41_461

8/8/2019 41_461

1/13

J. Gen. Appl. Microbiol., 41, 461-473 (1995)

PERFORMANCE OF A MULTISTAGE FERMENTORWITH CELL FILTERING AND RECYCLING FOR

CONTINUOUS ACETIC ACID PRODUCTION

AKIO NISHIWAKI* AND JOHN R. BOURNE'Department of Materials Chemistry and Bioengineering, OyamaNational College of Technology, Oyama 323, Japan' Technisch-Chemisches Laboratorium ETH , CH-8092 Zurich, Switzerland

(Received October 17, 1994; Accepted September 19, 1995)

The steady-state performance of a multistage fermentor with cell filteringthrough a membrane and recycling of concentrated cells is studied nu-merically for continuous production of acetic acid. The tanks-in-seriesmodel is used to describe the flow behaviour of culture broth in themultistage fermentor. Kinetic expressions and parameter values are takenfrom the literature. The effects of the total number of stages, the dilutionrate, the bleed ratio, the recycle ratio and the feed concentrations asoperating conditions on fermentor characteristics such as the concentra-tions of total and viable cells as well as substrate and product in eachstage, the cell viability, the acetic acid productivity and the substrateconversion were examined under the conditions of equal tank volumesand a recycle ratio equal to or greater than one. An increase in thenumber of stages and decreases in the bleed and recycle ratios and in thefeed concentration of product enhance the productivity. The relationsbetween the maximum productivity and the corresponding optimumdilution rate and between the corresponding outlet concentrations of thefour components and the optimum dilution rate are presented as figures.Equations for the average cell viability and the critical dilution ratecausing cell washout are also obtained. Furthermore, the minimum feedconcentration of substrate for its complete consumption is mentioned.Compared to a single tank fermentor, staging and cell recycle increasesubstrate utilisation and acetic acid productivity. The computed perform-ance of the fermentor configuration proposed in this study is sufficientlypromising for the continuous production of acetic acid that it should nowbe checked experimentally.

* Address reprint requests to: Dr . Akio Nishiwaki, Department of Materials Chemistry andBioengineering, Oyama National College of Technology, 771 Nakakuki, Oyama 323, Japan.

461

8/8/2019 41_461

2/13

462 NISHIWAKI and BOURNE VOL. 41

In recent years, various attempts to improve the productivity of acetic acid bycontinuous fermentation have been made (3-6). One way of obtaining highproduction rates is to maintain more viable microbial cells in a fermentor comparedto conventional batch or continuous production of acetic acid. The uses ofimmobilized cells and cell recycle with membrane separation are favourable alter-natives for this purpose. Although these two methods for high cell-density cultureare popular in researches aimed at efficient ethanol fermentation, however, thelatter method is not yet familiar for the case of acetic acid production. Mostrecently, Park and Toda (4) investigated high cell-density fermentation of aceticacid by using a membrane recycle bioreactor system and reported that a theoreticalmaximum acetic acid productivity of 123.1 kg m-3 h- I at a dilution rate of 3.52 h 'without bleeding was obtained in their simulation. In such a reactor system, amembrane filter module is attached to a single continuous stirred tank fermentorwith a semi-closed loop for cell recycling.The use of a tanks-in-series or a multistage column fermentor instead of thesingle tank in the above system may be expected to bring an overall increase inacetic acid productivity. For ethanol fermentation, Ghose and Tyagi (1) showedthat productivity was increased by using two stirred tanks in series in place of asingle tank fermentor. Also, Lee et al. (2) demonstrated that ethanol productivitycould be further improved by using cell recycling together with one or two tanks.However, the effect of product inhibition, especially on specific product formationrate, in acetic acid fermentation is quite different from that in ethanol fermentation,thus resulting in a remarkable difference between these two processes. AlthoughPark and Toda (4) also recommend to reuse the bleed which is rich in viable cellsfrom the first cell-recycle fermentor in the following fermentor for further aceticacid production, it was not shown quantitatively how high productivity can beattained by a multiple stage system. With recent notable developments in mem-brane performance, multistage fermentor-separator operations will become moreimportant as a practical method to enhance acetic acid productivity. Therefore, ananalysis of the reactor performance of multistage systems is required for rationaldesign and operations.

