Phase-field simulation of counter-current spontaneous imbibition in a fractured heterogeneous porous medium

Abstract

Spontaneous imbibition is well-known to be one of the most effective processes of oil recovery in fractured reservoirs. However, the detailed pore-scale mechanisms of the counter-current imbibition process and the effects of different fluid/rock parameters on this phenomenon have not yet been deeply addressed. This work presents the results of a new pore-level numerical study of counter-current spontaneous imbibition, using coupled Cahn–Hilliard phase field and Navier–Stokes equations, solved by a finite element method. A 2D fractured medium was constructed consisting of a nonhomogeneous porous matrix, in which the grains were represented by an equilateral triangular array of circles with different sizes and initially saturated with oil, and a fracture, adjacent to the matrix, initially saturated with water and supported by low rate water inflow. Through invasion of water into the matrix, oil drops were expelled one by one from the matrix to the fracture, and in the matrix, water progressed by forming capillary fingerings, with characteristics corresponding to the experimental observations. The effects of wettability, viscosity ratio, and interfacial tension were investigated. In strongly water-wet matrix, with grain contact angles of θ < π/8, different micro-scale mechanisms were successfully captured, including oil film thinning and rupture, fluids’ contact line movement, water bridging, and oil drop detachment. It was notified that there was a specific grain contact angle for this simulated model, θ = π/4, above it, matrix oil recovery was negligible by imbibition, while below it, the imbibition rate and oil recovery were significantly increased by decreasing the contact angle. In simulated mixed wet models, water, coming from the fracture, just invaded the neighboring water-wet grains; the water front was stopped moving as it met the oil-wet grains or wide pores/throats. Increasing water-oil interfacial tension, in the range of 0.005-0.05 N/m, resulted in both higher rate of imbibition and higher ultimate oil recovery. Changing the water-oil viscosity ratio (M), in the range of 0.1–10, had a negligible effect on the imbibition rate, while due to co-effects of capillary fingering and viscous mobility ratio, the model with M = 1 had relatively higher ultimate oil recovery.

Pore-scale study of counter-current imbibition in strongly water-wet fractured porous media using lattice Boltzmann method

“…At the solid surfaces, no-slip boundary condition is imposed by using the half-way bounceback scheme 53 and the desired contact angle is achieved by using the wetting boundary condition proposed by Xu et al 24 , which modifies the direction of the colour gradient ∇ρ N at the boundary to match the specified contact angle θ . These boundary conditions are to maintain a counter-current imbibition environment in which the oil in the matrix can only flow into the fracture that supplies water, which have been widely adopted in the previous numerical and experimental studies of counter-current imbibition 4,9,23,54 . Among various factors that influence the capillary imbibition, surface wettability is of vital importance for both imbibition rate and ultimate oil recovery, and its effect has been thoroughly investigated by Rokhforouz and Amiri 4 .…”

“…The counter-current imbibition occurs more often although it is less effective in terms of oil recovery. The spontaneous imbibition is known to be affected by many factors including the wettability 4 , the porosity, permeability and heterogeneity of the matrix [5][6][7][8][9][10][11] , the viscosity ratio of the wetting to non-wetting fluids 12,13 and their interfacial tension 14,15 , as well as initial saturation and boundary conditions 10,14,16 , etc. The spontaneous imbibition in conventional porous media has been extensively studied [17][18][19][20] due to its wide existence in various disciplines such as oil recovery, polymer composite manufacturing, soil science and subsurface hydrology.…”

“…Jafari et al 9 also used the phase-field method to investigate the effects of water injection velocity, fracture aperture, and grain shape during counter-current spontaneous imbibition. In these pore-scale simulations, the solid grains in the matrix are generally idealized as simple circular 4,9 or square cylinders 23 . However, the pore structures in natural rock matrix are extremely complex and irregular.…”

Pore-scale investigation of selective plugging mechanism in immiscible two-phase flow using phase-field method

“…COMSOL Multiphysics [66] software has become a reliable tool for solving two-phase flow problem, which includes interface capturing methods (e.g., phase-field, and level set) [56,61,63,67]. Navier-Stokes equations coupled with a diffuse interface method are available in the microfluidics module of the software.…”

“…Numerical studies of governing mechanisms of two-phase flow in porous media have been conducted by many researchers [42,43]. Pore-network modeling [44][45][46], smoothed particles hydrodynamics [47,48], Lattice Boltzmann (LB) [49,50], quasi-static [51,52] and direct numerical simulation approaches based on interface capturing techniques such as Volume of Fluid (VoF) [46,53,54], level set [55] and phase-field [56][57][58][59] are the most common approaches which have been developed to simulate the multiphase flow in porous media. A detailed study of advantages and drawbacks of these techniques can be found elsewhere [60].…”