-in-series model with back flow to simulate the cultivation in airlift bioreactors and to discuss their steady state performance. In the previous study, a mathematical model based on tanks in series model was developed to simulate the gluconic acid fermentation in a 10.5 dm3 internal loop airlift bioreactor (Znad, B´aleˇs, Markoˇs, & Kawase, 2004), the previous work was done without considering the oxygen in the gas phase and assuming a constant value of the pressure in the bioreactor. The present study aims at further developing this model by taking into account the oxygen in the gas phase and the variations of the pressure along the different sections of the bioreactor. Furthermore, testing the applicability of the model to simulate the gluconic acid fermentation in two different airlift bioreactors 10.5 dm3 and 35 dm3 , focusing on the scale up effects on the process performance, kinetic parameters and model predictions.

considered as a flow through a series of equal sized, wellmixed stirred stages or tanks and the parameter describing non-ideal flow are the number of stages. The model is represented schematically in Fig. 1. The bottom section (i = 1) is treated as a well-mixed stage. The riser section (i = 2 . . . M − 1) described as tanks-in-series with back flow. Since the

2. Mathematical model for airlift bioreactors The correct design and scale-up of an airlift reactor must be based on considering it as the sum of different regions, each with a characteristics flow pattern, therefore, the airlift bioreactor system can be modeled by dividing it into the riser, gas separator (top section), downcomer, and the bottom section, as shown in Fig. 1. An ideal continuous stirred tank reactor (CSTR) model used for the top and bottom sections, while tanks-in-series model used for the riser and the downcomer of the reactor. In this simulation, a tanks-in-series model describes the mixing characteristics. In this model, the flow is

Fig. 1. Schematic diagram of the tank-in-series model for the airlift bioreactor.

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flow in the downcomer (j = M + 1 . . . N) is relatively well defined, the backflow in the downcomer is neglected. In other words, M − 2 stages with backflow are used to characterize mixing in the riser. Consequently, mixing in the downcomer is represented by N − M stages without backflow. The backflow parameter (b) is defined as the ratio of the backflow rate to the net forward liquid flow rate, which is given as the difference between the liquid flow rate coming from the lower stage and that returning to the lower stage. The backflow parameter is assumed to be constant at every stage. The stages in the riser are numbered upwards and those in the downcomer are numbered downwards. The following assumptions were made while deriving the mathematical model equations, these are: 1. There are no radial gradients in liquid and gas phase. 2. Isothermal conditions in the reactor (constant temperature). 3. Reaction occurs just in the liquid phase. 4. Variation of the hydrostatic pressure along the reactor’s axis is taken into account. 5. The value of the equilibrium dissolved oxygen concentration, Cl∗ , was not constant, due to the changing of the total pressure vertically with positions. 6. The gas hold up in the top and bottom sections are equal to the gas hold up in the riser. 7. The gas hold-up and mass transfer coefficients almost constant along the riser and downcomer. 8. Ideal behavior of the gas phase. 2.1. Model equations The tanks-in-series model with backflow provides simultaneous first order ordinary differential equations, which are material balances of the micro-organism, glucose, gluconic acid, dissolved oxygen, and oxygen in the gas phase for hypothetical well mixed tanks or stages. The unsteady state material balances of these components can be written as given below. 2.1.1. Bottom section (i = 1) For the micro-organism, glucose, and gluconic acid (C = X, S, and P) dCl Q bQ = CN + C2 dt Vb (1 − εgr ) Vb (1 − εgr ) −

(1 + b)Q C1 + rC,1 Vb (1 − εgr )

(2)

For the dissolved oxygen (Cl )

Vb εgr

dY1 = Qgd YN + Qg,in Yin − [Qgd + Qg,in ]Y1 dt Vb ∗ − (kl a)r [Cl,1 − Cl,1 ](1 − εgr ) m O2

(4)

According to Henry’s law, the partial pressure of oxygen in the gas phase at equilibrium is proportional to the concentration of oxygen in the liquid film, that is, ∗ Cl,i =

PO2 ,i Pi = Yi Hc Hc

(5)

where Pi and Yi are, respectively, the total pressure and the mole fraction of oxygen in the gas phase at stage i. Therefore, Eqs. (3) and (4), can be rewritten in the following form: dCl,1 bQ Q = Cl,N + Cl,2 dt Vb (1 − εgr ) Vb (1 − εgr )
 (1 + b)Q Pb − Cl,1 + kl a Y1 − Cl,1 + rO,1 Vb (1 − εgr ) Hc (6) and Qgd Qg,in Qgd + Qg,in dY1 = YN + Yin − Y1 dt Vb εgr Vb εgr Vb εgr   1 − εgr Pb − (kl a)r Y1 − Cl,1 εgr mO2 Hc

