Mathematical modelling and optimization of hydrogen continuous production in a fixed bed bioreactor

Chemical Engineering Science 57 (2002) 3819–3830www.elsevier.com/locate/ces

Mathematical modelling and optimization of hydrogen continuousproduction in a 'xed bed bioreactor

E. Palazzi, P. Perego, B. Fabiano∗

DICheP Chemical and Process Engineering Department “G.B. Bonino”, University of Genoa, via Opera Pia 15, 16145 Genova, Italy

Received 29 January 2002; received in revised form 16 April 2002; accepted 19 July 2002

Abstract

The purpose of this paper is to investigate, both theoretically and experimentally, hydrogen production from agro-industrial by-productsusing a continuous bioreactor packed with a mixture of spongy and glass beads and inoculated with Enterobacter aerogenes. Replicatedseries of experimental runs were performed to study the e6ects of residence time on hydrogen evolution rate and to characterize thecritical conditions for the wash out, as a function of the inlet glucose concentration and of the 7uid super'cial velocity. A further series ofexperimental runs was focused on the e6ects of both residence time and inlet glucose concentration over hydrogen productivity. A kineticmodel of the process was developed and showed good agreement with experimental data, thus representing a potential tool to design alarge-scale fermenter. In fact, the model was applied to the optimal design of a bioreactor suitable of feeding a phosphoric acid fuel cellof a target power.? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Bioreactors; Fermentation; Hydrogen production; Immobilization; Optimization; Packed bed

1. Introduction

Alternative renewable energy forms are gaining increas-ing importance to complement and, possibly, substituteconventional energies, of fossil origin. Energy productionusing biomass is to be regarded as a potential, unpollutingenergy source. In particular, molecular hydrogen is consid-ered a suitable fuel for a future climate-constrained world(Tsygankov, Borodin, Rao, & Hall, 1999). Hydrogen can beproduced chemically, electrochemically, as a by-product ofoil/coal processing, or by the use of microorganisms. Whileother methods of production have been used industrially ando6er the advantage of scale economy, microbial productionis a relatively new technology still untested on a large scale.There are two systems to obtain microbial hydrogen

production, namely photochemical and fermentative. Theformer consists in producing by means of photosyntheticmicroorganisms such as algae (Kumazawa & Mitsui, 1981)and photosynthetic bacteria (Miyake & Kawamura, 1987;Sasikaia, Ramana, & Raghuveer Rao, 1992; Segers &Verstraete, 1983; Stevens, Vertonghen, de Vos, & Ley,

∗ Corresponding author. Tel.: +39-010-353-2585;fax: +39-010-353-2586.

E-mail address: [email protected] (B. Fabiano).

1984). The latter is carried out by fermentative hydrogenproducing microorganisms, such as facultative anaerobes(Brosseau & Zajic, 1982; Tanisho, Wakao, & Kosako,1983; Tanisho, Suzuki, & Wakao, 1987) and obligateanaerobes (Karube, Urano, Matsunaga, & Suzuki, 1982;Taguchi, Chang, Takiguchi, & Morimoto, 1992; Taguchi,Chang, Mizukami, Salto-Taki, & Hasegawa, 1993).Hydrogen production by fermentation seems to be a very

expectable method in comparison with the photochemi-cal one, because of the higher rate of hydrogen evolution(Tanisho et al., 1987). Other advantages of the fermenta-tive hydrogen production lie on the possibility of utilizingas substrate industrial and/or agricultural wastes and of ob-taining other metabolites suitable for valorization, such asorganic acids and alcohols.Clostridia and Escherichia coli are probably the most ex-

tensively studied in order to be used as fermentative hydro-gen producing organisms. Clostridium butyricum has beenreported to evolve hydrogen at a rate of 7:3 mmol g−1cells h

−1

under anaerobic cultivation of wastewater from an alcoholfactory (Tanisho, Kamiya, & Wakao, 1989).The metabolism of glucose by Enterofacter aerogenes

is amply known to follow the Embden–Meyerho6 pathway(Gottschalk, 1986). The 'rst step, corresponding to gly-colyses, produces pyruvate; in the subsequent fermentative

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S0009 -2509(02)00322 -6

3820 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

pathways, the result of anaerobic and microaerobic glucosemetabolism is a mixed acid fermentation, with conversionof pyruvate to acetate, ethanol, CO2, hydrogen, acetoin and2,3-butanediol. Hydrogen is formed through the reactionHCOOH → CO2 + H2, in which the degradation of for-mate is catalyzed by formate hydrogenlyase, a membranebound multyenzyme complex of which hydrogenase is a part(Schlegel & Schneider, 1985). In particular, the theoreticalmaximum hydrogen productivity on glucose fermentationcorresponds to 4 mol H2 mol

