anaerobic mixed cultures

Pergamon PII:

Chemical Engineerin,3 Science, Vol. 52, No. 14, pp. 2313-~2329. 1997 i*: 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0009 2509/97 $I7.0(1 - 0 0 0

S0009-2509(97)00055-9

Characterization and modelling of coimmobilized aerobic/anaerobic mixed cultures J. Meyerhoff, G. John, K.-H. Bellgardt and K. Schfigerl* Institut fiir Technische Chemie, Universit/it Hannover, Callinstr. 3, D-30167 Hannover, Germany (Received 4 April 1996; accepted in revised form 15 January 1997) Abstract--The aerobic fungus Aspergillus awamori and the anaerobic bacterium Zymomonas mobilis were coimmobilized in alginate beads and cultivated in a synthetic medium in stirred tank and airlift tower loop reactors. In the coimmobilized mixed culture, the fungus grows in the outer aerobic shell and on the surface of the beads. The fungus converts starch and maltose to glucose. Glucose is consumed by both of the microorganisms. Z. mobilis, growing in the anaerobic core of the beads, partially converts glucose to ethanol, which is consumed by the fungus after the glucose has been exhausted. The coimmobilized mixed culture forms a stable steady state. Biological parameters of the free and immobilized monocultures on soluble starch, maltose and glucose as substrates, and the effective diffusion coefficients of starch, maltose, glucose, and ethanol as well as oxygen within the beads were experimentally determined. The coimmobilized aerobic/anaerobic mixed culture was mathematically modelled. The model describes substrate uptake, growth, and product formation, both, microscopically and macroscopically. Four typical cultivations in stirred tank and airlift tower loop reactors were investigated. The agreement between simulation and measurements was satisfactory. The boundary between the anaerobic and the aerobic section moves outward during the batch phase. A sensitivity analysis illustrates the significance of single parameters. © 1997 Elsevier Science Ltd. All rights reserved

Keywords: Mixed culture; coimmobilization; mathematical modelling; Z. mobilis; A. awamori.

INTRODUCTION

Several researchers dealt with immobilized microorganisms (reviewed in: Hartmeier, 1986). Colinmobilized enzyme/microorganism systems were used for performing multistage reactions in a single reactor (Hartmeier, 1984). Anaerobic mixed cultures play a role in the waste water treatment. Coimmobilized mixed cultures were seldom investigated. Martin and Perlman (1976), Beunink and Rehm (1988), Tanaka et al. (1986), Kuroshawa et al. (1989), and Kuroshawa and Tanaka (1990) reported on such systems. The aim of the present paper is to characterize and to model Aspergillus awamori and Zymomonas mobilis coimmobilized in Ca-alginate gel beads. In contrast to the cultures in the papers cited before, this system forms an aerobic/anaerobic mixed culture and has not been thoroughly examined so far. This kind of system may acquire increasing significance especially in the environmental biotechnology.

*Corresponding author.

The strict aerobic fungus grows in the outer shell as well as on the surface, whereas the anaerobic bacterium that is used for the production of ethanol is found in the centre of the beads (Fig. 1). The microorganisms use a common substrate, glucose, which is produced by the fungal amylases from starch and maltose, respectively, and is consumed by both species. In general, use of immobilized systems is an easy way to retain high biomass concentrations in the reactor. In the present case, further advantages are: reduced inhibition effect of glucose on the amylase production and the hydrolysis of starch, immediate conversion of glucose to ethanol which lowers the residual glucose concentration in the reactor and decreases the chance for contamination. Therefore. an extraction of glucose that would be neccessary for a twostage submerged cultivation with a first aerobic reactor for starch degradation and a second anaerobic reactor for ethanol production is not required here. The population balance between the two species is influenced by the concentration of dissolved oxygen which penetrates to some extent into the alginate

2314

J. M e y e r h o f f et al.

ethanol

starch

MATERIALS AND METHODS

Microorganisms, immobilization and process monitoring Zymomonas mobilis strain DSM 424 (ATCC 10988) and Aspergillus awamori strain DSM 63272 were ap-

aerobic

,'~,~s~ anaerobic

Fig. 1. Schematic picture of A. awamori and Z. mobilis mixed culture coimmobilized in gel beads.

beads. Transport processes in the gel influence cell growth and product formation. A large number of papers have dealt with the diffusion of oxygen (e.g. Chang and Moo-Young, 1988; Gosmann and Rehm, 1988; Omar, 1993a, b; Hooijmans et al., 1990; Miiller et al., 1994) as well as with diffusion of sugars, ethanol and starch into the beads (e.g. Estap6 et al., 1992; Lebrun and Jinter, 1993; Hannoun and Stephanopoulos, 1986; Sakaki et al., 1988) and in general with diffusion in gels (e.g. Westrin and Axelsson, 1991; Dailili and Chau, 1987; Ruggeri et al., 1991; Seki et al., 1993; Radovich, 1985). Only a few investigations considered coimmobilized aerobic and anaerobic microorganisms and their interrelation to mass transfer processes (Tanaka et al., 1986, Kurusawa and Tanaka, 1990). A model for the mixed culture was set up in order to attain a better understanding of the details of the culture. A valid model generally can give some insights into non-measurable properties. So far, no models for a coimmobilized aerobic/anaerobic mixed culture have been set up. The approach presented here shows certain parallels to the description of growing pellets of filamentous microorganisms such as fungi or Streptomyces. Diffusion of substrates and oxygen into a sperical pellet may become limiting, so concentration gradients along the pellet radius develop. The model by Buschulte and Gilles (1990) and Buschulte (1991) describes the pellet growth of Streptomyces tendae by means of a system of partial differential equations. A similar model by Meyerhoff and Bellgardt (1995b) connects the microscopic description of pellet growth with the macroscopic mass balance in the cultivation medium and serves as a first concept for the design of the model for coimmobilized A. awamori and Z. mobilis.

The model will be used to estimate the magnitude of important kinetic parameters and to study the principal effect of different process conditions on biomass growth and ethanol production. It is expected to get a first insight into the process behaviour which can direct future experiments for further model verification.

plied. The preparation of their precultures is given by John et al. (1996). The microorganisms were coimmobilized in 3% Ca-alginate (Protanal LF 20/60 Protan Biopolymers, Drammen, Norway). The immobilization procedure is described by John et al. (1996). The coimmobilized mixed cultures were cultivated in synthetic medium in a 3 1 stirred tank and airlift tower loop reactor, respectively, at 30°C. The aeration rate was 1 vvm air or air/nitrogen mixture (John and Sch/.igerl, 1996). The reactors were provided with stirrer speed-, temperature- and pH-control, pO2-electrode, mass flow meter (Brooks), and off-gas analyser (Unor 6N, Maihak, and Oxygor 6N, Maihak). The instruments of the stirred tank and airlift loop reactors were connected to a VAX-computer network and operated with a real time software RISP (Realtime Integrated Software Platform) for process control, data logging, evaluation, and graphical display. Glucose was analysed with a glucose analyser Model 27 (Yellow Spring Instruments, OH). The concentration of total sugars (starch, oligosaccharides and monosaccharides) was determined as glucose after a heat treatment (2 min at 95°C) and hydrolysis by glucoamylase by treating 100 lal sample with 100 ~tl glucoamylase solution (100 mgm1-1) for 12-14 h at 37°C. The concentration of non-glucose sugars (starch and oligosaccharides) was calculated as difference between the concentrations of total sugars and the concentration of glucose. Ethanol concentration was determined by gas chromatography (Perkin Elmer Sigma 38 GC + Sigma 15 Data Station, ALLTECH glas column PT SILAR 10C on Gaschrom QII). Cell mass determination The biomasses of A. awamori and Z. mobilis in

suspension cultures were determined by weight after separating, rinsing and drying of the cells. This dry cell mass concentration of Z. mobilis C~vm'M was correlated with the optical density (OD) of the free cell suspensions: czYm, M =

0.233OD578(gl-1).

