BIOTECHNOLOGY AND BIOENGINEERING VOL. XV (1973)

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Analysis of Membrane Reactor Performance for Hydrolysis of Starch by Glucoamylase

INTRODUCTION

Recently Shah and Remmenl analyzed the performance of a membrane reactor (i.e., porous wall reactor with suction) for the case of a first order reaction. The concept of the membrane reactor is presently useful for a number of enzymatic reactions,2.3 in particular the hydrolysis of starch to glucose by the enzyme glu~oamylase.~ This is a reaction of potential industrial interest and there are commercial membranes available such as PM-10 (Amicon Corp., Lexinmn, Mass.), HFA-200 (Abcor Inc., Cambridge, Mass.), and OSMOTIK-215 (Calgon- Havens Systems, Sen Diego, Calif.) which can efficiently separate glucose from the enzyme and starch. Since starch hydrolysis is, in general, more complex than first order, in this communication we extend the analysis of Shah and Remmenl for this reaction.

THEORETICAL

Because the hydrolyis of the branched fraction of starch is relatively slow only laminar flow condition is considered here. Furthermore, since the membranes available are usually produced in film, we present the analysis for flow through a thin channel geometry such as the one illustrated by Figure 1. We make the same assumptions as the ones made by Shah and Remmenl and use the same nomenclature. Thus, the governing mass balance equations for the starch and enzyme are:

and

(2) bX by by

Since no model for the depolymerization of branched starch is available, a simpli- fied expression is used in eq. (1). The reaction rate is first order with respect to enzyme concentration and proportional to an average enzyme activity k,. Notice that eqs. (1) and (2) are coupled through the reaction term. The required velocity profile is given by Berman6 as

b (cm) b icsv) b2cE + - = D R Y

u = (;) [ao - 2][1 - (a>'] (3)

441 0 1973 by John Wdey & Sons, Inc.

442 BIOTECHNOLOGY AND BIOENGINEERING VOL. XV (1973)

PERMEATE POROUS SUPPORT

MEMBRANES

SOLUTIONAT 4 4 ?" W 4 9 ? 4 9 L /

UNIFORM 'y ENZYME AND STARCH t x ?.- CONCENTRA-p ENZYME TION,CE~, ,~ ,1",, STARCH ~ + ~ GLUCOSE ~ 6d cso POROUS

SUPPORT PERMEATE

Fig. 1. Schematic of a membrane reactor.

The relevant boundary conditions are:

ca = c.0; CE = CEO, a t x = 0, any y (5 )

dca dCE - = 0, at y = 0, any x by dY

(7) dC

dY D,"= R v . ~ , at y = h, any x

d C E D E - = R E V ~ E , a t y = h, any x dY

Equation (6) implies symmetry with respect to midplane. In the absence of experimental data, the model for transmembrane flux used by Shah and Remmenl is still used here. Equations (7) and (8) imply that fluxes of starch and enzyme through the membrane are noninteracting.

It is obvious that a simple analytical solution for the system of eqs. (1)-(8) is not possible, and a numerical solution was obtained with a digital computer. The finite difference method used has been described by Shah.6

RESULTS

In order to make the analysis relevant, data available in the literature are used. A model consisting of a thin channel reactor with membrane spacing of 60 mils (h = 30 mils) is selected as typical of such units.? Since reports in the literature297 indicate that fluxes between 1 and 20 gal/ft2-day may be obtained for ultra- filtration of the present types of macrosolutes, a value of vw = 10 gal/ft*-day is used here. Complete enzyme rejection ( R E = 1.0) and partial starch rejection ( R , = 0.9) are assumed. These values are estimated from the data reported in ref. 8.

No data were found in the literature for the diffusion coefficients of glucoamy- lase and the branched fraction of starch in water. A value of DE = 5.7 x 10-7 cm2/sec for glucoamylase is chosen as an average of the data reported for Q and fl-amylase.g A value of D, = 10-6 cm2/sec is assumed for the starch, based on diffusion coefficients of polysaccharides of similar molecular weights." The enzyme activity reported by Smiley et aL11 is considered typical of glucoamylase

COMMUNICATIONS TO THE EDITOR 443

and based on his data a value for k , of 0.154 (gram glucose formed)/(gram enzyme protein-sec) is calculated. A 1% branched starch solution is considered desirable for the present system, for reasons given e l ~ e w h e r e . ~ ~ ~ * Thus a value of cso = 10 g/liter is used in this analysis.

With the above fixed parameters, the variables that remain are the inlet veloc- ities 5 0 , the length of the reactor x, and the inlet enzyme concentration C E O .

