효소적 에스터화 반응을 위한

수분 활성도 전산제어 시스템의 모델링 및 시뮬레이션

원 기훈, 이 선복*

포항공과대학교 환경연구소, 포항공과대학교 화학공학과*

Modeling and Simulation of the Computer-Aided Water Activity Control System

for Solvent-Free Enzymatic Esterification Reactions

Keehoon Won and Sun Bok Lee*

Institute of Environmental and Energy Technology, POSTECH,

Department of Chemical Engineering, POSTECH*

Introduction

Enzymatic catalysis in non-aqueous solvents is such a rapidly developing research area that it has attracted interest from chemists, biochemists, and chemical engineers [1]. Under these conditions, the industrial utility of enzymes is improved because of enhanced thermostability, ease of product and enzyme recovery, the ability to catalyze reactions that are impossible in aqueous solution and so on. However, if feasible, it would be technologically more attractive to perform the enzymatic reaction in solvent-free media, namely mixtures of the substrates themselves without any bulk solvents. This approach can combine the advantage of non-aqueous enzymology with the high levels of productivity. In addition recent environmental legislation is severely restricting the use of many traditional organic solvents.

For the successful implementation of such a solvent-free system, there should be a driving force for the reaction to proceed in the desired direction until completion. In the case of ester synthesis this is usually achieved by removal of water produced during the reaction. Several techniques have been suggested in the literature for water removal, such as headspace evacuation [2], pervaporation [3], adsorption [4], and sparging of dry air gas through the reaction medium [5].

When implementing any such synthesis, one has to remember that excessive dehydration of the reaction mixture can lead to a dramatic deterioration of enzyme performance. This is the case since water plays a major role in enzymatic catalysis, and more specifically, in the maintenance of the unique catalytically competent conformation of the enzyme. It has been amply demonstrated that enzyme activity and stability depend critically on water activity. Too low water activity can not provide flexibility enough for enzymes to function in non-aqueous systems. However, the high level of enzyme hydration does not always accompany the increase of its activity. In many cases, the reaction rate decreases sharply at high water activity. Recently enzyme agglomeration was shown to make the largest contribution to this serious loss in catalytic efficiency [6]. Consequently, it would be more desirable to control water activity in the system at an optimum rather than to exclusively remove water produced by the reaction. We have developed a computer-aided water activity control system using air bubbling for lipase-catalyzed esterification reactions in solvent-free media. In the present study, modeling and simulation of the control system will be described.

Experimental

Lipozyme IM , Rhizomucor miehei lipase immobilized on anion-exchange resin, was a generous gift from Novo Nordisk (Bagsvaerd, Denmark) and used as received. n-Capric acid and n-decyl alcohol were purchased from Sigma (St. Louis, Mo, USA). Silica gel was from Shinyo (Osaka, Japan). All the chemicals were used without further purification.

Esterification reactions were carried out in the following manner. Enzyme powders (1.0 g) were suspended in 100 ml of n-decyl alcohol for some 30 min. Enzymatic esterifications were started by the addition of the substrate mixture (22 ml of n-decyl alcohol and 62 ml of n-capric acid). All the reactions were performed at 30 ℃ and 500 rpm.

A schematic diagram of the water activity control system is shown in Figure 1. Compressed air passed through an air filter (0.2 □m). The air flow rate was controlled by a mass flow controller (MFC). The inlet air stream was split by a Y connector into two flows, which had different humidity: one obtained water by bubbling through distilled water in two bottles in series; the other lost water by flowing through silica blue in other two bottles in series. But only one of these two flows was allowed to enter the enzyme reactor through the sintered glass disc at the bottom of the reactor. Sparged air either provided water for the reaction medium or removed water from it.

Figure 1. A schematic diagram of the computer-aided water activity control system.

Consequently water activity can be controlled by manipulating the flow rate and type of air supplied into the enzyme reactor. Both of them were determined by the output value from a feedback digital controller. The controlled variable, say water activity, was measured, and then sent in the form of digital signals to the digital computer where the measured output value was compared to the desired, or set point, value. Based on the error, the deviation between desired and measured value, control action was determined. The sign and magnitude of the output determine the kind and flow rate of inlet air gas, respectively.

