Palladium is an important material for separation of hydrogen from other gases, separation of hydrogen isotopes, and for hydrogen storage. Its main advantages are its high selectivity and rapid, highly reversible uptake and release of hydrogen at near ambient temperatures and pressures. Toward a more comprehensive understanding of its behavior, we present particle and continuum multiphysics mathematical models of the coupled reactive transport of hydrogen isotopes in the context of a single palladium sphere, and of flow in a packed palladium hydride bed. The models consider rates of chemical reactions and mass transport within a hydride bed, and incorporate a multistep reaction mechanism involving the metal bulk, metal surface, and gas phases. A unique feature in this formulation is that the chemical reaction model accounts for all absorption, adsorption, and diffusion activation energies. In particular, the adsorption energy is believed to depend strongly on the composition and atom-scale structure of the surface. We perform a parametric study to evaluate the effects of temperature, surface adsorption energy, and hydride particle radius on the isotope exchange kinetics. The models are useful in designing optimal hydride beds operating at various temperatures, with varied hydride particle size, and surface conditions. (C) 2014 Elsevier Ltd. All rights reserved.