The pore diffusion model that describes unsteady-state adsorption, diffusion, and reaction in a porous catalyst is in the form of a parabolic partial differential equation. To relieve computational loads, approximate ordinary differential equations are often used and they can be derived from the transfer function between the surface and average concentrations in the particle. The transfer function shows half-order behaviors at the high-frequency range. The rational transfer functions cannot describe well this half-order behavior. Here, introducing the half-order term to rational transfer function candidates for approximation, models valid throughout low- and high-frequency ranges are derived. Since the proposed approximate models are valid globally, they can be applied to reactive porous catalysts easily. They can also be used for noninteger shape factors that will show better performances for adsorbents different from ideal geometries of infinite slab, infinite cylinder and sphere, and for biporous adsorbents. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2540-2548, 2013