−1glucose, as reported by Thauer,

(1977):

C6H12O6 + 2H2O→ 2CH3COOH + 2CO2 + 4H2

Continuous fermentation process is expected to allow ane6ective improvement of hydrogen production, as reportedby several researchers for di6erent fermentations from re-newable materials (Patel & Madamwar, 1995; Tanisho &Ishiwata, 1995). Two basic categories can be identi'ed:suspended cell processes, taking place in continuous stirredtank reactors, and 'xed 'lm processes, realized by im-mobilized cell reactors. The former can present negativephenomena i.e. wash-out and product inhibition, which areto be overcome by the application of cell recycle, reducedpressure or membrane reactors. The latter represents a lesscomplex and expensive solution and o6ers advantages, suchas greater cell longevity, making it possible to work withnon-conventional reactors, such as tower bioreactors, incontinuous or semi-continuous processes (Cruz, Almeida,Araujo, Giordano, & Hokka, 2001). Improvement of hy-drogen production by self 7occulated cells in a packed bedreactor was recently reported by Rachman, Nkashimada,Kakizono, and Nishio (1998), while the use of immobilizedEnterobacter cloacae IIT-BT 08 on lignocellulosic solidmatrices, was reported by Kumar and Das (2001). In a pre-vious work (Palazzi, Fabiano, & Perego, 2000), preliminaryexperimental runs were performed to verify the feasibilityof hydrogen production by a continuous column bioreactor.On the basis of these results, further series of experimentswere performed, with the aim of quantitatively de'ning thecritical operating conditions, as well as the optimal valuesof 7ow rate and inlet glucose concentration, to the end ofhydrogen production. Starting from a brief account on the'rst series of experimental runs, this work describes themain results of the next ones and the development of a sim-ple kinetic model, employed to design a bioreactor suitableto feed a phosphoric acid fuel cell (PAFC) of 5 kW.

2. Materials and methods

2.1. Microorganism

Pure culture of E. aerogenes (NCIMB 10102) used forthis study was maintained on nutrient agar slants at 4◦Cand subcultured monthly. The cells were then incubated

Table 1Yield of starch hydrolysate (values are referred to the dry extract equalto 69.5% (w/w))

Component Value

Glucose 85.0% (w/w)Maltose 2.6% (w/w)Trisaccharides 0.7% (w/w)Oligosaccharides 6.85% (w/w)Ashes 3.8% (w/w)Proteins (N × 6:25) 1.05% (w/w)Ca2+ 0:305 (mg g−1)Mg2+ 0:129 (mg g−1)Na+ 71:50 (mg g−1)K+ 1:090 (mg g−1)

aerobically at 37◦C, in shake 7asks on a rotary shaker at150 rpm and harvested at the stationary phase.The pre-culture medium consisted of 1.5% glucose, 0.2%

yeast extract, 0.5% peptone, 0.5% NaCl, 0.1% beef extract,all in weight per cent; the cells were aseptically inoculatedinto the fermenter 12 h after they had been harvested.

2.2. Culture media

The starch hydrolysate, kindly supplied by Roquette ItaliaS.p.A. of Cassano Spinola (Italy), was prepared by enzy-matic hydrolysis of corn starch. The procedure consisted ofan enzymatic pre-treatment with a heat-resisting �-amylase,until a concentration of 15–20% equivalent dextrose (ED)was obtained. A subsequent sacchari'cation at 60◦C withamyloglucosydase nearly allowed the complete hydrolysisof the starch, as shown in Table 1. The medium used forthe continuous fermentation runs was obtained by dilut-ing corn starch hydrolysate with tap water until the de-sired fermentable sugar concentration was achieved, andby adding the following salts: 6:0 g l−1 KH2PO4, 2:0 g l−1

(NH4)2SO4 and 0:4 g l−1 MgSO4 · 7H2O; sodium citrate

dihydrate and NaOH were used to bu6er the medium atpH = 5:5.

2.3. Reactor con9guration

A schematic diagram of the experimental equipment is re-produced in Fig. 1. The bioreactor is a laboratory-scale of thecontinuous 7ow column type. It was assembled by packinga sterile water-jacketed glass column (54 cm long × 4 cminner diameter) with a mixture of spongy and glass beads.The presence of glass beads proved to be very important inorder to minimize the pressure drop and improve the unifor-mity of biomass growth. Filling material was supported bytwo grid plates of stainless steel, at the bottom and at the topof the active height, L, of the column. Fresh medium wasintroduced from the bottom of the reactor using peristalticpumps and the temperature was maintained by pumping wa-ter at 40◦C through the water jacket of the column.

