Mathematical Model and Application of Spontaneous and Forced Imbibition in Shale Porous Media-Considered Forced Pressure and Osmosis

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.