A Novel Multi-Scale Heat and Mass Transfer Framework for Packed Bed Reactor-Based CO2 Hydrogenation to Methane and Methanol: Insights into Transport Phenomena, Catalyst Effectiveness, and Reactor Performance

<jats:p>The catalytic hydrogenation of carbon dioxide (CO2) has emerged as a promising carbon utilization strategy for the sustainable production of methane and methanol, thereby facilitating the transition toward a low-carbon energy economy. The performance of packed bed reactors employed for CO2 conversion is strongly governed by the interaction of hydrodynamic behavior, heat transfer, mass transfer, and catalyst effectiveness. Consequently, a detailed understanding of transport phenomena is essential for optimizing reactor design, improving catalyst utilization, and ensuring efficient industrial-scale operation. In the present study, a comprehensive heat and mass transfer analysis of a fixed packed bed reactor loaded with Ni/Al2O3 catalyst is performed under representative operating conditions for CO2 hydrogenation. Hydrodynamic characteristics are evaluated through pressure-drop estimation using the Ergun equation, while bed porosity, bulk density, residence time, gas hourly space velocity, and axial dispersion effects are systematically investigated. The study further examines internal and external mass transfer mechanisms through the determination of effective diffusivity, Knudsen diffusivity, combined diffusivity, pore diffusion time, Sherwood number, mass transfer coefficient, mass Biot number, Thiele modulus, and catalyst effectiveness factor. Heat transfer behavior is analyzed using the Reynolds, Prandtl, Nusselt, Biot, and thermal Peclet numbers together with the overall heat transfer coefficient and thermal resistance network. The calculated results indicate negligible intraparticle diffusion resistance, near-complete catalyst utilization, low pressure losses, and efficient thermal distribution within catalyst pellets. Furthermore, the relative contributions of diffusion, convection, and conduction are quantified to identify the dominant transport mechanisms controlling reactor performance. The engineering significance of each dimensionless parameter is critically examined to establish direct links between transport phenomena and reactor productivity, thermal stability, reactant conversion, and process scalability. The findings provide valuable guidelines for the design, optimization, and scale-up of packed bed reactors intended for CO2 methanation and methanol synthesis applications. The developed analytical framework offers a robust foundation for future investigations involving advanced reactor modeling, process intensification, renewable hydrogen integration, and industrial carbon capture and utilization technologies.</jats:p>