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

Abstract

SummaryIt is important to consider the additional pressure drops associated with non-Darcy flows in the near-wellbore 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 (β-factor). While the β-factor is regarded as a property of porous media, detailed study on the effect of pore geometry has not been performed. This study characterized the effect of geometry on the flow transition and the β-factor using lattice Boltzmann simulations and stochastically constructed 2D porous media models. The effect of geometry was identified from a large set of data within a porosity range of 8–35%. It was observed 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. The β-factor increased with decreasing porosity or an increasing level of heterogeneity. Inspection of flow patterns revealed both steady vortices and onset of unsteady motions in the Forchheimer regime. The latter correlated well with published points-of-transition. In developing a dimensionally consistent correlation for the β-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 fact that it is the contrast between pore bodies and throats that dictates the flow properties of many porous media. In this study, we used the square root of the permeability and the fluid-solid contact length as the two characteristic lengths.