The purpose of this work was to elucidate numerically the effects of variousoperating parameters on the characteristics of tanks-in-series and multistagecolumn fermentors with cell separation and recycle for acetic acid production.

PERFORMANCE EQUATIONSThe continuous steady-state operation of a multistage fermentor with cell

filtering and recycling for acetic acid production is considered. As shown in Fig. 1,a fermentor in this system is composed of either N completely mixed tanksconnected in series with equal working volumes or a column partitioned into Nstages with equal spacings. Fresh medium supplied to the first stage (or tank) isconsidered to be sterile. In the fermentor, cell growth and death, substrate

8/8/2019 41_461

3/13

1995 Multistage Fermentor for Acetic Acid 463

consumption and product formation proceed. The culture stream from the Nthstage is introduced to a filtering module to separate cells in the culture through amembrane and the concentrated cells are then recycled to the first stage. Therecycle flow rate is denoted by rF. To maintain a stable operation, part of theculture broth is withdrawn from the Nth stage. The bleed flow rate is denoted byBE Without such bleeding, a steady-state in total cells cannot be achieved becauseof an unlimited accumulation of non-viable cells.In deriving the mass balance equations for viable and total cells, substrate andproduct, the following assumptions were made:

(1) Kinetic expressions for acetic acid fermentation and their parametervalues are available in the literature (4) and are stated below.(2) For the column-type fermentor, the culture broth in each stage isperfectly mixed and backmixing between adjacent stages is negligible. Hence, theflow behaviour of the culture in the whole column as well as that in multiple tanks

is expressed by the tanks-in-series model.(3) Membrane separation is perfect and thus the filtrate stream contains nocells.(4) The liquid residence time in the recycle loop is negligible.(5) No resistance to mass transfer exists and the rate of fermentation isdetermined by its kinetics.According to Park and Toda (4), the specific growth rate can be expressed bythe following equation with product inhibition and without the substrate saturation

constant in the Monod expression:[ -,im {1- (P~Pm)} (1)

where ,um= O.26 h ', Pm= 63.5 kg m 3 and n = 3.61.

(a) (b)Fig.(a)

1N

Scheme of a multistagetanks-in-series fermentor.

fermentor with cell filtering and recycling.(b) Multistage column fermentor.

8/8/2019 41_461

4/13

464 NISHIWAKInd BOURNE VOL.1Also, the specific rates of cell death, acetic acid production and ethanolconsumption are represented by Park and Toda (4) as follows, respectively:

y=klexp(k2D) (2)where k1-0.059h -1 and k2-0.325h.

v=a+b,u-cp2 (3)where a =1.92 h-1, b = 386.8 and c =1,347 h.

qs=v/Yps (4)where Yp~s1.18 kg kg 1, implying that this yield coefficient was constant. Parkand Toda (4) used Sf=47.4 kg m-3 and Pf= l0 kg m-3 as feed concentrations intheir experiments and determined the above kinetic parameter values.Based on the above assumptions and kinetics, the steady-state mass balancesfor total cells, viable cells, substrate and product in the first and the ith stages canbe described as follows:

D 1X1=0 (5)i1, r$XrN- (l +r)X~1 + NDr$XN-(l+r)X1+ 1 (u1-y)X1=0 (6)ND

1Sf+rSN- (1 +r)S1- ND gSlX1 0 (7)Pf+rPN-(l+r)P1+ 1 L1X1=0 (8ND )

i2,3, ...,N, (l+r)Xr1-1-(l+r)Xt~+ 1 ~c,Xi=O (9ND )+r X,_1- l+r X~+ l ,ul-r X,=O 10

(1+r)S1-1-(l+r)Si- ND gs,X1=O (11)