E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830 3821

Fig. 1. Schematic diagram of the experimental set-up. (1) Immobilized cell bioreactor; (2) substrate vessel; (3) substrate exit line; (4) hydrogensampling/analysis system; (5) NaOH vessel; (6-7-8) feeding pumps; (9) thermostating water inlet line; (10) thermostating water exit line.

2.4. Immobilization

The spongy support material employed in this study was asynthetic commercial sponge (Wettex, Sweden). Followingsterilization, from the sponge were obtained particles of av-erage dimensions: 5×5×2 mm3. The speci'c water absorp-tion w was 12:58 g water g−1 support. The water absorptionwas experimentally determined using some spongy particlesidentical to the ones utilized for the fermentation process.The samples were vigorously washed with water and driedto constant weight md, by heating to 105◦C and by placingthem in a drier for 1:5 h before weighing. The samples, en-tirely covered with distilled water, were boiled for 2 h avoid-ing any contact with the heated bottom of the container. Af-ter the boiling period, the samples were cooled to room tem-perature and were kept completely immersed in water for aminimum of 12 h. The saturated weight mw [g] was deter-mined by weighing the samples 'lled with water, excludingthe external drops on their surfaces, and the water absorp-tion was calculated using the relation: w = (mw − md)=md.The cells contained within some spongy samples of 1 cm2

were eluted with distilled water until a volume of 100 ml.The mean concentration of the immobilized cells, QX wasobtained by multiplying the mean dry weight per unit areaof the samples (determined using the dry weight procedurefor 20 ml of this suspension) by the total known area of thesupport, and by dividing by the working volume of the re-actor. The resulting global characteristics of the reactor arereported in Table 2.

Table 2Details of the reactor

Characteristic Symbol and unit Value

Cross section A (cm2) 12.5Working volume V (cm3) 475Liquid inside spongy support Vi (cm3) 255Liquid inside bed channels Ve (cm3) 113Volume of glass beads Vv (cm3) 80Spongy support apparent volume Vs (cm3) 27

2.5. Operating conditions

All the experiments were carried out at 40± 0:5◦C. Thefermenter and the fermentation medium were sterilized byautoclaving at 120◦C for 20 min. The pH of the mediumwas controlled by a Leeds and Northurp apparatus and keptat the value 5:5±0:1 by a Sigma pump, which injected a 'nestream of 0:1 N NaOH solution into the reactor, at the centreof the transverse section, at two points, respectively, locatedat 13 and

23 of the column axis. There was no evidence of

contamination in any of the runs carried out, as determinedby examination of the free cells, under optical microscope.

2.6. Analysis

The free-cell concentration was determined by 'lteringa known volume of culture broth on 0:2 �m autoclavable

3822 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

'lters. The 'lters were dried at 105◦C until no weight changebetween consecutive measurements was observed.The concentrations of sugars in the broth, as well as their

contents in the natural substrate, were determined by meansof the HPLC Hewlett Packard 1100 using an IR detector.A column Hypersil 200× 4:6 was used at 35◦C with 80:20acetonitrile/water as the mobile phase, at a 7ow rate of1:0 cm3 min−1.The volume of gas produced was measured by means

of liquid level displacement. Hydrogen was determined bya gas chromatograph Perkin–Elmer Sigma 3 (Milan, Italy)equipped with a thermal conductivity detector (TCD) and a2 m stainless column packed with Porapak Q (50/80 mesh).The operational temperatures at the injection port, the col-umn oven and the detector were 100, 70 and 100◦C, respec-tively. Nitrogen was used as the carrier gas, at a 7ow rateof 30 cm3 min−1.

3. Experimental results

3.1. Main results of the 9rst series of experiments

The 'rst series of experimental runs was carried out bymeans of a column characterized by a height L=38 cm andinlet glucose concentration G0 =20 mg cm−3. A full reportof this study is given in Palazzi et al. (2000), together withan extensive discussion on the main e6ects of 7uid dynamicson the cell growth. The most signi'cant results of the afore-said experiments are reported in Table 3. In particular, thevalues of feed 7ow rate, V , hydrogen evolution rate, H2g;p,mean cell concentration, QX , and outlet glucose concentra-tion, GL, were directly measured, while the values of super-'cial velocity, v0, speci'c hydrogen productivity, QrH2 ; QX , andhydrogen global yield, QYH2 , were calculated, respectively,by means of the equations:

v0 =VA; (1)

QrH2 ; QX =H2gQXV

(2)

QYH2 =H2g

V (G0 − GL): (3)