(7)

The dissolved oxygen concentration in an airlift reactor is significantly influenced by the effect of liquid height on oxygen partial pressure. The total pressure in each stage is represented by the sum of the atmospheric pressure and the liquid height. The total pressure at the bottom section is defined as (Ho et al., 1977):  Pb = Pa + κ ht (1 − εgt ) + (hr + hb )  ×

1−

  1 (1 − εgr ) 2(M − 1)

(8)

where Pa is the atmospheric pressure, κ (conversion factor) = 0.000968 atm/cm H2 O and Hc (Henry’s constant) = 25 l atm/g O2 2.1.2. Riser section (i = 2 . . . M − 1) For the micro-organism, glucose, and gluconic acid (C = X, S, and P).   dCi bQ = Ci+1 − Ci dt [Vr /(M − 2)](1 − εgr )

Q dCl,1 bQ = Cl,N + Cl,2 dt Vb (1 − εgr ) Vb (1 − εgr ) (1 + b)Q ∗ − − Cl,1 ) + rO,1 Cl,1 + kl a(Cl,1 Vb (1 − εgr )

For the oxygen gas phase

+ (3)

  (1 + b)Q Ci−1 − Ci + rC,i [Vr /(M − 2)](1 − εgr )

(9)

H. Znad et al. / Computers and Chemical Engineering 28 (2004) 2765–2777

For the dissolved oxygen (Cl )

For the dissolved oxygen (Cl )

bQ dCl,i = [Cl,i+1 − Cl,i ] dt [Vr /(M − 2)](1 − εgr )

Q dCl,i = [Cl,i−1 − Cl,i ] dt [Vd /(N − M)](1 − εgd )
 Pi + kl a Yi − Cl,i + rO,i Hc

(1 + b)Q [Cl,i−1 − Cl,i ] [Vr /(M − 2)](1 − εgr )
 Pi + kl a Yi − Cl,i + rO,i Hc +

(10)

For the oxygen gas phase Qgd + Qg,in dYi [Yi−1 − Yi ] = dt [Vr /(M − 2)]εgr   1 − εgr Pi − (kl a)r Yi − Cl,i εgr mO2 Hc

(11)

For the ith stage in the riser, the total pressure is defined as (Ho et al., 1977):  Pi = Pa + κ ht (1 − εgt ) + (hr + hb )  ×



1−

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(18)

For the oxygen gas phase Qgd dYi = [Yi−1 − Yi ] dt [Vd /(N − M)]εgd   1 − εgd Pi − (kl a)d Yi − Cl,i εgd mO2 Hc

(19)

For the ith stage in the downcomer, the total pressure is (Ho et al., 1977),     2i − 1 Pi = Pa + κ ht (1 − εgt ) + (hr + hb ) (1−εgd ) 2(N − M) (20) where rC,i = rX,i , rS,i , rP,i



2i − 1 (1 − εgr ) 2(M − 2)

(12)

2.1.3. Top section (i = M) For the micro-organism, glucose, and gluconic acid (C = X, S, and P)  dCM Q(1 + b)  = CM−1 − CM + rC,M dt Vt (1 − εgr )

The kinetic models presented in (Znad, Blaˇzej, B´aleˇs, & Markoˇs, 2004) will be used in this simulation to describe the gluconic acid fermentation, the model given by Eqs. (21)–(29). rX,i =

dXi = µ i Xi dt

(21)

rS,i =

dSi dXi = −γ − λXi dt dt

(22)

rP,i =

dPi dXi =α + βXi dt dt

(23)

rO,i =

dCl,i dXi = −δ − φXi dt dt

(24)

(13)

For the dissolved oxygen (Cl ) Q(1 + b) dCl,M = [Cl,M−1 − Cl,M ] dt Vt (1 − εgr ) 
PM + kl a YM − Cl,M + rO,M Hc

2.2. Kinetic model

(14)

i=1→N

For the oxygen gas phase

where the specific growth rate (µi ) is,

Qgd (Qgd + Qg,in ) Qg,out dYM YM−1 − YM − YM = dt VM εgr VM εgr VM εgr   1 − εgr PM (15) − (kl a)r YM − Cl,M εgr mO2 Hc

and

The total pressure for the top section is (Ho et al., 1977),

γ=

1 α + YXS YPS

(26)

