Kinetics of continuous starch hydrolysis in a membrane reactor

Biochemical Engineering Journal 6 (2000) 233–238

Kinetics of continuous starch hydrolysis in a membrane reactor D. Paolucci-Jeanjean a , M.P. Belleville a , G.M. Rios a,∗ , N. Zakhia b a

Laboratoire des Matériaux et des Procédés Membranaires (LMPM UMR 5635), ENSCM, 276 rue de La Galéra, 34097 Montpellier cedex, France b CIRAD/AMIS, 73 rue Jean-François Breton, 34032 Montpellier cedex 5, France Received 4 January 2000; accepted 2 September 2000

Abstract Following a previous study on kinetics of enzymatic starch hydrolysis with Termamyl 120 l (Novo Nordisk) in batch reactor, this paper deals with kinetics in a continuous recycled membrane reactor (CRMR). Starting from results obtained in various working conditions, an equation relating the production rates of small oligosaccharides (DP ranging from 1 to 5) to the sum of concentrations of oligosaccharides with a higher degree of polymerisation is proposed. This equation looks like the one already reported for a batch system, with the exception that in the CRMR the enzyme activity varies: an exponential decay of activity as a function of time must be introduced to smooth carefully data points. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Membrane bioreactor; Starch; Hydrolysis; Enzyme; Kinetics

1. Introduction The enzymatic hydrolysis of starch is usually carried out in a batch reactor following a two-step procedure including liquifaction and saccharification [1]. Each step needs a specific enzyme which must be separated and inactivated after each run. Recently, it has been shown that the process can be performed in only one-step thanks to amylase enzymes such as Termamyl (Novo Nordisk), able to directly produce dextrins from native starch. Another improvement of hydrolysis follows from the use of a membrane reactor which allows to operate in a continuous way and to reuse enzymes. The continuous recycled membrane reactor (CRMR) is the most attractive option as hydrolysis can be carried out while separating syrups from enzymes and non-hydrolysed starch [2]. This paper deals with kinetics of starch hydrolysis with Termamyl in a CRMR. It constitutes the natural continuation of the work already published on the hydrolysis in batch conditions [3] to which it refers on several occasions. Most of kinetics studies involving an enzymatic reaction make the assumption that the production rate obeys the classical Michaelis–Menten Eqs. [4–7]: r= ∗

kES Vm S = Km + S Km + S

Corresponding author. Tel.: +33-3-67-14-72-70; fax: +33-3-67-14-72-71. E-mail address: [email protected] (G.M. Rios).

(1)

with r is the production rate (g dm−3 h−1 ), E the enzymatic concentration (cm3 dm−3 ), S the substrate concentration (g dm−3 ), and Vm (g dm−3 h−1 ), Km (g dm−3 ), k (g cm−3 h−1 ) the kinetic constants. The comparison of best-fitting values Vm , Km and k obtained with batch and membrane reactors constitutes a good means to detect some differences between enzyme activity in both systems. As an example, a lower value of k in the CRMR as observed by Deeslie and Cheryan [4] for kinetics studies of protein hydrolysis by Pronase, points out the existence of a higher loss of enzyme activity in the CRMR. On their side Sims and Cheryan [6] in an attempt to model hydrolysis of liquified starch by glucoamylase AMG, obtained a constant Km two to seven times higher in the CRMR, which indicates a reduced affinity of the enzyme for the substrate in the continuous reactor. However, in many cases the basic Michaelis Menten model does not work correctly and a more complex relation must be preferred. In order to take into account a competitive product inhibition during protease hydrolysis of water soluble fish proteins, Nakajima et al. [8] used the following equation: r=

kES Km (1 + C/K1i ) + S

(2)

where K1i is an inhibition constant (g dm−3 ) and C the product concentration (g dm−3 ). With this model, kinetic constants were identified for batch and membrane systems

1369-703X/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 1 3 6 9 - 7 0 3 X ( 0 0 ) 0 0 0 9 2 - 9