Nomenclature: a, parameter in Eq. (3) (h-'); b, parameter in Eq. (3); B, bleed ratio; c, pa-rameter in Eq. (3) (h); D, dilution rate (h-'); F, volumetric flow rate of medium feed (m3h-'); k1,parameter in Eq. (2) (h-'); k2, parameter in Eq. (2) (h); n, parameter in Eq. (1); N, total numberof stages or tanks; P, product (acetic acid) concentration (kg m-3); Pr, productivity of acetic acid(kg m-3h'); qs, specific consumption rate of ethanol (kg kg-' h-' ); r, recycle ratio; S, substrate(ethanol) concentration (kg m-3); v, cell viability; X, viable cell concentration (kg m-3); X~, total cellconcentration (kg m-3); Yp~s,yield of acetic acid based on ethanol consumed (kg kg-'); Z, dimen-sionless distance. [Greek letters] j3, factor by which cells in the recycle stream are concentrated bymembrane filter; r, specific death rate (h-'); i, specific growth rate (h-'); v, specific production rateof acetic acid (kg kg-' h-'). [Subscripts] av, average; c, critical; f, feed; i, ith stage or tank; m,maximum; min, minimum; opt, optimum.

8/8/2019 41_461

5/13


(l+r)P,_1-(1+r)P,+ 1 v~X;=O (12ND )In these balance equations, the dilution rate D refers to the volumetric feed

rate F divided by the total working volume of either all tanks in series or the wholecolumn. Also, Lt, v; and qs~ n the ith stage are denoted in Eqs. (1), (3) and (4) withP =P~, respectively.From the mass balance for either viable or total cells around the filter module,the following relation is obtained:

This expression shows that the cell separator factor $ is fixed by selecting boththe bleed ratio B and the recycle ratio r as operating conditions and increases withthe decreases of B and r.The concentrations of total and viable cells, substrate and product in eachstage for a given set of N, D, B, r, Sf and Pf are obtained by solving numerically Eqs.(5)-(12) combined with Eqs. (1)-(4) and (13). As a numerical technique, theNewton-Raphson iterative method is applicable. The ith-stage substrate concentra-tion S~ s also calculated from the corresponding ith-stage product concentration P,by means of the constant mass yield of product from substrate Yp~s:

P; -PfY 5= (14)Sf-S;which is derived from Eqs. (4), (7), (8), (11) and (12).When N ==1, he following equations (4) are obtained by setting N= 1 in Eqs.(5)-(8) and using Eqs. (1) and (13) :=BD+r (15)

P=Pm {1-(IJ/,1m)} l~n (16)X =D(P-Pf)/v (17)

X~_ (BD + y)X/BD (18)S=Sf-q5X/D (19)

The concentrations of the four components for N=1 are calculated from Eqs.(16)-(19) in turn after obtaining the values of y and , t from Eqs. (2) and (15),respectively. These concentrations are independent of the recycle ratio r.When r - DO s a special case of the multistage system, the resultant equationsderived from Eqs. (5)-(12) by setting r = DO nd using Eq. (13) are identical toEqs. (15) and (17)-(19).

The acetic acid productivity Pr is defined as follows:Pr-D(PN-Pf) (20)

8/8/2019 41_461

6/13

466 NIsHIwMU and BOURNE VOL. 41This definition means that acetic acid in the bleed stream is recoverable as

product.Operating parameters are the total number of stages N, the bleed ratio B, the

recycle ratio r and the feed concentrations Sf and Pf. The following fermentoranalysis is carried out under the conditions of equal tank volumes and r >_ 1. Also,the ranges 25-47.4 and 0-15 kg m-3 are used for Sf and Pf, respectively.

RESULTS AND DISCUSSIONConcentrations in stages

Figure 2 shows an example of the calculated concentrations of total cells,viable cells, substrate and product, Xt;, X,, Si and F, respectively, in each stage, withthe total number of stages N as a parameter. The abscissa Z refers to thedimensionless distance from the top of a column fermentor as shown in Fig, lb.For a tanks-in-series fermentor, the ith tank is equivalent to the ith stage of thecolumn. Xr~ and X~ in each stage are larger than those for N=1 and increase withan increase of N. Also, their stepwise concentration profiles for each N along thewhole fermentor are almost flat. On the other hand, the corresponding axialprofiles of S; and P~ are greater for a larger N. As can be seen from the values of

Fig. 2. Concentrations of total and viable cells, substrate and product in eachstage with total number of stages as a parameter.

