Mathematical models for the mechanical properties of a CoMoP/AI0 hydrotreating catalyst in the sulfidation process are developed with response surface methodology, A Doehlert design is performed tocollectively study the effects of sulfidation temperature, time and heating rate on the mean strength, Weibull modulus and pellet density, Analysis of variance reveals that the models developed for the mean strength and Weibull modulus are adequate, The validity of the models is also verified by experimental data, Analyses of response surfaces show that in the great part of the experimental domain examined, as the sulfidation temperature increases the mean strength decreases, while the Weibull modulus increases at first and then decreases, The middle level of the sulfidation time results in smaller mean strength and higher Weibull modulus, The Weibull modulus decreases with increasing heating rate; however, the effect of the heating rate on the mean strength is statistically less pronounced, It is concluded that there is a great potential for improving the catalyst mechanical reliability in the sulfidation process, while the pellet density does not vary significantly.

The mechanical strength of solid catalysts is distributed over a wide range of values. The suitability of the normal, lognormal and Weibull distributions to model the catalyst strength variation was judged by three goodness-of-fit criteria: the coefficient of determination, Akaike information criterion and Kolmogorov–Smirnov test. It is concluded that the Weibull distribution is most universal to represent the catalyst strength data, though sometimes it may not be the optimal candidate. It is elucidated that the catalyst strength variation results from the brittle fracture nature of the mechanical failure of solid catalyst materials. The low-strength/probability part of the catalyst strength distribution is the key domain for the mechanical reliability, while the mean strength that has traditionally been taken as a measure of the catalyst strength is of less importance. It is also pointed out that a mechanical strength distributed in a narrow window, i.e., with a high Weibull modulus, is beneficial to industrial applications of solid catalysts.