Pore-Scale Simulations of Simultaneous Steady-State Two-Phase Flow Dynamics Using a Lattice Boltzmann Model: Interfacial Area, Capillary Pressure and Relative Permeability

The dynamics of simultaneous flow of immiscible two-phase fluids at the steady state in the capillary force-dominated regime were investigated. It was described by the key state variables, including interfacial area between fluids, capillary pressure and relative permeability, as functions of fluid saturation. Based on the two-dimensional pore-scale simulations using the Shan-Chen multi-component lattice Boltzmann model (SCMC-LBM), the steady-state interfacial area, capillary pressure and relative permeability versus saturation relationships subjected to flow conditions, such as initial fluid distribution, saturation history and magnitude of hydraulic gradient, were examined. Also, the intrinsic differences in the interfacial area and capillary pressure versus saturation curves between at dynamic equilibrium in the steady-state infiltration and at quasi-static equilibrium in the transient displacement were explored. As the SCMC-LBM simulations revealed, the relative permeabilities of both fluids were insensitive to initial fluid distribution or saturation history because of the simultaneous steady-state flow dynamics, but dependent on the magnitude of hydraulic gradient due to the existence of a threshold hydraulic gradient. The hysteresis behaviours of interfacial area-saturation and capillary pressure–saturation curves were captured in the transient displacement but absent in the steady-state infiltration, and the unique interfacial area-capillary pressure–saturation surface at dynamic equilibrium did not tend to overlap with the one at quasi-static equilibrium. The hysteretic capillary pressure behaviour for these two flow patterns was of great theoretical and practical significances.