An Approximate Solution for a Transient Two-Phase Stirred Tank Bioreactor with Nonlinear Kinetics

An Approximate Solution for a Transient Two-Phase Stirred Tank Bioreactor with Nonlinear Kinetics

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An Approximate Solution for a Transient Two-Phase Stirred Tank Bioreactor with Nonlinear Kinetics Francisco J. Valde ´ s-Parada, Jose ´ A Ä lvarez-Ramı ´ rez, and J. Alberto Ochoa-Tapia* Universidad Auto ´noma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, Me ´xico D.F., Me ´xico, C.P. 09340 The derivation of an approximate solution method for models of a continuous stirred tank bioreactor where the reaction takes place in pellets suspended in a well-mixed fluid is presented. It is assumed that the reaction follows a Michaelis - Menten-type kinetics. Analytic solution of the differential equations is obtained by expanding the reaction rate expression at pellet surface concentration using Taylor series. The concept of a pellet’s dead zone is incorporated; improving the predictions and avoiding negative values of the reagent concentration. The results include the concentration expressions obtained for (a) the steady state, (b) the transient case, imposing the quasi-steady- state assumption for the pellet equation, and (c) the complete solution of the approximate transient problem. The convenience of the approximate method is assessed by comparison of the predictions with the ones obtained from the numerical solution of the original problem. The differences are in general quite acceptable. Introduction The stirred tank reactor (STR), batch or continuous, is considered an efficient setup for analysis of overall conversion rates in bioprocesses ( 1 ). Most of the reactions carried out in this class of reactors are catalyzed by enzymes. One of the limiting factors when using enzymes at an industrial scale is the cost ( 2 ). However, it can be reduced if the enzymes can be reused, which can be done when enzymes are immobilized ( 3 ). Some methods for immobilization are adsorption, covalent bonding, or entrapment. Another is encapsulation by coating liquid droplets containing enzymes with some semipermeable material formed in situ. Immobilization by adsorption or by covalent bonding often helps to stabilize the molecular configurations of an enzyme against alterations including thermal deactivation. Immobilized enzymes tend to be less sensitive to pH changes than are free enzymes, and this is especially important when they are suspended in aqueous solutions. Heat transfer between the immobi- lized enzymes and the medium is good enough so that the isothermal assumption for the system is reasonable. Most carriers have high porosity and large internal surface areas so that a relatively large amount of enzymes can be immobilized in a given volume of carrier. An immobilized enzyme - carrier complex (IECC) can be modeled as a heterogeneous catalytic system; thus in many parts of this work we will use the term “pellet” in the same way we use “IECC”. The oxygen and other solutes transported in the enzyme complex are subject to external resistance as well as pore diffusion-reaction effects, and for that reason the effectiveness factor is a useful parameter to characterize the immobilized enzyme pellet.
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This note was uploaded on 03/10/2011 for the course CBI 101 taught by Professor O.tapia during the Spring '11 term at UNAM MX.

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An Approximate Solution for a Transient Two-Phase Stirred Tank Bioreactor with Nonlinear Kinetics

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