Unstable systems

Nonideal continuous stirred-tank reactor

Details

Last Updated on Thursday, 24 October 2013 08:41

Published on Wednesday, 23 May 2012 13:58

Written by Jaroslav Kolařík

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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. 

Parameters:

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

n = m = 0.75, V = 1 l, k1 = 10 s-1, k2 = 10 l/mol, q = 0.033 l/s

A nominal operating point (for the linearization):

cf = 6.484 mol/l, ce = 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,  C_e(t) is the concentration in the exit stream (controlled variable), and C_f(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.