Table 3Values of hydrogen evolution rate, average cell concentration, outlet glucose concentration, speci'c hydrogen productivity, and hydrogen yield obtainedduring the 'rst series of continuous fermentation runs (G0 = 20 mg cm−3)

Run V v0 H2g QX GL QrH2 ; QXQYH2

(cm3 h−1) (cm h−1) (mmol h−1) (mg cm−3) (mg cm−3) (mmolH2 h−1 g−1cell) (mmolH2 mg

−1G )

1 4 0.32 1.30 8.18 0.61 0.33 0.0172 12 0.95 2.34 7.76 4.78 0.63 0.0133 24 1.91 3.92 5.58 8.48 1.48 0.0144 32 2.55 3.54 4.20 5.38 1.77 0.00765 40 3.18 4.06 3.02 8.15 2.83 0.0086

The most interesting result regards the quasi-linear increas-ing of the speci'c hydrogen productivity with the feed 7owrate. In fact, the super'cial velocity increase simultaneouslyenhances the rate of mass transport phenomena between thebulk and the cells and depresses the slow side-reactions re-utilizing hydrogen, with respect to glucose decomposition.Unfortunately, the average cell concentration in the bed de-creases when v0 increases, until the conditions for the com-plete wash-out of the biomass are reached, in correspon-dence to a critical value of the super'cial velocity, v0c, ofabout 3:5 cm h−1. As discussed in the following kinetic sec-tion, the critical velocity appears to be an increasing func-tion of the substrate concentration. An appropriate choiceof the last one could then allow to appropriately increasethe feed 7ow rate and/or the cell concentration, so to obtainsigni'cant reductions of the reactor volume in an industrialprocess. In fact, the controlled addition of the substrate is es-sential to achieve maximum production of the desired prod-uct, in order to avoid underfeeding as well as overfeedingof the substrate (Sengupta & Modak, 2001).Then, further series of experiments have been pro-

grammed, to the purpose of de'ning, from a quantitativeviewpoint, the optimal operating conditions. The experi-mental runs were performed by utilizing an active columnheight L equal to 10 cm, owing to the fact that the greaterpart of the cells sprouts into the 'rst portion of the reactor,as pointed out in the previous work (Palazzi et al., 2000).

3.2. Experiments performed to study the criticalconditions

A second series of 've experimental runs was carried outto clearly individuate the critical operating conditions of thebioreactor, which is the situations in which it cannot morecorrectly run. The critical conditions were characterized bythe critical values of two parameters, namely the super'cialvelocity and the outlet glucose concentration, operatively de-'ned according to the following procedure. All experimentswere carried out at di6erent glucose inlet concentrations;after reaching a steady-state condition, the feed 7ow ratewas continuously increased, up to a situation in which theprocess shows some symptoms of instability, correspond-ing to the beginning of the biomass wash-out at the reactor

E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830 3823

Fig. 2. Critical glucose concentration as a function of the critical super'cial velocity (• experimental—calculated).

Table 4Values of hydrogen evolution rate, average cell concentration, outlet glucose concentration, critical glucose concentration, speci'c hydrogen productivity,and hydrogen yield obtained during the third series of continuous fermentation runs

G0 V v0 H2g QX GL Gc QrH2 ; QX QYH2(mg cm−3) (cm3 h−1) (cm h−1) (mmol h−1) (mg cm−3) (mg cm−3) (mg cm−3) (mmolH2 h

−1 g−1cells) (mmolH2 mg−1G )

30 32 2.55 5.9 14.9 8.1 4.5 3.2 0.008430 40 3.18 7.1 14.2 8.9 4.8 3.9 0.008440 96 7.64 18.3 17.6 14.5 7.6 8.3 0.007540 120 9.55 20.8 17.0 16.4 9.3 9.8 0.007350 160 12.7 28.6 15.8 25.2 13.0 14.5 0.007250 200 15.9 27.8 14.1 30.4 18.1 15.8 0.0071

outlet. The critical velocity, v0c, and the critical glucose con-centration, Gc, were, respectively, de'ned as the super'cialvelocity and the outlet glucose concentration in the afore-said conditions. The experimental results allowed to drawthe best-'tting curve in Fig. 2, showing the dependence ofGc on v0c.

3.3. Experiments addressed to individuate the optimaloperating conditions

In order to minimize the reactor volume and individuatethe optimal operating conditions needed to obtain a givenhydrogen production, the system behaviour was studied byperforming a third series of six experimental runs, using rel-atively high values of glucose concentration and super'cialvelocity. The most signi'cant results of experiments are re-ported in Table 4. It must be remarked that in these runs

we selected operative conditions rather far from the criticalones; the values of the critical glucose concentration cor-responding to the super'cial velocity used during the ex-periments were obtained by means of the best-'tting curvereported in the above-mentioned Fig. 2.

