Abstract
The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.
Highlights
Immiscible two-phase flow seepage in porous media is a physical process, which often appears in environmental, geotechnical, and petroleum engineering
The conventional theory for simulating this physical phenomenon can be summarized in two types of formulation: (1) for the Enhancement of Oil Recovery (EOR) in petroleum engineering, the theory consists of two sets of mass and momentum conservation equations for both wetting and non-wetting fluid phase, and the experimental determination of capillary pressure/relative permeability–saturation curves (Pc-S/Kr-S) [1,2]; (2) for the environmental and geotechnical engineering, the soil suction is usually taken as a negative pore water pressure, due to setting atmosphere pressure as reference zero for air
The transient flow conditions were generated by suddenly applying varies of the magnitude of pressure boundary conditions between the top for non-wetting phase fluid and the bottom for wetting phase fluid on the 2D porous package
Summary
Immiscible two-phase flow seepage in porous media is a physical process, which often appears in environmental, geotechnical, and petroleum engineering. The conventional theory for simulating this physical phenomenon can be summarized in two types of formulation: (1) for the Enhancement of Oil Recovery (EOR) in petroleum engineering, the theory consists of two sets of mass and momentum conservation equations (continuity equations and Darcy’s law) for both wetting and non-wetting fluid phase, and the experimental determination of capillary pressure/relative permeability–saturation curves (Pc-S/Kr-S) [1,2]; (2) for the environmental and geotechnical engineering, the soil suction is usually taken as a negative pore water pressure, due to setting atmosphere pressure as reference zero for air. The measurement of the Pc-S curve or SWRC critically determines the prediction of the hydro-mechanical behavior of unsaturated soil
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