Improved formulations for coupled convection-difusion with exorthemic reaction in packed beds

This work presents an improved pseudo-homogeneous formulation for fixed-bed catalytic reactors with exothermic reactions. The standard two-dimensional model is reformulated using the Coupled Integral Equation Approach (CIEA) to obtain an optimized 1.5 D model, which is subsequently solved through the Generalized Integral Transform Technique (GITT). Unlike purely numerical methods subject to mesh dependency, the proposed hybrid approach offers an efficient analytical-numerical procedure where accuracy is controlled solely by the truncation orders. Initial analysis indicated that N = 20 eigenvalues were sufficient for the GITT convergence, under diffusion-dominated conditions. The study demonstrates that the CIEA formulation remains valid for Biot numbers up to 10, effectively incorporating radial gradient effects into the axial distribution. This capability allows for precise predictions of the thermal hotspots, elucidating a critical role of reactor design. Results indicate that lower aspect ratios promote better axial heat distributions, mitigating hotspots even at constant Peclet numbers, an insight frequently lost in standard lower-dimensional models. Comparison against a purely numerical method, the Method of Lines (MOL), indicates relative errors below 0.2% in critical regimes. This work provides a physically consistent and highly efficient tool for reactor engineering, proving that limiting the computational cost does not require compromising the physical description of the problem.