Modeling of antibiotics production in magneto three-phase airlift fermenter

Biochemical Engineering Journal 7 (2001) 7–16

Modeling of antibiotics production in magneto three-phase airlift fermenter Z. Al-Qodah∗ , W. Lafi Department of Chemical Engineering, Amman College for Engineering Technology, Al-Balqa’ Applied University, P.O. Box 340558, Marka, Amman, Jordan Received 13 December 1999; accepted 2 September 2000

Abstract A mathematical model is developed to describe the performance of a three-phase airlift reactor utilizing a transverse magnetic field. The model is based on the complete mixing model for the bulk of liquid phase and on the Michaelis–Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase airlift reactor with P. chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At relatively high magnetic field intensities a certain discrepancy in the model solution was observed when the model over estimates the product concentration. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Mathematical modeling; Magnetic stabilization; Magneto airlift reactors; Penicillin production; P. chrysogenum

1. Introduction Whole cell immobilization technology has generated considerable interest in the field of bioreactor design and operation. The technology has lead to the design of new reactor configurations to accommodate the resultant immobilized cell conformation in the form of relatively large spherical particles. Currently, fluidized beds and airlift bioreactors are being considered as promising reactor types that are suitable for carrying out bioprocesses with immobilized whole cells. Low shear stresses compared with mechanically stirred vessels characterize these reactors. For this reason, these reactors seem to be very attractive to shear sensitive filamentous microorganisms such as P. chrysogenum. The airlift loop reactor is considered as an alternative to the fluidized bed reactor in the search for a well-mixed and non-mechanically stirred immobilized cell reactor. An external (as opposed to an internal) loop reactor is the most widely used configuration as this design has a more regular and well defined flow pattern in addition to better degassing at the top of the reactor [1]. Similar to the three-phase fluidized bed reactors (FBR), airlift reactors suffer from the occurrence of large gas bubbles. Such problems produce potentially disadvantageous ∗ Corresponding author. Tel.: +962-6-487-4545; fax: +962-6-489-4292. E-mail address: [email protected] (Z. Al-Qodah).

outcomes. These outcomes include a broad residence time distribution, imperfect contact of fluid phases, and a considerable back mixing of solids, which may reduce conversion via adsorption of reactants and products [2,3]. For ideal behavior, where adverse effects are minimized while maintaining the advantages, airlift loop reactors should have plug flow in the gas phase and no back mixing in the solid phase. An airlift reactor is expected to be modified to that behavior by providing a solid-phase of magnetic particles and applying the principle of magnetic stabilization. The application of the magnetic field to a bed of ferromagnetic particles induces magnetic cohesive forces among the particles, imposes anisotropy in their arrangement along the field lines and suppresses bubble formation [4,5]. Studies that give quantitative descriptions of the hydrodynamic behavior of magnetically stabilized beds (MSBs) have asserted that such operation improves the contact between the fluid and the solid phases in the bioreactor. This reactor exhibits a combination of the best characteristics of both fluidized and packed beds [6–8]. Very limited information is available in the literature regarding fundamental characteristics of three-phase systems in the presence of magnetic field. Sada et al. [9] applied an axial magnetic field to a three-phase fluidized bed to keep magnetite containing beads in the column over a wide range of fluid velocities. They found that the aggregation of the magnetic beads in this case was not as pronounced as that in

1369-703X/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 6 9 - 7 0 3 X ( 0 0 ) 0 0 0 9 5 - 4

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Nomenclature Ab A∗ B Bs C C∗ Cb CB

Ci Ci∗ Cf Co Cp Cs Cx dp Daw De Hd Hr J J∗ Km Ks L Lo Ms N Q Q∗ r rf rp rs R Re Rl Shs T

