MODELING AND NUMERICAL ANALYSIS OF DEAD-CORE PHENOMENA IN CHEMICAL REACTOR ENGINEERING

Abstract

Diffusion-reaction processes in chemical reactors are often modelled by differential equations of diffusion-reaction type that describe the change in time and space of concentrations of chemical species. In this work, dead-core phenomena, i.e. depleting of chemical species due to the strong catalytic reactions, are studied analytically and numerically for single reactions with power-law kinetics of fractional order. In the first part of this work, dead-core phenomena are presented for 1-D diffusion-reaction problems for catalytic pellets. The point-wise convergence of the classical solution of non-stationary problems to the solution of the steady-state limit is shown analytically which constitutes the basis for the construction of an appropriate time-marching scheme to solve numerically stationary diffusion-reaction problems. In the second part of this work, 2-D reactor problems are studied. The spatial discretization is based on Finite Element Method (FEM) where the modified Crank-Nicolson method is used for the time-marching approach. The developed numerical scheme is implemented in MATLAB using Partial Differential Toolbox (PDE Toolbox). The simulation re sults confirm the theoretical predictions. Also, the phenomenon of dead-cores at the boundary is studied numerically for the model of chemical reactor with a catalytic membrane.