We will briefly outline the effects of each of these parameters on the performance indexfA defined by Shah and Remmen.' The values of these parameters are in ranges considered to be of practical interest.

The length of the reactor is an arbitrary variable but will depend in general on the degree of conversion desired for a given reaction rate and longitudinal inlet velocity. Similarly, the enzyme concentration used may be based on a conversion requirement for a given reactor length and velocity Go. The following ranges of variables are considered suitable for the system a t hand: reactor lengths between 5 and 100 cm, enzyme concentrations of 0.5 to 5.0 g/liter, and longitudinal inlet velocities of 0.1 to 5 cm/sec. These values are in general agreement with pub- lished reports on this sort of system.4~8 Figures 2 and 3 show the effects of varying these parameters on the performance indexfA. In these figures, the dotted lines indicate the best performance (in plug flow) of solid wall reactors operating under similar reaction conditions. It can be easily deduced from these figures that except under conditions of large inlet enzyme concentration, the membrane reactor gives a better performance index than the best performance index achieved by a solid wall reactor.

0 I 2 3 4 5 LONGITUDINAL VELOCITY, ii$cm/sec)

Fig. 2. Effect of longitudinal velocity on reactor performance; C E O = 0.8 g/liter.

444 BIOTECHNOLOGY AND BIOENGINEERING VOL. XV (1973)

0 10 20 30 4 0 50 60 70 00 90 100 110 120 REACTOR LENGTH, X (CmS)

Fig. 3. Reactor performance as a function of enzyme concentration and distance along membrane; i i o = 1.0 cm/sec.

CONCLUSIONS

Under the reaction conditions generally reported in the literature, the hydro- lysis of starch into glucose by the enzyme glucoamylase is carried out better in a membrane reactor than in a solid wall reactor. Another asset of the membrane reactor is that it separates the enzyme from the glucose produced and allows recycling and continuous reuse of the enzyme.

We therefore recommend the use of the membrane reactor for the enzymatic hydrolysis of starch into the glucose.

Ca

CE D. DE

h k. RE R,

f A

U

ii

Nomenclature

starch concentration, g/liter enzyme concentration, g/liter molecular diffusion coefficient of starch, cm2/sec molecular diffusion coefficient of enzyme, cm2/sec performance index of reactor, defined in ref. 1 half-width of channel, cm average enzyme activity, gram glucose formed/gram enzyme protein-sec enzyme rejection coefficient starch rejection coefficient longitudinal velocity, cm/sec average value of u over the channel a t a given value of 2, cm/sec

COMMUNICATIONS TO THE EDITOR 445

v z y Subscripts o E enzyme s starch w

velocity component in ydirection, cm/sec longitudinal distance from channel inlet, cm transverse distance from channel midplane, cm

channel inlet, i.e., z = 0

channel wall, i.e., at the membrane surface

The help of the University of Pittsburgh Computer Center is gratefully ac- knowledged.

References

1. Y. T. Shah and T. Remmen, Int. J. Heat Mass Transfer, 14,2109 (1971). 2. T. I(. Ghose and J. A. Kostick, Biotechnol. Bioeng., 12,921 (1970). 3. S. P. O’Neill, J. R. Wykes, P. Dunnill, and M. D. Lay, Bwtechnol. Bioeng.,

4. T. A. Butterworth, D. I. C. Wang, and A. J. Sinskey, Biotechnol. Bioeng.,

5. A. S. Berman, J. Appl. Phys, 24, 1232 (1953). 6. Y. T. Shah, Znt. J . Heat Mass Transfer, 14, 921 (1971). 7. R. L. Goldsmith, Znd. Eng-Chem., 10, 113 (1971). 8. A. S. Michaels, L. Nelsen and M. C. Porter, in Membrane Processes in

Industry and Biomedicine, M. Bier, Ed., Plenum Press, New York, 1971, p. 197. 9. C. T. Greenwood and E. A. Milne, in Advances in Carbohydrate Chemistry,

M. L. Wolfrom and R. S. Tipson, Eds. Academic Press, New York, 1968, p. 281. 10. H. A. Sober, Ed., Handbook of Biochemistry, The Chemical Rubber Co.,

Cleveland, Ohio, 1968. 11. M. J. Bachler, G. W. Strandberg, and K. L. Smiley, Biotechnol. Bioeng.,

12, 85 (1970). 12. P. Bernfeld, in Advances in Enzymology, F. F. Nord, Ed., Interscience,

New York, 1951. G. P. CLOSSET Y. T. SHAH J. T. COBB

13, 319 (1971).

12, 615 (1970).

Dept. of Chemical Engineering University of Pittsburgh Pittsburgh, Pennsylvania 15213

Accepted for Publication September 29, 1972