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The modeling of flow and heat transfer in porous media systems have always been a challenge and, the extended Darcy transport models for flow and equilibrium and non-equilibrium energy models for heat transfer are being used for macro-level analysis, however, the limitations of these models are subjected to porous geometry. The forced convective flow of an incompressible viscous fluid through a channel filled with four different types of porous geometries constructed using the Triply-Periodic-Minimal-Surface (or TPMS) model, are presented in this study. Four TPMS lattice shapes namely; Diamond, I-WP, Primitive, and Gyroid are created with identical porosity, and three different types of porous media are further generated for each porous geometry to investigate the relationship of shape-tortuosity, microporosity, and pore size on permeability and inertial drag factors. A pore-scale direct numerical simulation approach is performed for the first two types of porous media by solving the Navier-Stokes equations. The specific microporosity is quantitatively induced in the solid region where Darcy-Forchheimer-Brinkman model is solved, whereas the Navier-Stokes equations is solved for the fluid region in the third type of porous media. The results reveal that the validity of Darcy flow regime is very narrow up to Re ~ 4 for the Primitive lattice (Type 1) while for Diamond lattice (Type 2), it extends up to Re ~ 20. For Re > 20, Darcy regime is not valid for any lattice types. For lower porosity (Type 1, ε = 0.32) the inertial drag is found to be minimum in I-WP lattice and maximum in Gyroid lattice while, for higher porosity ( Type 2, ε ~ 1), Primitive lattice has minimum and I-WP lattice has maximum value of inertial drag, respectively.