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CSTR operations entailing high nonlinearity and complexity such as multiple input and output steady-states present a real challenge to chemical engineers and process designers. The input multiplicity in chemical reactions leads to control probems such as process instability and low efficiency. Therefore, it is of critical importance to predict and avoid the multiplicity regions during reactor operation. Since the bifurcation analysis of biochemical processes with nonideal mixing has been carried out by the authors in the previous publication (Yang, C. Y., D. C. Tsai, and Y. S. Chien. 2021. “The Strategy Developed for High Conversion and the Multiplicity Problems of Biochemical Reaction in a Real CSTR with Cholette’s Model.”  International Journal of Chemical Reactor Engineering  19: 1245–70), the goal of the present work is to use Sturm’s method, Routh stability criteria and the discriminator roots method with the tangent analysis method to derive the input multiplicity conditions in substrate inhibition in a real CSTR based on Chollete’s model. Four kinetic schemes are used in the analysis as examples to show that all three methods can precisely obtain the bifurcation starting point for the input multiplicity. In addition to the multiple input steady-states, the start-up diagram obtained by the discriminator root method is of critical importance to avoid operating in the input multiplicity regions.

Investigation into a multiple input/output bifurcated biochemical reaction with substrate inhibition in a real CSTR based on Cholette’s model