Estimation of Thiele Module and Effectiveness Factor. Theoretically, the Thiele module (Φ = R(kγ/Dm)1/2) can be calculated for the given particle diameter, reaction rate constant, and effective diffusivity of gases. In the current study, kr can be estimated by eliminating internal diffusion using very fine sawdust particles. For a given particle pore size, the diffusivity of volatiles, Dm, can be first approximated by the Knudsen diffusion coefficient, Dk, from