Applicable Investigation of SPH in Characterization of Fluid Flow in Uniform and Non-Uniform Periodic Porous Media

Abstract

Today, the use of numerical modeling for characterizing properties of porous media and related concepts has been widely extended, especially in subsurface flow issues such as geological CO2 storage and petroleum recovery. Therefore, in this study, the fundamental problem of laminar fluid flow through uniform or non-uniform and periodic array of cylinders was functionally investigated using the smoothed particle hydrodynamics (SPH) method as a modern and applied method of modeling in order to develop the past studies and introduce a complementary numerical tool alongside laboratory methods. All modeling processes were performed in the form of dimensionless processes for generalization and applicability at different scales. The results were used to characterize properties of porous media and to investigate basic properties such as fluid velocity, permeability, streamlines, and hydraulic tortuosity. Accuracy of modeling was shown in comparison with the results obtained in the literature. In this study, the potential of the method has been investigated in order to show the ability in modeling characteristic laboratory experiments of porous media and the possibility of using it instead of them. For this purpose, three periodic models of uniform and randomly distributed non-uniform porous media with arrays of circular, square, and diamond-shaped cylinders in a porosity range of 30–95%, with different types of cylinder distribution at the pore scale, were investigated. New equations were proposed for permeability as a function of porosity. Moreover, the method of tortuosity calculation was investigated directly through the time history of properties in the SPH method, and shape factors were obtained for the studied porous media models. The results showed that the geometry of a square cylinder with distribution in a square grid led to a higher permeability than circular and diamond-shaped grids. In contrast, diamond-shaped geometry with distribution in a hexagonal grid led to higher permeability than the other two models. Furthermore, diamond-shaped geometry had higher tortuosity, and circular and square geometries had almost identical tortuosity. Increasing the size of the modeling domain and decreasing the size of cylinders (i.e., decreasing resolution) reduces effects of the shape and the geometry of cylinders and achieves the same results. Random and non-uniform distribution of cylinders within porous media reduces fluid velocity, permeability, tortuosity, and shape factor (p) compared to the uniform models.