Enzymatic reaction in supercritical carbon dioxide internal mass transfer limitation

Enzymatic reaction in supercritical carbon dioxide internal mass transfer limitation

High Pressure Chemical Engineering Ph. Rudolf von Rohr and Ch. Trepp (Editors) 9 1996 Elsevier Science B.V. All rights reserved. 103 E n z y m a t i...

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High Pressure Chemical Engineering Ph. Rudolf von Rohr and Ch. Trepp (Editors) 9 1996 Elsevier Science B.V. All rights reserved.


E n z y m a t i c R e a c t i o n in Supercritical C a r b o n Dioxide Internal M a s s Transfer Limitation P. Bernard and D. Barth Laboratoire de Thermodynamique Chimique et Appliquee-E.N.S.I.C. l, rue Grandville - BP 451 - 54001 NANCY C6dex, France 1. INTRODUCTION Enzymatic reactions in non-aqueous solvents are subjected to a wide interest A particular class of these solvents is the supercritical fluid (1) such as carbon dioxide that has many advantages over classical organic solvents or water: no toxicity, no flammability, critical pressure 7.38 Mpa and temperature 31 ~ and allowing high mass transfer and diffusion rates. Several authors have shown the stability and the catalytic activity of enzymes in supercritical carbon dioxide (SC CO2) [2 to 25]. Some authors [14,17,18] have shown the difference of activity of enzyme in SC CO2 and in organic solvent. The intrinsic catalytic properties of enzymes are modified either during immobilization or atter they were immobilized [25-27]. In heterogeneous catalysis such as is carried out by immobilized enzymes, the rate of reaction is determined not simply by pH, temperature and substrate solution, but by the rates of proton, heat and substrate transport, through the support matrix to the immobilized enzyme. In order to estimate this last phenomenon, we have studied the internal mass transfer limitation both in hexane and in SC CO2, with different enzymatic support sizes. 2. M A T E R I A L AND M E T H O D S

Myristic acid was purchased from Sigma (St Louis, MO) and ethanol (99.85 %) from Prolabo (France). Ultra pure carbon dioxide (99.995 %) was purchased from Airgaz (France). The lipase (E.C. was a commercial enzyme from Mucor miehei kindly supplied by Novo Nordisk (Denmark). This lipase (Lipozyme TM) is immobilized on Duolite A568 (Rohm and Hass). The resin particles have a size comprised between 300 to 600 ~m. In order to see if a phenomenon of internal mass transfer occurs during the enzymatic esterification, we sieved the support into different size series. The average granulometry was determined by Coulzer Sizer method (Table 1). Table 1 Nitrogen content of the enzymatic support Support series (lam) Average size (lam) % (N/CHN)

0-200 181 11.93

200-250 212 11.96

250-300 239 12.05

300-400 310 11.93

400-500 396 11


2.1. Supercritical fluid reactor (Figure 1) Before each experiment, the jacketed stainless steel (Top Industrie, Dommarie-Les-Lys, France) reactor is opened. A precise amount of substrates and water (Table 2) are introduced within the reactor. After sealing, pressurization is achieved by pumping liquid carbon dioxide (Minipump, Dosapro-Milton Roy, Pont-St-Pierre, France) to the desired final pressure (12.5 MPa). The reactor is then isolated from the CO2 circuit. Then 20 mg of lipozyme TM of various diameter distributions (Table 1) is introduced in the reactor with an original system, giving the zero time of the reaction and the stirring is switched on. A 6-way HPLC valve (Rheod /ne 7125) permits to withdrawn 50 tal sam ~les for analysis without depressurization. Cold bath Pump Heatbath


273 K 60 bar

273 K

323 K 125 bar

l, CO2 tank

293 K 60 bar

Pressure 17X gauge

HPLC Valve

U Injection device

Sttrred reactor

Figurel Laboratory reactor flow-sheet 2.2.Two liquid-phase reactor The reaction was carried out in a glass with a round bottom, in order to prevent the enzyme support attrition, filled with 100 ml n-hexane, in which substrates, water and enzyme were added. The reaction mixture is incubated and agitated with magnetic stirring.

2.3. Experimental reaction conditions Hexane and SC CO2 experiments were performed in a batch mode reactor (100 cm3). In both cases, added enzyme and substrate quantities, reaction volume and temperature were similar as shown in table 2. Table 2 Experimental conditions in hexane and SC CO2 cases Hexane SC C02 (a) (b) l0 [Myristic acid] (mM) 4 4 100 [Ethanoll (mM) 8 8 44 [Water] (mM) 1.1 44 20 Lipozyme TM (mg) 20 20 323 Temperature (K) 323 323 12.5 Pressure (Mpa) 0.1 12.5 300 Stirring (rpm) 1000 300

105 Only the quantities of water introduce in both solvents are not similar, because the water is necessary for the active enzyme conformation and not for the reaction. The water effect was studied elsewhere [ 13,14]. From these measurements, the conversion rate was determined from the ratio between ethyl myristate production and myristic acid feed. Then the inital velocity was graphically measured. 2.5. Analytical method

The samples were analysed by capillary gas chromatography GC 6000 (Carlo Erba) with FFAP-CB phase (Chrompack) that is special for free fatty acid analysis. The FID temperature was 235~ the injector was an on-column system and the oven gradient was 40~ during 2 min, then increasing to 210~ at 45~ The injected quantity was 21,tl with no dilution. 2.6. Enzyme content

