Unstable systems

Nonideal continuous stirred-tank reactor

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System description

This process is represented by a continuous stirred-tank reactor (CSTR) with nonideal mixing described by Cholette’s model. The process can be illustrated according to the following figure. 


Presented parameters are described in detail in the mathematical model given below.

n = m = 0.75, V = 1 l, k= 10 s-1, k2 = 10 l/mol, q = 0.033 l/s

A nominal operating point (for the linearization):

c= 6.484 mol/l, c= 1.8 mol/l, c = 0.2387 mol/l

Mathematical model

A simplified mathematical model of the process dynamics can be described by the following nonlinear differential formulas (Liou & Chien, 1991; Padma Sree & Chidambaram, 2006):

where C(t) is the concentration of the reactant in the well-mixed zone,  Ce(t) is the concentration in the exit stream (controlled variable), and Cf(t) is the feed concentration (manipulated variable). Further, n is the fraction of the reactant feed that enters the zone of perfect mixing, and m is the fraction of the reactor total volume V where the reaction occurs. Constants k1 and k2 describe the reaction rate, and q is the inlet flow rate.

Linearization of the nonlinear model around the above given nominal operating point gives the transfer function model as:

Simulation files

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Information sources

LIOU, Ching-Tien; CHIEN, Yu-Shu. The effect of nonideal mixing on input multiplicity in a CSTR. Chem. Eng. Sci., vol. 46, no. 8, pp. 2113-2116, 1991.

PADMA SREE, R., CHIDAMBARAM, M. Control of Unstable Systems. Oxford: Alpha Science, 2006, 297 p. ISBN 1-84265-287-7.

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