The energized hydraulic fracturing technology of “energizing, hydraulic fracturing, shut-in, and flowback” has achieved good development results in some shale oil fields. The mechanisms of forced imbibition (FI) under forced pressure (the difference between hydraulic fluid pressure and original pore pressure) need to be further studied; especially, the difference and boundary of various mechanisms in forced soaking are still unclear. The wettability of pores is different, the reservoir shows strong mixed wettability, and the permeability of clay mineral pores has osmotic pressure. This paper analyzes the imbibition forces in distinct types of pores, and the dynamic models of spontaneous imbibition (SI) and FI in a single capillary tube are established. Based on the fractal theory and capillary bundle model, the mathematical models of SI and FI at the core scale are established, and semi-analytical solution models considering different forces are proposed, especially considering forced pressure and osmosis. In addition, the above mathematical models are fitted and verified by imbibition experiments and NMR, which ensured the accuracy and validity of the mathematical models. In this paper, the sensitivity analysis of different factors to oil displacement rate and oil recovery by imbibition is quantitatively evaluated. The research shows that the imbibition rate of FI is faster than that of SI, and the ultimate oil recovery is also higher. Smaller pores mainly control the imbibition rate, which increases with oil–water interfacial tension and forced pressure. However, the imbibition rate decreases with increasing water-phase viscosity and fractal dimension.

Due to the fracturing fluid imbibition and primary water, oil−water two-phase fluids generally exist in shale nanoporous media. The effects of water phase on shale oil recovery and geological carbon sequestration via CO 2 huff-n-puff is non-negligible. Meanwhile, oil−CO 2 miscibility after CO 2 huff-n-puff also has an important effect on oil− water two-phase flow behaviors. In this work, by considering the oil− CO 2 competitive adsorption behaviors and the effects of oil−CO 2 miscibility on water wettability, an improved multicomponent and multiphase lattice Boltzmann method is proposed to study the effects of water phase on CO 2 huff-n-puff. Additionally, the effects of oil−CO 2 miscibility on oil−water flow behaviors and relative permeability are also discussed. The results show that due to Jamin's effect of water droplets in oil-wetting pores and the capillary resistance of bridge-like water phase in water-wetting pores, CO 2 can hardly diffuse into the oil phase, causing a large amount of remaining oil. As water saturation increases, Jamin's effect and the capillary resistance become more pronounced, and the CO 2 storage mass gradually decreases. Then, based on the results from molecular dynamics simulations, the influences of oil−CO 2 miscibility on oil−water relative permeability in calcite nanoporous media are studied, and as the oil mass percentage in the oil−CO 2 miscible system decreases, the oil/water relative permeability decreases/ increases. The improved lattice Boltzmann model can be readily extended to quantitatively calculate geological CO 2 storage mass considering water saturation and calculate the accurate oil−water relative permeability based on the real 3D digital core.