overall surface area of the particles (m2 ) dimensionless surface area magnetic field intensity (mT) saturation magnetic field intensity (mT) dimensionless substrate concentration in the bulk of the liquid dimensionless substrate concentration at the surface of the particle substrate concentration in the bulk of the liquid (kg/m3 ) dimensionless exit substrate concentration in the presence of an applied magnetic field (dimensionless) substrate inlet concentration (kg/m3 ) dimensionless substrate inlet concentration substrate concentration in the biofilm (kg/m3 ) substrate concentration in the bulk of the liquid (kg/m3 ) specific heat (kJ/kg) substrate concentration at the surface of the bead (kg/m3 ) biomass dry density (kg/m3 ) particle diameter (mm) molecular diffusivity of lactose in water (m/s) effective diffusivity of lactose in the biofilm (m2 /s) height of the downcomer (m) height of the downcomer (m) substrate flux into biofilm (kg/m2 h) dimensionless substrate flux into biofilm saturation constant (kg/m3 ) external mass transfer coefficient for the transport of lactose (m/s) bed height (m) initial bed height (m) saturation magnetic intensity (mT) particle numbers of a kilogram of magnetic beads feed flow rate (m3 /h) dimensionless feed flow rate distance inside the biofilm (m) radius of the biofilm (m) radius of the biofilm (m) radius of the magnetic support (m) radius of the magnetic bead (m) Reynolds number overall rate of substrate consumption (kg/h) Sherwood number (dimensionless) dimensionless number (Vmax R2 )/(De Co )

Ug Ul UL Umf Umfo Vmax W X Xv Ymax Yx/l Yp/l

gas superficial velocity (m/s) liquid circulation velocity (m/s) liquid velocity (m/s) minimum fluidization velocity (m/s) minimum fluidization velocity in absence of magnetic field (m/s) maximum reaction rate (kg lactose/kg cell/s) weight of magnetic beads loaded into the bioreactor (kg) dimensionless distance in the biofilm cell density in the biofilm (kg/m3 ) maximum yield coefficient (kg/kg) growth yield coefficient (kg cels/kg lactose) product yield coefficient (kg penicillin/kg lactose)

Greek letters bulk density of the magnetic particles ρb (kg/m3 ) molded density of the magnetic ρs particles (kg/m3 ) ε bed porosity (dimensionless) biofilm porosity (dimensionless) εf gas holdup (dimensionless) ε gb liquid holdup (dimensionless) εl ε so initial solid holdup (dimensionless) initial bed voidage (dimensionless) εo maximum growth rate (s−1 ) µmax β parameter (Km /Cb ) δ biofilm thickness

liquid–solid systems. Hu and Wu [10] have studied the characteristics of three-phase fluidized beds in an axial magnetic field. Based on visual observations, they described the fluidization patterns and bed expansion under the influence of both the magnetic field intensity and the fluid velocities. The performance of a three-phase magnetically stabilized bed bioreactor utilizing a transverse magnetic field has been studied by Al-Qodah [11]. Some correlations regarding the effect of magnetic field intensity, fluid velocities on bed expansion and the minimum fluidization velocity were developed. Recently, Ivanova et al. [12] studied the performance of a magnetically stabilized bed reactor with immobilized yeast cells. According to these researchers higher ethanol concentration and ethanol productivity were obtained. Subsequently, Colin et al. [13] applied an axial magnetic field to an immobilized enzyme reactor. They found that the over-all mass transfer rate was significantly improved. In a more recent work, Thompson and Worden [14] have studied phase holdup, liquid dispersion and gas-to-liquid mass transfer in a three-phase fluidized bed utilizing an axial magnetic field. They found that, KL a either keeps constant or increases as the magnetic field increases, depending on

Z. Al-Qodah, W. Lafi / Biochemical Engineering Journal 7 (2001) 7–16

the operating flow regime. In addition, they reported that the gas holdup decreased by as much as 20% of its value in the fluidized regime as the field intensity increases due to bed contraction and formation of preferred channels. Furthermore, a fourfold decrease in the axial dispersion coefficient was observed in the channel regime. The effect of the magnetic field on the hydrodynamics of three-phase gas–liquid–solid airlift reactors, as an approach to improve their behavior, was investigated by Al-Qodah [15]. The application of the magnetic field to a three-phase airlift fermenter was found to improve the mass transfer characteristics, and to affect liquid circulation velocity, bed expansion, gas bubbles coalescence and solid phase distribution inside the reactor. The conclusion was made that a magneto airlift fermenter could be used as a suitable vessel for carrying out aerobic bioprocesses with immobilized cells such as filamentous fungi. For this reason, the aim of this study is to develop a mathematical model that describes the performance of a three-phase magneto airlift fermenter with immobilized cells and to compare the performance predicted by the model with experimental results. A real process of immobilized P. chrysogenum in a three-phase airlift fermenter, utilizing a magnetic field, to produce penicillin G, will be tested in the magnetized airlift reactor in order to verify the mathematical model.

