A mole based pellet model has been formulated to describe the evolution of species mole fraction, pressure, velocity, total concentration, temperature and mole diffusion flux in porous pellets for the steam methane reforming (SMR), sorption-enhanced steam methane reforming (SE-SMR) and desorption processes. In the case of molar based pellet model, a rigorous analysis reveals that both the mass- and mole averaged velocities occur in the equation system. On the other hand, the mass based counterpart contains only the mass averaged velocity. The effect of velocity definition inconsistency is elucidated in this work. The gas-solid reactions taking place within the reactive particles for the SE-SMR process, make the sorption micro-particles grow during the reaction process due to the solid formation, thus the pellet void-fraction is reduced as the reaction proceeds. This effect may reduce the effective reaction rate due to increased diffusion limitations. The changes in void-fraction is taken into account in the proposed pellet model for the SE-SMR- and desorption processes. The reaction efficiency factors determining the diffusion limitations of different reactions in the SMR-, SE-SMR- and desorption processes are calculated by the proposed pellet model, and used in the pseudo-homogeneous fixed bed reactor model. The effects of pressure, steam to carbon ratio, inlet temperature variation and inlet gas flow rate on the reactions were studied on the fixed bed reactor level. The objective of this work is to perform a numerical study elucidating the effects of the operational conditions by introducing a one-pellet design; one pellet holding both catalytic and sorbent properties, with application to the SE-SMR process in the fixed bed reactor. It is assumed that the carbonation reaction is kinetics controlled, neglecting the product layer diffusion effects. However, the porosity changes due to the solid product formation are considered. The later effect influences on the internal limitations. The SE-SMR process is not completely chemical kinetics controlled, as the internal diffusion limitations are significant due to the porosity variation. The approximate values of the efficiency factors for carbonation reaction is around 0.81 and for the desorption it is around 0.017. The mole based pellet- and fixed bed reactor models were used to evaluate the potential of carbon formation across the pellet and in the bulk gas phase of the fixed bed reactor. There is no solid carbon formation within the pellet or in the bulk phase of the reactor with steam to carbon ratio of 3.5. (c) 2012 Elsevier B.V. All rights reserved.