D=1.2 h-`, B=0.1, r=2, Sf=47.4kgm_3 and Pf=0. Broken lines indicate N=1.

8/8/2019 41_461

7/13


S, and P,, the substrate consumption and product formation in the first stage for themultistage fermentor are reduced compared to N=1. Thus, because productinhibition in the first stage is reduced, the cell growth proceeds further and viablecells increase with increasing N compared to N=1. Such increases lead to substrateconsumption and acetic acid production to a high level in the following stages. Asa result, the outlet concentrations SN and PN decrease and increase with increasingN, respectively.

Examining the concentrations of the four components in each stage for B lessthan that in Fig. 2, it is found that the corresponding X, for each N in this caseincreases slightly, while X

8/8/2019 41_461

8/13

468 NIsHIWAKI and BOURNE VOL. 41

later. At any constant D less than D~, except D very close to D~, both X1N and X~are higher when more stages are used. PN decreases with increases in D and alscbecomes higher for larger N values, as in the above case of cell concentrations. Theeffects of D and N on SN are the inverse of those on PN.Cell viability

The viability of cells is the fraction of viable cell concentration relative to totalcell concentration. The cell viability v; in each stage refers to X1/Xr~nd the averagecell viability vav n the whole fermentor to the arithmetic mean of v,. Figure 4 showsa calculation example of the viabilities v~and vas. For each N, the stepwise profileof v; along the entire fermentor tends to a convex one with increasing N and thusvN becomes less than the corresponding vas. However, differences between thesetwo values for each N and also between vavvalues for different N stages are withir.10o, although vav ncreases slightly with the increase of N. Examining the effects ofthe dilution rate D, the bleed ratio B and the recycle ratio r on vas, it is found thatthe value of vav ncreases with increasing D and B and is almost independent of r.

The equation for giving vas, which is defined here as a constant v~ (-X/X1)can be obtained by setting X, =Xrwav in Eqs. (5), (6), (9) and (10) and combiningthem to eliminate Lt and then Xr~by substitution. Using Eq. (13), moreover, thfresultant equation for vav s represented as follows:

1NND l+r) 1- 1- Bl+rvav- B IN (21)ND(1+r) 1- 1- l+ r +y

When N-1 or r= oo, Eq. (21) is reduced to:= BDD+ y (22)

Fig. 4. Cell viability in each stage and average cell viability infermentor with total number of stages as a parameter.

D = l.2 h-', B =0.1, r=1, Sf=47.4 kg m-3 and Pf=0. Solid andindicate viability in each stage and average viability, respectively. Theindicates N=1.

the wholedotted linesbroken line

8/8/2019 41_461

9/13


This equation is identical to that obtained from Eq. (18) for N=1. The valuesof vav calculated from Eq. (21) agree well with the arithmetic means of v; in Fig. 4and also under other conditions.Critical dilution rate

When the value of D becomes larger than a certain critical dilution rate D~, asmentioned above in Fig. 3, cell washout occurs. From calculation results forvarious conditions, it can be seen that the effects of N and r on D~ are not significant,while the effect of B on D~ is great.