λ=

β + mS YPS

(27)

PM = Pa + 0.5κhM (1 − εgr )

(16)

2.1.4. Downcomer section (i = M + 1 . . . N) For the micro-organism, glucose, and gluconic acid (C = X, S, and P)   dCi Q = Ci−1 − Ci + rC,i dt [Vd /(N − M)](1 − εgd )

µi = µm

(17)

δ= φ=

Si Cl,i Ks Xi + Si KO Xi + Cl,i

(25)

α YPO

(28)

β + mO YPO

(29)

1 YXO

+

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The specific growth rate used in this work Eq. (25), indicates that growth rate depends on two limiting substrates, i.e., glucose and dissolved oxygen.

kl a = 1.27 × 10

2.3. Hydrodynamic and mass transfer correlations The liquid velocities in the airlift bioreactor were calculated using the method described in detail by Chisti (1989),

0.5 2ghD (εgr − εgd ) (30) Ulr = KB (Ar /Ad )2 (1/(1 − εgd )2 ) where


Ad KB = 11.40 Ab

(31)

hL 1 − εg

(32)

The superficial liquid velocity, Eq. (30), could be converted to the linear liquid velocity in the riser (Vlr ) and the downcomer (Vld ), Vlr =

Ulr 1 − εgr

Vlr (1 − εgr )Ar = Vld (1 − εgd )Ad

(33) (34)

The overall gas hold up is a mean of the gas hold up from the riser, downcomer, top, and bottom sections. εg =

Vr εgr + Vd εgd + Vt εgt + Vb εgb VL

(35)

−4




PG VL

0.925

ρL gUgr PG = VL 1 + (Ad /Ar )

[Vr + Vd + Vt ]εgr + Vb εgb VL

(kl a)r Ar + (kl a)d Ad Ar + A d

(kl a)d = Ψ (kl a)r

The mathematical model supplies a set of N first-order differential equations and for five components (biomass, glucose, gluconic acid, dissolved oxygen, and mole fraction of oxygen in the gas phase), the total no of equations will be 5 × N 1st ODEs, these equations to be solved simultaneously using the Athena Visual Workbench software package (Stewart and Associates Engineering Software, Inc.). However, for computer simulation, further correlations and parameters are required of these: Geometrical parameters, kinetic model, mass transfer and hydrodynamic parameters. These values have been evaluated using suitable relations for the airlift reactor, under our conditions, Sections 2.2 and 2.3. Fig. 2 shows the equations and parameters used for simulation.

(36)

(37)

For the axial dispersion coefficient of the liquid phase Towell and Ackerman (1972) as cited in Lubbert and Godo (2001) found: (38)

(42)

2.4. Method of solution

The following additional equation is necessary for calculation of εgr and εgd :

0.5 Dax = 2.61Dr1.5 Ugr

(41)

The value of Ψ was fixed at 0.8, as recommended by Chisti (1989).

The overall gas holdup was obtained with equation (Chisti, 1989),
0.499 −3 PG εg = 4.334 × 10 (37) VL

εgd = 0.89εgr

(40)

(kl a)r and (kl a)d values were selected in such a way that the following two equations were satisfied:

assuming that εgr = εgb = εgt εg =

(39)

where

kl a =

0.79

The height of the dispersion hD was calculated from the known height hL of the gas-free liquid and the overall gas holdup; thus, hD =

The overall oxygen transfer coefficient was calculated by the following equation (Chisti, 1989),

Fig. 2. Equations and parameters used for simulation.

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Table 3 Basic parameter of the airlift reactor (Kroˇsl´ak, 2000) VL (dm3 )

D (m)

hL (m)

hr (m)

Dr (m)

Ad /Ar

hL /D

10.5 35

0.108 0.157

1.24 1.82

1.145 1.71

0.070 0.106

1.23 0.96

11.5 11.59

Vr (dm3 )

Vd (dm3 )

4.404 15.08

5.417 14.47

Vt (dm3 )

Vb (dm3 )