The substrates and product were determined by GC analysis. At predetermined intervals, about 0.5 ml of suspension was taken from the reaction medium and centrifuged to settle enzyme particles. 0.4 □l of sample diluted with cyclohexane was analyzed by GC with a flame ionization detector and a HP-INNOWax capillary column (inside diameter: 0.32 mm and length: 30 m). The column temperature was programmed to be increased from 160 ℃ to 240 ℃ at 20 ℃/min and maintained at 240 ℃ for 3.0 min. Injector and detector temperature were 250 ℃ and 260 ℃, respectively. Helium as a carrier gas was supplied into the column at 3.8 ml/min.

Modeling

The dynamic model was developed by writing the following material balance on the water in the reaction system.

[eqn: {d{C}_{w,t}} over {dt}=V {k}_{L}a LEFT ( {C}`_{w,m} ^{*}- {C}_{w,m} RIGHT ) + {M}_{w} rE]

[eqn: {C}_{w,t}=V {C}_{w,m}+E {C}_{w,e}]

where Cw,t is the total water content in the reaction system (mg), V is the reaction volume (ml), kLa is the volumetric water transfer coefficient (min-1), Cw,m* is the water concentration equilibrated with the inlet air in the reaction medium (mg/ml), Cw,m is the water concentration in the reaction medium (mg/ml), Mw is molecular weigh of water, r is the rate of water formation (mol/g of enzyme·min), E is the enzyme amount (g), and Cw,e is the water concentration on the enzyme particles (mg/g).

Assuming a rapid equilibrium of water between each phase (the enzyme particles, the reaction medium, and the headspace in the reactor), the variable Cw,e becomes a function of Cw,m. Hence the above differential equation can be solved with respect to only one variable Cw,m.

Results and Discussion

In the previous work, we constructed the computer-aided water activity control system using both humidified air and dried one for the first time. A change in the water concentration in the system is governed by the above material balance. Water transfer between the air and the reaction medium and water formation by the ester synthesis are responsible for variation of the water concentration. Water transfer rate is expressed in terms of a concentration gradient times a volumetric mass transfer coefficient dependent on a flow rate of air. From this model the water concentration in the reaction system is easily found to be affected by the kLa value. The measurement of relative humidity not water concentration with the relative humidity sensor compelled us to find the relationship between them. Similarly what we can manipulate is the flow rate of supplied air not the volumetric water transfer coefficient, so that correlation between them was also determined. Consequently relative humidity is a controlled variable and the air flow rate a manipulated variable.

The model parameters were estimated through nonlinear regression analysis of experimental data. However, they depended on the composition of the reaction medium and varied as the reaction proceeded. For simplicity, it was assumed that all the time-varying parameters changed linearly to the reaction conversion. The model was solved using the fourth order Runge-Kutta method implemented in a software Simulink□ 2.2 (The MathWorks, Inc., USA)

Figure 2. Experimental data and model simulation of the performance of the computer-aided water activity control system. PID control: (a) Kc = 3000 sccm/%, □I = 6000 min, □D = 1 min, and time interval = 2 min; (b) Kc = 1000 sccm/%, □I = 6000 min, □D = 0 min, and time interval = 2 min.

Figure 2 shows the comparison between the values of relative humidity under PID control with two different parameters and model simulation results. As shown in Figure 2, the experimental data were in good agreement with model predictions.

Acknowledgement

The authors wish to acknowledge the financial support of the Korea Research Foundation made in the program year of 1998.

References

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3. Van der Padt, A., Sewalt, J. J. W., and Van't Riet, K.: J. Membr. Sci., 80, 199 (1993).

4. Ergan, F., Trani, M., and Andre, G.: Biotechnol. Lett., 10, 629 (1988).

5. Jeong, J. C. and Lee, S. B.: Biotechnol. Technique, 11, 853 (1997).

6. Kim, M. G. and Lee, S. B.: J. Mol. Catal. B: Enzymatic, 2, 127 (1996).