Conversion‐time relations for fluid–solid reactors with shrinking‐core kinetics

Abstract

The problem of finding expressions linking conversion and residence time for systems of fluid–solid reactions with shrinking-core kinetics is revisited. The classical formulae are revised for the three classical cases with different ratelimiting resistances: mass transfer in the film, chemical reaction and diffusion through the ash layer. It is demonstrated that, for a single particle size, the classical Taylor’s expansions of the conversion as a function of the dimensionless residence time can be conveniently replaced by other mathematical functions to solve the problem of inaccuracy and multiple roots of the polynomials. The proposed correlations give accurate solutions. Pairwise correlations permit getting the conversion from the residence time, and the residence time from a given conversion, with no multiple roots, for the cases of a continuous reactor with plug flow or perfectly mixed flow, for the three cases of rate-limiting resistances. The obtained results demonstrate that classical Taylor expansions yield significant errors for small residence times, whereas the newly proposed correlations avoid this issue and provide greater accuracy across the whole range. From the point of view of numerical calculus, the new correlations are simpler and reduce computational effort by eliminating the need to calculate numerous polynomial terms.