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Nomenclature A a a0 bn bn0 00 bn,av bn00 C Ci Ci ,lim Ci ,ret Ci ,ret,lim

Ci ,ret,lim,av

Cn,0

Cn,perm

Cn,perm,av

Cn,ret

Cn,ret,av

Cr E Eact Eb Em k kn K K1i Km J mn

surface area of the membranes (m2 ) current enzyme activity of the retentate (g cm−3 min−1 ) initial enzyme activity of the retentate (g cm−3 min−1 ) constant defined Eq. (4) (dm3 cm−3 h−1 ) coefficient defined Eq. (6) (dm3 cm−3 h−1 ) constant defined Eq. (10) (dm3 cm−3 h−1 ) constant defined Eq. (13) (dm3 cm−3 h−1 ) product concentration (g dm−3 ) concentration of the oligosaccharide with a DP equal to i (g dm−3 ) limit concentration of the oligosaccharide with a DP equal to i (g dm−3 ) concentration of the oligosaccharide with a DP equal to i in the retentate (g dm−3 ) limit concentration of the oligosaccharide with a DP equal to i in the retentate (g dm−3 ) average concentration of the oligosaccharide with a DP equal to i in the retentate (g dm−3 ) concentration of the oligosaccharide with a DP equal to n in the feeding solution (g dm−3 ) concentration of the oligosaccharide with a DP equal to n in the permeate (g dm−3 ) average concentration of the oligosaccharide with a DP equal to n in the permeate (g dm−3 ) concentration of the oligosaccharide with a DP equal to n in the retentate (g dm−3 ) average concentration of the oligosaccharide with a DP equal to n in the retentate (g dm−3 ) reactant concentration (g dm−3 ) enzymatic concentration (cm3 dm−3 ) concentration of active enzymes (cm3 dm−3 ) enzymatic concentration in the batch reactor (cm3 dm−3 ) enzymatic concentration in the membrane reactor (cm3 dm−3 ) kinetic constant (g cm−3 h−1 ) constant (dm3 cm−3 h−1 ) kinetic constant (h−1 ) kinetic constant (g dm−3 ) kinetic constant (g dm−3 ) Permeate flux (dm3 h−1 m−2 ) DP of the smaller oligosaccharide leading to n DP product

production rate (g dm−3 h−1 ) production rate of the oligosaccharide with a DP equal to n (g dm−3 h−1 ) average production rate of the oligosaccharide with a DP equal to n (g dm−3 h−1 ) substrate concentration (g dm−3 ) time (h) kinetic constant (g dm−3 h−1 ) reaction volume (dm3 )

r rn rn,av

S t Vm VR

Greek letters α constant defined Eq. (3) (h−1 ) β constant defined Eq. (3) (h−2 ) ε constant (dimensionless) constant defined Eq. (13) (dimensionless) εn φ constant defined Eq. (15) (dimensionless) τ space time (h) average space time (h) τ av successively. It appears that in the second case k had to be divided by 10 in order to take into account a main loss of enzyme activity. Sometimes, time must also be integrated in the reaction rate. Thus, for starch hydrolysis into maltose in a CRMR, Houng et al. [9] proposed the following equation: kE e(−αt+βt ) S Km (1 + C/K1i ) + S 2

r=

(3)

where α (h−1 ) and β (h−2 ) are two constants. As shown elsewhere [3], such expressions directly derived from the original Michaelis–Menten relation are unable to fit correctly experimental results for starch hydrolysis when large concentrations of substrate are concerned (100 g dm−3 ). The production rate of oligosaccharides with a DP ranging from 1 to 5 better follows the equation:   ∞ ∞ X X Ci − Ci,lim  E (4) rn = bn  i=mn

i=mn

where rn is the production rate of the oligosaccharide with a DP equal to n (g dm−3 h−1 ), Ci the concentration of the oligosaccharide with a DP equal to i (g dm−3 ), Ci ,lim the limit (i.e. final) concentration of the oligosaccharide with a DP equal to i (g dm−3 ), bn (dm3 cm−3 h−1 ) a constant. The value of mn corresponds to the DP of the smaller oligosaccharide leading to product with a DP equal to n (hereafter P∞ noted n DP product) through hydrolysis. As the sum i=mn Ci represents the total concentration of oligosaccharides P with a DP higher than mn in the reaction mixture, ∞ i=mn Ci,lim corresponds to the concentration of the oligosaccharides with a DP higher than mn which cannot be hydrolysed by the enzyme (highly branched sugars). Thus,

