Tortuosity and mass transfer limitations in industrial hydrotreating catalysts: effect of particle shape and size distribution

The tortuosity factor of -alumina supports and catalysts used in hydrotreating applications was evaluated in the liquid phase with three different techniques: pulse field gradient-NMR (PFG-NMR), inverse liquid chromatography (ILC) and catalytic experiments in a batch reactor. In order to satisfy the specific experimental constraints associated with each technique, tortuosity factors were evaluated in a wide range of operating conditions: temperature was varied from 295 K to 613 K, catalyst particles were used as-synthesized (trilobe extrudates) or crushed, and the liquid composition was either pure toluene, n-heptane/squalane mixtures, or squalane/2,5-bis-(octadecyl)thiophene mixtures. It is demonstrated that not taking into account both the shape factor and the size distribution of the particles can lead to significant errors in the tortuosity factor. For both parameters, the optimal mean spherical radius depends on the contribution of internal diffusion to the overall performance. When internal diffusion is the limiting step, a new expression for the mean radius of the distributed particle is proposed and validated by comparison between ILC and PFG-NMR results. This expression is transposable to any catalytic system, making it possible to measure the tortuosity factors using either microscopic or macroscopic methodologies. Moreover, the tortuosity factors obtained with ILC and NMR are in good agreement with the one estimated from the catalytic experiments, showing that mass transfer parameters can be extrapolated from non-reactive to reactive conditions.