2. Mathematical modeling 2.1. Solid-phase model The following assumptions are made for formulating the model describing the transport and reaction of the substrate to and in the biofilm: 1. The magnetic beads are spherical in shape and uniform in size. 2. The biofilm is assumed to be homogeneous matrix and to have a uniform thickness and constant density. 3. The magnetic support and the magnetic field have no adverse effects on the immobilized cells [11]. 4. Lactose diffusivity in the biofilm is independent of concentration. 5. No preferential adsorption of the substrate or the product on the magnetic support is present. 6. Substrate and product inhibition is absent. 7. The substrate utilization rate within the biofilm follows the Michaelis–Menten relationship. 8. The mass of the immobilized cells in the diffusion layer is neglected, and Fick’s law follows. Based on these assumption and when steady states are reached in the bioreactor, the concentration profile of glucose inside the biofilm can be described by the following equation:   Vmax Cf De ∂ 2 ∂Cf r − =0 (1) 2 ∂r Km + Cf r ∂r

9

where Vmax =

µmax Cx Yx/l

(2)

The boundary conditions for the outer surface of the biofilm takes the boundary layer resistance into account: At the surface of the biofilm, i.e. r = R = rs + δ ∂Cf = Ks (Cb − Cf |r=R ) (3) ∂r Eq. (3) implies that at the surface of the biofilm, the substrate flux diffused from the diffusion layer equals that diffusing into the biofilm. At the stratum of the biofilm no substrate flow through the magnetic support is assumed: Thus, at r = r s

De

∂Cf =0 (4) ∂r This means that there is no concentration gradient of the substrate at the startum of the biofilm. 2.2. Liquid-phase model The two main properties that characterized magnetically stabilized beds in airlift columns from those in fluidized beds are the relatively high gas velocities needed to fluidize the bed and the relatively high liquid circulation velocity compared with the feed stream. Liquid circulation is caused by the density difference between the contents of the riser and downcomer. These two factors suggest that the completely mixed flow model can be applied the liquid phase, although the solid phase particles are stationary. Generally, such model could be applied to a stirred tank reactor, a fluidized bed reactor with a high recycle ratio [16], or a fluidized bed with a draft tube [17], and to an airlift column. In addition to the complete mixing of the liquid phase and the steady state approximations, the following assumptions are made in order to formulate a model describing the substrate concentration in the bulk liquid phase in the three-phase bed: 1. The reactor operates in the stabilized regime, i.e. the immobilized magnetic-beads are stationary. This suggests the absence of backmixing in the solid phase. 2. The bed operates under isothermal conditions. 3. No reaction takes place in the downcomer or in the two-phase region above the bed. 4. Rigorous mixing in the bulk liquid occurs due to the rising bubbles and the circulated liquid stream. Based on these assumptions, lactose concentration in the bulk liquid phase can be described by the following mass conservation equation: Q(Ci − Cb ) − Ks Ab (Cb − Cs ) = 0

(5)

The overall rate of lactose consumption is given by Rl = Ks Ab (Cb − Cs ) = NWπ rp2 J

(6)

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where J = De

dC |r=rf Dr

(7)

Consequently, Q(Ci − Cb ) = NWπR 2 J

(8)

The model equations can be transformed to dimensionless form by the introduction of the following parameters: Cf Cs Ci Km Cb , S= , C∗ = , Ci∗ = , β= , Co Co Co Co Cb Ks R A r , A = 4πR 2 NW, A∗ = 2 , X = , Shs = R De R JR (Vmax R 2 ) Q , Q∗ , T = . J∗ = (De Co ) (RDe ) (De Co ) C=

The equation of the biofilm becomes:   S 1 ∂ 2 ∂S X −T =0 2 ∂X β +S X ∂X

(9)