D. Paolucci-Jeanjean et al. / Biochemical Engineering Journal 6 (2000) 233–238

expression (4) is similar to that of a classical first-order reaction rate r = KCr

(5)

where K (h−1 ) is the kinetic constant and Cr the reactant concentration. In this article, we endeavour to check the ability of such a model to describe also kinetics of starch hydrolysis in CRMR.

2. Material and methods 2.1. Pilot-plant and operating conditions Hydrolysis was performed in a pilot plant shown in Fig. 1. The reactor was equipped with three Carbosep M4 membranes (molecular weight cut-off: 50 kD — Orelis, France) which reject enzyme and non-hydrolysed starch and let hydrolysates pass. The total surface area of the membranes is equal to 0.067 m2 and the cross-section area is 8.5×10−5 m2 . At the start of experiment, the buffer tank was filled with a native starch solution. The enzyme was added at concentration E1 and a preliminary batch prehydrolysis was conducted in order to decrease viscosity and diminish further membrane fouling. Then, pumping of the vessel content through the separation module was started and products permeated through membranes while enzymes and non-hydrolysed starch were recycled back: that was the beginning of the continuous process at which a second addition of enzyme (E2 ) was operated, leading to a total initial catalyst concentration E = E1 + E2 . The volume of liquid inside the apparatus was kept constant and equal to 6 dm3 by continuously feeding with fresh native starch

235

suspension, thanks to an electrovalve connected to level sensors located inside the buffer tank. Temperature was kept at 80◦ C, all reaction long with a tangential flow rate, high enough to limit polarisation effects (about 3 m s−1 , i.e. a recirculation rate of 15 dm3 min−1 ) and a classical transmembrane pressure around 1 bar. All experiments were followed by a complete membrane regeneration based on basic and acid washings. 2.2. Enzyme, substrate and product analysis Cassava starch used in this work was issued from Manihot ultissima pohl species and produced in Thailand by Thai Wah Public Co. (Bangkok). A commercial preparation of thermostable exo-␣-amylase Termamyl 120 l from Bacillus licheniformis was provided by Novo Nordisk. At regular time intervals, samples were removed from the reaction mixture and analysed by HPLC with a Bio-Rad HPX42A column, leading to hydrolysate compositions. Enzyme activity was also checked at regular intervals. A complete description of working conditions and experimental results thus obtained have been already reported in a previous paper [10]. These are precisely the data which constitute the base on which the theoretical developments have been elaborated.

3. Discussion 3.1. General considerations The starting idea is to prove the ability of an expression similar to the Eq. (4) to describe starch hydrolysis in CRMR, i.e.   ∞ ∞ X X Ci,ret − Ci,ret,lim  E (6) rn = bn0  i=mn

i=mn

where rn is the production rate of the oligosaccharide with a DP equal to n (g dm−3 h−1 ), Ci ,ret and Ci,ret,lim the actual and limit concentrations of the oligosaccharide with a DP equal to i in the retentate (g dm−3 ), bn0 (dm3 cm−3 h−1 ) a constant and mn the DP of the smaller oligosaccharide leading to the n DP product through hydrolysis (see Table 1). The CRMR is considered as an ideal continuous stirred tank reactor and the mass balance for each oligosaccharide may be written as JACn,0 + rn VR = JACn,perm + VR

dCn,ret dt

(7)

Table 1 Values of mn

Fig. 1. Schematic diagram of the CRMR.