0.554 4.37

0.125 0.647

3. Experiments

4. Results and discussion

Two internal-loop airlift bioreactors made of glass with a working volume of 10.5 dm3 and 35 dm3 was used. The details of the bioreactor geometry are given in Table 3. The scheme of the experimental equipment is depicted in Fig. 3 (Kroˇsl´ak, 2000). The micro-organism Aspergillus niger CCM 8004 was used in this study. The mycelium grew in a pellet form. The inoculum was prepared in a shaked flask for 48 h. The bioreactor was inoculated with 2% of volume. The reactor temperature was kept at 30 ◦ C. Air was used as the gas phase. The airflow rate of 15 dm3 min−1 and 34 dm3 min−1 (at 298 K and atmospheric pressure) was applied in a 10.5 dm3 and 35 dm3 bioreactor, respectively. Concentrations of gluconic acid and glucose in the sample solution were analyzed using high performance liquid chromatography (HPLC). The concentration of biomass was calculated from the mycelial dry weight, which was determined by a gravimetric method. The concentration of dissolved oxygen in the fermentation broth was measured by an oxygen probe (Jenway, England). Then, the measured concentration was corrected to the pressure of the place where the probe was located and to the composition of the fermentation broth at the temperature and pressure in the place of the measurement, and finally corrected to the partial pressure of oxygen in the aeration medium (Kroˇsl´ak, 2000).

4.1. Determination of the model parameters

Fig. 3. Schematic diagram of the experimental apparatus (Kroˇsl´ak, 2000).

The values of gas-hold ups, mass transfer coefficients, and liquid circulation rate in an internal loop airlift bioreactor are needed for computer simulations. These values can be evaluated using Eqs. (30)–(42) under our experimental conditions. The obtained results are given in Table 4. 4.2. Estimation the number of stages in the riser and the downcomer To specify the number of stages in the riser including the top and bottom stages, i.e., M, Eq. (1) has been employed, as explained in Table 5. The extent of longitudinal mixing in the downcomer is approximated as a plug flow and represented by 10 stages (N − M = 10) (Prokop, 1969), where N represents the total number of stages in the airlift bioreactor. The seven stages in the riser are numbered 2–8 upwards, the 10 stages in the downcomer are numbered 10–19 downward, and the 1st and 9th stages represent the bottom and top sections, respectively, of the airlift bioreactor. 4.3. Simulation of gluconic acid production in 10.5 dm3 and 35 dm3 ALBR Comparison between the experimental and simulation results in 10.5 dm3 and 35 dm3 airlift bioreactor are shown in Figs. 4 and 5, respectively. Where the biomass, gluconic acid, glucose, and dissolved oxygen concentrations in the fermentation broth are plotted as a function of time. During the exponential growth phase, the biomass concentration exponentially increases with cultivation time and the corresponding substrate concentration rapidly approaches zero. Growth rate decelerates due to depletion of glucose and dissolved oxygen near the end of the exponential growth phase. The prediction of the model is quite clear and can finely describe the gluconic acid ferment in a 10.5 dm3 airlift bioreactor. Furthermore, in a 35 dm3 airlift bioreactor, Fig. 5, the model predicts very well the consumption of the glucose (substrate) and the production of the gluconic acid. However, it’s failed to predict the biomass growth during the period (15–38 h), this is may be contribute to the experimental error in determining the biomass concentrations, where the accuracy of biomass measurements may be questionable during that period. Time courses of the dissolved oxygen concentrations in Figs. 4 and 5 are very interesting, where different

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Table 4 Numerical values of the parameters used in the model WL (dm3 )

Ql (m3 s−1 )

Qg (m3 s−1 )

εgr

εgd

(kl a)r (s−1 )

(kl a)d (s−1 )

Vlr (m s−1 )

Vld (m s−1 )

10.5 35

5.866 × 10−4 17.318 × 10−4

2.566 × 10−4 5.670 × 10−4

0.078 0.0816

0.069 0.073

0.0273 0.0294

0.0219 0.0235

0.1655 0.2138

0.1333 0.2197

Table 5 Evaluating the number of stages in the riser (M) WL (dm3 )

hD (m) Eq. (32)

Ugr = Qg /Ar (m s−1 )

Dax,r (m2 s−1 ) Eq. (38)

Per = Vlr hD /Dax,r

M, with b = 0, Eq. (1)