This relation holds true only for OD < 0.5. Therefore, at high cell concentrations the suspension was diluted to keep OD < 0.5. Definite amounts of beads were dissolved in 500 g l-X Na-polyphosphate and the cell mass per bead was determined by weight after separation, rinsing and drying of the cell mass. The cell mass concentration of immobilized A. awamori was determined with this method. However, the cell concentration of immobilized Z. mobilis had to be determined by microscopical counting after the dissolution of the gel bead with Na-polyphosphate. There was a linear

Coimmobilized aerobic/anaerobic mixed cultures relationship between the cell count and the (dry) cell mass cAsp,M, x . C A~p'M= 9.9 × 10-lo cell count ml-1

(g l-1).

In coimmobilized mixed cultures, only the cell mass of A. awamori was determined by weight, because the amount of Z. mobilis cells was very low and could not completely be separated from the fungus surface.

2315

the non-linear least-squares fitting according to the Levenberg-Marquard algorithm (Press et al., 1988). The above procedure is only valid if the mass transfer resistance in the liquid film at the surface of the beads can be neglected. According to Ranz and Marshall (1952), the following relationship holds true between the Sherwood number (Sh = [~dp/D), Reynolds number (Re = vdp/v) and Schmidt number ISc = v/D) in well-stirred systems:

Sh = 2 + ().6Re°'5 Sc 0'33 . Determination of the effective diffusion coefficients of the substrates and the product in the beads The density of the beads was determined in a pycnometer and their size measured by their projection on a transparent foil. In order to measure the diffusion coefficients of substrates (glucose, maltose and starch) and product (ethanol), 80 g beads was suspended in 150ml water in a stirred vessel, 150ml solution of glucose, maltose, starch or ethanol was added to the suspension and the concentration change of the solute was monitored as a function of the time. The concentration of the solute inside the bead was described by the diffusion equation (Crank, 1975)

~'C /'~2C 2 OC'~ ~-t- = Deff (x~r2 -{- 7 (?~-rJ]

(1)

with the initial conditions: C=0

\ r3

fort=0andr>Rb

(31

for t ~>0and r = 0

(4)

Ve (?C ~?tM = Nk4nR2D~ rf ~~?C r fort>~Oandr=Rb.

(5) The analytical solution of eq. (1) is given by Crank (1975):

( CM=CM(0)~

~ 6~(1+ ~,e-O~q"~t/R~ 1 +,=,

9+9~+~2q2

j (6)

where q, are the non-trivial solutions of tan q, =

3q,

3 + ~q2

Vv

Vv

where •,, is the energy dissipation rate per unit of mass. In aerated reactors without mechanically stirring, the energy dissipation rate is only a function of the aeration rate. For example, for an aeration rate of 1.5 lmin-~, the superficial gas velocity amounts to 8.8 × 10 3 m s- 1. With an overall volume of 3 1. an energy dissipation rate per unit mass c,, = 3 . 7 x 1 0 - 2 m 2s a a n d a S h e r w o o d n u m b e r S h = 347 as well as a mass transfer coefficient [4 = 9.4x 10- 5m s ~ were obtained. According to these calculations and the experimental finding that the diffusion coefficients in the beads were independent of the stirring rate, the external mass transfer resistance of the beads was neglected in the shake flasks, the stirred-tank reactor as well as in the airlift loop reactor (for detailed calculations see John, 1995).

(7)

c~is the capacity ratio (ratio of liquid volume to bead volume):

V~k Nk4/3nR~

(10}

(2)

and boundary conditions: ~C --=0

Here fl is the mass transfer coefficient, dp the particle diameter, v the slip velocity, r the kinematic viscosity, and D the molecular diffusivity. Harriott (1962) calculated the slip velocity c from the settling velocity of the particles v,. The mass transfer coefficient/~ evaluated from vt is by a factor of 1.5-8 lower than the effective [~ for stirred tanks. By using the lowest factor, 1.5, tbr the mass transfer coefficient, D = 2.6x 10 -5 ms -~ was obtained for the beads in the stirred tank. According to Stinger and Deckwer (1981), the following relationship holds true for the Sherwood number of the mass transfer from the medium to the surface of the solid particles suspended in aerated reactors:

Sh = 2 + 0.545 3x//Sc {e,,d~, )0.2,,4

fort=OandO
C~t(0)=C u

(9)

(8)

k is the partition coefficient of the solute between the liquid phase and the gel, which was determined experimentally, q,-values were evaluated numerically by the Newton procedure (Ebert and Ederer, 1985). D~ff was calculated by regression analysis using

Determination of the effective diffusion coefficient of dissolved oxygen in the beads The pseudo-steady-state oxygen concentration profiles in the gel-immobilized microorganism were determined by Hooijmann et al. (1990). Beuling et al. (1995) investigated the influence of cells on the diffusion coefficients using microelectrodes. Based on these methods, Hellendoorn et al. (to be submitted) determined the diffusion coefficient of oxygen in the coimmobilized system of A. awamori/ Z. mobilis system with microelectrodes. In Fig. 2, such oxygen concentration profiles are shown.

2316

J. Meyerhoff et al. 1.20 1.00 0.80 0.60

0 0.40 0.20 0.00 0.00

0.20

0.40

0.60

0.80

1.00

r/R Fig. 2. Oxygen microprofllesin immobilizedA. awamori as a function of time: t = 10.5 h (O); t = 11.5 h (A); t = 12,7 h (n); t = 13.6 h (~); t = 14.5 h (~); t = 15.5 h (IS]);R = 2 mm (Hellendoorn et al., 1996).

Cultivation conditions in stirred-tank and airlift loop reactors The cultivations were performed in 2.2 1 medium in the 3 1 stirred-tank reactor with 2% substrate (starch, maltose or glucose) and 440 g (20% w/v) beads (with 1.25 × 106 fungal spores + 0.5 mg bacterial cell mass per gram alginate as inoculum at 30°C, pH 5.5 and 400 rpm). The cultivations were carried out with different gas compositions: 0.5 vvm air, 0.5 vvm gas mixture (20% a i r + 8 0 % N2) and 0.5vvm (10% air + 90% N2). In the 31 airlift loop reactor, 2.51 medium and 500 g beads with the same initial composition of the coimmobilized cells, than in the stirred-tank reactor, was applied. The cultivation was performed with 0.5 vvm air and gas mixture (20% air + 80% N2), respectively, at pH 5.5 and 30°C (John, 1995).

