An accurate numerical model is proposed to simulate flow through cylindrical fixed-bed reactors with randomly packed porous non-spherical particles. The length scale for flow outside the porous particles (made of open-cell foam) is O(10(2)) higher than the size of the internal micro-pores of the particles. To capture the flow at these two different length scales, a multiscale modeling approach, derived using volume averaging theory (VAT), is developed. The flow through and around the porous particles is computed as a single hydrodynamic field in a Cartesian computational domain. The flow within the inter-particle space is fully resolved, whereas, flow at the scale of the intra-particle micro-pores is not resolved and instead represented by closure terms. Random packings of cubic and cuboid particles in cylindrical columns of different diameter are generated using a glued-sphere Discrete Element Method (DEM) approach. The packing structures for different particle-column combinations are analysed. The effects of particle size/shape, column diameter and internal porosity of the particles on the overall pressure drop and flow distribution are investigated. The macroscopic Reynolds number (based on the particle equivalent diameter and the superficial velocity of the bed) is varied from 0.1 to 400. The effect of Reynolds number on pressure drop is analyzed, as well as the reduction in pressure drop due to the presence of the intra-particle pores. In addition, our numerical simulations have helped to elucidate the detailed fluid-solid interaction in complex bi-disperse, dual porosity porous media.