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.

This work presents an application of Mixed-Integer Linear Programming (MILP) in the efficient management of water resources for urban supply. Based on the analysis of recent studies, the model by Korotaj and Vašak was selected, which addresses the predictive control of water distribution systems through sequential linear programming. The study was adapted and formulated as a linear optimization problem with binary variables representing pump activation decisions and continuous variables for flow rates, tank levels, and losses. The implementation was carried out in the GAMS environment using fictitious data to simulate operational conditions of a simplified system composed of one tank and two pumps in parallel. The objective was to minimize the total cost, considering time-varying electricity tariffs and costs associated with water losses. The results showed that the model found operational strategies that prioritize the use of stored volume, activating pumps only when necessary, ensuring adequate tank levels, and minimizing operational costs.