10.5 35

1.339 1.972

0.0667 0.0643

0.0125 0.0228

17.744 18.46

≈9 ≈9

profiles have been predicted by the model, at the bottom (solid line) and the top (dashed line) of the ALBR. This point will be discussed later in this paper. 4.4. Application of the model for scale up and optimization In view of the predictive capability of the model, Figs. 4 and 5, the model may be used as a scale-up and optimization tool to evaluate the influence of various design variables and kinetic parameters on the expected performance of the ALBR. 4.4.1. Scale-up effect on the kinetic parameters Scale-up of bioprocesses involves the transfer of a process developed in the laboratory to production scale, where

the product can be produced in large quantities. To predict the performance of large-scale operation the effect of the increased size of the bioreactor has to be considered. The scale dependent parameters are related to mass transfer, and the mass transfer resistance is expected to increase with scale. The fact that the magnitude of a transport resistance changes with the scale of operation has important consequences for the environment of the micro-organisms. Even though the factor influencing the microbial growth kinetics in principle are scale independent, they are in practice scale dependent, because parameters such as oxygen transfer, mixing and shear stress determine the environment of the cells in the large bioreactor. Therefore, the microbial growth kinetics observed in laboratory scale experiments often does not agree with the kinetic observed in pilot-scale or industrial scale fermentation.

Fig. 4. Comparison of simulated (solid line) and experimental (points) profile of the biomass (A), gluconic acid (B), substrate (C), dissolved oxygen (D) in a 10.5 dm3 airlift bioreactor, at an airflow rate of 15 dm3 min−1 .

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Fig. 5. Comparison of simulated (solid line) and experimental (points) profile of the biomass (A), substrate (B), gluconic acid (C), dissolved oxygen (D) (no experimental data) in a 35 dm3 airlift bioreactor, at an airflow rate of 34 dm3 min−1 .

Del Re, Di Giacomo, Spera, and Veglio (2003), found in their work differences in the estimated kinetic parameters for shake flask 100 ml, stirred tank bioreactor 3 dm3 , and airlift bioreactor 3.5 dm3 , without mentioned reasonable reasons for that and recommended further test for this feature. Oliveira, De Castro, Visconti, and Giudici (1999) applied their developed mathematical model for the small scale process of ethanol production to the experimental data obtained in the large scale process to evaluate the scale up effect on the kinetic parameters. They found that there are no significant differences between the kinetic parameters obtained in the two scales of the process, in spite of major deviations between some of the kinetic parameters. In this study, to evaluate the scale up effects on the kinetic parameters. The kinetic parameters estimated of 2 dm3 and 5 dm3 batch stirred bioreactor, 10.5 dm3 and 35 dm3 airlift bioreactors are presented in Table 6. The kinetic parameters estimated from experiments in 2 dm3 and 5 dm3 STR (Znad, Blaˇzej et al., 2004), have been used in the present simulation for predicting the gluconic acid fermentation in 10.5 dm3 and 35 dm3 airlift bioreactor. However, unfortunately, agreement between the simulation and experimental results was too poor, this is can be attributed to the fact mentioned above, i.e.,

the microbial growth kinetics are scale dependent especially for different kinds of bioreactors used. Therefore, adjusting these kinetic parameters, are necessary to get better agreement. In our previous work, the author suggested that the kinetic parameters estimated for 10.5 dm3 ALBR (Znad, B´aleˇs et al., 2004), could be used for predicting the fermentation of gluconic acid in different airlift bioreactors scales. Therefore, according to Table 6 there are no significant differences between kinetic parameters obtained in different scales of the airlift bioreactors 10.5 dm3 and 35 dm3 (the same kind of the bioreactor). Major deviations were observed for the parameters β and φ. This is in agreement with the study of Oliveira et al. (1999). 4.4.2. Effect of the airflow rate on the GA fermentation The effect of airflow rate on gluconic acid productivity (GAP) and biomass growth is shown in Fig. 6. Gluconic acid productivity was defined as the maximum gluconic acid concentration divided by the correspondent fermentation time, the duration of fermentation was kept constant at 60 h. It can be seen that GAP and the biomass increased with airflow rates in the range of 3–85 dm−3 min−1 . At aeration rate of 3 dm3 min−1 , the GAP and the biomass produced are 0.32 g dm−3 h−1 and 0.49 g dm−3 ,

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Table 6 Values of the kinetic parameters obtained from different process scale Parameter

Kinetic parameters for 2 dm3 and 5 dm3 STR (Znad, Blaˇzej et al., 2004)

Kinetic parameters for 10.5 dm3 ALBR (Znad, B´aleˇs et al., 2004)

