Isothermal effectiveness factor—I: Analytical expression for single reaction with arbitrary kinetics. Slab geometry

Abstract

An analytical simple algebraic expression for isothermal effectiveness factor (η) in a porous pellet is presented. Arbitrary kinetic expressions are investigated and the external mass transfer effect is also considered. The resulting analytical expression is found after matching asymptotic expressions of η valid for large and small values of Thiele modulus. The agreement between approximated and numerical results is surprisingly good. For most cases analyzed maximum deviation are below 3% for power law type kinetic expressions provided the reaction order is greater than 0.5. More severe limitation arises for Langmuir-Hinshelwood kinetic expressions. In actual facts the proposed analytical expressions is unable to predict effectiveness factor greater than one. Nevertheless, as will be shown in future works, this very simple procedure can be safely used to predict the effectiveness in more complex situations such as those where activity distribution must be considered or where the kinetic parameters will be function of composition and/or spatial coordinates.