Pore-Scale Two-Phase Flow Simulations:Numerical Schemes And Applications

Two-phase flow phenomena in porous media are widely appeared in oil and gas field development.A deep understanding of two-phase flow problem is of great significance to oil and gas field development.The Darcy’s law describes the two-phase flow in porous media from a macro scale,but it cannot directly describe the structure of porous media and the fluid in pores.Therefore,it is necessary to explore the two-phase flow in porous media from the pore scale.In this work,the pore-scale numerical method is used to investigate fluid flow in porous media.At first,we construct some linear,decoupled schemes for the hydrodynamics coupled phasefield model by using the scalar auxiliary variable(SAV)approach.The unconditional energy stability is rigorously proved.Numerical results show that the constructed numerical schemes are more accurate than traditional schemes.Second,the phase-field moving contact line(MCL)model is derived through the first law of thermodynamics,associated thermodynamic relations and the Onsager variational principle.Two different phase-field MCL models are considered,namely,the NBC-based phase-field MCL model with matched density and the GNBC-based phase-field MCL model with non-matching density.We develop a linear and decoupled scheme for the case of matched density and a nonlinearly coupled scheme for the case of non-matching density,respectively.Again,the unconditional energy stability is rigorously proved.Numerical results show that our scheme is more accurate than the traditional schemes.Third,we construct effective and energy-stable schemes for the hydrodynamics coupled phase-field surfactant model with matched and non-matching density.For the case of matched density,a linear and decoupled first-order scheme is developed,while a linearly coupled first-order scheme is constructed for the case of non-matching density.We further develop linear and decoupled second-order schemes for both matched density and non-matching densinty cases.The firstorder schemes are unconditionally energy stable while the second-order schemes are conditionally energy stable.Numerical results show that the constructed schemes sucessfully simulate the adsorption of surfactants on the interface between fluids and reduce the interfacial tension.Fourth,we proposed the phase-field moving contact line model with soluble surfactants.With chemical potentials derived from the free energy functional,we analytically obtain certain equilibrium properties of surfactant adsorption.A nonlinearly coupled scheme with unconditional energy stability is developed.Using the proposed model and numerical scheme,we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface.It is observed that droplet forms three typical flow states as a result of different surfactant bulk concentrations and defect strengths,and a phase diagram for the three flow states is presented.Finally,we investigate the fluid flow in digital rock at the high water cut and the imbibition process in porous media.An energy capillary number and a phase-diagram is proposed to identify the regime transition of the imbibition,and they are evidenced by the quantitative analysis of invasion morphologies.