A RELAXATION METHOD FOR SOLVING REACTION PROBLEM IN AN ISOTHERMAL TUBULAR REACTOR WITH ONE-DIMENSIONAL EDDY DIFFUSION

A numerical method is proposed for solving an isothermal equimolar vap or phase parallel reaction problem in a tubular reactor with one dimen sional eddy diffusion under the boundary conditions given by Danckwert s. This problem is described by simultaneous second order ordinary dif ferential equations, and is transformed to a set of nonlinear simultan eous algebraic equations by expansion using the central finite differe nce operator, The Newton-Raphson method has been frequently used to so lve these equations in spite of the difficulties of complicated deriva tion of Jacobian matrix and selecting adequate initial values. The pro posed method is based on the relaxation method and consists of two cal culation loops; i) to correct the compositions of segmentation points of a reactor using a theta method with component material balances and ii) to repeat the point-by-point calculation in the sequence shown by Mori et al. in the solution of multistage, multi-component distillati on problems. The method provides stable solution with a brief algorith m regardless oi the number and rate equation of reactions, and is less sensitive in selecting initial values. The usefulness of the method i s demonstrated by some numerical examples.