Dynamic response of an isothermal three-phase slurry reactor—II. The PM-PM-HS/ID model: analytical solutions for two kinds of batch operation

Abstract

The dynamics of an isothermal batch, three-phase slurry reactor with a first-order reaction occurring in uniform spherical catalyst particles have been investigated. Two kinds of batch operation were considered: variable and constant reactant concentrations in the gas phase. Analytical solutions were presented in both cases. The solutions are based on the PM-PM-HS/ID model, which considers perfect mixing (PM) in both gas and liquid phases, homogeneous suspension (HS) of the catalyst particles, and intraparticle diffusion (ID). The solutions are valid for any mode of input perturbation with non-negative and constant initial conditions. For an input perturbation with which the catalyst particles are suddenly introduced into the reactor after the gas and liquid are in equilibrium, the gas reactant in the liquid phase reveals two responses for both kinds of batch operation. In the case of constant gas reactant in the gas phase, the critical condition which distinguishes two responses can be expressed explicitly, and is independent of liquid—solid mass transfer coefficient and intraparticle diffusion coefficient. This makes it possible to determine experimentally the rate constant from the critical condition without evaluating these two mass transfer processes simultaneously.