The dynamics of chemical reactors in porous media

Abstract

Is ignition or extinction the fate of an exothermic chemical reaction occurring in a bounded region within a heat conductive solid consisting of a porous medium? In the spherical case, the reactor is modeled by a system of reaction-diffusion equations that reduces to a linear heat equation in a shell, coupled at the internal boundary to a nonlinear ODE modeling the reaction region. This ODE can be regarded as a boundary condition. This model allows the complete analysis of the time evolution of the system: there is always a global attractor. We show that, depending on physical parameters, the attractor contains one or three equilibria. The latter case has special physical interest: the two equilibria represent attractors ("extinction" or "ignition") and the third equilibrium is a saddle. The whole system is well approximated by a single ODE, a "reduced" model, justifying the "heat transfer coefficient" approach of Chemical Engineering.