Adjusted kinetic parameters for 35 dm3 ALBR, this work

µm α γ Ks β λ δ φ KO

0.3610 2.580 2.1768 21.447 0.1704 0.2937 0.2724 0.0425 0.001061

0.3610 4.5865 3.9868 21.239 1.3757 0.9560 1.2699 0.0614 0.004134

0.3610 4.5865 3.9868 21.239 0.7392 0.7251 1.2699 0.1436 0.00481

respectively. Then increased with airflow rate and stabilized at 2.50 g dm−3 h−1 and 5.23 g dm−3 , respectively, at an airflow rate of 68 dm3 min−1 . Beyond 68 dm3 min−1 the effect of airflow rate on the biomass growth and GAP was not significant. This can be attributed to the fact that high airflow rates can lead to high gas hold ups, enhanced bulk mixing and improved DO and mass transfer which promotes the biomass growth and consequently GA, and when the airflow rate exceeded 68 dm3 min−1 , the increase in the biomass growth with air flow rate reduced, because high airflow rate produce a high shear stress, which could potentially lead to cellular damage, consequently reducing their ability to produce gluconic acid. Furthermore, another reason can be mentioned here, that higher airflow rates resulted in higher respiration rates, potentially leading to a significant decrease in glucose source (substrate) availability for any purpose, including gluconic acid synthesis, Fig. 6. Therefore, an optimum airflow rate range (3–68 dm3 min−1 ) is suitable for GA fermentation in a 35 dm3 ALBR, and the experimental value used was 35 dm3 min−1 . In the previous work (Znad, B´aleˇs et al., 2004), an optimum airflow rate range from 9 dm3 min−1 to 45 dm3 min−1 , have been predicted by the model for GA fermentation in a 10.5 dm3 ALBR, and the experimental value used was 15 dm3 min−1 .

4.4.3. Axial dissolved oxygen profile Variation in dissolved oxygen potentially affects the local and the overall productivity of bioreactors; hence, quantification of axial changes is necessary. Fig. 7 shows the variation of the dissolved oxygen concentration, pressure, and the mole fraction of oxygen in the gas phase. At the bottom section of a bioreactor (stage 1) the liquid is poor in oxygen, while both the pressure and the molar fraction of oxygen in the gas are maximal. In the riser (2–8 stage) the dissolved oxygen in the liquid phase ascends because air is supplied in the riser and gas–liquid mass transfer occurs. Also, the rate of oxygen absorption may be higher than the rate of oxygen consumption by the micro-organism and as a result there is a build-up of the dissolved oxygen in the liquid phase along the riser, Fig. 7. However, as the fluids rise, the driving force becomes smaller because pressure and oxygen content in the gas phase decrease (Fig. 7). When both rates are equal, the concentration profile is at its maximum (stage 9) and from this point on the DO decreases. Therefore, the dissolved oxygen profiles descend in the downcomer (10–19 stage), in which no gas dispersion occurs and the consumption of micro-organism is higher than the mass transfer rate. Consequently, in the downcomer, oxygen is significantly consumed and as a result the

Fig. 6. Effect of airflow rate on the gluconic acid productivity, biomass and substrate concentrations at 60 h of fermentation, in a 35 dm3 ALBR.

Fig. 7. Axial variation of DO concentration (solid line), oxygen in the gas phase (dashed line) and pressure (doted line) in a 10.5 dm3 airlift bioreactor at an airflow rate of 15 dm3 min−1 after 55 h of fermentation.

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dissolved oxygen concentration in the downcomer decreases significantly. Fig. 8 shows the variation of the dissolved oxygen concentration with time and the number of stages. At the beginning of fermentation the DO concentration is constant along the bioreactor, however, during the course of fermentation the concentration will change, as presented in Fig. 7. In tall loop bioreactors, i.e., one of industrial scale, a detrimental effect on the fermentation kinetics may occur if the cells are exposed to low or zero dissolved oxygen concentration. This may occur in a gas-free downcomer or even in one where εgd is relatively small if the liquid residence time therein is sufficiently long such that the dissolved oxygen is depleted by microbial uptake (respiration) before the liquid reaches the bottom of the downcomer. Therefore, for a large scale airlift bioreactor it may be necessary to either provide for gas carryover from the riser into the downcomer, or to separately sparge gas into the downcomer (at a point above the bottom) such that εgd > 0. Thus, the maximum potential liquid circulation rate may not be achievable in practice. To show the effect of the bioreactor height on the axial dissolved oxygen concentrations, three airlift bioreactors have been considered, small (10.5 dm3 and 1.24 m height), medium (35 dm3 and 1.8 m height) and large one (200 dm3 and 3 m height). The results illustrated in Fig. 9, reveal that the shorter reactor (dashed line) has, relatively, a more uniform DO concentration than the taller one (solid line). The DO concentration in the large airlift bioreactor is higher because of the greater oxygen partial pressure caused by the liquid head. Furthermore, in the taller airlift bioreactor, the mean bubble residence time is longer and a larger fraction of oxygen is absorbed by the liquid phase. The results of the simulation showed that the lowest levels of DO occur at the base of the bioreactor, this is in agreement with Hatch’s experimental observation (Hatch, 1973) and theoretical ob-