(10)

At X = 1, ∂S = Shs (C − C∗ ) ∂X

(11)

The steady state equation of the substrate, which diffused from the bulk liquid into the bioparticles, can be expressed as J∗ =

Q∗ ∗ (C − C) A∗ i

ε = 0.42 Exp[0.012B]

(12)

2.3. Method of solution The finite difference method is used for the solution of Eqs. (9)–(12). The fully explicit second order scheme of approximation is applied. The Newton–Raphson method is used to linearize the nonlinear term in Eq. (9). This model can be easily extended for various reaction kinetics of practical importance, namely Michaelis–Menten kinetics with substrate and/or product inhibition.

(13)

It is evident that the bed porosity increases as the magnetic field intensity increases. The values of the magnetic field used are less than 35 mT in order to operate in the stabilized regime. Above this value the bed needs high fluid velocity to be expanded. In addition, particle agglomeration is significant above this value. The bed height is related to the bed porosity by the following equation: L=

At X = r s /R, ∂S =0 ∂X

The effect of the magnetic field intensity on the bed porosity can be described by the following correlation which, was obtained from the hydrodynamic study of the reactor under the effect of the magnetic field:

εso Lo 1−ε

(14)

The effluent concentration of the substrate, C was found to decrease as the bed height increases, owing to the increased contact time between the substrate and the biocatalyst in the bed. The following proposed equation describes the relation between the exit concentration and the bed height:   Lo CB = 0.1934 Exp 1.627 (15) C L The mass transfer coefficient is evaluated from the correlation proposed by Diwivedi and Upadhay [18]:     0.365 UL −1/3 0.765 Shs + (16) Ks ε Re0.82 Re0.386 The effective diffusion coefficient of the substrate in the biofilm is evaluated from the correlation proposed by Tang and Fan [17]:   1 − 0.43Xv0.93 (17) De = Daw 11.09 + 0.29Xv0.72 The penicillin-G concentration is calculated from the following balance equation: CP = (1 − Cb )Yp/l

(18)

The values of the second group parameters are shown in Table 1.

2.4. Selection and estimation of model parameters

3. Materials and methods

The parameters included in the set of Eqs. (9)–(12) can be separated into two main groups. The first group includes the hydrodynamic parameters, the bed porosity and the bed height. These parameters are strongly dependent on the magnetic field intensity. The second group includes the parameters of the reaction kinetics, the substrate diffusivity in the biofilm and the physical dimensions of the reactor and the magnetic beads. These parameters do not depend on the magnetic field intensity.

3.1. Maintenance of the microorganism All chemicals, unless stated otherwise, were purchased from Sigma Co. (Poole Dorest, UK). The culture P. chrysogenum was obtained as freeze-dried ampoules from the Department of Applied Microbiology at Jordan University of Science and Technology, which was stored at 4◦ C as a silica gel stock. The procedure for microorganism maintenance was performed in a manner

Z. Al-Qodah, W. Lafi / Biochemical Engineering Journal 7 (2001) 7–16 Table 1 Values of some model parameters Parameter Daw Xv R Co Lo Km Vmax εso εf δ ρl µmax B

