Steady states of a continuous-flow adiabatic chemical reactor

Abstract

Flow reactors are widely used in the chemical industry for purposes of catalytic reactions [1,2]. Calculation of reactors of this type, even in one-dimemional approximation, is complicated and possible only with the use of numerical methods [1, 3]. Such calculations make it possible to find the steady-state distribution of temperature and concentration in the chemical reactor if one exists; in general, however, there may be other steady-state regimes which may be preferable from the standpoint of obtaining a different degree of conversion of the starting product, operating stability, etc.

In this connection special interest attaches to the question of the existence and number of steady-state solutions of the system of equations describing the reactor process.

This problem was previously considered in [4–7]. Thus, in [4, 5] it was pointed out that in certain special cases more than one steady-state regime may exist. In [6, 7] the question of sufficient conditions of uniqueness was investigated. In [7] it was shown that the steady-state regime is unique in the ease of short reactors or a dilute mixture of reactants. In [8] the problem of the existence and uniqueness of the steady-state regime was examined for a chain reaction model with direct application of the general theorems of functional analysis.

The present paper includes an analysis of a very simple mathematical model of an adiabatic chemical reactor in which an exothermic or endothermie reaction takes place. It is established that in the case of an endothermic process a unique steady-state regime always exists. In the exothermic case the problem of the steady-state regime also always has a solution which, however, may be nonunique; the possibility of the existence of several steady-state regimes, associated with the form of the temperature dependence of the heat release rate, is substantiated.