Exploring Nonlinear Reaction Kinetics in Porous Catalysts: Analytical and Numerical Approaches to LHHW Model

Abstract

The article examines a mathematical model for porous catalysts incorporating nonlinear reaction kinetics. Central to this model is the nonlinear steady-state reaction-diffusion equation. The Taylor series method derives the analytical solution for species concentration in various nonlinear Langmuir-Hinshelwood-Haugen-Watson (LHHW) models, each characterized by distinct fundamental rate functions. From this analysis, we derive both straightforward and approximate polynomial expressions for concentration and effectiveness factors. Furthermore, we compare numerical simulations to the analytical approximations, demonstrating a strong correlation between the numerical results and theoretical predictions. We also compute the concentration and effectiveness factors for the LHHW-type models. The analytical solutions offer valuable insights for optimizing catalytic and biochemical system designs, such as fixed/fluidized-bed reactors, fuel cells, and catalytic converters. They support advances in sustainable chemical production, wastewater treatment, biomedical devices, and energy systems. These results reduce reliance on trial-and-error methods, enabling cost-effective scale-up and improved catalyst longevity. Overall, the findings align well with the aim of statistics, optimization, and information computing for efficient system modeling and design.