The equation for D~ can be derived by setting P; =Pf fora; in Eqs. (6) and (10)and combining them to delete X~ by substitution. Furthermore, using Eq. (13), theresultant expression for D. is written as:

D~= 'tT ,~N (23)N(1+r) 1- 1- lB+r

where u refers to Eq. (1) with P =Pf and y to Eq. (2) with D =Dr. Thus, since theright-hand side of Eq. (23) also contains D~, the value of D~ is determined by atrial-and-error method. When N =1 or r = c, Eq. (23) results in Eq. (15) with D

= D~. The values of D~ calculated from Eq. (23) agree exactly with those in Fig. 3.It is found that Eq. (23) is also applicable for other conditions.Productivity

Figure 5 shows the acetic acid productivity Pr as a function of the dilution rateD with the total number of stages N and the feed concentration of product Pf asparameters. As D increases, Pr for each N and Pf increases and has its maximumat a certain L). Then Pr decreases steeply. As shown by the dotted lines, the

Fig. 5. Effect of dilution rate on acetic acid productivity with total number ofstages and feed concentration of product as parameters.B=0.05, r=2, Sf=47.4kgm-3 and Pf=10 (A) and 0 (B) kgm-3. Broken linesindicate N=1. Dotted lines refer to the relation between maximum productivity andoptimum dilution rate.

8/8/2019 41_461

10/13


attainable maximum productivity Prm becomes higher with increasing N and withdecreasing Pf. Also, the optimum dilution rate Doptgiving Prm is almost independ-ent of N and is larger for a smaller Pf. Hence, multistage fermentors are superiorto single-stage fermentors.

Such values of Prm and Doptwere determined for various sets of N, B, r, Sf andPf as operating conditions. Figure 6 presents the relation between Prm and DoptwithN, B and r as parameters in the case of Sf= 47.4 kg m- 3 and Pf= 0. For N = 3 and5, only the lines of r =1 are shown in the figure. Prm for multiple stages is higherat any B and r compared to that for N=1 and increases with decreasing both B andr. Although Prm becomes high with increasing N, the increase of Prm per stage formultiple stages is largest when N = 2. Both Prm and D0 at r = for each N areidentical to those for N=1 at the same B. The effects of N and r on Dopt arecomparatively small or negligible.Figure 7 shows the corresponding final-stage concentrations of product andsubstrate, PN and SN, respectively, i.e., equal to the concentrations in the filtrate andbleed streams, at the same Dopt as those in Fig. 6 for Prm. PN at a constant Bincreases with increasing N and with decreasing r. Also, except for the range of Blarger than about 0.2, PN at constant N and r becomes slightly higher for a smallerB. PN in most cases is over 40 kg m-3, which is the minimum acetic acid concentra-tion used for vinegar (4). The relation between SN and Dopt eems nearly symmetricwith respect to a horizontal line of about 27 kg m-3 against the case of PN.Similarly, Fig. 8 shows the corresponding final-stage concentrations of total cellsand viable cells, XtNand XN, respectively, at the same Doptas those in Fig. 6 for Prm.Ac R h,.rr mc.ccm~ll Y .. ra~cac firct ararlrlallu and than rc r rlly rlrla tc crrnwlnn

total

0opt (h-Fig. 6. Relation between maximum productivity and optimum dilution rate withnumber of stages, bleed ratio and recycle ratio as parameters.

Sf 47.4kgm_3 and P 0. The broken line refers to N=1.

8/8/2019 41_461

11/13


accumulation of non-viable cells. AtN also increases with increasing IV and withdecreasing r. The effects of N, B and r on XN are similar with those on Prm in Fig.6 and the relation between XN and D0 for constant N and r values is almost linear.

In the case that the feed concentration of product Pf is nonzero, both Prm andD0Pt are found to decrease with increasing Pf. Also, the influences of B and r onthem for a constant Pf are similar to those in Fig. 6. On the other hand, there is noeffect of the feed concentration of substrate Sf on Prm and D0 because Eqs. (5), (6),(9) and (l0) are independent of Sf and S1.

Fig. 7. Correspondingsame optimum dilution rates

final-stage concentrationsas those in Fig. 6.

of product and substrate at the

Fig. 8. Corresponding final-stagesame optimum dilution rates as those in

concentrations ofFig. 6.

total and viable cells at the

8/8/2019 41_461

12/13


Substrate conversionUsing Eq. (14) with i =N and Eq. (20), overall substrate conversion at thefermentor outlet is written as:

Sf-SN _ PN-Pf _ Pr 24YpsSf YpsSfD ( )I IThis equation means that the effects of N, B and r on the substrate conversion

for a constant Sf are the same as those either on PN at a constant Pf or on Pr at aconstant D. For example, as can be seen from Fig. 7 for SN and PN at D0 givingPrm, the substrate conversion becomes high with increasing N and with decreasingB and r. Also, from Fig. 5, by comparing Pr values at a constant D, the substrateconversion is found to increase with decreasing Pf. In this figure, each left end ofthe solid and broken lines corresponds to complete substrate consumption (See Fig.3 for P -O).

