Modeling of multicomponent mass diffusion in porous spherical pellets: Application to steam methane reforming and methanol synthesis

The main purpose of this paper is the derivation and evaluation of various diffusion flux models. For this aim, a comprehensive catalyst pellet problem has been simulated for two test cases: the steam methane reforming (SMR) and the methanol synthesis, as these two important chemical processes cover various aspects of a chemical reaction. The pressure, temperature, total concentration, species composition, viscous flow, mass and heat fluxes within the porous spherical pellet are included in the transient pellet model. Mass diffusion fluxes are described according to the rigorous Maxell–Stefan and dusty gas models, and the respectively simpler Wilke and Wilke–Bosanquet models. Simulations are performed with these fluxes defined according to both the molar averaged and mass averaged definitions. For the mass based pellet equations, a consistent set of equations is obtained holding only the mass averaged velocity. On the other hand, the closed set of molar based pellet equations hold both the molar averaged and mass averaged velocities as the fundamental energy balance and the momentum balance (Darcy law) are derived according to the mass averaged velocity definition, whereas the diffusion fluxes are defined relative to the molar averaged velocity. Identical results of the molar and mass based pellet equations were not obtained; however, the deviations are small. It is anticipated that these discrepancies are due to some unspecified numerical inaccuracies. However, efficiency factors have been computed for both processes and the values obtained compare well with the available literature data. Furthermore, efficiency factor sensitivity on parameters like pore diameter, tortuosity, temperature and pressure have been accomplished, and the classical simplifications of the pellet equations have been elucidated: isothermal condition, constant pressure, and neglecting viscous flow. The following conclusions are established for the reactor operating conditions used in the present work. The methanol synthesis: The simulation results of the methanol synthesis indicate that the classical assumptions are very fair for this process. Moreover, both Wilke and Wilke–Bosanquet models are good replacements for the more rigorous Maxwell–Stefan and dusty gas models. However, the simulation results are affected by Knudsen diffusion, thus the diffusion flux is most appropriately described by the Wilke–Bosanquet model. The SMR process: Knudsen diffusion hardly influences the results of the highly intraparticle diffusion limited SMR process. As the Wilke model does not necessarily conserve mass, we recommend the Maxwell–Stefan model because the simpler Wilke closure deviates with several percents. However, it is not elucidated whether these deviations are numerical problems arising from the large gradients of this process, or related to the choice of diffusion model. Isothermal and isobaric conditions can be assumed within the particle, but significant external temperature gradients are observed. Convective fluxes are much less than the diffusive fluxes, hence viscous flow can be neglected.