MATHEMATICALMODEL Overview The model describes the situations in one single bead. A simulation run starts with low concentrations of Z. mobilis and A. awamori biomasses equally distributed within the gel bead (3 mm diameter). At first, A. awamori hydrolyses some starch to glucose, which diffuses into the bead. It is assumed that the growth of A. awamori is limited by oxygen and glucose, so A. awamori will grow only in the outer regions of the bead. This consequently leads to a depletion of oxygen in the centre of the gel bead. The absence of oxygen allows Z. mobilis to grow and to form ethanol, provided that glucose still suffices. After some time, glucose, oxygen and the two biomasses develop radial concentration gradients. The growth of fungal biomass is not constrained to the gel bead but may also extend into the medium. This as well is modelled in analogy to diffusion. Mass balances of substrate, biomass, CO> and ethanol are simply derived from those of a single bead by multiplying them with the number of beads per

liter fluid-phase volume. This is done on the supposition that all beads are equal, or that the simulated bead represents an average. In a strict definition, all state equations should be partial differential equations. All variables that vary with time and radius should therefore be written as, e.g. Co(r, t), but the time dependency was generally omitted for a better readability. For practical reasons, all calculations were discretized in time and space. The spherical space of the bead is subdivided into 30 concentric radial layers of equal thickness. This was done as in the model by Meyerhoff and Bellgardt (1995a, b) for Penieillium chrysogenum pellets. Growth and substrate uptake At time t = 0, dry biomass and substrate concentrations are equal for all radii. The concentration of Z. mobilis CZYm(r, t = 0) is known to start at 13 mg a per I gel volume, whereas the initial concentration of A. awarnori CxAsp(r, t = 0) is unknown and must be estimated. Substrate concentrations Cs(r, t = 0) and Co(r, t = 0) in the bead equal those in the medium. Both microorganisms are assumed to grow according to Monod kinetics. The balance equation (11) contains a transport term, Qx [see eq. (26)], for the radial extension of the hyphae and their outgrowing of the beads. Growth of A. awamori is limited by glucose and oxygen, whereas Z. mobilis is inhibited by the presence of oxygen; so eq. (12) contains an inhibition term ~C x(r) Asp __ &

,,Asp /'~Asp/~ /-*max ~,~X \ / J

× c~Cx(r)z m ~t

Co(r) + Qx(r), Ko + Co(r)

,,ZymF, Zym [r] P" . . . .

X

Cs(r) KAsP s + Cs(r)

V,'

(11)

Cs(r ) Kj Kzy= + Cs(r) K~ + Co(r) (12)

Coimmobilized aerobic/anaerobic mixed cultures Both organisms consume glucose but only A.

awamori is responsible for oxygen uptake. Maintenance terms are set up only for A. awamori because the presumptive contribution of Z. mobilis to the total maintenance uptake rate is negligible. Ethanol formation is assumed to be growth-rate-dependent [-see eq. (27)] and contributes to the substrate uptake rate of Z. mobilis, Qzym, accordingly. The local uptake rates within the gel bead are Q3SP(r I =

#Asp A s p / 'U~I max rt-~X

Yxo

Cs(r ) K ~ sp

Co(r)

+ Cs(r) Ko + Co(r)

+ m ° K oCo + ~oo(r) C~c~n(r)

(13)

2317

(i.e. volume of solids per volume), [3,,i: p,~, = 1 / v , ~

+

Cxym(r')pz, ) + 11 - ~a,.)

•

118}

Px is the density in gram dry biomass per ml of living biomass, pxAsp was set to 0.31 g dry biomass per ml (value for Penicillium chrysogenum; Packer et al., 1992), pZym to 0.25gm1-1 and the porosity of the alginate bead, t;alg, to 0.75 [for 3% alginate, see eq. (31)]. Neale and Nader (1973) describe the effective diffusion coefficient in a model system [eq. (19)], which is also taken as an approximation for the situation in the alginate bead. 2 - 2p< Deff(ri) = Deff(p,, i ) =

QZYm(r) = 0

D .... J121 + ,----'

j = O, S.

for oxygen and

(19)

,,Asp / ~ A s p / ~ QsAsp(r) _ ,u x ~,-I

Cs(r) Co(r) K A*p + Cs(r) Ko + Co (r)

YAF

Cs(r) CxA~P(r) + Cs(r)

+ msASp

K Ass p Zym

Qs

f //Zym ~max

(14)

Equation (17) is solved by the orthogonal collocation method (Villadsen and Stewart, 1967; Villadsen and Michelsen, 1978) using 14 collocation points and the boundary conditions (j = O, S): C j J, ....... = C~a

/lZym \ t~max

and

~77r}r=O = 0 "

(20)

(r) = ~-~-~ ÷ ~ p s ) czym(r) Cs(r)

K1

x Kzym + Cs(r) KI + Co(r) for glucose. A mass balance for glucose in the bulk medium is calculated from the weighed integral of eqs (14) over the bead volume multiplied with the bead concentration in the medium, cB. Because of the radial discretization, the integral is replaced by summation over all n radial layers (volume v~). The total glucose uptake rate Q~ is then given by

In the beginning, rmax equals Rb but later on, the maximal radius rmax increases since A. awamori outgrows the alginate bead [see eq. (11)]. In order to reduce computation time, the radial concentration profiles are calculated only after every 10 min of simulated cultivation time. In this recursive calculation, the radial substrate concentration profiles themselves act on the growth rates [eqs (11) and (12)] and substrate consumption rates [eqs {13) and (14)], which in turn react on the concentration profiles, and so on.

Hydrolysis of starch Q ~ = c~

~, (QA~V(ri) + Qzym(ri))vi

(15)

i=1

The balance of medium glucose can be found in the following section [eq. (21)]. Similarly, the total dry biomass is

Glucose in the medium is not measurable unless more glucose is broken down from starch than can be consumed by the microorganisms:

dC~ dt

- +QsT×I.II-Q~.

(21)

n

C~t = cB ~ (cA~P(r,) + cZym(ri)) vi.

(16)

i=1

From the consumption rates given in eqs (13) and (14), radial concentration profiles for oxygen and glucose can be calculated. One assumes quasi-stationary conditions (j = S, 0):

OCj(r),)D~tt, j(r) 1 ~ (r 2 c)Cj(r) ?r Or + D~cf'J(r)Ti-~r \ ~r / = Qj(r) zym + Qj(r) g~p.

(17)

The effective diffusion coefficient Def[, j is thought to be dependent on the local volume density in the bead

By the numerical factor 1.11 g g - l the addition of water during starch hydrolysis of long polymer chains ( > 1000 glucose units} is taken into account. Q~ is given by eq. (15). A. awamori secretes amylase into the medium which is responsible for the hydrolysis. Because the actual enzyme secretion rate is not known, it was simply assumed that starch break-down is proportional to the dry biomass of ,4. awamori. According to the model, only the fraction of hyphae which is in close contact to the starch particles is induced to produce the enzyme but the starch globules are too large to diffuse into the denser parts of the hyphal mesh. A critical maximum biomass concentration Cx, cri, is

J. Meyerhoff et al.

2318

therefore employed to describe the imaginary border at r~.,~t beyond which starch does not diffuse. Only biomass outside the border is taken into account when calculating the break-down rate of starch, Qs~. Furthermore, our own experiments and Koska and Kaczkowski (1989) suggest that severe oxygen limitation in the medium inhibits enzyme secretion. The starch concentration in the medium is given by

dCg -dt

the outer hairy zone are not taken into account. Particularly in the airlift loop reactor, shear forces play a minor role. Z. mobilis is regarded as completely immobilized; growth outside the bead would mean that the singlecell microorganism is lost into the medium.

Ethanol production Product formation is coupled to the growth rate of

Q~

(22)

Z. mobilis (type I according to Gaden's classification of product formation types; Gaden, 1959). Production is then modelled:

with the rate for break-down,

Q~T =

CBqST ....

