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A fundamental analysis of continuous flow bioreactor and membrane reactor models with non‐competitive product inhibition. II. Exponential inhibition
Author(s) -
Nelson Mark Ian,
Lim Wei Xian
Publication year - 2010
Publication title -
asia‐pacific journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.348
H-Index - 35
eISSN - 1932-2143
pISSN - 1932-2135
DOI - 10.1002/apj.485
Subject(s) - bioreactor , dimensionless quantity , product inhibition , steady state (chemistry) , membrane reactor , substrate (aquarium) , constant (computer programming) , exponential growth , residence time (fluid dynamics) , residence time distribution , chemistry , product (mathematics) , yield (engineering) , continuous stirred tank reactor , continuous flow , by product , thermodynamics , chemostat , flow (mathematics) , membrane , physics , mechanics , mathematics , non competitive inhibition , biochemistry , engineering , mathematical analysis , biology , computer science , enzyme , organic chemistry , bacteria , ecology , geometry , programming language , geotechnical engineering , genetics
The steady‐state production of a product produced through the growth of microorganisms in a continuous flow bioreactor is presented. A generalised reactor model is used in which both the classic well‐stirred bioreactor and the idealised membrane bioreactor are considered as special cases. The reaction is assumed to be governed by Monod growth kinetics subject to non‐competitive product inhibition. Inhibition is modelled as a decaying exponential function of the product concentration. This reaction scheme is well documented in the literature, although a stability analysis of the governing equations has not previously been presented. The performance of a well‐stirred bioreactor with microorganisms death is also not currently available in the literature. The steady‐state solutions for the models have been obtained, and the stability has been determined as a function of the residence time. The key dimensionless parameter (γ) that controls the degree of non‐competitive product inhibition is obtained by scaling of the equations, and its effect on the reactor performance is quantified in the limit when product inhibition is ‘small’. The parameter γ is a scaled inhibition constant ( K p ) that depends upon the substrate and product yield factors and the Monod constant ( $\gamma = {\alpha_{s}\over \alpha_{p}} \cdot {K_{s}\over K_{p}}$ ). Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.