The use of a modified Petrov-Galerkin method for gas-sold reaction modelling

A new numerical technique for simulating gas-solid reactionsincluding diffusion through the reactant and product layers,reaction on the shrinking surface and internal reaction is presented.Some transformations are introduced, and this model can be reducedto dimensionless form including a selfadjoint, singularly perturbed,two-point boundary-valve problem and two initial-value problems.A combination of the Petrov-Galerkin finite element method andpredictor-corrector method is applied to solve the problem.It is shown that the shrinking-core model including both surfacereaction and product layer diffusion can arise for low initialrelative permeability and the diffusion-controlled shrinking-coremodel occurs when the product layer diffusional resistance islarge relative to the surface reaction. This method is simpleand there is no limit on the range of the parameters. Computedresults are numerically evaluated for comparison with resultsof previous authors.