Value

Dimension

0.69 × 23.5 0.00045 10 0.12 2.5 0.0017 0.58 0.57 0.0002 1200 0.12 Varies

10−9

m2 /s kg/m3 m kg/m3 m kg/m3 kg/s kg – – m kg/m3 h−1 mT

analogous to that used in Jones et al. [19]. Portions of the silica gel were dispersed onto the surface of sporulation agar in 500 ml Erlenmeyer flasks. The inoculated flasks were incubated at 26◦ C and 220 rpm in gyratory water path (New Brunswick Scientific, NJ) for 72 h. Spores were removed from the flasks with 5 ml saline solution. The spore suspension obtained was used to inoculate the activated carbon magnetic beads or used in submerged culture fermentation. 3.2. Preparation of the magnetic support Magnetic particles were prepared in the same manner as described earlier [20]. Some of their characteristics are shown in Table 2. The magnetic particles consist of a ferromagnetic core of magnetite (Fe3 O4 ) covered by a stable layer of activated carbon, or zeolite, by using epoxy resin as an adhesive. Spherical magnetic beads with narrow size distribution were obtained. In addition, the magnetic beads are sterilizable, because the attached activated carbon, or zeolite, layers are stable and sustain the sterilization temperature. 3.3. Immobilization method The magnetic beads were first treated with 1% NaOH and with 1% HCl then washed with distilled water to neutral pH. After sterilization at 121◦ C in the presence of water, (3 ml water/1 g beads), 270 g of the magnetic beads were cooled and mixed with 800 ml of spore suspension with P. chrysogenum spore concentration of 1.1×108 spores/ml. This mixture was incubated at 26◦ C in a rotary shaker incubator at 120 rpm for. After the fixation process (1.5 h) the liquid was decanted and the beads were washed with abundant quantity of sterile water to remove the unfixed cells.

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A growth medium was prepared in the same manner as in Ariyo et al. [21]. It was added to the magnetic beads in the same proportions. The growth medium contains: 20 g sucrose, 10 g lactose, 5 g mycological peptone (oxoid), 13 g (NH4 )2 SO4 , 3 g KH2 PO4 , 0.5 g Na2 SO4 , 0.55 g EDTA, 0.25 g MgSO4 ·7H2 O, 0.05 g CaCl2 ·2H2 O, 0.25 g Fe2 SO4 ·7H2 O, 0.02 g MnSO4 ·4H2 O, 0.02 g ZnSO4 ·7H2 O, and 0.005 g CuSO4 ·5H2 O in 1000 ml of distilled water. The mixture of the growth medium and the loaded magnetic beads were incubated for 12 h at 26◦ C and 180 rpm to promote spore germination without loss of the spores from the magnetic beads. After 48 h of continuous growth, 200 ml of the medium were decanted and the same volume of a fresh medium is added to compensate for the exhausted substrate. The magnetic beads were then washed with 2 volumes of potassium phosphate buffer, pH 7. The washed magnetic beads were transferred to the reactor under sterile conditions. 3.4. Continuous fermentation equipment A schematic diagram of the experimental setup is shown in Fig. 1. The external loop three-phase bioreactor was made of glass and consisted of a riser and a downcomer tube with inner diameters of 0.045 and 0.018 m, respectively. The heights of the riser and downcomer, Hr and Hd , were 0.7 and 0.78 m, respectively. The riser and the downcomer were located 0.10 m apart. The column was surrounded by a water jacket, which was connected to a thermostat (Grant Instruments, UK) in order to maintain a constant fermentation temperature of 37◦ C. The degassing section consisted of a transparent cylinder with an inner diameter of 0.12 m and a height of 0.15 m and was equipped with an air filter. This part was carefully designed in order to improve the degassing process in such a way that circulation of the fine gas bubbles through the downcomer stream was prevented. This degree of degassing was accomplished by taking the downcomer flow from a point 0.10 m below the top of the riser, as is shown in Fig. 1. The total volume of the bioreactor including the riser, the downcomer, the degassing section, tubing and joints was 2.4 l. A perforated non-magnetic stainless steel grid of 0.0003 m pore diameter was mounted on the base of the riser to support the magnetic beads and distribute the fluid. The bottom of the downcomer extended below the supporting grid and connected to the riser at a point 0.10 m below the gas distributor. This distance between the gas distributor and the bottom of the downcomer produced a sufficient head

Table 2 Characteristics of the magnetic particles used in this study Material used to cover magnetite

ρ b (kg/m3 )

ρ s (kg/m3 )

Shape factor

dp (mm)

Umfo (m/s)

Ms (mT)

Color

Porosity, ε o

Cp (J/kg)

Activated carbon 1 (AC1) Activated carbon 2 (AC2) Zeolite (Z)

