In petroleum, geological and environmental science, flow through porous media is conventionally studied complementarily with numerical modeling/simulation and experimental corefloods. Despite advances in numerical modeling/simulation, experimental corefloods with actual samples are still desired for higher-specificity testing or more complex mechanistic studies. In these applications, the lack of advances in physical modeling is very apparent with the available options mostly unchanged for decades (e.g., sandpacks of unconsolidated packing materials, industry-accepted substitutes with fixed/mismatching petrophysical properties such as Berea sandstone). Renewable synthetic porous media with adjustable parameters are the most promising but have not advanced adequately. To address this, a methodology of advanced physical modeling of the fundamental parameters of dominant mineralogy, particle size distribution, packing, and cementation of a target natural porous media is introduced. Based upon the tight physical modeling of these four fundamental parameters, the other derived parameters of interests including wettability, porosity, pore throat size distribution, permeability, and capillary pressure can be concurrently modeled very close as well by further fine-tuning one of the fundamental parameters while holding the rest constant. Through this process, concurrent multi-parametric physical modeling of the primary petrophysical parameters including particle size distribution, wettability, porosity, pore throat size distribution, permeability, capillary pressure behavior in a target sandstone becomes possible.