Co~ CsMT+ Ksr mxA4P CoM + Ko, ST

dC~ = CB gpx ttZYm(~ZYm(~"~l~" dt i=1

c~

(23)

which depends on the biomass of A. awamori that produces amylase:

mxA~p =

~

cA~P(rl)vi" (24)

{ilCx(rO~ Cx,cvit,rl>

r(crit }

Radial extension of the fungal biomass The growth A. awamori hyphae is not restricted to the gel bead. The inner parts of the hyphal mesh are immobilized by alginate but growth on the outside of the bead develops a hairy zone extending into the medium. This process of radial extension equals that observed in fungal pellets. Unfortunately, measurements of the extension process are difficult to perform. From microphotographs of the beads, one can assess a radial increase by a factor of 1.5-2 within 100 h of cultivation. Gradual oxygen limitation promotes radial extension of the hyphal mesh. This can be explained by two mechanisms, a preferred growth of the hyphae into the direction of the oxygen gradient and a higher substrate level in the outer layers of the bead due to reduced substrate consumption in the inner oxygen-limited parts. The radial extension is treated in analogy to diffusion of biomass along its concentration gradient. This useful approach has already been chosen by Buschulte and Gilles (1990) for modelling the growth of Streptomyces pellets. The biomass transport coefficient is directly proportional to the specific growth rate of A. awamori. In the present case, it is assumed that the medium concentrations of glucose and oxygen determine the value of the transport coefficient, Dx:

Dx

A~p C g CsM =fax#max CM ° d- Ko C~ T± K Asps

x

Cs(ri) KI Ks + Cs(ri) K, + Co(ri)"

(27)

An expression in which the product formation rate is proportional to the biomass concentration of Z. mobilis instead to the specific growth rate is equally well suited. In fact, on the basis of present data, one cannot decide whether one of the before-mentioned alternatives or even a combination of both (the Luedeking-Piret equation) is most appropriate to describe the experimental data.

Carbon dioxide formation The model equation for the carbon dioxide production rate (CPR) is composed of two growth-ratedependent terms, one for A. awamori and one for Z. mobilis, and a maintenance term. Again, as in eqs (13) and (14), maintenance metabolism of Z. mobilis is omitted. Since ethanol production is modelled as growth-rate-dependent, the CO2 yield due to ethanol formation can be assembled together with the CO2 yield due to the growth of Z. mobilis. The common yield coefficient is Y ~cm. n (y1A~y~ , ,-~ dCASp(ri)d~ YzYcmldCZY~(ri)dtVi CPR = cB i~=l l)i -[

+ mcCASP(r,)c, • ,.) .

(28)

The experimental CPR is calculated as CPR -

pFG (xin

TVFR ~x CO2

1 -- X-inO 2 ._.~_xXCOz]xcn02 ex

1 --

02

x (mol 1- i h - 1).

XCO2

/

(29)

(25)

Oxygen wherefd~ is a model parameter. Biomass transport of A. awamori is given by 1 //

Qx(r) : U x ~ z r ~

~CASp(r)

2 ~2cAsp(r)'~

+r

~ r2

).

(26)

As before, calculations are discretized in time and space. Shear forces that chip off hyphae from

Mass balances for oxygen in the medium have not been set up to avoid additional model parameters. Instead, a function of pO2 (t) was used in the simulation program which is approximated to the experimental data [Figs 5(b), 8(b), 9(b) and 10(b)]. CoM(t) is simply obtained by:

CoM(t) = pO2(t) C8/lOO.

(30)

2319

Coimmobilized aerobic/anaerobic mixed cultures C* is the maximal dissolved oxygen c o n c e n t r a t i o n in the m e d i u m at the given pressure, gas c o m p o s i t i o n and temperature.

40

Gauss-distribution 3,075mm + 0,168

30

A A

Process simulation F o u r experiments were simulated by m e a n s of the model developed. Two sets of data from experiments in the stirred-tank reactor and two from the airlift loop reactor were used. The simulation p r o g r a m was written in V A X - F O R T R A N using IMSL-library routines (IMSL, H o u s t o n , Texas) and run on a VAX 3100 (Digital).

A

19

A

zx A

__l 2,6

I 2,7

,

I 2,8

,

I 2,9

3,0

I 3.1

,

I

,

3,2

I

z~ ,

3,3

~

zx

~L_~__

34

35

bead diameter [mm] Fig. 3. Size distribution of the gel beads.

RESULTS AND DISCUSSION

Characterization of the beads: d!ffusivities of the suhstrates and the product The bead size distribution was fairly narrow (Fig. 3). The diffusivities of the substrates and the p r o d u c t were determined for beads, p r e p a r e d from 3% alginate solution, 3.08 m m in m e a n diameter, 10.0 mg weight and 1.04 g c m - 3 density. In Table 1, the partition coefficients of the solutes k, their effective diffusivities Deff and the D~f6Dmax'ratios are compiled, where D m a x is the diffusivity of the solutes in water. Derf = ~D . . . . where ~ is the labyrinth factor, which depends on the alginate concentration (in %L For glucose the following holds true: ,5 = 0.947

-

0.090Calginat

Since according to Hugo (1974), ~ = (5~:~jg - 1F'4, thus for the porosity, Calg = 0 , 9 5 8

--

0.072Calgi,,,e

was obtained. F o r maltose, Deff/Dma x = 0.52 and for ethanol, D~ff/Dmax = 0.77 were obtained. Diffusivities of glucose, maltose, starch and ethanol at different solute concentrations are compiled in Table 2. M e a s u r e m e n t s were carried out with glucose and Z. mobilis in gel beads alone as well as in the presence of spores of A. awamori. In the latter case, Z. mobilis

e.

Table 1. The partition coefficients of glucose, its effective diffusivities D e ft in the beads, and Deff/Dma,-ratios at different alginate concentrations and mixing rates f; Dm,x = 8.1 × 10 - 6 cm: s - l C~]gi.... (%) 1.5 3.0 4.5 3.0 3.0 3.0

k 1.00 0.98 0.96 0.96 0.99 0.97

Deft (cm2s 1) 6.8 × 5.1 x 4.6 X 4.7 x 5.4 x 4.9 x

10 -6

10 -6 l0 -6

10 6 10 6 10 6

De,/D . . . . 0.84 0.62 0.57 0.58 0.66 0.60

f(min -1) 500 500 500 500 750 1000

Table 2. Mean effective diffusivities D e ft t × 10- 6 cm2s- ]) of glucose, maltose, starch and ethanol at various solute concentrations in water (W) and in cultivation medium (M) without starch and with starch (MS) Solute Glucose W Glucose M Glucose MS Glucose MZ Glucose MZA Maltose W Starch W Ethanol W

(31)

5g1 1

10 g 1- 1

20 g 1-1

3.95 _+ 0.26 4.58 _+ 0.23 3.82 _+ 0.43 n,d. n.d. 3.54 _+ 0.18 3.50 + 0.16 9.59 _+ 0.52

4.23 _ 0.21 3.83 + 0.26 4.71 _+ 0.17 4.39 _+ 0.28 4.48 _+ 0.23 3.44 + 0.15 3.82 _+ 0.17 9.38 _+ 0.50

4.84 _+ 0.44 4.78 + 0.24 4.54 _+ 0.19 n.d. n.d. 3.56 + 0.15 3.83 _+ 0.21 9.40 _+ 0.41

Note: Beads with immobilized Z. mobilis (MZ) (20 mg cell mass/' 40 g gel). Beads with immobilized Z. mobilis (20 nag cells mass/40 g gel) in presence of 5 x 107 spores of A. awamori (MZA).