1750 1905 2100

3020 3230 3500

0.9 0.9 0.8

0.9 1.05 1.2

1.26 1.48 1.83

230 230 230

Black Black Green

0.42 0.41 0.40

362 370 478

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(PAA), 3.95 g K2 SO4 and 0.25 g MgSO4 ·7H2 O. The pH of the fermentation medium was adjusted to 6.8 with 2 M KOH before sterilization. This medium was fed to the riser at a point just below the supporting grid by a peristaltic pump (Gallen–Kamp, UK). The dilution rates based on the net volume of the magnetic beads and those based on the whole reactor were 0.094 and 0.00625 h−1 , respectively. Antifoam 204 was used to minimize foaming in the bioreactor when necessary. Gas superficial velocity was maintained at 2.2 cm/s. This velocity is sufficient to induce liquid circulation between the riser and the downcomer. The magnetic field intensity was measured using a Hall sonde magnetometer (Leybolo–Heraeus, Germany). During the course of fermentation samples were collected periodically from the effluent stream, then frozen and later analyzed for lactose, penicillin G, phenylacetic acid and biomass. 3.5. Analytical methods

Fig. 1. Experimental apparatus: (1) distribution section; (2) polyethylene particles; (3) cascade; (4) flanges; (5) cooling water inlet; (6) water jacket; (7) cooling water outlet; (8) degassing section; (9) product outlet; (10) riser; (11) magnetic particles; (12) magnetic system; (13) supporting grid; (14) gas inlet; (15) feed inlet; (16) downcomer.

pressure, so as to prevent the gas phase from entering the downcomer. Filtered air was injected through a (+) shape distributor of a nominal pore size of 50 ␮m located 0.005 m below the supporting grid. This design was observed to give an even distribution of gas bubbles over the entire cross section of the riser. The magnetic system was made of a cast steel core and 1500 copper coils made of a copper wire of 0.9 mm. Glass wool was used as an insulator among the layers of coils. The core consisted of 180 painted cast steel sheets each of 0.9 mm thickness. The cast steel sheets were formed in a suitable geometry in order to house the riser. The net height of the magnetic system was 0.2 m and its net weight was 40 kg. The dc current could be varied from 0 to 2.5 A and the corresponding magnetic field intensity changed from 0 to 80 mT. The production medium contained in g/l: 10 g lactose, 6.8 g KH2 PO4 , 1.21 g NH4 Cl, 1.0 g phenyl acetic acid

Lactose in the samples was hydrolyzed by ␤-galactosidase from E. coli. An enzyme kit based on glucose kinase and glucose-6-phosphate dehydrogenase (Boiheringer Mannhein GmbH Biochemica, Mannhein, Germany) measured the released glucose. To determine the produced penicillin G and phenylacetic acid in the broth, an off-line analysis for filtered samples was conducted by an HPLC (Hewlett Packard, Waldbronn, Germany). The HPLC was equipped with an S5C8 column (Hichrom Ltd., Reading, UK) eluted with a mobile phase containing 0.15 M potassium dihydrogen orthophosphate and 20% (v/v) acetonitrile. Detection of both materials was at 210 nm. Free biomass in the bioreactor medium was measured by filtering a 25 sample on a 0.45 ␮m, 25 mm diameter filter paper (MSI, Westboro, MA) by syringe filtration followed by drying the sample at 105◦ C until constant weight. There are two modes of bed stabilization: magnetizing first and magnetizing last. Experiments in the present study were conducted in magnetizing first mode.

4. Results and discussion 4.1. Numerical simulations The following analysis focuses on the characterization of penicillin antibiotic production by immobilized P. chrysogenum cells in a three-phase magneto airlift bioreactor. To accomplish this task a series of numerical experiments were performed covering a number of magnetic field intensities (B < 35 mT) and fluid flow rates. In this study, the effect of the magnetic field intensity on bed height in addition to the rate of substrate consumption and penicillin production is discussed. Fig. 2 shows the effect of the magnetic field intensity on the bed height, which is considered to be an important

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Fig. 2. Simulated effect of magnetic field intensity on the magnetized bed height.

