A method is presented for the analysis of a reaction between a porous solid and a gaseous reactant where the kinetic expression is linear in the concentration and where appreciable concentration gradients are established in the pore system as a result of diffusive transport rate. Two cases are treated mathematically: a single cylindrical pore initially of uniform diameter and a porous solid initially containing uniform cylindrical pores with random intersections. The mathematical solutions to the latter case are used to interpret the experimental results reported in the literature on the gasification of graphite rods with carbon dioxide. Values of the computed effective diffusivity are an order of magnitude smaller than the bulk diffusivity at the same temperature and pressure.
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Eugene E. Petersen (1957) studied this question.
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