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Transient responses of reaction–desorption process were predicted from mathematical solutions of modeling equations for CSTR (continuously stirred tank reactor) containing core–shell adsorbent particles. Analytical solutions on the core–shell particles were derived for core–shell spherical, cylindrical, and slab-type morphologies, assuming inert-cores. Unlike continuous adsorber, CSTRs for reaction–desorption process containing spherical particles exhibited the slowest reduction rate of concentration of adsorbate, because the amount of adsorbed component on the particles is the largest among three kinds of particle shapes. Factors affecting the transient concentration in bulk medium of reaction–desorption process were investigated by adjusting inert-core thickness, inlet flow rate, initial concentration of reactant in inflow stream, amount of adsorbent, and Thiele modulus. Concentration profile inside the particles as well as average intra-particle concentration could be also predicted for comparison with bulk concentration of CSTR. For non-linear isotherm and non-linear reaction kinetics, concentration of active component could be predicted by solving non-linear coupled differential equation using finite element method. For connected CSTRs in series, systems of reaction-diffusion equations were solved by finite element method to study the effect of number of connected reactors. When the number of reactors was sufficiently large, the reactor system could be approximated to fixed bed reactor for reaction–desorption process.

Modeling of reaction–desorption process by core–shell particles dispersed in continuously stirred tank reactor (CSTR)