DP (n)

1

2

3

4

5

mn

6

6

7

7

6

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where J is the permeate flux (dm3 h−1 m−2 ), A the surface area of the membranes (m2 ), VR the reactor volume (dm3 ), Cn,0 , Cn,perm and Cn,ret the concentrations of the n DP oligosaccharide in the feed, permeate and retentate streams respectively (g dm−3 ) and t the time (h). Because there are no low DP (1–5) oligosaccharides in the feeding solution, and because these compounds once formed do not accumulate in the retentate (their concentrations are identical on permeate and retentate sides), the equation may be simplified at steady-state as follows:

Table 2 P∞ 0 Values of bn,av, i=mn Ci,ret,lim,av , and corresponding regression coeffi2a cients R

rn τ = Cn,perm

10% except for glucose. In that case, the obtained value of (25 g dm−3 ) is lower than the expected one (30–33 g dm−3 ). In fact, the concentration of glucose in the reactor is always very low and its production rate very slow [10] which probably enhances inaccuracies in chromatographic analysis, in turn responsible for the observed discrepancy. the choice of the first value for glucose PBecause ∞ −3 C i=mn i,ret,lim,av (25 g dm ) leads for the developments which follow to often incoherent results, whereas the use of the second (30 g dm−3 ) provides things much more acceptable, this is the last choice which was made hereafter. If one compares the average values ofP the sums obtained
∞ during modelling of hydrolysis in batch i=mn Ci,lim av and
P∞ membrane i=mn Ci,ret,lim,av av reactors for mn equal to 6 or 7 (Table 3), it may be observed that they are equal within 6% for mn = 6 and present a difference of 26% for mn = 7. In fact, there is no reason so that they are perfectly identical, even if their order of magnitude must be the same; indeed the privileged retention of high DP oligosaccharides in CRMR, and the fact that reaction is not complete in it, can explain significant differences with batch apparatus.

(8)

where τ is the space time (h). Owing to the fact that fouling develops continuously throughout experimental runs and thus modifies resistances at wall progressively, the performance of the reactor moves slowly in the course of time: it is in fact more appropriate to speak about a quasi-steady-state at any time, rather than to refer strictly to a pure steady operation [10]. To take into account of this evolution, kinetics studies have been led hereafter starting from two distinct approaches: either interpreting time average values of concentrations and space time (the so-called “time average kinetics studies”) or considering instantaneous data under the quasi-steady-state assumption (hereinafter referred to as “instantaneous kinetics studies”). 3.2. Time average kinetics studies The average production rate rn,av (g dm−3 h−1 ) can be obtained from the following equation: rn,av =

Cn,perm,av τav

(9)

where Cn,perm,av is the average concentration of the oligosaccharide with a DP equal to n in the permeate (g dm−3 ), τ av the average space time (h). Being given the form of the sought production rate expression   ∞ ∞ X X 0  Ci,ret,av − Ci,ret,lim,av  E (10) rn,av = bn,av i=mn

DP (n)

1

0 bn,av (dm3 cm−3 h−1 ) P∞ −3 i=mn Ci,ret,lim,av (g dm ) 2 R

0.064 0.216 0.272 0.137 0.296 25 33 22 24 30 0.999 0.998 0.987 0.993 0.997

3

4

5

a θ = 80◦ C, pH = 5.8, S = 100 g dm −3 , 1.8 ≤ E ≤ 5.5 cm 3 dm −3 , 0 V R = 6 dm3 .