2320

J. Meyerhoff et al.

produced acetaldehyde as well, which impaired the growth of the fungus. No effect of the immobilized Z. mobilis on the diffusion coefficients was found in the investigated range. The surface of the beads was covered with a biofilm of the fungus. Therefore, the bead diameter could not be determined exactly so definite calculations of D~ff were not practicable. The diffusion coefficients of starch, maltose, glucose and ethanol on the one hand, and of oxygen on the other hand are close to their coefficients in pure water and in good agreement with the results of other authors (Chang and Moo-Young, 1988; Gosmann and Rehm, 1988; Omar, 1993a, b; Hoijmans et al., 1990; M/iller et al., 1994; Hellendorn et al., 1995; Estap6 et al., 1992; Lebrun and Junter, 1993; Hannoun and Stephanopoulos, 1986; Sakaki et al., 1988). Biological parameters of the microorganisms The biological parameters of Zymomonas mobilis at different substrate concentrations were determined by separate measurements. (Table 3). Linear relationship between the CO2 concentration (Cc) formed and the cell mass concentration (Cx) were obtained: ZCc (mol 1-1 ) = )'0.007 + 0.17C zym'M for 2% glucose [.0.031 + 0.21C zym'M for 4% glucose. Between the CO2 concentration and C Zym' M the following approximate relationship was found: ECc(mol1-1) = 0.0013 + 0.0239C zym'M (gl-X).

Table 3. Cultivation parameters of freely suspended Zymomonas mobilis on glucose in stirred-tank reactor Parameters

Substrate (%)

PZym(h- 1) yZ~,, (gg 1) Yes (gg 1) Yvx (g g- 1) Qp (g g- 1h- 1) QZym(g g-X h-l)

0.5

2.0

4.0

0.73 0.034 0.47 10.7 7.84 18.9

0.49 0.053 0.36 6.65 3.14 9.23

0.34 0.042 0.44 10.4 3.54 8.15

However, the ratio ~,Cc/C~ m'M was only constant in the range of t = 30080h. A respiration quotient RQ = 0.85 was obtained for this cultivation period. The biological parameters of suspended and immobilized A. awamori are shown in Table 4. Coimmobilized mixed cultures A. awamori and Z. mobilis prefer different cultivation conditions. The optimal growth conditions of Z. mobilis are 30035°C, pH 5.0°5.5 (Rogers et al., 1982), and of A. awamori, 25°C and pH 4.5 (Chiquetto et al., 1992). To find the optimum for the coimmobilized mixed culture, temperature, pH and the ratio of the fungus to bacterium cell mass were varied. The highest ethanol concentration was obtained at initial pH 5.5, but the pH effect was weak in the pH range 4.5-5.5 as well as in the temperature range 30035°C. With increasing temperature, however, the maximum concentration was obtained earlier. With increasing spore concentration from 2.5x 105 to 2.5 x l0 T per 40 g gel, the overall cell mass concentration was not influenced unequivocally, but the maximum ethanol concentration increased from 3.6 to 6.0 g 1-1. With increasing bacterial inoculum concentration 5-40mg per 40 g gel at 5 x 107 spore per 40ggel, the maximum ethanol concentration increased from 3.8 to 5.3 g1-1 . To investigate the stability of the cultures, repeated batch cultivations were performed in shake flasks. The coimmobilized fungus/bacterium system was stable up to 200 h (John et al., 1996). The performances of the cultivations in shake cultures are given by John et al. (1996) and in stirred-tank and airlift tower loop reactors by John and Schfigerl (1996). General description of the coimmobilized mixed culture The cooperation of the fungus and the bacterium is schematically depicted in Fig. 4. The amylase produced by A. awamori hydrolyses starch or maltose to glucose which is consumed by both of the microorganisms. Therefore, the hydrolysis occurs in the homogeneous liquid phase as well as in the heterogeneous phase (biofilm and bead shell). The amylase is inhibited at a high glucose concentrations. Glucose is used by A. awamori for cell growth and by Z. mobilis for cell growth and ethanol formation. Under anaerobic

Table 4. Cultivation of the freely suspended and immobilized A. awamori on synthetic medium with starch substrate in gaslift loop reactor (0.5 vvm air)

max. cA~p(g 1 1) Time at max. cAsv (h) pk~p (h- 1) Fraction of immobilized cell mass (%) yA~, (g g- ~) Yxc (g g- 1) RQ

Immobilized cells

Freely suspended cells

142 42 0.09 96.0 0.64 2.84 0.84

13.4 65 0.10 0.54 3.16 0.85

Coimmobilized aerobic/anaerobic mixed cultures

02

2321

1iucos,

starch

i

cell mass, CO 2

~ Aspergillus awarnori] 2--o

;2 o=,..

02

glucose

e-

.o °~ d~ trllll

cell mass, C02

i Zymomonas mobilis

'

I

T i

acetaldehyde ethanol Fig. 4. Schematic diagram on the cooperation and competition of A. awamori and Z. mobilis in coimmobilized mixed culture.

conditions, the bacterium does not consume ethanol. The fungus, however, takes up ethanol as soon as the glucose is exhausted. Using glucose as substrate, Z. mobilis grows, produces ethanol and - - in presence of oxygen - - acetaldehyde as well, which prevents the fungal spores from germination. In the outer shell of the beads, the fungus grows under aerobic conditions. The bacterium can only exist in the anerobic centre of the beads. When starch or maltose are used as substrates, the growth of the fungus is controlled by the hydrolysis rate of starch and maltose as well as by the oxygen transfer rate into the biofilm and bead shell. The growth of the bacterium and ethanol formation are controlled by the hydrolysis rate. The ratio of the two microorganisms c a n be controlled by the spore concentration to bacterial inoculum mass as well as by level of dissolved oxygen in the liquid, i.e. by the gas composition, used for aeration.

The coimmobilized aerobic fungus and anaerobic bacterium formed a stable mixed culture when starch or maltose were used as substrates. The growth of the bacterium started after the spores of the fungus had germinated. The growth rate of the microorganisms was controlled by the conversion rate of starch and maltose, respectively, to glucose. At high glucose concentrations the amylase activity was inhibited. Therefore, the glucose concentration never attained high values. The biomass concentration attained a level which was necessary to produce a sufficient amount of amylase for the formation of glucose. Comparison of the measured data with the model simulations. Figure 5 displays experimental data and simulation results for an experiment with the coimmobilized culture of Aspergillus awamori and Zymomonas mobilis in an 31 airlift loop reactor, aerated with air. This and

2322

J. Meyerhoff et al. a

suggest that A. awamori starts to consume ethanol for growth. This p h e n o m e n o n is not considered in the present model. Simulation of the carbon dioxide production rate 1 poses some problems in this case [-Fig. 5(b)]. The 0 ~ plateau at t = 25 h and the maximum at t = 35 h in _1~_.~ the experimental data have no obvious correspondence in the growth curve. On the supposition that - 2 ~ CPR is mainly determined by the growth rates and -3 that model parameters like YxA~ p and Y~'cm have constant values all the time, it is impossible to achieve -4 a better agreement between simulation and experi-5 ment. CPR is mainly determined by growth activity of

3 2

25 2O

Cxv

7a

10OCsM 12

10

20 t [h] 30

40

50

A. awamori.

b 0,012140 0,008120

g 0,o04. -

100

0,000~

80 ~

-o, i -0,012 0

oO°oc

10

20 t[h] 30

dO

6O

-50

Fig, 5. Experimental data (symbols) and simulation results (lines) of an immobilized mixed cultivation in the airlift loop reactor, aeration with air. (a) (11) Concentration of soluble starch, C~; (A) concentration of ethanol, Cg; (O) concentration of glucose, CsU; (T) total dry biomass concentration, CxM;(b) (11) Carbon dioxide production rate, CPR; (©) oxygen tension in the medium, p02. Parameter values of the simulation are given in Table 5. p02 in the medium [Fig. 5(b)] was not simulated but put into the program according to the line that fits the pO2 data points. Dashed line: CPR that is due to growth and maintenance of A. awamori alone.

