•Developed a multi-scale Computational Fluid Dynamics (CFD) model for analysing catalytic heterogeneous reactions within porous monoliths.•Conducted pore-scale simulations to study flow and concentration profiles for optimized design. In this research work, a multi-scale CFD model is developed for a catalytic heterogeneous reaction under continuous flow in a porous monolith. For this purpose, the Knoevenagel condensation was chosen as a model reaction. The model is based on a homogenization approach as well as pore scale modelling by coupling convection, diffusion and reaction within macro-meso porous hierarchical monoliths. The model's accuracy was determined through successful validation against previously available experimental data in the literature. Subsequently, the model was employed to examine the influence on reaction rates of structural and key process parameters like temperature, flow rates and macro/meso porosity. To analyze flow patterns and concentration profiles at the macro pore level, pore-scale simulations were conducted through image processing and CFD modeling of 25x25 µm Scanning Electron Microscopy (SEM) images of the monoliths. These simulations yielded an in-depth comprehension of pore flow and concentration behavior at the macro-meso level, offering valuable insights for optimizing pores in hierarchical structures.