4. Mathematical model

For an e6ective design and scale-up of the bioreactor,the de'nition of an appropriate kinetic model of the processis required. The experimental results indicate that a criticalfactor for the process e6ectiveness is the adaptation of cellsto the reactor environment. On the other hand, glucose isthe most important source of material and energy for thecell growth, when large amounts of this substrate are atdisposition of the biomass, as in the experimental conditions

3824 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

here adopted. Then, a suitable kinetic model must correctlydescribe, 'rst of all, the interactions between the biomassand glucose steady-state balances.Making reference to the reactor in'nitesimal element

dV = A dz (4)

shown in the already-mentioned Fig. 1, the glucose balancein the bulk 7uid can be written as

v0 dG =−rG dz; (5)

where rG is the glucose consumption rate in the volume dV .The biomass balance, on the other hand, is given by

rX = rd (6)

being rX and rd, respectively, the rate of cell growth andcell disappearance.Since in all experiments the residence time was relatively

low, we assume that the rate of cell growth be proportionalto the glucose consumption one:

rX = YX rG; (7)

where YX is an appropriate cell yield coeUcient.Moreover, we also assume that the rate of cell disappear-

ance be proportional to its concentration:

rd = kdX; (8)

where kd should depend on v0, since the cell disappearancecan be due to natural death, as well as to the detachmentfrom the support, owing to mechanical stress.By combining Eqs. (6)–(8), one obtains

rG = cX; (9)

where c = kd=YX depends on v0.It can be easily noticed that the biomass and glucose bal-

ances, described by Eqs. (5) and (9), are linked via the glu-cose consumption rate rG. This term should theoretically de-pend, in a rather complicated way, on both X and G, as wellas on v0, in particular as regards the e6ects of the intersti-tial velocity on the biomass. Under the assumption of linearrelationship (whose validity is discussed in the following),Eq. (9) can be expressed in the form

X = aG − b; (10)

where a and b are empirical coeUcients depending on v0.From the de'nition of Gc, Eq. (10) can be rewritten as

X = a(G − Gc): (11)

By virtue of Eqs. (9) and (11), the glucose balance can berewritten as follows:

v0 dG =−ac(G − Gc) dz: (12)

By integrating the last equation between the inlet and zthsection of the column, one 'nally obtains

G = Gc + (G0 − Gc) exp(−ac

v0z)

: (13)

In correspondence to the boundary condition z = L, the lastequation gives, in particular, the theoretical value of theglucose outlet concentration

GL = Gc + (G0 − Gc) exp(−ac

v0L)

: (14)

It is noteworthy observing that the model foresees that theglucose outlet concentration,GL, can reach the critical value,Gc, only in the limiting case of a reactor of in'nite length.According to our de'nition, on the contrary, Gc is the valueof GL when the reactor (of 'nite length) becomes insta-ble. However, this approximation of the model is practicallyunimportant, since the value of Gc corresponding to our def-inition should be very near the asymptotic one, owing to theexponential decay of G along the reactor.The mean glucose concentration in the bioreactor, calcu-

lated as

QG =1L

∫ L

0

[Gc + (G0 − Gc) exp

(−acv0

z)]dz (15)

is given by

QG = Gc +v0acL(G0 − GL): (16)

Both the 'rst and the second experimental series indicatedthat the better conditions for hydrogen production corre-spond to values of QG around 20 mg cm−3.Substituting forG expression (13) in Eq. (11) one obtains

X = a(G0 − Gc) exp(−ac

v0z)

: (17)

The theoretical behaviour of X along the reactor is consistentwith the 'rst experimental results, as well as with the secondones, thus con'rming the hypothesis, which expression (10)is based upon. The mean value of the cell concentrationinside the reactor can be calculated from Eqs. (11) and (16)as follows:

QX =v0cL(G0 − GL): (18)

Eqs. (10), (16) and (18) were used to evaluate the parame-ters a; b and c from the experimental data, according to thefollowing procedure:

• c is directly calculated, by means of Eq. (18);• a is obtained from Eq. (14), after substituting in it thevalue of c;

• b is calculated by means of Eq. (10), after substituting init the value of a.

The values of a; b and c obtained, in this way, as wellas those of the global hydrogen yield, QYH2 , can be linearlycorrelated with the super'cial velocity v0 according to theequations:

a= a1 + a2v0 = 1:51− 0:056v0; (19a)

b= b1 + b2v0 = 5:73 + 0:35v0; (19b)

c = c1 + c2v0 = 0; 016 + 0; 14v0; (19c)

E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830 3825

Fig. 3. Dependence of empirical coeUcients a; b and c on super'cial velocity and best-'t to experimental data.

