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 $0.4<T_h<4$. Therefore, the effectiveness factor analyzed is between 1 and $1/T_h$; 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.

The textile industry is known for its excessive water consumption and environmental impact. One of the major challenges it faces is managing pollution generated by dyes, particularly bifunctional dyes, such as sumireact supra yellow s-hbu, with a red appearance and sumifix supra lemon-yellow e-xf, with a yellow appearance. This study aimed to investigate the decolorization kinetics of synthetic solutions of said bifunctional dyes, which comprise triazine and vinylsulfon. We conducted various tests, including modifications of pH, the addition of TiO₂ P-50 nanoparticles, exposure to solar radiation, limited contact with oxygen, and eolic agitation. The initial solutions had a concentration of 1000 ppm of textile dye. The study showed that the reaction order for the “red” solutions in the R6 and R9 reactors and all the yellow solutions was ½. The concentration of nanoparticles and pH had a significant impact on the reaction rate. The yellow solutions with a concentration of 800 ppm and pH levels of 3.15, 4.13, and 2.25 demonstrated 100% color discoloration, followed by solutions with a concentration of 400 ppm and pH levels of 3.15, 2.25, and 4.13. The analysis of variance confirmed the reaction rate constants for the yellow solutions and emphasized the significance of pH in this process.

The objective of this research is to find the effectiveness factor of the catalyst particles for the most favorable conditions of the phthalic anhydride production in a fixed bed reactor, with the aim of achieving the highest rate of phthalic anhydride production compared to other secondary products and analyzing the areas of lower effectiveness for the modification of the reactor design. Initially, the material and the energy balances in the catalytic bed are solved to obtain the concentration and temperature profiles based on the radius and length of the reactor, using polymath software(Polymath^® v6.2 Software Minitab 19 Matlab 2019) with the data from literature. Once the profiles reproducibility was verified using the initial data (inlet temperature, pressure in the reactor, reactor wall temperature, reactor radius and mass flow rate) the experimental design 3⁵ carry out, which generates 243 “experiments”, whose response variable (phthalic anhydride concentration) was obtained using Matlab. Subsequently, the variables were analyzed using the Minitab 18^® that, through the response surface analysis method, allowed us to obtain the optimal values of the tested variables. Then, Subsequently, material and energy balances coupled with Fourier and Fick’s laws, along with the effectiveness factor equation, were applied, resulting in the generation of 9 coupled differential equations. Upon implementing the finite difference method, this yielded 90 nonlinear algebraic equations, which were solved using the Polymath software. A total of 78 particles were preselected based on their radial and axial positions to determine the effectiveness factor profile, with values ranging from 0.83 to near unity. The lower values correspond to the points with higher temperature, as evidenced by the calculations performed.