Function space methods for analysis of nonadiabatic tubular reactors with axial mixing-I. Uniqueness criteria of the steady state and computation of the steady state profiles

Abstract

Use is made of abstract function spaces to investigate the uniqueness of the steady state of nonadiabatic tubular reactors with axial mixing. For the study, the system differential equations are first transformed into integral equations. The properties of the integral operators are then investigated in the space of square integrable functions in order to obtain sufficient conditions for the uniqueness of solution of the system equations. A uniqueness criterion is obtained by use of the Contraction Mapping theorem, which permits one to compute the steady state profiles of reactor temperature and concentration by means of successive iteration with the transformed integral system equations. The computation involved here is quite simple compared to the numerical solution of the system differential equations with split boundary conditions. Numerical examples are given to investigate the effects of various system parameters on the steady state profiles of reactor temperature and concentration.