SHAPE GENERALIZED ISOTHERMAL EFFECTIVENESS FACTOR FOR FIRST-ORDER KINETICS

A generalized effectiveness factor equation (Eq. (32)), in terms of modified Bessel functions, is derived for a catalyst pellet of arbitrary shape. The derivation is based on utilizing an appropriate one-dimensional approximation for the Laplacian in an arbitrary shaped body subjected to a uniform external concentration field. The comparison of the result with the available expressions for various geometries is highly satisfactory. It unifies the expressions for the three fundamental shapes, viz., infinite slab, infinite cylinder and sphere, and also compares very well with the exact solutions for finite shapes over the entire range of the Thiele modulus.