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Fig. 9. Axial variation of DO concentration in three different scales of airlift bioreactor after 55 h of fermentation.

Fig. 10. Effect of backflow on the axial dissolved oxygen in the riser of 34 dm3 ALBR.

servation of Ho et al. (1977). It can be seen that in the large bioreactor (solid line) there is a stage of gas desorption at the top of the riser (stage 8), but in the small bioreactor (solid line) there is absorption up to the separator occurs (stage 9), This fact was observed also by Merchuk and Stein (1981) in their hypothetical bioreactors. Fig. 10 shows the effect of increasing the backmixing on the axial dissolved oxygen concentration along the riser. It is seen from Fig. 10, that the backflow reduces the concentration changes in the riser. It is possible that the backflow causes an enhancement in liquid back-mixing and as a result the overall mixing in the riser tends to be perfect (constant dissolved oxygen). Therefore, Due to an increase in backflow, as expected, the airlift bioreactor behaves more like a completely mixed reactor.

5. Conclusions Fig. 8. Dissolved oxygen concentrations profile along the airlift bioreactor under unsteady state conditions in a 10.5 dm3 airlift bioreactor.

In this study, an extension of a previously developed model for airlift bioreactors is presented, to describe the

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fermentation of gluconic acid in two different scales of internal loop airlift bioreactor, 10.5 dm3 and 35 dm3 . The scale up effects on the performance, kinetic parameters and model predictions of gluconic acid fermentation in airlift bioreactors were studied. The model has been tested against experimental results satisfactorily. The model is suitable to predict the effect of airflow rate on the process. Optimum airflow rates range 3–68 dm3 min−1 was favorable to GA fermentation in 35 dm3 internal loop airlift bioreactors, beyond which the process will not be economical. The kinetic parameters for the airlift bioreactors of 10.5 dm3 and 35 dm3 (the same kind of bioreactor) remained practically unchanged, while that of STR and ALBR (different kind of bioreactors) have been changed significantly. Also the model has predicted the effect of the bioreactor scale on the axial dissolved oxygen. The axial DO concentration changed significantly along the bioreactor during the course of fermentation, particularly for large scale ALBR and after the starting the fermentation process. The scale of the bioreactor and the backmixing influences the shape of the axial DO profile. A shorter or small bioreactor shows relatively more uniform axial DO concentrations than the taller or large one, in which a greater variation in DO with the height occurs. Higher backflow make the bioreactor behaves more like a completely mixed bioreactor. The influence of the pressure profile along the bioreactor should be considered, especially in the large bioreactors having a non-ideal flow pattern in the liquid phase. Neglecting the pressure profile can lead to the wrong design of the bioreactor. The model is useful for the optimum design and operation of an airlift bioreactor, and can be adapted to another fermentation systems rather than GA fermentation. The results of this study encourage another process scale up and demonstrate the high predictive capability of the proposed model. For a further improvement of the model accuracy, a more suitable correlation for the mass transfer coefficient, gas hold ups, in a real fermentation system should be taken into account in the model.

Acknowledgement This work was supported by the Slovak Grant Agency for Science VEGA (Grant No. 1/0066/03).

References Adler, I., Deckwer, W. D., & Schugerl, K. (1982). Performance of tower loop bioreactors—II. Model calculations for substrate limited growth. Chem. Eng. Sci., 37, 417–424. Andre, G., Robinson, C. W., & Moo-Young, M. (1983). New criteria for application of the well-mixed model to gas–liquid mass transfer studies. Chem. Eng. Sci., 38, 1845–1854. Chisti, Y. (1989). Airlift bioreactors. London: Elsevier.

