Thiele modulus having regard to the anomalous diffusion in a catalyst pellet

In the present paper, Thiele modulus (TM) for a catalytic reaction with the anomalous diffusion of a reagent in a catalyst pellet is introduced. Different cases of the TM are considered related to the anomalous diffusion process governed by a diffusion equation with the space-fractional, time-fractional, and space-time fractional derivatives. In addition, each fractional derivative is used according to the Caputo and the Riemann-Liouville definitions. Closed-form expressions of the TM for each definition of the fractional derivative are provided. For the time-fractional derivative, the TM is obtained under the assumption of the reaction dynamics nonlinearity. We demonstrate and critically discuss the applicability of the TM obtained for the reaction-diffusion equation with non-integer order derivatives to the evaluation of the parameters of the heterogeneous catalytic process.