3.3. Instantaneous kinetics studies
P∞ Starting from i=mn Ci,ret,lim,av av previously obtained, and based on instantaneous values of permeate concentrations and space times — Cn,perm and τ , — an expression of bn0 versus time is now looked for. It is worth keeping in mind that the result of this investigation will be dependent on the time interval chosen for averaging (6 h in our case). The instantaneous rate is given by

i=mn

it seems interesting to plot rn,av /E as a function of the sum of average concentrations of oligosaccharides with a DP P C . higher than mn in the retentate, ∞ i=mn i,ret,av For all the oligosaccharides with an intermediate DP between 1 and 5, a linear regression wasPmade which led to the values 0 −3 (dm3 cm−3 h−1 ), ∞ of bn,av i=mn Ci,ret,lim,av (g dm ), and regression coefficients given in Table 2. The values of mn being, respectively, equal to 6 for oligosaccharides of DP 1, 2 and P 5, and to 7 for products of DP 3 and 4 (Table 1), the sum ∞ i=mn Ci,ret,lim,av must be the same for oligosaccharides of DP 1, 2 and 5 on the one hand, and 3 and 4 on the other hand. This is checked to within

2

rn =

Cn,perm τ

(11)

Table 3 Comparison modelling of
sums obtained during
hydrolysisa in P∞ of average P∞ batch i=mn Ci,lim av and membrane i=mn Ci,ret,lim,av av reactors mn

Batch P∞ reactor
i=mn Ci,lim

Membrane reactor
P∞ i=mn Ci,ret,lim,av

6 7

33.5 30

31.5 23

av

Difference (%) av

6 26

a θ = 80◦ C, pH = 5.8, S = 100 g dm −3 , 1.8 ≤ E ≤ 5.5 cm 3 dm −3 , 0 m 0.17 ≤ E b ≤ 1 cm3 dm−3 , V R = 6 dm3 .

D. Paolucci-Jeanjean et al. / Biochemical Engineering Journal 6 (2000) 233–238

Fig. 2. Napierian logarithm of bn0 as a function of time for oligosaccharides with a DP ranging from 1 to 5 (θ = 80◦ C, pH = 5.8, S0 = 100 g dm−3 , E = 1.2 cm3 dm−3 , V R = 6 dm3 ).

237

Fig. 3. Evolution of the napierian logarithm of current over initial enzyme activity ratio in the retentate during continuous hydrolysis of starch (θ = 80◦ C, pH = 5.8, S0 = 100 g dm−3 , V R = 6 dm3 ).

and bn0 is plotted as a function of time bn0 = P∞

i=mn Ci,ret −

rn P∞

i=mn Ci,ret,lim,av




E

(12)

Whatever the experimental run as well as the oligossacharide, it appears that bn0 is an exponential function of time as shown in Fig. 2: bn0 = bn00 e−εn t/τav

i=mn

This expression is quite similar to the production rate found for batch hydrolysis with the exception that the enzymatic concentration E has been replaced by E e−εt/τav . This suggests that there would be a continuous decay of the active enzyme concentration in the reactor. The value of ε found in this study is nearly equal to 0.30. Experimental measurements of enzyme activity in the retentate have been carried out at E = 3.7 and 5.5 cm3 dm−3 . Results clearly show that activity obeys a law of exponential decay of the type (Fig. 3 and Eq. (15)) a = a0 e

−φt/τav

E (cm3 dm−3 )

1.8

2.7

3.7

5.5

ε φ

0.32

0.30

0.31 0.29

0.29 0.28

a

(13)

where τ av is the average space time (h) and bn00 (dm3 cm−3 h−1 ), ε n (dimensionless) two new constants. The five straight lines associated to ln(bn0 ) versus time variations are parallel which means that the ratio εn /τav is constant regardless of the DP of oligosaccharide. As the average space time has a fixed value for each run, one can infer that ε n is a constant that will be simply noted ε in what follows. The instantaneous production rate of each product can thus be written as   ∞ ∞ X X Ci,ret − Ci,ret,lim,av  E e−εt/τav (14) rn = bn00  i=mn

Table 4 Values of ε and φ for different experimentsa

(15)

where a and a0 are the running and initial activity in the retentate (g cm−3 min−1 ) while φ is a dimensionless constant. In addition, φ is very closed to ε (see Table 4) which confirms that the constant ε is effectively linked to the loss of enzyme activity in the model. Considering statistic errors due to multiple regressions, one can assert from results shown in Table 5 that bn00 is independent of the enzymatic concentration and identical to

θ = 80◦ C, pH = 5.8, S0 = 100 g dm−3 , V R = 6 dm3 .