Fig. 4. Simulated effect of the magnetic field intensity on lactose exit concentration at steady state at three different flow rates.

parameter that affects the extent of the bioconversion. The expectation was that, as the bed height increased the contact time between the substrate and the immobilized cells would increases. This effect is shown in Eqs. (13)–(15). It is evident in Fig. 2 that, as the magnetic field intensity increases from 1 to 32 mT; the bed height increases 50%. This prediction indicates that both penicillin production and lactose utilization increase as the magnetic field intensity increases as is implied by Eq. (15). Figs. 3 and 4 show the effect of the magnetic field intensity on the steady state exit concentration of penicillin and lactose at three different flow rates. Figs. 3 and 4 show that, at a medium flow rate of 16 ml/h, the exit dimensionless lactose concentration decreases by about 45.8% and that of lactose penicillin increases by about 50.6%, as the magnetic field intensity increases from 1 to 35 mT. These results indicate

that the application of a magnetic field increases the rate of substrate utilization and the rate product formation, and this can be attributed to the effect of the magnetic field on the bed height and the resulting increase in the residence time in the reaction zone. In addition, it is evident in Figs. 3 and 4 that, as the medium flow rate increases, both the substrate utilization and penicillin production decrease. For example, at a magnetic field intensity of 35 mT, lactose concentration increases by about 49.8% and that of penicillin decreases by about 20%, as the flow rate increases from 16 to 26 ml/h. Conversely as the flow rate increases the residence time of the substrate in the bed decreases and this in turn reduces the extent of conversion.

Fig. 3. Simulated effect of the magnetic field intensity on penicillin exit concentration at steady state at three different flow rates.

4.2. Continuous penicillin production Prior to the continuous penicillin production runs a preliminary set of experiments was performed in order to determine the maximum possible spore loading on the magnetic beads. The results indicate that the biomass yield was 29, 22 and 20 mg protein/g of (AC1), (AC2) and (Z) beads, respectively. This means that the (AC1) provides higher cell concentration than the other two bead types. In addition these beads have a relatively low density and are easy to fluidize and suspend in the bioreactor. For these reasons, (AC1), i.e. activated carbon magnetic beads (R = 0.00045 m) were used to immobilize P. chrysogenum for continuous production of penicillin. Five continuous runs were conducted in the magneto airlift bioreactor. These runs were carried under the same conditions. Only the value of the applied magnetic field intensity was varied from run to run. The initial bed height was 0.12 m. In each run, the magnetic field of certain value was applied, then the flow rate of air was gradually increased until the bed was fluidized. After that point, the

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Fig. 5. Experimental exit concentration of penicillin for different values of magnetic field intensity.

air flow rate was reduced to a value of 2.2 cm/s. During this process of increasing the gas velocity to the minimum fluidization velocity, Umf , and reducing the velocity to a value of 2.2 cm/s, the bed remained in an expanded state under the effect of the magnetic field. As a consequence, the residence time of the fresh medium feed to the bioreactor increased as the magnetic field intensity increases. Each run continued 120 h. Penicillin production was noted to start to decrease after 100–110 h from start up. The reason for this behavior may be attributed to the fact that P. chrysogenum is a genetically unstable and to the loss of viability of the biomass due to the age. Fig. 5 shows the variations of the penicillin concentration in the bioreactor effluent as a function of time on line at steady state at five magnetic field intensities of 0, 10, 17, 23, and 35 mT. It is evident in Fig. 5 that penicillin concentration increases as the time increases in the first 100 h, then the concentration becomes constant for a short time before starting to decrease. These results agree with those of Jones et al. [19]. In addition the applied magnetic field seems to have a positive effect on penicillin concentration. The maximum penicillin concentration increased from 390 to 510 mg penicillin/l (31% increase) as the magnetic field intensity increased from 0 to 35 mT. The reason for this change can be referred to the effect of the magnetic field intensity on the bed height and the bubble sizes in the riser. As discussed above, the height of the stabilized bed increases as the magnetic field increases. This change in bed means that the substrate residence time in the bed increases as the magnetic field intensity increases. Consequently, Penicillin production rate will increase as the magnetic field intensity increases. In addition, the overall volumetric mass transfer coefficient of oxygen, KL a is positively affected by the application of the magnetic field owing to the effect on gas holdup, bubble sizes and bed height [22]. Stabilizing magnetic beads by the field lines is well known to reduce bubble sizes as they rise through the stationary magnetic particles of limited by the

Fig. 6. Experimental exit concentration of lactose for different values of magnetic field intensity.