Del Re, G., Di Giacomo, G., Spera, L., & Veglio, F. (2003). Integrated approach in the biotreatment of starch wastes by Rhizopus oligosporus: Kinetic analysis. Desalination, 156, 389– 396. Erickson, L. E., Lee, S. S., & Fan, L. T. (1972). Modelling and analysis of tower fermentation processes. I. Steady state performance. J. Appl. Chem. Biotechnol., 22, 199–214. Hatch, R. T. (1973). Experimental and theoretical studies of oxygen transfer in the airlift fermentor. Ph.D. thesis, MIT. Ho, C. S., Erickson, L. E., & Fan, L. T. (1977). Modeling and simulation of oxygen transfer in airlift fermentors. Biotechnol. Bioeng., 14, 1503–1522. Kanai, T., Uzumaki, T., & Kawase, Y. (1996). Simulation of airlift bioreactors: Steady-state performance of continuous culture processes. Comput. Chem. Eng., 20, 1089–1099. Kroˇsl´ak, M. (2000). Modeling of the fermentation in the airlift reactors. M.Sc. thesis, Slovak University of Technology, Bratislava. Lavric, V., & Muntean, O. (1987). Rev. Chem., 38, 807–814. As cited in Uzumaki, T., & Kawase, Y. (1994). Modeling and scale up of airlift bioreactors, 3rd German/Japanese symposium bubble column. Lefrancois, L., Mariller, C. G. T., & Mejane, J. V. (1955). Effectionnements aux Procedes de Cultures Forgiques et de Fermentations Industries Brevet D’Invention, France, No. 1,102,200, Delivree le 4 Mai. Lubbert, A., & Godo, S. (2001). Bubble column & airlift loop bioreactor. In P. Kieran & M. Beroviˇc (Eds.), Bioprocess engineering course notes (pp. 151–167). Supetra, Island of Braˇc, Croatia: The European Federation of Biotechnology. Luttman, R., Thoma, M., Buchholz, H., & Schugerl, K. (1983a). Model development, parameter identification, and simulation of SCP production processes in airlift tower reactor with external loop—I. Comput. Chem. Eng., 7, 43–50. Luttman, R., Thoma, M., Buchholz, H., & Schugerl, K. (1983b). Model development, parameter identification, and simulation of SCP production processes in airlift tower reactor with external loop—II. Comput. Chem. Eng., 7, 51–63. Merchuk, J. C. (1993). In K. Scuger (Ed.), Biotechnology (2nd ed.). Weinheim: VCH. Merchuk, J. C., & Stein, Y. (1981). A distributed parameter model for airlift fermentor. Effects of pressure. Biotechnol. Bioeng., 23, 1309– 1324. Merchuk, J. C., Stein, Y., & Mateles, R. I. (1980). Distributed parameter model of an airlift fermentor. Biotechnol. Bioeng., 22, 1189– 1211. Oliveira, S. C., De Castro, H. F., Visconti, A. E. S., & Giudici, R. (1999). Continuous ethanol fermentation in a tower reactor. Bioprocess Eng., 20, 525–530. Onken, U., & Weiland, P. (1983). Airlift fermenters: Construction, behavior, and uses. Advances in biotechnological processes: vol. 1. New York: Alan R. Liss. Pigache, S., Trystram, G., & Dhoms, P. (1992). Oxygen transfer modeling and simulation for an industrial continuous airlift fermentor. Biotechnol. Bioeng., 39, 923–931. Prokop, A., Erickson, L. E., Fernandez, J., & Humphrey, A. E. (1969). Design and physical characteristics of a multistage, continuous tower. Biotechnol. Bioeng., 11, 945–966. Todt, J., Lucke, J., Schugerl, K., & Renken, A. (1977). Gas holdup and longitudinal dispersion in different types of multiphase reactor and their possible application for microbial processes. Chem. Eng. Sci., 32, 369–375. Towell, G. D., & Ackerman, G. H. (1972). Proceedings of the 5th European 2nd International Symposium on Chem. Reat. Eng., B3 (pp. 1–13). Turner, J. R., & Mills, P. L. (1990). Comparison of axial dispersion and mixing cell models for design and simulation of Fischer–Tropsch slurry bubble column reactors. Chem. Eng. Sci., 45, 2317–2324.

H. Znad et al. / Computers and Chemical Engineering 28 (2004) 2765–2777 Znad, H., Blaˇzej, M., B´aleˇs, V., & Markoˇs, J. (2004). A kinetic model for gluconic acid production by Aspergillus niger. Chem. Paper, 58, 23–28.

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