Modelling combined diffusion and surface resistances in adsorbent particles: zero length column for spherical and slab geometries

Mass transport in nanoporous materials is a key property that allows to improve the performance of many gas separation processes and design more efficient heterogeneous catalytic reactors. In many instances a combination of surface resistance and internal diffusion are present. The combined model for surface barrier and diffusion in a ZLC system is discussed in detail and the analytical solutions valid for the traditional and the partial loading experiments have been derived for the spherical and slab geometries. The model reduces to the limiting forms of pure diffusion when \(\frac{k{R}_{p}}{D}>100\), and pure surface barrier when \(\frac{k{R}_{p}}{D}<1\). This study has shown that most literature studies have analysed ZLC responses incorrectly based on an effective combined dimensionless parameter. Two methods are described to obtain the parameters from the long-time asymptotic behaviour of the response curves. Both approaches have been demonstrated on curves generated from the full model solution and experimental data on an etched sample of Y zeolite. Both the analysis of the model and of the experimental results confirm that to characterize combined surface barriers and diffusion one should perform at least experiments at two different flowrates where the system is kinetically controlled, and crucially a partial loading experiment with a time to the switch which should be at least an order of magnitude smaller than the smallest of the diffusion and surface barrier times.