Table 5 Average values of bn00 and corresponding relative standard deviation (RSD) obtained during modelling of hydrolysis in the CRMR and comparison with bn corresponding to batch experimentsa DP (n)

1

bn00

2

3

4

(membrane reactor) 0.346 0.821 0.825 0.443 RSDb (%) 26 19 17 13 0.391 0.745 0.824 0.579 bn (batch reactor) RDc (%) −12 10 0 −23

5 1.079 15 1.14 −5

a θ = 80◦ C, pH = 5.8, S = 100 g dm −3 , 1.8 ≤ E ≤ 5.5 cm 3 dm −3 , 0 m 0.17 ≤ E b ≤ 1 cm3 dm−3 , V R = 6 dm3 . b RSD: relative standard deviation for b00 value. n c RD: ralative difference between b and b00 values. n n

bn previously obtained for batch hydrolysis (Table 5). This underlines the similarity between the laws for production of small oligosaccharide in batch and membrane reactors.

4. Conclusion From previous findings, it is concluded that the production rate of small oligosaccharides (n between 1 and 5) may be calculated with the same expression in batch and continuous reactors   ∞ ∞ X X Ci − Ci,lim  Eact (16) rn = kn  i=mn

i=mn

where rn is the production rate of the considered oligosaccharide (g dm−3 h−1 ), Ci the concentration of the oligosaccharide with a DP equal to i (in the retentate for the CRMR)

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(g dm−3 ), Ci ,lim the limit concentration of the oligosaccharide with a DP equal to i (in the retentate for the CRMR) (g dm−3 ), mn corresponds to the DP of the smallest oligosaccharide leading to the production of a sugar with a DP equal to n, Eact the concentration of active enzymes (cm3 dm−3 ), always equal to the initial concentration in the batch reactor or continuously decreasing according to Eact = E e−εt/τav in the CRMR, kn a constant (dm3 cm−3 h−1 ). The values of kn are similar in both reactors, whereas limit concentrations are different due to retention of high molecular weight products by the membrane and limited reaction yield in the CRMR. It is worth noting that the CRMR kinetics modelling allows to predict the loss of enzyme activity at any time. Thus, enzymatic activity measurements become useless. In addition, this modelling constitutes an invaluable asset on the way to be further investigated of a complete simulation of the reactor at work. This simulation would require that one expresses the production rates of oligosaccharides with a DP equal or higher than 6 as a function of the concentrations of the different species in the retentate, and that one takes

into account the accumulation in the reactor of the oligosaccharides with a DP >6.

References [1] A. Reeve, in: F.W. Schenck, R. Hebeda (Eds.), Starch Hydrolysis Products, VCH Publishers, New York, 1992, p. 79. [2] D. Paolucci-Jeanjean, M.P. Belleville, G.M. Rios, N. Zakhia, Starch/Stärke 51 (1) (1999) 25. [3] D. Paolucci-Jeanjean, M.P. Belleville, G.M. Rios, N. Zakhia, Biotechnol. Bioeng. 68 (1) (2000) 71–77. [4] W.D. Deeslie, M. Cheryan, Biotechnol. Bioeng. 23 (1981) 2257. [5] P. Bressolier, J.M. Petit, R. Julien, Biotechnol. Bioeng. 31 (1988) 650. [6] K.A. Sims, M. Cheryan, Biotechnol. Bioeng. 39 (1992) 960. [7] R. Lopez-Ulibarri, G.M. Hall, Enz. Microb. Technol. 21 (6) (1997) 398. [8] M. Nakajima, T. Shoji, H. Nabetani, Process Biochem. 27 (1992) 155. [9] J.Y. Houng, J.Y. Chiou, K.C. Chen, Bioprocess Eng. 8 (1992) 85. [10] D. Paolucci-Jeanjean, M.P. Belleville, N. Zakhia, G.M. Rios, Biochem. Eng. J. 5 (2000) 17.