The numerical solution of equations governing diffusion and reaction inside a porous catalyst

[摘要] This work investigates the transient behavior of a chemically-reacting system inside a porous catalyst particle. For simplicity, the associated reaction rate is assumed to be first order exhibiting an Arrhenius temperature dependence. Two separate sets of boundary conditions are imposed: equilibrium boundary conditions; and Newtonian mass and heat transfer resistance boundary conditions. Three different geometries corresponding to three basic shapes of catalyst particles are considered: an infinite slab of finite thickness; an infinite cylinder of finite radius; and a sphere of finite radius. The above system is governed by two coupled, nonlinear, parabolic partial differential equations. The solution of these equations is accomplished by means of a Galerkin Crank-Nicolson approximation utilizing Hermite cubic polynomials as basis functions which transforms the original problem into the more tractable one of solving two nonlinear sets of algebraic equations. The computational mechanics associated with this technique are subsequently compared with those intrinsic to a standard finite difference technique. For all of the examples investigated, this former algorithm is found to require less expenditure of computing time than does this alternate procedure to achieve a given level of accuracy in the solutions obtained.

[发布机构] Rice University