Noncatalytic reaction of a bed of pellets made from solid powder particles with gaseous reactant was modeled mathematically. Gaseous reactant diffusion through the pores made between powder particles and reaction on powder surfaces was considered in modeling. Three solution techniques, finite difference, finite volume, and orthogonal collocation, were used to solve the governing equations. The capability of these methods was studied for a wide range of chemical reactions and flow conditions through defining three exemplary cases that were obtained using different values for effective diffusivity through the pellet, Thiele modulus, and superficial velocity of the reacting gas entering the reactor.