Pore-Scale Investigation and Application of Two-Phase Low-Velocity Non-Darcy Flow in Low-Permeability Porous Media

The widely applied empirical Darcy’s law in geotechnical engineering faces significant challenges in describing low-velocity flow processes in low-permeability porous media such as tight sandstones containing irreducible water. A deep understanding of low-velocity non-Darcy two-phase flow behavior in low-permeability porous media is essential for evaluating the development of ultra-low-permeability reservoirs. In this study, seven low-permeability three-dimensional digital cores with distinct pore structures were constructed based on realistic ultra-low-permeability sandstones. Using the lattice Boltzmann method, pore-scale investigations of water displacing oil were conducted. Low-velocity two-phase flow behavior under varying wettability conditions, pore structures, and fluid viscosities was simulated. The underlying mechanisms of low-velocity non-Darcy flow in ultra-low-permeability sandstones were examined, leading to a modified low-velocity non-Darcy flow equation. This improved model was subsequently applied to numerical simulations of ultra-low-permeability reservoirs. The results demonstrate that non-Darcy effects manifest primarily as nonlinearities in seepage curves, representing a marked departure from conventional Darcy’s law. Low-velocity non-Darcy (LVND) flow is predominantly constrained by the influence of complex pore-throat structures and capillary forces on fluid distribution. The dynamic equilibrium among capillary forces arising from residual water saturation, viscous forces, and pressure gradients constitutes the fundamental mechanism governing the onset of LVND flow. Enhanced nonlinear behavior is observed with increasing viscosity of the invading phase and elevated capillary forces. Substantial discrepancies in reservoir production dynamics are identified between LVND and classical Darcian regimes. Through pore-scale numerical simulations, this study systematically elucidates LVND behavior during bi-phasic flow in low-permeability porous media, while identifying critical controlling factors. These findings provide scientific rationale and technical support for addressing geological engineering challenges in tight sandstone formations.