Analysis of the Effectiveness Factor in a Fixed-Bed Tubular Reactor System: Catalytic Dehydrogenation of Cyclohexanol

Abstract

The modeling and simulation of the catalytic dehydrogenation process of cyclohexanol in a fixed-bed catalytic reactor is presented, leading to finding the relationship between the effectiveness factor, the Thiele modulus, and the Weisz–Prater modulus of the catalyst particles with respect to their axial and radial position, for which the external conditions of concentration and temperature around each particle were previously obtained by applying the material and energy balances in the catalyst bed considering a two-dimensional pseudo-homogeneous model with radial diffusion. Subsequently, the material balances are established in terms of the molar flux density and conversion, the energy balance in terms of the heat flux density, Fick’s law, Fourier’s law, and the differential form of the effectiveness factor non-isothermal for each particle chosen based on the proposed meshing. The Thiele modulus calculated for most of the points is between 0.8 and 0.25, with a tendency towards the lower limit, and the theoretical values established as the limit for the Thiele modulus fluctuate between 0.4<Th<4. Therefore, the effectiveness factor analyzed is between 1 and 1/Th; this indicates that both the reaction speed as well as the diffusion speed within the particle have an influence on the intraparticle process, which is confirmed by the calculation of the Weisz–Prater modulus whose values are not <<1 nor >>1. The results obtained are subjected to a statistical test leading to analyzing whether there are significant differences both in the Thiele modulus, as well as in the effectiveness factor with respect to the radius and length of the reactor. It has been determined that there are no significant differences between the effectiveness factor with respect to the radius of the reactor; however, according to the analysis of variance, there are significant differences in the effectiveness factor with respect to length and, likewise, there are significant differences in the Thiele modulus and the Weisz–Prater modulus with respect to radius and length.