Abstract There has been a growing trend to couple different levels of modelling, such as going from first-principle calculations to the meso (e.g. kinetic Monte Carlo - KMC) and macro scale (e.g. computational fluid dynamics - CFD). In the current investigation, we put forward a CFD study of CO2 hydrogenation to methanol for heterogeneous reacting flows in reactors with complex shape geometries, coupled with first-principle calculations (density functional theory - DFT). KMC operation simulations were also performed to obtain insight into the uppermost layer conditions during the reaction. With computational fluid dynamics, the focus was placed on the non-uniform catalytic reduction of carbon dioxide to formate, which we treated with a detailed mean-field first-principle microkinetic model, analysed, and corroborated with experiments. The results showed a good consistent agreement with experimental data. The formulated methodological approach paves the way towards full virtual multiscale system descriptions of industrial processing units, encompassing all conventional stages, from catalyst design to the optimization of mass transfer parameters. Such a bridging is outlined for carbon capture and utilization.