The role of interphase boundary in permeability estimation for saturated (unsaturated) porous media

Abstract

The single-phase and immiscible two-phase flows through porous media play crucial roles in natural and industrial systems, such as, NAPL contaminant transport in groundwater, and enhanced recovery of oil and gas from reservoirs. The cornerstone of the porous media flow of incompressible fluid(s) is the Darcy equation, which assumes the no-slip boundary condition in the laminar regime for the saturated porous media, and is extended by simply introducing the relative permeability to the flow of multiple immiscible fluids. This flow equation is well-established for the viscous flow, but many other physical phenomena, including liquid-solid interaction and fluid-fluid interface dynamics, are still not clearly accounted for. nFor this reason, the validity of the Darcy equation is often challenged. For example, the pre-Darcy flow (power law relationship), the threshold pressure gradient, the irreducible water saturation and the higher-than-expected water flow rate usually take place in low-permeability saturated porous media; and the hysteresis of relative permeability with respect to the flow pattern, capillary number, wettability and pore size distribution is frequently observed in the capillary force-dominated regime. In order to better understand the underlying physics of porous media flow, this study takes advantage of pore scale simulations based on the lattice Boltzmann model to investigate the effects of adhesive liquidnsolid interaction (and the resulting film fluid) and capillary force at fluid interfaces on the permeability estimation for the saturated (unsaturated) porous media. nnTo this end, this study mainly comprises three parts of research work: (1) A lattice Boltzmann model based on an exponentially decaying force function is established for describing the adhesive liquid-solid interaction at the particle level. The effects of interaction strength (distance) on the slip length and the permeability ratio are investigated. A modified permeability function is derived with consideration of the slip length in the capillary tube. These investigations are further extended to the porous media composed of square grains in order to reduce spurious velocities. (2) The Shan-Chen multi-component lattice Boltzmann model is used to investigate the influences of flow conditions (initial fluid distribution, saturation history and magnitude of hydraulic gradient) on the characteristic of simultaneous steady-state flow of immiscible two-phase fluids (interfacial area, capillary pressure and relative permeability) in the capillary force-dominated regime. Also, the intrinsic differences of interfacial area and capillary pressure between cases at dynamic equilibrium and quasi-static equilibrium are explored. (3) Two-dimensional pore scale simulations of simultaneous steady-state two-phase flow in the capillary force-dominated regime are conducted. The fluid distribution (wetting fluid-solid, non-wetting fluid-solid and fluid-fluid interfacial areas) as well as the capillary pressure versus saturation curve as affected by fluid and geometrical properties (wettability, adhesive strength, pore size distribution and specific surface area) is analysed. Also, how these properties influence the relative permeability versus saturation relation through apparent effective permeability and threshold pressure gradient is explored. nnThe pore scale simulations based on the lattice Boltzmann model reveal the following facts: (1) Both the slip length and the permeability ratio follow a power law function of interaction strength (distance). The slip length is found to be independent of the pore diameter and smaller in porous media than in capillary tube. The permeability ratio considering the slip length can be estimated. The permeability ratio increases significantly as the pore diameter decreases, indicating a great importance of liquid-solid interaction for the tight porous media. (2) The hysteresis behavior of capillary pressure-saturation curve is captured in the transient displacement but absent in the steady-state infiltration; and the unique interfacial area-capillary pressure-saturation surface at dynamic equilibrium does not tend to overlap with the one at quasi-static equilibrium. The steady-state relative permeabilities of both fluids are also found to be insensitive to initial fluid distributions but dependent on the magnitude of gravity due to the existence of a threshold gravity. (3) The thin wetting fluid film formed around the solid surface due to the adhesive fluid-solid interaction results in the reduction of the wetting fluid mobility. Also, the adhesive interaction provides another source of capillary pressure in addition to capillary force, which, however, does not affect the mobility of the non-wetting fluid. In the steady-state infiltration, both the wetting and non-wetting fluids are subjected to the capillary resistance.The findings obtained from the lattice Boltzmann simulations shed light on the roles of the adhesive interaction and the capillary force occurring at the interphase boundaries in the permeability estimation for saturated (unsaturated) porous media, and are of substantial value for hydrologists and soil scientists as well as petroleum and environmental engineers.nn