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.

Alkaline sodium silicate (Na-silicate) is environment-friendly and possesses water-like viscosity during the injection stage for in-depth reservoir treatment to enhance sweep efficiency. Gel setting time (t_g) and gel strength are interrelated. Factors that accelerate t_g are Na-silicate content (wt%), low pH, presence of divalent ions and temperature. Pressure drop across the gel accelerates syneresis; however, the gel appeared to remain intact. Presence of Ca²⁺ and Mg²⁺ ions is shown to increase gel strength. With a Na-silicate content of 4.5 wt%, for example, at a pH of 10.3 and a temperature of 20 °C, gel strength almost tripled and was reached about eight times faster at the combined tested concentration of 0.009 M, based on the average effect from the coexistence of both ions. Low-salinity water (LSW) has an ion composition of 25-fold diluted seawater, did not show precipitation, and could accordingly be a candidate for a pre-flush before the injection of a Na-silicate solution in the event of a field application. This is important since LSW for enhancing oil recovery is a popular method in oil industry. A suggested predictive tool (simple graphical method) to estimate the effect of different factors on gelation time and gel strength is presented.