the following figures were drawn by picking only the simulation results of every 5 h of cultivation time and using linear interpolation in between. Parameters were identified with a view to an optimized fit of Csu, Ceu, Cs~ and Cxu . Simulation results show a good correspondence to the experimental data. There is no explicit lag phase in the model, yet it takes about 20 h until there is a noticeable increase in biomass. Soon afterwards, the medium glucose concentration reaches its maximum when more glucose is produced than can be consumed. The maximum of the glucose concentration corresponds to intensive growth of Z. mobilis what can be concluded from the steep increase of the C~-curve. Ethanol production and growth of Z. mobilis cause a sudden decrease of the glucose concentration. At about t = 35 h, starch has been used up, so growth and ethanol production come to a standstill. In the experiment, a drop of Cvu and a further weak increase in the biomass concentration

Figures 6(a) and (b) show the simulated biomass concentration profiles of A. awamori and Z. mobilis, respectively. A. awamori soon leaves the alginate bead (r < 1500 #m) and ends off growth at r = 2300/~m. These are purely simulation results to which no corresponding experimental data exist but photographs of a typical bead taken after 36 h show that these results are within realistic limits (John, 1995). Z. mobilis starts to grow almost uniformly distributed throughout the bead. Growth is slightly inhibited between r = 1000 and 1500 pm. After t = 30 h, a maximum of C zym develops in this region, as soon as the oxygen concentration is low enough but as long as glucose concentration is still sufficient for growth.

~

~

~-30 -25 .20 _-.15 •10 rJ .5

4027

~ ~ ] .0 ¢~ ~ ~ r-- c~

Radius[~tm]

b 2

tlhl 0 " ~

~

I"~''~" ¢~ ~ ~ R~dius[~m]

Fig. 6. Simulated radial concentration profiles of the biomass concentrations: (a) Dry biomass concentration of A. awamori; (b) dry biomass concentration of Z. mobilis. The thickened line marks the edge of the alginate bead.

2323

Coimmobilized aerobic/anaerobic mixed cultures a .5 -4,5 -4 -3,5 -3 -2,5 -2 -1,5 -1 -0,5

CM /~ v

I B"-"I,.~ C M /,,

•

"-~

~-" 1

5

2

~

12

-2

10 8

~I

..M 4~

--

2 ~m

'1~-

-.2

Radius [gin]

6

~

;o Z

40 0

10

20

30

40 t[hl

50

60

b

100

60

-3 0

0,004-

. ~ "

CPR [ 120

;.= o,

f8o

o,oooRadius [grn]

~

~" ~

~

tthl

Fig. 7. Simulated radial concentration profiles of the substrate concentrations: (a) glucose concentration; (b) oxygen tension• The thickened line marks the edge of the alginate bead. Due to the extension of the A. awamori layer, the radius of the maximal concentrations moves outwards.

Substrate profiles are depicted in Figs 7(a) and (b). It should be noted that there is almost no decrease in the glucose concentration along the radius at t = 18 h but later on at t = 27 h - - s t a r t i n g from the same C~t--glu cose drops to zero at the centre of the bead. This change is due to the activity of Z. mobilis, which has its peak at t = 23 h. On the contrary, A. awamori contributes only few to the glucose concentration gradient because of a relatively high value of rasp --XS " The penetration depth of oxygen, on the other hand, decreases quickly from 1500 #m at t = 4,5 h to about 250/~m at t = 13 h and ends with about I00/~m at t = 30 h. Figures 8(a) and (b) show results of another experiment performed in the airlift loop reactor, aerated with 20% air/80% nitrogen. The reduction of the oxygen supply is to limit the growth activity of A. awamori and to support ethanol production by Z. mobilis (John and Schfigerl, 1996). However, under conditions of oxygen limitation it was observed that the mycelial layer outside the gel bead thickens but has only a loose structure. The viscosity of the broth is highly increased to the end of the cultivation. The thickness of the fungal mycelium impairs diffusion of glucose into the bead and causes Z. mobilis to produce ethanol on a lower level than expected. In the simulation, the mycelium extends up to r = 3000 pm but only to a maximum concentration of C Asp = 12 g l - 1.

60

r.) -0,002 •

pO;

I 0

-0,0040

10

20

30 40 t [hi

50

60

Fig. 8. Experimental data (symbols; see caption of Fig. 5) and simulation results (lines) of an immobilized mixed cultivation in the airlift loop reactor, aeration with 80% N2, 20% air. Parameter values of the simulation are given in Table 5. pO2 in the medium [Fig. 8(b)] was not simulated but put into the simulation program according to the line that fits to the p02 data points.

Figures 9 and 10 show simulation results and data of two experiments in the small stirred-tank reactor. In Fig. 9, the simulated biomass concentration seemingly exceeds the measured one from t = 40 h onwards. There are, however, increasing amounts of the mycelium chipped off and suspended in the medium (t = 4 0 h : 1.6g1-1; t = 60h: 3.6g1-1). The concentration of suspended dry biomass is measured separately. Data points of C ~ in Fig. 9 only mean the amount of immobilized biomass. In both experiments, the starch concentration begins to drop without an analogous increase in the glucose or biomass concentration in the first 15-20 h. This discrepancy in the mass balance becomes obvious in the simulation. All in all, simulation results are in good correspondence to the experimental data. Model parameters F o u r different cultivations could be described satisfactorily by the same model. We therefore claim the model to be valid in the range of experimental conditions that have been tested. It is not necessary to alter

J. Meyerhoff et al.

2324 a

a

4

25 6 20! 4 8

15z

~

C~

, -4

10 20 30 40 50 60 70

0 ~r~t -4 b~" 1

5

?4

q-2,0

10 20 30 40 50 60 70 80 90 t[h]

~ -2,5

t [h]

b

~ •

~

0,002~

--.,r

0'000~w'- ~

~ -o,oo2j -0,004J . . . . . . 0 1020

•140 .120 '100

8o

4060 ~~'-L

~ ~ . . 3040506070 t [h]

0

Fig. 9. Experimental data (symbols; see caption of Fig. 5) and simulation results (lines) of an immobilized mixed cultivation in the stirred-tank reactor, aeration with air. Parameter values of the simulation are given in Table 5. pO2 in the medium [Fig. 9(b)] was not simulated but put into the simulation program according to the line that fits to the pOa data points. some of the model equations to account for each individual experiment; differences in these conditions can be described with variable sets of parameter values. Some tentative parameter values were taken from the literature and our own measurements (John, 1995; John and Schiigerl, 1996) but most of them had to be identified or corrected individually. Model parameters are given in Table 5. Many parameter values, such as the yield coefficients, do not differ very much or are even constant. The greatest variability is shown by the specific growth rates rmax ttAsp and P Zym . . . . the Monod constant for oxygen, K0, the maintenance coefficients mc and ms, and the transport coefficient fax. Values for #max zym are very close to data in the literature (e.g. Lee et al., 1980; Rogers et al., 1982). Contrary to Z. mobilis, there are almost no data on #max Asp available from the literature. Zetelaky-Horvbah (1978) specifies /~m,x Asp = 0.214 h -1 which is much lower than values from our own parameter identification. This is explicable from the definition of the specific growth rate

1 dCx Cx dt

0,008 ~

~ .

