Mean Velocity Calculation for Single-Phase Flow in Porous Media Based on Minkowski Functionals

Studies of flow dynamics in complex disordered media are very important in many practical areas, such as materials science, soil science, groundwater engineering, chemical engineering, and especially petroleum and gas engineering. Integral geometry methods are a useful tool for studying complex media. In this work, it is shown that, for a given porous media class, the by-layer mean flow velocity for any sample within the same class can be characterized as a function of Minkowski functionals, allowing to avoid costly natural core flood experiments or numerical simulation for screening purposes. This paper proposes the flow characterization method based on integral geometry. This method allows for obtaining the single-phase fluid flow velocity characterization models across a wide range of porous media classes for a quick estimation of the mean by-layer velocity distribution purely by extracting the geometrical measures from binary sample images. Samples from gas reservoirs are chosen as the relevant porous media examples, with regard to the growing importance of this type of reservoir caused by the global shift towards natural gas as a key energy source. Direct comparison with numerical simulation based on Stokes equation was made with commercial class software. The results demonstrate that the proposed algorithm has a relatively high degree of statistical significance and closely captures mean velocity trends. That provides a useful tool for quick, robust modelling for screening, agile calculations, and upscaling tasks.