Abstract
An approximate analytical expression for estimating the effectiveness factors of non-catalytic gas-solid reactions is proposed. The new expression is derived from the analytical solution for simple first order reactions (Ishida and Wen 1968. Comparison of kinetic and diffusional models for solid-gas reactions. AIChE Journal 14, 311–317. http://dx.doi.org/10.1002/aic.690140218). The scaled Thiele modulus concept is introduced to account for the variations of the reaction rate form that differs from the first order. The validity of the new expression is demonstrated for the reactions of different orders and of different forms via comparisons against a complete particle-reactor model using the collocation method for solving heat and mass fluxes inside the particles. In addition, the proposed approach is applied to redox reactions of ferric oxide where non-isothermal condition, net consumption of gaseous reactant, and parallel reactions are encountered. The results show that the effectiveness factor method compared well with the orthogonal collocation method over a wide range of Thiele moduli, reaction orders and reaction forms. Therefore, the proposed expression can serve as a generic replacement for more complex and computationally expensive combined particle-reactor modelling which is often employed in reactor systems with significant intra-particle diffusion resistances.