•IOO

-r~' o,oo6

.8o

0,004 J

a~

,~E 0,002t

~

°,°°°i

_ _ . 2 •

].1 ~ - - - -

0

2 C -2~

b 0,004]

A ~0

t

2 ~ ]-1,0 -2

0

C 15!L

6 -"-" 0,0 -~" 4 ~ -0,5

1~~ 10o

0

~0,5

2

.

.

.

,..~" - ~

"60

k~

.40 ~

"

.

°o,°o°2 \ 0 10 20 30 40 t [hi

: o0 50 60 70

Fig. 10. Experimental data (symbols; see caption of Fig. 5) and simulation results (lines) of an immobilized mixed cultivation in the stirred-tank reactor, aeration with 80% N2, 20% air. Parameter values of the simulation are given in Table 5. p O 2 in the medium [Fig. 10(b}] was not simulated but put into the simulation program according to the line that fits to the pOz data points.

Because oxygen is limiting in most parts of the bead, there is in fact only a very small fraction of hyphae which contributes to growth (or to dCx/dt, respectively) and which therefore should be considered in the factor 1/Cx, whereas in practical measurements of /~ or/~ . . . . non-growing biomass is subsumed under Cx as well. In case of a high fraction of inactive biomass, the apparent value of # ~ consequently may be much lower than the actual one which prevails only at the outer edge of the bead. The apparent specific growth rate of A. awamori in the present experiments is always below 0.1 h The differences in Ko may point to the capability of A. awamori to adapt to very low oxygen tensions in the medium. This is especially remarkable in Fig. 10, where there is still noticeable growth at t > 40 h even though pO2 is below 5% ( = 0 . 0 0 8 m g l - 1 ) . From t = 50 h, some mycelium starts to grow on the oxygen electrode, therefore preventing it from yielding reliable results. Differences between the parameter values that dez y m , yA~p) are relatively great. In termine CPR (mc, Y xc two cases (Figs 9 and 10), the simulation closely corresponds to experimental data, whereas the quality of the other two simulations falls behind, perhaps because the above-mentioned parameters do not have constant values over time. It was intended to set up

Coimmobilized aerobic/anaerobic mixed cultures

2325

Table 5. Model parameters and initial values

Aeration Cxasp (0) (g 1 1) Csv(0) (g 1 - l) C*(g1-1) ~A~ (h ~) ItZY]' (h ~) yZ~m

Ye.~ yA~p

yZ~, mc(h ~) mo (h 1) ms (h 11 K Asp (gl 1) K zym (gl- ~) Ko(g1-1) K i ( g l l) qST. . . . (h 1) Ksx.o(gl 1)

jj~ (Itm 21 ('x.~i~ (gl l) dr (h)

Figs 5-7

Fig. 8

Fig. 9

Fig. 10

Air 0.9 25.0 8.6154x10 3 0.6 0.365 0.056 9.1 2.5 0.4 1.2x10 4 0.05 0.048 0.1 0.13 l x l 0 ~t

Air/N2 0.8 22.0 1.7231x10 -3 0.79 0.115 0.056 9.2 12.0 0.7 1.8x10 -4 0.06 0.05 0.05 0.1 3x10-~, 5 x 1 0 _s 0.97 5x10-4 1100 19.5 0.05

Air 0.9 22.0 8.6154x10 3 0.58 0.138 0.056 7.0 3.5 0.37 5.7x10 5 0.06 0.012 (/.05 0.1 6 x 1 0 -6

Air/N 2 0.09 22.0 1.7231x10 3 0.88 0.22 0.09 9.2 3.0 0.13 2x10 5 0.06 0.1 0.05 0.1 1.7x10 ~ 4x10 3 1.5 2.7x10 4 825 19.5 0.05

lxl0

-4

1.25 IXI0 8 2250 17.5 0.07

6x10-4

1.31 5 x 1 0 -3 1675 19.5 0.05

Sensitivity analysis

0.8 22.0 1.7231×10 -~ 0.7 (I.25 0.056 9. l

0.06 0.(15 0.05 0.13 lxl0 ~ lxl0 ~ 1.25 5×10--~ 150(1 19.5 0.05

Constants: CzYm(0) = 0.013 g l 1; KST = 5.0 g l- 1; Yes = 0.3; YxA~ ,0 = 0.5; Yx'o = 0.8: c~ = 13,877 1 ~; Do ..... = 20 x 10 s cm 2 s

1: Ds.max = 5 . 0 x

10

6 cm 2 s-i

a global model (i.e. a model which is valid for the discription of the whole cultivation period), so a possible variation of p a r a m e t e r values during time was not analysed.

Sensitivity analysis In the following section, the consequences of variations in the p a r a m e t e r values are to be assessed. O n e could simply j u d g e h o w m u c h the e t h a n o l concentration changes after one or m o r e p a r a m e t e r s have been varied but the reader's a t t e n t i o n should also be focussed on h o w the d e v e l o p m e n t of the cultivation a n d not only how the final o u t c o m e is changed. To keep the n u m b e r of examples small, only selected variations of one p a r a m e t e r value at a time are s h o w n in the following figures [Figs 1 l(a)-(f)]. Reference ('standard') p a r a m e t e r s are given in Table 5, the assumed external oxygen c o n c e n t r a t i o n s were the same as in Fig. 8(b). C P R was omitted from the analysis. Figure l l(b) shows simulation results with reduced initial c o n c e n t r a t i o n of starch, CST(0). Until t = 30 h, the simulation behaves identically to the reference [Fig. l l(a)]. Afterwards, the glucose c o n c e n t r a t i o n reaches only a lower m a x i m u m . E t h a n o l a n d the biomass c o n c e n t r a t i o n stagnate from t = 4 0 h at a lower level t h a n in Fig. ll(a). Figure l l(c) depicts simulation results u n d e r the condition that pO2 is always 2 0 % higher t h a n in the reference simulation [Fig. l l(a)]. This leads to an

increased initial growth activity of A. awamori and starch hydrolysis is accelerated. As expected, more oxygen in the m e d i u m depresses ethanol f o r m a t i o n while the biomass c o n c e n t r a t i o n a n d the fraction of A. awamori increase. The effects of variant oxygen tensions in the m e d i u m are m o r e distinct t h a n those of deviating values of the diffusion coefficient Do . . . . . This is in accordance with modelling analyses on pellet d e v e l o p m e n t of Penicillium chrysogenum (Meyerhoff et al., 19951. Figure l l ( d ) illustrates the effect of lowering the initial c o n c e n t r a t i o n of A. awamori. G r o w t h a n d starch hydrolysis take place more slowly. The maxi m u m c o n c e n t r a t i o n of glucose is lower t h a n in the reference simulation while the final ethanol concent r a t i o n is on a similar level. An increase in the final ethanol c o n c e n t r a t i o n can be observed when/~ZmYmor qsx . . . . are a u g m e n t e d (Figs l l(e) a n d (f)]. In the former case, starch hydrolysis a n d C ~ are almost not influenced, whereas the glucose m a x i m u m shrinks c o m p a r e d to the reference because more glucose is converted to ethanol. The latter p a r a m e t e r variation simulates accelerated starch hydrolysis. This causes glucose to accumulate faster and reach higher c o n c e n t r a t i o n s and, according to eq. (28), glucose limitation of ethanol f o r m a t i o n is (partially) lifted. CST(0), Cx(0), pO2 a n d o t h e r m e d i u m concentrations c a n - - w i t h i n l i m i t s - - b e influenced directly by the operator. Other parameters such as specific reaction

2326

J. Meyerhoff et al.

a 2 0 ~ ~ r

//~--

CpM

10

4

30

40

60

50

t [51

e~

15-

4~

"~ .... ~C.~lO" C ~ ~

CxM

2L

-6

,-4 70

"-8

12

-6

10

,4

8

]2

4

.... 00 10

f ~ 20'

1

o~

-r

' . . . . . . . . . 20 30 40 50 60

C M

/

~M

t5P

15

T~

_

_

_

~

V

/

. . . .

o

M

Cx 30

-2 , -4

L

5O

40

20-

O0

70

60

CpM

.

