The objective of this thesis is the development of an integrated methodology for the design and construction of synthetic porous structures that bear the same microscopiccharacteristics with sandstone, as well as their laboratory characterization in terms of their permeability. Initially, an inhouse software developed at the Applied Fluid Mechanics Laboratory of the School of Mineral Resources Engineering was used to stochastically reconstruct 3D digital structures based on well-established porosity spatial distributionalgorithms in combination with commercially available stereolithography file design programs to design samples of geological porous media at the pore-scale. The digital domains were designed with different values of three characteristic parameters: the porosity, the spatial correlation length of the solid phase, and the spatial correlation pattern. A 3D printing (additive manufacturing) methodology based on the photopolymerization of a suitable resin was used to fabricate 3D porous structures with the above well-defined characteristics. The printed 3D structures were then characterized in our laboratory in terms of their Darcy permeability using a flow setup combining a precision pump and differential manometer with a very good measuring resolution. By comparing the measured permeability values with the values predicted by theoretical models and literature data, it was found that this approach is suitable for the design of porous domains with excellent control over their microscopic features in order to construct geological pore models with tunable macroscopic properties. Our study demonstrated a good convergence between the theoretically expected permeability values and the laboratory measured values of the samples.