Abstract
This paper presents a dimensionless reaction–diffusion–energy model for a non-isothermal fixed-bed reactor. The model integrates chemical kinetics, mass transfer, heat transfer, and wall heat exchange within a unified framework. It is formulated in terms of dimensionless parameters, including the Damköhler, Peclet, Lewis, and Biot numbers, enabling the analysis of coupled transport and reaction processes within a consistent parametric space. To evaluate the stability of operating regimes, an integral energyefficiency index ne is introduced, quantifying the balance between heat generation and heat removal. Numerical results show that increasing the Damkohler number enhances conversion but also intensifies temperature gradients. Higher temperature sensitivity leads to stronger thermal feedback and the formation of pronounced temperature maxima. An optimal operating region (Da=2) is identified, where ne reaches a maximum (0.74–0.76), indicating that maximum conversion does not coincide with maximum energy efficiency. Model validation against data from an industrial phosphine oxidation reactor shows deviations within 5–7%, confirming its predictive capability. The proposed approach can be used for reactor design, optimization, and thermal regime analysis, providing a computationally efficient alternative to more complex models while preserving physical fidelity.