Analysis and shape inequalities for gas‐solid reactions with changing volume

Abstract For gas‐solid noncatalytic reactions following the sharp‐interface model, some fundamental aspects, not discussed previously in the literature, are presented for particle shapes where diffusion processes are described by a single space dimension. A detailed structure analysis of the solution for monotone nonlinear kinetics reveals interesting differences in the dynamics of the interfacial reaction front, including local maxima and minima in the rate of reaction interface motion, depending on particle shape and expanding or shrinking particle size. Rigorous shape inequalities on the interfacial reactant concentration, the motion of the reaction front and the particle conversion for the sphere and slab, and cylinder and slab geometries are obtained for any nonlinear monotonically increasing reaction kinetics and a wide range of parameter values. By taking advantage of these inequalities, the fraction of original solids of spherical or cylindrical shape, which remains unconverted at the exit of a fluidized‐bed reactor, is bounded by the corresponding quantities related to the slab shape. As an example, a first‐order reaction of the gaseous reactant is considered, where expressions for the reactor are obtained analytically, without any assumptions about possible controlling regimes. These analytical bounds for reactor conversion closely approximate the numerical solutions for design purposes.