Monod kinetics product inhibition

Conversion rate data obtained under a wide range of operating conditions may be worked out to provide a kinetic expression, most typically expressed according to well established models for bioprocess kinetics first and second order, Monod, Haldane, product-inhibited, etc. 

With sufficient food and harmonious environment, cells multiply freely. However, no matter how much food is available, eventually either cells crowd each other out or their waste products inhibit their growth. We call this product poisoning. Hence, Monod kinetics always is a special case of a more general rate form which includes product poisoning. A simple equation of the general rate form for this situation is... 

The shape of the performance curve for a continuous stirred-tank fermenter is dependent on the kinetic behaviour of the micro-organism used. In the case where the specific growth rate is described by the Monod kinetic equation, then the productivity versus dilution rate curve is given by equation 5.137 and has the general shape shown by the curve in Fig. 5.58. However, if the specific growth rate follows substrate inhibition kinetics and equation 5.65 is applicable then, at steady state, equation 5.131 becomes ... 

Figure 6.25. Demonstration of the advantage of CPFR over CSTR by calculating the volume ratio in dependence of conversion reached (C) as a function of biokinetics using the simple Monod equation and varying the ratio Sq/K and also product inhibition kinetics with variation of Sq/Kj. A. Moser, 1985c, reprinted with permission from Conservation and Recycling, vol. 8, No. 1/2, Pergamon Press, Oxford.)...

Han, K., Levenspiel, O., 1988. Extended Monod kinetics for substrate, product, and cell inhibition. Biotechnology and Bioengineering 32, 430—437. 

Because of the failure of the Monod equation to find universal applicability, many researchers have suggested variations on the form of this equation in attempts to better characterize the kinetic behavior of substrate-limited growth of microorganisms. There are several more complex mathematical models that take into account not only inhibition by substrates and/or products of biochemical reactions, but also other factors, such as cell death and cell maintenance effects and multiple limiting substrates (5,6). 

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