QYH2 = y1 + y2v0 = 0; 0086− 0; 00011v0: (19d)

Fig. 3 depicts the linear dependence on the super'cial veloc-ity of the above-mentioned empirical parameters a; b and c,together with the calculated values of the correlation coeU-cient R2, representing the goodness of 't. Fig. 4 shows theglobal hydrogen yield as a function of the super'cial veloc-ity. It must be remarked that, rigorously, the global hydro-gen yield is a function of the starting glucose concentration,the super'cial velocity and the average cell concentration.However, in our operative range, the hydrogen yield wasfound to be mainly dependent on the super'cial velocity.Therefore, on the basis of the purpose of this study and for aformal analogy, we choose to approximate the dependenceof the hydrogen yield by a linear function of the super'cialvelocity only, obtaining a goodness of 't that is almost thesame as for the other parameters.

5. Reactor design

5.1. Design variables

As already reported in the introduction, the aim of ourresearch is to study the feasibility of a fermentation processable to realize an hydrogen production H2g;p=100 mol h

−1,to feed a PAFC of 5 kW. The kinetic model developed in the

previous section will be applied in the following, to designin an optimal way a cylindrical bioreactor suitable to thisend.In the experiments we freely choose four variables,

namely the 7ow rate and concentration of the feed, inaddition to the length and the cross section of the reactor.Since in our design problem the required hydrogen

production is 'xed, only three variables remain at our dis-position for the process optimization. Let G0; v0 and thefractional glucose conversion, �G, be the free variables ofthe process.The fractional glucose conversion, de'ned as

�G = 1− GL

G0(20)

can range from zero to a critical value:

�Gc = 1−Gc

G0: (21)

In dealing with the design problem, it is convenient to ex-press as a function of the free variables the other signi'cantprocess variables, as shown in the following.The residence time can be easily obtained by eliminating

GL from Eqs. (14) and (20):

�=Lv0=1acln[

11− �G=�Gc

]: (22)

3826 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

Fig. 4. Hydrogen global yield as a function of the super'cial velocity and best 't to experimental data.

The feed 7ow-rate required to meet with the desired hydro-gen production is given by

V =H2g;p

YH2G0�G: (23)

At last, the cross section, length and volume of the bioreactorcan be, respectively, calculated as

A=Vv0=

H2g;pYHv0G0�G

; (24)

L= v0�=v0acln[

11− �G=�Gc

]; (25)

V =H2g;p

acYHG0�Gln[

11− �G=�Gc

]: (26)

5.2. Range of the free variables

To better understand the further developments, it is ap-propriate to brie7y discuss on the range of the free variables.The most important restriction on the free variables is rep-resented by Eq. (21), which, taking into accounts Eqs. (10),

(19a) and (19b), can be rewritten as

�Gc = 1−1G0

b1 + b2v0ca1 + a2v0c

(27)

or else, by solving it with respect to v0c:

v0c =[a1G0(1− �Gc)− b1][− a2G0(1− �Gc)− b2]

: (28)

For a given G0, the curve in Fig. 5 graphically representsEqs. (27) and (28). The convex region, which is delimited bythis curve and the axes, represents the range of the feasibledesigns. The point P in 'gure, for example, individuates acouple of values v0 and �G, which can be freely chosen torealize a correctly operating bioreactor. In correspondenceto the aforesaid value of �G, di6erent feasible solutions canbe obtained (the range is represented by the segment passingby P and parallel to the abscissae axis), by increasing v0from zero to the critical value v0c, given by Eq. (28) for�Gc=�G. Conversely, if v0 is 'xed, considering the segmentpassing by P and parallel to the ordinatae axis, �G can beincreased from zero to a critical value �Gc , given by Eq. (27)for v0c = v0.Fig. 5 indicates as well the limiting values of the criti-

cal conversion �∗Gcand of the critical velocity v∗0c, obtained

by imposing v0c = 0 in Eq. (27) and �Gc = 0 in Eq. (28),

E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830 3827

Fig. 5. Range of feasible design, at 'xed inlet substrate concentration, according to the critical conditions approach.

respectively, as

�∗Gc= 1− 1

G0

b1a1

; (29)

v∗0c =a1G0 − b1−a2G0 + b2

: (30)

The last equations clearly show that the range of �G andv0, and, consequently, the region of the feasible processes,extends as G0 increases. Some quantitative indications onthe range of the free variables can be obtained by analysingthese equations from a numerical point of view.In particular, Eq. (29) indicates that the inlet glucose con-

centration must exceed the limiting value:

G∗0 =

b1a1

� 4; 1 mg cm−3

and that almost a complete conversion could be obtained(�∗Gc

→ 1) when G0 is very high. On the other hand, thesuper'cial velocity should be, in any case, lower than theasymptotic value:

v∗0c →a1−a2

� 27 cm h−1

obtained by virtue of Eq. (30).