magnetic field inter particle voidage. As a result, the specific surface area, a, of the bubbles increases and their rising velocity decreases, as the magnetic field intensity increases. Fig. 6 gives the variation of lactose concentration with time for different magnetic field intensities. The lactose concentration at a time of 100 h is observed to decrease from 2.2 to 0.2 g as the magnetic field intensity increases from 0 to 23 mT. This change means that substrate utilization in the bed increased as the magnetic field intensity increased. The total amount of free cells in the reactor liquid was, at steady state, i.e. at 100 h from the start, about 0.3 g or 5% of the total biomass loaded on the magnetic beads. These data indicates that the immobilized cells are strongly attached to the bead surface, and detachment of these cells occurred in a relatively small rate. This behavior fulfills one of the main assumptions formulated for modeling of a continuous processes with immobilized cells, i.e. bioconversion the free cells is negligible compared with that by the immobilized cells. 4.3. Comparison between the theoretical and experimental results Figs. 7 and 8 show a comparison between the theoretical results obtained from the numerical solution of the proposed model at steady state and the experimental results obtained from a real bioproduction of penicillin by immobilized P. chrysogenum. It is evident in Figs. 7 and 8 that qualitatively the model simulation represents a good match with the experimental data. However, a quantitative comparison shows some points of discrepancy between the theoretical and the experimental results. In order to illustrate these differences, the plots in both Figs. 7 and 8 can be divided into three regions, according to the magnetic field intensity. These regions corresponds to low (<10 mT), moderate (from 10 to 25 mT) and high (>25 mT) magnetic field intensities. The

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ferences between the mathematical and experimental results is product inhibition. As the product concentration rises in the bed it may reduce the biomass activity. In addition, and as mentioned above, P. chrysogenum used in this investigation is genetically unstable strain and penicillin productivity usually decrease after more than six to seven residence times [23]. However, as far as the operation in the stabilized bed regime is concerned, which is the case in this study, the accuracy of the mathematical model is still satisfactory. In addition, the use of a dimensionless model is suitable for scale up purposes, in order to apply magnetic stabilization process in a larger scale bioreactor. Fig. 7. Comparison between the predicted and experimental concentrations of penicillin.

mathematical predictions in the first and second region are clearly in good agreement with the experimental results. The average difference between the theoretical and experimental data does not exceed 10%. It should be noted that the two empirical correlations, Eqs. (13) and (14), used to calculate the bed porosity and the bed height represent the conditions in a stabilized bed, i.e. the second region. In the third region, the relatively larger differences could be attributed to the fact that the bed behavior in this region is not similar to the stabilized bed. The magnetic field intensity in the third region is high enough to expand the bed, but causes a relatively high degree of particle agglomeration. Particle agglomeration results in the reduction of the bed specific surface area and the solid phase mass transfer limitation, thus reducing the mass transfer effectiveness factor below unity. The mathematical model in this region over estimates penicillin concentration and underestimates lactose concentration, as the effect of the magnetic field intensity on specific surface area is not taken into account in the model. Another factor that may cause dif-

5. Conclusions The experiments carried out and numerical simulation have allowed an assessment of the effect of a uniform transverse steady magnetic field on the bioproduction of antibiotics by immobilized P. chrysogenum on magnetic beads in a three-phase airlift bioreactor utilizing a transverse magnetic field. The experimental and numerical results show that antibiotic production is improved by the application of the magnetic field, owing to the significant changes in the hydrodynamic behavior of magnetized beds over conventional systems. The following conclusions can be drawn from the present investigation: 1. Liquid flow in a three-phase magneto airlift bioreactor can be successfully described by the complete mixing flow model. 2. The application of a magnetic field to a three-phase magneto airlift bioreactor with immobilized cells improves the performance of the bioreactor with respect to the degree of conversion of the limiting substrate. 3. Bioproduction of antibiotics and substrate utilization increase as the magnetic intensity field increases. This fact is explained by the hydrodynamics of the magnetostabilized system such as the increased bed height and there by the increased contact time. 4. Magnetically stabilized beds should be operated in the stabilized regime in order to avoid bed aggregation at high magnetic field intensities. References

Fig. 8. Comparison between the predicted and experimental concentrations of lactose.

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