Inertial Effect on Spontaneous Oil-Water Imbibition by Molecular Kinetic Theory

Imbibition is one of the most common physical phenomena in nature, and it plays an important role in enhanced oil recovery, hydrology, and environmental engineering. For the tight reservoirs, the imbibition method has an obvious advantage in fracturing, shut-in, and huff-puff development. Although the current imbibition studies focus on oil recovery, and the inertial effect in imbibition is neglected and its mechanism is also unclear. In this paper, the inertial effect on spontaneous oil-water imbibition at micron-scale is studied by molecular kinetic theory (MKT). The frictional coefficient in the model is a fitted parameter to match the experimental data during the total imbibition process. Then, the simulation of the initial imbibition stage is conducted and the inertial effect on imbibition is identified by the difference between the model considering the inertial effect (CI) and the model neglecting the inertial effect (NI), or by the proportion of inertial force to the total resistance. Results show that (i) with an increase in the water phase viscosity, the inertial effect time shortens, maximum imbibition height and rate decrease, and thus the inertial effect on imbibition weakens; (ii) with an increase in the oil phase viscosity, the inertial effect time changes little, the maximum imbibition height and rate decrease slightly, namely, the inertial effect depends slightly on the oil phase. (iii) with an increase in the capillary wettability (hydrophilicity), the inertial effect time shortens, the maximum imbibition rate first increases and then decreases, and the inertial effect on imbibition weakens. This work sheds light on the inertial effect on oil-water imbibition by MKT, considering the effects of dynamic contact angle, water phase viscosity, oil phase viscosity, and wettabilities, which is helpful to understand the role of inertia in the oil-water or oil-fracturing fluid imbibition process.