I--

15.

/

.

Cs

~10-

/" .

,

20

•

, .~-.

,

30 40 t [h]

.

,

50

•

,

60

d 20/

15-

.

12

6

10

4

8

2

6~" 4~

4--' 0 ~

2

-2L=.

0

-4

, -2

-6

, -4

-8

70

12

]6

10

-14

8

]2

4-a

~10=~< 5 - ~

10

2

20

12

-6

10

~4

8

J2

~

-7

/

[

M

2L 0

4-4

-2 10

20

30 40 t [h]

50

60

-4 70

~-8

Fig. 11. (Continued)

C~r

10

J -8

t N]

C

.--~

t::

5

-8

67--"

~c,~ ~10'

~

~-4

70

t [h]

2 ~.)m - 2 : ~ .

20

-2 ~

-2

M

~

0 --

* -6

~10

/

2

-2

6T"

0,-.-"7_ s 0 10

8

67,--~

-4

15 ¸ ~

~

6 4

0

/

. . . .

C~

12 10

-1-,,

M

C~

Csr ,,~

o

b 20-

~

2 ~.)~]_2 :r~

M

Cx

20

2 0 - ~

4 "~

M

10

e /

64-"

. . . . .

0

q6

8

t ..... ~

12

30 40 t [b]

50

60

-2 2

0

4-4

-2

t -6

-4

J -8

70

Fig. 11. Examples of the sensitivity analysis. All model parameters are given in Table 5: (a) reference simulation; (b-f) variation of one single parameter, (b) lower C~(0)= 16 gl-1; (c) pO2 always 20% higher; (d) lower CxAsP(0)= 0 . 4 g l - l ; (e)higher /~Zym=0.35h-1; (f) higher qsr .... = 1.5 h -1 .

rates, kinetic and stoichiometric constants cannot easily be controlled by the experimentalist and variations are predominantly of theoretical interest. The complexity of the model system prevents a brief summary of the parameter sensitivity. In general, alterations of the specific reaction rates have the greatest effects. Alteration of one parameter value usually cannot be compensated by alteration of another. As far as ethanol formation is concerned, this is mainly dependent on sufficient glucose supply. Any conditions that restrain starch hydrolysis or support glucose consumption by A. awamori will diminish ethanol production. CONCLUSIONS As a model system for coimmobitized aerobic/anaerobic mixed cultures, A. awamori and Z. mobilis coimmobilized in Ca-alginate beads were characterized experimentally mainly in respect to mass transport processes. Effective diffusion coefficients of carbon substrates in the gel were determined and found to be markedly lower than the diffusivities in pure water. The coimmobilized mixed culture was shown to be in a stable steady state• The model of the microscopic processes (growth, substrate transport and uptake, and ethanol production) is suited for describing whole cultivations in small stirred tank and airlift tower loop reactors. It helps to understand the most important factors that influence growth and production of the mixed culture. By using the experimentally determined transport parameters, such as diffusion coefficients, the process

Coimmobilized aerobic/anaerobic mixed cultures could be described well by a model based on simple kinetics. The accuracy of the estimated kinetic parameters must still be improved by further measurments, preferably of the profiles of cell distribution and of the other relevant concentrations within the beads. It was found that ethanol production will be high if glucose can be provided early in the cultivation before the biomass of A. awamori dominates the glucose consumption. Optimization procedures should focus on finding the most favourable relation between the activities of the two microorganisms. Since A. awamori serves only to break down starch and to shield Z. mobilis from oxygen, the fungal activitiy should, however, been controlled, e.g. by reducing pO2 or by selecting A. awamori strains that have lower

QM p pO2

Future experiments might investigate the distribution of the two organisms in the beads during the process. Thin sectioning, staining and microscopic examination and measuring concentration profiles might be possible approaches. Unfortunately, it is not possible to follow the history of one single bead in a cultivation.

Vv V~ x Yes

R Rb Re RQ r Sc Sh T t t'~ v

Yex Yxc

Acknowledgements

G. J. thanks the Fonds der Chemischen Industrie for a scholarship and the authors acknowledge the support by the European Economical Community (Contract No. ERBCIPA-CT92-4010tand the Max Buchner Foundation of the DECHEMA. NOTATION

CB

C CM

c~

CPR dp

D Dm~x Ox

F(; k K KI tn

mXA~.,' tl

N qn

Q Qx

number of gel beads per liter medium volume, 1 local concentration, g 1concentration in the medium, g l maximal concentration of dissolved oxygen at the current, partial pressure in the gas phase, g 1- t carbon dioxide production rate, g 1- ~h particle diameter, m diffusion coefficient, m 2 h - 1 maximum diffusivity in water at 2Y'C. m2h 1 transport coefficient of biomass, m 2 h parameter, m 2 gas flow at the inlet, l h partition coefficient liquid/bead, dimensionless Monod constant, g linhibition constant, g 1specific maintenace rate, h biomass of A. awamori that hydrolyses starch, g number of radial layers, number of beads, dimensionless coefficient of approximation series, dimensionless local uptake rate, g 1- a h transport term due to hyphal extension, h 1

Yxo Yxs

,3,,7

total uptake rate in the medium, g I ~h pressure at the gas inlet, Pa partial pressure of oxygen in the liquid phase, % gas constant in eq. (29) J K - ~mol radius of the gel bead,/~m Reynolds number, dimensionless respiration quotient, dimensionless radius, #m Schmid number, dimensionless Sherwood number, dimensionless temperature at the gas inlet, K time, volume of a radial layer, 1 slip velocity, m2s 1 settling velocity, mZs 1 volume of the liquid phase in the reactor. 1 total volume of the gel. 1 molar fraction, dimensionless yield coefficient, g ethanol per g glucose consumed, g gyield coefficient, g ethanol produced per g biomass formed, g gyield coefficient, g biomass per g carbon dioxide, g g yield coefficient, g biomass per g oxygen consumed, g g yield coefficient, g biomass per g glucose consumed, g g

Greek letters

fl a,~g am # v p,, Px

ratio of liquid volume to bead volume, dimensionless mass transfer coefficient, m 2 s porosity of the alginate bead, 11 energy dissipation rate per mass, m 2 s 1 specific growth rate, h - 1 kinematic viscosity, m - 2s volume density (volume of biomass per total volume), 1lbiomass density (dry biomass per I wet cells), g I - l labyrinth factor, dimensionless

Subscripts and Superscripts Asp Aspergillus awamori alginate variable in the alginate get C carbon dioxide crit critical value eft effective value ex at the gas outlet in at the gas inlet M in the liquid medium max maximum value O oxygen P product, ethanol S glucose ST starch X biomass Zym Z ymomonas mobilis

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J. Meyerhoff et al. REFERENCES

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