Dead-core and non-dead-core solutions to diffusion-reaction problems for catalyst pellets with external mass transfer

We present semi-analytic approaches for solving two-point boundary value diffusion-reaction problems for catalytic pellets in the case of external mass transfer. The nonlinear reaction term is of the power-law type with fractional reaction exponent. The presence of such reaction term can lead to the formation of the so-called dead zone where no reaction occurs. We derive novel semi-analytical dead-core and non-dead-core solutions for catalyst pellets of planar, cylindrical, and spherical geometries with external mass transfer. We verify our approach by numerical simulations and study the effects of the Thiele modulus, reaction order, and Biot number on profiles of reactant concentration. We also compare the solutions for pellets of various shapes and prove that the largest dead-zone occurs in pellets with planar geometry for the same set of process parameters.