5.3. Process optimization

In this section, the optimal conditions for the realizationof a bioreactor able to meet with the required hydrogen pro-duction will be discussed. To this end, the region of thetheoretically feasible process will be explored, so as to in-dividuate the values of the free variables G0; �G and v0that minimize the reactor volume. Eq. (26) indicates that,by virtue of Eq. (21), the reactor volume monotonicallydecreases when G0 increases. Then, at 'rst sight, signi'-cant reductions of the reactor volume could be obtained bychoosing values of G0 as high as possible. Although we donot theoretically recognize severe restrictions on the sub-strate concentration in the feed, up to a concentration ofabout 90 mg cm−3, a practical limitation is certainly dueto the increasing of the solution viscosity with G0, whichcould promote the conditions for the bed instability. More-over, as already remarked, this parameter should be ad-justed so that the mean glucose concentration in the reactorbe not too far from 20 mg cm−3. As shown in the follow-ing, the aforesaid requirements can be met if G0 is in therange 35–50 mg cm−3.Eq. (26) also indicates that, when decreasing �G, the re-

actor volume monotonically decreases, down to the limiting

3828 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

Fig. 6. Reactor volume as a function of super'cial velocity, in correspondence to di6erent substrate concentrations.

value, in correspondence to the boundary condition �G → 0:

V ∗ =H2g;p

acYHG0�Gc

: (31)

For G0 =50 mg cm−3 and v0 =10 cm h−1, V ∗ assumes theminimum value

V ∗min � 0; 24 m3;which represents the limiting value of the reactor volumeneeded for the realization of the process. It is interesting toobserve that, in decreasing �G down to zero, the residencetime and the reactor length also decrease down to zero, whilethe 7ow rate and the reactor cross section increase up toin'nity, according to Eqs. (22)–(25).Conversely, when �G increases up to �Gc , the residence

time as well as the reactor length and volume increase upto in'nity, while the 7ow rate and the reactor cross sectiondecrease down to the critical values:

V c =H2g;p

YHG0�Gc

; (32)

Ac =H2g;p

v0YHG0�Gc

: (33)

It is evident that the design of practically feasible processesrequires that the values of �G be chosen conveniently farfrom the limiting values 0 and �Gc . A numerical explorationindicates that the range of practical interest for the glucoseconversion is: 0:56 �G6 0:8.

The dependence of the reactor volume on v0 is certainlythe most interesting relationship from the point of view ofthe process optimization, since, given G0 and �G, it becomesminimum for a particular value of v0. As an example, Fig. 6shows a typical behaviour of V (v0), for �G=0:5 and di6erentvalues of substrate concentration, namely G0 = 35, 40 and45 mg cm−3.By applying the complete model, Table 5 shows some of

the minimum values of the reactor volume, when G0 and v0vary in the range of interest, together with the most importantdesign variables. Among the situations here considered, aminimum reactor volume of 0:37 m3 can suUce to realizethe desired hydrogen production, by converting the 50% ofa 50 mg cm−3 glucose solution, feeded to it with a 7ow rateof 0:53 m3 h−1.This volume is lower of an order of magnitude, with re-

spect to the values estimated in the previous works (Perego,Fabiano, Ponzano, & Palazzi, 1998; Palazzi et al., 2000),probably due to both the widening of the experimental 'eldand the process knowledge and to the systematic applica-tion of an optimization procedure. Many of the solutions inTable 5 are comparable with the one corresponding to theminimum volume, and some of them could be even pre-ferred, if the waste treatment be a primarily scope of theprocess. It should however be noted that from a plant view-point some of the resulting 'xed beds are characterized byhigh ratios section over height. Such a kind of reactors canpresent non-uniform residence time distribution, hence the

E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830 3829

Table 5Minimum reactor volume and corresponding values of super'cial velocity, in correspondence to some interesting values of G0 and �G

G0 �G Vopt v0 A V Gm

(mg cm−3) dimensionless (m3) (cm h−1) (m2) (cm3 h−1) (mg cm−3)

35 0.5 0.62 8 9.3 0.74 16.70.6 0.75 8 7.7 0.62 13.90.7 0.98 7 7.4 0.52 11.40.8 1.69 5 8.9 0.44 8.1

40 0.5 0.51 9 7.3 0.66 19.50.6 0.60 8 6.7 0.54 17.30.7 0.77 7 6.5 0.46 14.40.8 1.22 6 6.6 0.39 10.0

45 0.5 0.43 9 6.5 0.58 23.20.6 0.50 9 5.4 0.49 19.70.7 0.63 8 5.1 0.41 16.50.8 0.95 6 5.8 0.35 12.9

50 0.5 0.37 9 5.8 0.53 26.80.6 0.43 9 4.9 0.44 23.00.7 0.54 8 4.6 0.37 19.50.8 0.77 7 4.6 0.32 14.5

practical realization should foresee the choice of severalsmaller parallel operating 'xed bed reactors. Finally, it isinteresting to observe that the value of v0 that minimizes Vin the di6erent situations only slightly depends on G0 anddecreases when �G increases.

