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

Abstract

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

Insight in kinetics from pre‐edge features using time resolved in situ XAS

“…An implicit analytical solution of Eq. with a constant gas concentration ( and at a given temperature results in where …”

Reacting porous solids with phase segregation

“…However, oversimplified approaches are often selected (Parisi and Laborde, 2004;Gbor and Jia, 2004;Kruggel-Emden et al, 2010), typically trying to describe the experimentally determined rate of particle conversion with a model that does not properly account for the prevailing phenomena while using the physical parameters as numerical fitting parameters. We recently discussed quantitatively the incorrect predictions arising from a simpler model extrapolated outside the boundaries imposed by their constitutive assumptions (Melchiori and Canu, 2014). Here we present a continuous model accounting for a multistep chemistry that is shown and applied in the context of chemical looping combustion (CLC).…”

“…The second approach consists in solving the microscopic conservation equations for the gas and the solid species within the single particle (Szekely and Evans, 1971), considering the porous phase as pseudohomogeneous, with a local concentration of accessible surface per unit volume that determines the local reaction rates of the solids. Although in many cases the shrinking core model was proven to approximate the results of the continuous models quite or reasonably well (Ishida and Wen, 1971;Do, 1982), non-negligible errors can result when it is not used properly (Melchiori and Canu, 2014). Several authors (Sadhukhan et al, 2010;Niksiar and Rahimi, 2009;Patisson and Ablitzer, 2002) agree that the accuracy of more detailed continuous models is needed to achieve a proper description of gas-solid reacting systems.…”

Kinetics of Multi‐Step Redox Processes by Time‐Resolved In Situ X‐ray Diffraction

“…The shrinking core model, commonly applied for solid-gas reactions [19,20], is a topo-chemical model based on the assumption of spherical particles with a spherical front of reaction during transformation, as is also applied for solid-solid reactions [21]. The shrinking core model, commonly applied for solid-gas reactions [19,20], is a topo-chemical model based on the assumption of spherical particles with a spherical front of reaction during transformation, as is also applied for solid-solid reactions [21].…”

“…Since the main focus of this work is to illustrate the extraction of kinetic information for multi-step solid-solid processes from in situ XRD, a shrinking core model is applied for each phase transformation. The shrinking core model, commonly applied for solid-gas reactions [19,20], is a topo-chemical model based on the assumption of spherical particles with a spherical front of reaction during transformation, as is also applied for solid-solid reactions [21]. Eq.…”