Semi-analytical expressions for the concentrations and effectiveness factor for the three general catalyst shapes

In this contribution, a Langmuir–Hinshelwood–Hougen–Watson (LHHW) type kinetic model is discussed for simple one-dimensional geometry of porous catalysts such as a sphere, infinite cylinder, and flat pellets. The system is described in finite-range Fickian diffusion and nonlinear reaction kinetics to produce a nonlinear reaction–diffusion equation. This paper aims to employ efficient and reliable approximate analytical methods to derive semi-analytical expressions for species concentrations and the effectiveness factor for the underlying kinetic model. The accuracy of the derived approximate analytical expressions of the concentrations is validated by directed comparison with derived numerical simulations. The analytical expressions will simplify investigating the effect of various parameters on the concentration and effectiveness factor.