6. Conclusions

This study demonstrates the technical feasibility of a con-tinuous process for the hydrogen production via fermenta-tion, by means of E. aerogenes. The kinetic model devel-oped to describe the process 'ts very well with the exper-imental data, displays the limiting operating conditions forthe reactor stability and allows to deal with the design prob-lems without diUculties. The approach based on the criticalconditions appears e6ective in selecting the region of fea-sible design. The model could be used as scale-up criterionof large fermenters, allowing to describe operating condi-tions and size of the bioreactor. In particular, by applyingthe model to the optimal design of a bioreactor capable tofeed a phosphoric acid fuel cell of 5 kW, we have demon-strated that the required volume of the reactor is only about0; 4 m3, that is of an order of magnitude lower than the oneobtained in our preliminary researches. In our opinion, fur-ther substantial improvements of the process should not beexpected from the kind of reactor dealt with in this paper.

Notation

a empirical coeUcient de'ned in Eq. (10),mgcells mg

−1G

a1 empirical coeUcient de'ned in Eq. (19a),mgcells mg

−1G

a2 empirical coeUcient de'ned in Eq. (19a),mgcells mg

−1G cm−1 h

A reactor cross section, cm2

Ac critical cross section of the reactor, cm2

b empirical coeUcient de'ned in Eq. (10),mgcells cm

−3

b1 empirical coeUcient de'ned in Eq. (19b),mgcells cm

−3

b2 empirical coeUcient de'ned in Eq. (19b),mgcells cm

−4 hc consumption parameter in Eq. (9),

mgG mg−1cells h

−1

c1 empirical coeUcient de'ned in Eq. (19c),mgG mg

−1cells h

−1

c2 empirical coeUcient de'ned in Eq. (19c),mgG mg

−1cells cm

−1

G glucose concentration, mg cm−3

GL outlet glucose concentration, mg cm−3

Gm mean glucose concentration, mg cm−3

G0 inlet glucose concentration, mg cm−3

G∗0 limiting value of inlet glucose concentration,

mg cm−3

Gc critical glucose concentration, mg cm−3QG mean glucose concentration, mg cm−3

H2g hydrogen evolution rate, mmol h−1

H2g;p target hydrogen evolution rate, mmol h−1

kd disappearance coeUcient, h−1

L reactor length, cmmd support dried weight, gmw support saturated weight, grx rate of cell disappearance, mg cm−3 h−1

rG glucose consumption rate, mg cm−3 h−1

QrH2 ; QX speci'c hydrogen productivity, mmolH2 h−1 g−1cells

rd rate of cell growth, mg cm−3 h−1

3830 E. Palazzi et al. / Chemical Engineering Science 57 (2002) 3819–3830

v0 super'cial velocity, cm h−1

v0c critical super'cial velocity, cm h−1

v∗0c limiting value of the critical super'cial velocity,cm h−1

V reactor working volume, cm3

V ∗ limiting value of the reactor working volume, cm3

V ∗min minimum limiting value of the reactor working vol-

ume, cm3

Vi volume of liquid inside spongy support, cm3

Ve volume of liquid inside bed channels, cm3

Vv total volume of glass beads, cm3

Vs total spongy support apparent volume, cm3

w speci'c water absorption gwater g−1supportV feed 7ow rate, cm3 h−1

V c critical feed 7ow rate, cm3 h−1

X cell concentration, mg cm−3QX average cell concentration, mg cm−3

y1 empirical coeUcient de'ned in Eq. (19d),mmolH2 mg

−1G

y2 empirical coeUcient de'ned in Eq. (19d),mmolH2 mg

−1G cm−1 h

QYH2 hydrogen global yield, mmolH2 mg−1G

YX cell yield coeUcient, mg mg−1Gz longitudinal reactor coordinate, cm

Greek letters

� residence time, h�G fractional glucose conversion, dimensionless�Gc critical glucose conversion, dimensionless�∗Gc

limiting value of the critical glucose conversion,dimensionless

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