Examining the effect of Sf on the substrate conversion, it is found that theconversion increases with decreasing Sf and as a result, there exists a minimum feedconcentration of substrate Sfmin for complete substrate consumption in the finalstage. Hence, Sf for a feasible operation must be greater than Sfmin. Determiningsuch values of Sfminfor various given sets of N, D, B, r and Pf by changing Sf, thesevalues agree well with those from the following equation:

_ PrSfmin- Yp5D (25)

I which is obtained by setting SN = 0 in Eq. (24). For the same conditions, except Sf,as those in Fig. 6 for Prm and Dopt, Sf min ncreases with increasing N and withdecreasing B and r. Also, examining the effect of Pf on Sfmin, it is found that Sfminincreases with decreasing Pf.

CONCLUSIONS

Applying the tanks-in-series model and the kinetic expressions and parametervalues from the literature (4) to a multistage fermentor with cell separation andrecycle, its steady-state performance was investigated numerically for continuousacetic acid production. The effects of operating parameters on various fermentorcharacteristics were examined and the following results were obtained.

The viable cell concentration in each stage for multistage fermentors is highercompared to a single fermentor and increases with increasing the total number ofstages and with decreasing the bleed ratio. This raises the overall substrateconsumption and acetic acid production. The difference between the cell viabilityin each stage and the average cell viability in the whole fermentor is not significantand the average viability is given by Eq. (21). The critical dilution rate for thewashout of cells is expressed by Eq. (23). As presented in Figs. 5 and 6, themaximum acetic acid productivity increases with increasing the total number of

8/8/2019 41_461

13/13


stages and with decreasing the bleed ratio, the recycle ratio and the feed concentra-tion of product. Also, the optimum dilution rate giving the maximum productivityincreases with decreasing the bleed ratio and the feed concentration of product.Although the maximum productivity can be enhanced by reducing the bleed ratio,the total cell concentration then becomes very high, as shown in Fig. 8. Thesubstrate conversion increases with decreasing the feed concentration of substrate.There exists a minimum feed concentration of substrate for its complete consump-tion and Eq. (25) holds.The computed performance of the fermentor configuration proposed in Fig. 1is based on the kinetic model of Park and Toda (4) and is sufficiently promising forthe continuous production of acetic acid that it should now be checked experimen-tally.

REFERENCES

1) Ghose, T. K. and Tyagi, R. D., Rapid ethanol fermentation of cellulose hydrolysate. II. Productand substrate inhibition and optimization of fermentor design. Biotechnol. Bioeng., 21, 1401-1420(1979).2) Lee, J. M., Pollard, J. F., and Coulman, G. A., Ethanol fermentation with cell recycling:Computer simulation. Biotechnol. Bioeng., 25, 497-511 (1983).

3) Mori, A., Production of vinegar by immobilized cells. Process Biochem., 20, 67-74 (1985).4) Park, Y. S. and Toda, K., Simulation study on bleed effect in cell-recycle culture of Acetobacteraceti. J. Gen. App!. Microbiol., 36, 221-233 (1990).

5) Sun, Y. and Furusaki, S., Continuous production of acetic acid using immobilized Acetobacter acetiin a three-phase fluidized bed bioreactor. J. Ferment. Bioeng., 69, 102-110 (1990).6) Von Eysmondt, J., Vasic-Racki, D., and Wandrey, C., Acetic acid production by Acetogeniumkivui in continuous culture-Kinetic studies and computer simulations. App!. Microbiol. Biotech-no!., 34, 344-349 (1990).

Documents

41_461