General rate equation theory for gas–solid reaction kinetics and its application to CaO carbonation

Abstract

The kinetics of reactions between gases and solids are typically modeled using shrinking-core or shrinking-pore theoretical frameworks, in which the formation of a uniform solid product layer covering the entire solid surface with a sharp interface between the solid reactant and the product is assumed. However, theories involving a uniform solid product layer cannot predict the kinetic transition behavior that occurs in some gas–solid reactions. This work proposes that the growth of solid product islands occurs instead of the progressive formation of a uniform solid product layer in traditional shrinking-core and shrinking-pore models and establishes a general rate equation theory to model the kinetics of gas–solid reactions for solid reactants of various shapes. The growth of the product islands is calculated using the rate equation theory and is integrated into the shrinking-core model and shrinking-pore model, in which the microstructure of the solid reactant is also considered. Elemental steps of chemical reaction, surface diffusion and product layer diffusion are included in the general rate equation theory. The kinetic parameters included in the model are chemical reaction rate constant ks, surface diffusion coefficient Ds, and product layer diffusion coefficient Dp. The resulting model is analyzed at the limits where either the chemical reaction or product layer diffusion is the rate-controlling step. At very small or very high Ds values, the rate equation theory is equal to the kinetics-controlled regime or diffusion-controlled regime in traditional models; therefore, the traditional models represent special cases of this theoretical rate equation model. At intermediate Ds values, the so-called two-stage kinetic behavior occurs. The transition from the fast initial stage to the diffusion-controlled stage depends on the value of Ds, with the conversion at the transition point increasing with increasing Ds. The rate equation theory is demonstrated to successfully predict the CaO carbonation kinetics under a wide range of experimental conditions including temperature, CO2 concentration, sorbent type, and amount of added inert supports as well as for systems that exhibit a temperature rise during the carbonation reaction The rate equation theory is integrated into a particle model to account for the external diffusion of gas around the particle and intraparticle diffusion as well as the effect of particle structural changes on intraparticle diffusion, such as the pore plugging phenomenon. The developed rate equation theory is an analytical model that can be easily used in reactor-scale modeling or computational fluid dynamics simulations.