A mathematical model is derived for the shrinking core like conversion of solids in a reacting fluid. As a technical example for this type of reaction the model is used to evaluate kinetic experiments on the production of carbide-derived carbon from silicon carbide. Therefore the simultaneous influence of reaction as well as diffusion is combined with the residence time behaviour of the reactor (tubular reactor), the non-constant gas phase volume over the extent of reaction and the particle size distribution of the solid substrate. The derived model is validated for accuracy against known solutions of boarder cases (e.g. shrinking core model of a single sphere, fluid phase volume change without dispersion or shrinking core and limitation by reactant feed). (C) 2011 Elsevier Ltd. All rights reserved.