Analytical solutions of sharp interface models with nth order kinetics. Application to char conversion

Abstract

When a reaction occurs in a narrow layer of a porous particle, it is practical to simplify the calculation of the reaction rate by assuming global kinetic parameters based on the surface of the reaction front. The assumption of such simplified situation allows formulation of a sharp interface model (SIM). Though, there are three difficulties for the application of a SIM in reactor simulations: (1) No analytical solution is available for general SIM with nth order kinetics with respect to gas reactant. For reactor model simulation, with a variety of particles and operating conditions, a numerical model is still necessary to be applied, leading to numerical difficulties and time consumption; (2) The global surface kinetic coefficient is not a priori known. The reason is that this coefficient depends not only on the intrinsic reactivity, but also on physical factors such as the size and density of the solid, as well as operation conditions of the reactor like gas reactant concentration and temperature, varying during conversion of the particle; (3) The SIM is applicable when chemical reaction is rapid compared to intraparticle diffusion because in this situation the reaction occurs within a narrow region compared to the size of the particle. However, no quantitative criteria has been developed to delimit the conditions for application of SIM. In the present work these questions are answered. Char conversion (combustion and gasification) is taken as reference, but most conclusions are applicable to isothermal non-catalytic gas–solid irreversible reactions with a single gaseous reactant.