Improving the Quantitative Description of Reacting Porous Solids: Critical Analysis of the Shrinking Core Model by Comparison to the Generalized Grain Model

A numerical comparison between the shrinking core model and the grain model is carried out, in the case of a single noncatalytic gas-solid reaction within a spherical particle. The study is focused on the mathematical quantification of the divergence between the time dependent particle conversions predicted by the two models, taking into account the different relationships between kinetics and intraparticle diffusion. Sensitivity tests have been carried out, depending on the controlling regime (chemical, diffusive, intermediate). The comparison was extended to a generalized form of the grain model, in which the superficial area of the porous matrix can be described as nonspherical micrograins, with possible sintering phenomena occurring. The comparison between the two models is first made by trying to fit the shrinking core model kinetics to the more realistic continuous model. Finally, errors introduced by the shrinking core model extrapolated to particle sizes different from that used to identify its apparent kinetics are discussed and quantified. Unexpectedly, the largest errors introduced by the shrinking core model are in the intermediate regime, instead of the kinetic one, where it is farthest from the actual physics of the process. The results prove that the common choice of using a shrinking core model instead of a continuous model can lead to severe errors in the conversion prediction, also beyond the regime where its assumptions are clearly violated.