Modeling of Hollow Cylindrical Catalytic Pellets – Analytical Solutions for First Order Reaction

Abstract

Mathematical modeling of catalytic reaction was performed for hollow cylindrical pellets with infinitely long or finite length. For isothermal irreversible first order reaction, intra-particle concentration could be predicted from analytical solutions obtained by solving reaction-diffusion equations. Both intra-particle diffusional and surface film resistance were considered in the modeling equations. Factors affecting distribution of reactant concentration inside hollow cylindrical pellet surrounded in infinitely large medium were studied by adjusting thickness of hollow core (x’), aspect ratio (γ0), Thiele modulus (Φ), and Biot number (Bi). Transient concentration inside hollow cylindrical pellet with infinitely long and finite length was also derived by solving unsteady-state partial differential equation using separation of variables and eigenfunction expansion method, respectively. Analytical solutions could be also derived for effectiveness factor (η), which was increased with increasing x’ and decreasing γ0 due to decrease of active volume of the pellet. For hollow cylindrical pellet with finite length, η was derived as two different mathematical expressions, which are advantageous to evaluate eigenvalues for various x’ or γ0. For series reaction (A→B→C), secondary effectiveness factor (ηB→C) was derived for hollow cylindrical pellet for the first time to apply pseudo steady-state approximation for batch and fixed bed reactors. The performance of the catalytic reactors was predicted for consecutive reaction by adjusting x’ and Φ. Maximum concentration of intermittent product in batch reactor could be increased using hollow cylindrical pellets, compared to conventional cylindrical pellets. For simple reaction (A→B), transient concentration of reactant in exit stream was also predicted for fixed bed containing hollow cylindrical pellet with finite length. Reaction conversion at steady state was enhanced using the hollow pellets with smaller γ0, while pressure drop in bed was reduced, compared to conventional cylindrical pellets.

Keywords

• Hollow catalytic pellets
• Effectiveness factor
• Series reaction
• Batch reactor
• Fixed bed