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 analyti cally 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.