Lattice Boltzmann Simulation Of Non-Darcy Flow In Stochastically Generated 2D Porous Media Geometries

摘要

It is important to consider the additional pressure drops associated with non-Darcy flows in the near well bore region of conventional gas reservoirs and in propped hydraulic fractures. These pressure drops are usually described by the Forchheimer equation in which the deviation from the Darcy’s law is proportional to the inertial resistance factor ( -factor). While the -factor is regarded as a property of the porous media, detailed study on the effect of pore geometry has not been done. Many previous experiments and simulations were based on idealized systems such as packings of spheres. In this study, the effect of geometry was studied using a combination of lattice Boltzmann simulations and stochastically constructed 2D porous media models designed to simulate the geometric complexity of reservoir rocks. Based on the data obtained from about 1100 simulations run in 55 model geometries within a porosity range of 8-35%, a dimensionally consistent correlation for the -factor was established. The effect of geometry on the transition to non-Darcy flow and on the -factor was evident. It was discovered that the contrast between pore throat and pore body triggers an early transition to non-Darcy flows. Following a quick transition where the correction to the Darcy’s law was cubic in velocity, the flows entered the Forchheimer regime where the β-factor increased with decreasing porosity or increasing level of heterogeneity. Inspection of flow patterns revealed both steady vortices and onset of turbulent motions in the Forchheimer regime. The latter correlated well with published point-of-transitions. In developing the correlation for the -factor, we show that it is necessary to include two distinctive characteristic lengths to account for the effect of pore-scale heterogeneity. This finding reflects the simple fact that it is the contrast between pore bodies and throats that dictates the flow properties of many porous media. In this study, we have used the square root of the permeability and the fluid-solid contact length as the two characteristic lengths, a practical choice when direct measurement of the microscopic length scales is not available. This method can be used in the future to correlate three-dimensional numerical and experimental data.