We have formulated the hypothesis that the enzyme content of the different particle series is the same. In order to verify this hypothesis, the elementar analysis was realised for the different support sizes. As shown in table 1, the enzyme content measured as nitrogen is identical ; this equality was verified mathematically by the Student's law. 2.7. Effect of stirring on the reaction rate

By varying the speed of the stirrer from 200 to 500 rpm no effct on the reaction velocities is observed in SC CO2 or in n-hexane However, without stirring, the reaction velocities decrease 6 % and 13 % respectively. All further SC CO2 studies are performed at 300 rpm. So, no external diffusion limitation can be assumed; however, internal diffusion limitations may happen, as discussed in the following section. 3. THE GENERALIZED THIELE MODULUS Froment [29] et all have shown that the mass balance on a pellet should be written as : 1

Se D(S , )r(S, x/2 [~Sc 1"1- Lr(Se)


The generalized Thiele modulus is defined by : rl -

(1) 1


This concept should be applied to a Michaelis-Menten kinetic [30] : .2




1 Vmax Se + KM. Ln -KM- j



,-,(1+13e)2 ]3e_i_~(1+]3e)


with 13- KM

According to the result presented by J.M Engasser [29], we have plotted rl(~)versus for several values of 13~. Dumont demonstrated [ 14] that the esterification of myristic acid by ethanol has shown to follow Ping Pong Bi Bi kinetics with competitive substrate inhibition by ethanol :

106 VmAB r : AB + Kma A + K~AB(1 + B / Ki) (5) In this ease, it can be demonstrated, if one molecule has a higher diffusion coefficient, that modelisation should be realized as a single molecular reaction with a Michaelis-Menten mechanism : ethanol diffusion coefficient is higher than that of myristic acid in solution. r(Se)- rlr(Se) with r l -


3 ~)G cot g(3 ~G) - 1 3t~G

and D' = f(13o).D

r(So)- k So 2 kL2 t~G- D'



with f(13e)= 2


(7) L = --dP 6


1+13~ 13~ (13o-Ln(l+ 13o)


The apparent diffusion coefficient D' is determined by minimizing the difference between the experimental and the calculated apparent velocity versus dp 16. Then we have to determine two parameters: Km and Vma~. Vm~, does not depend on the particule size so these two parameters are determined by studying the influence of myristic acid concentration on apparent velocity. 2 VmaxSe 2 1 ~2 1 3 ~ 1 r(Se)- rlr(Se) - rl KM+ S----~ (13) +G = ~ (1 +13e)2 13o-Ln(1+13o) (14) 4. RESULTS AND DISCUSSION

The experimental results are summarized in table 3 and 4 for the two reaction media. In the case of SC CO2 we can study the concentration effect of ethanol on the diffusion coefficient: it is twice smaller in (a) than in (b). It has been shown that ethanol added to SC CO2 should contribute to increase a binary diffusion coefficient [30]. Table 3 Kinetic parameters and diffusion coefficients : comparison between hexane and CO2 SC [Myristic acid] = 4mM [Ethanol] = 8raM Hexane

D' (m2.s"1) V'max

(mmol.(s.kg) 1)

K*M Diffusion coefficient (m2.s-1)

2.37.10 "9 13.6 5.9

1.43.10 "9

[Myristic acid] = 10mM [Ethanol] = 100raM

SC CO2 C(a)

SC CO2(b)

4.34.10 "9 3.1 1.28 3.01.10 "9

10.6.10 "9 10.3 4.92 7.85.10-9

(a), (b) : see table 2 *dp=450Bm. We can observe (Table 4) that the concentration effect on Thiele modulus is very poor. Due to the Thiele modulus values, we can say that in SC CO2 an intermediate rate between the reactional and diffusional rates was apparent. The kinetic parameters, Vmaxand Kr,~, in both reaction media are very different : Vmaxis higher in n-hexane (13.6 mmol.(s.kg.) 1) than in SC CO2 (3.1 mmol.(s.kg.)) so n-hexane should be a better solvent than SC CO2. But the myristic acid diffusion coefficient is lower in n-hexane than in SC CO2 and we can observe the

107 unfavorable effect on the efficiency. The internal diffusion seems to be higher in n-hexane than in SC CO2 essentially if the particle size is greater than 310 l,tm. Table 4 Thiele modulus versus duolite particle size : comparison between hexane and CO2 SC. Thiele Modulus Particule size (l.tm) 181 212 239 310 396 464 (a), (b) : see table 2.

Hexane 0.50 0.68 0.87 1.46 2.38 3.27

SCCO2(a) 0.20 0.27 0.35 0.59 0.96 1.31 ,

SCCO2(b) 0.22 0.30 0.38 0.63 1.03 1.42 i

5. CONCLUSION We have demonstrated for the first time that we could apply the theory of generalized Thiele modulus to an enzymatic reaction both in n-hexane and SC CO2. The comparison between the two reaction media is not so clear: in n-hexane the ~ real )) reaction velocity is higher than that obtained in SC CO2. Nevertheless, the Thiele modulus values indicates a limitation due to the internal mass transfer rate +~ >> 1. Thus we observed, in the hexane case, a diffusional control, while in SC CO2 an intermediate rate between the reactional and diffusional rates was apparent. It therefore, seems that SC CO2 should be the solvent of choice in reactions catalyzed by immobilized enzymes, since it reduces problems with internal mass transfer. An other advantage is that the value of the inhibition constant is 43 mM in n-hexane and 120 mM in SC CO2 [14], so SC CO 2 should be more convenient if we have to work with higher ethanol concentration. The economic feasibility of an industrial scale lipase catalyzed reaction on CO2 may depend upon possible costs for high-pressure equipment. REFERENCES

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