Mathematical model of dynamic imbibition in nanoporous reservoirs

The oil-water imbibition equation in the nano-scale pores considering the dynamic contact angle effect, nanoconfinement effect, inertia effect, and inlet end effect was established, and the relation between the friction coefficient of solid-oil-water three-phase contact line and the fluid viscosity in the interface zone was derived. In combination with the capillary bundle model and the lognormal distribution theory, the imbibition model of tight core was obtained and key parameters affecting imbibition dynamics were analyzed. The study shows that in the process of nanopore imbibition, the dynamic contact angle effect has the most significant impact on the imbibition, followed by nanoconfinement effect (multilayer sticking effect and slippage effect), and the inertia effect and inlet end effect have the least impact; in the initial stage of imbibition, the effect of inertial force decreases, and the effect of contact line friction increases, so the dynamic contact angle gradually increases from the initial equilibrium contact angle to the maximum and then remains basically stable; in the later stage of imbibition, the effect of contact line friction decreases, and the contact angle gradually decreases from the maximum dynamic contact angle and approaches the initial equilibrium contact angle; as the pore radius decreases, the dynamic contact angle effect increases in the initial stage of imbibition and decreases in the later stage of imbibition; as the oil-water interfacial tension increases, the imbibition power increases, and the dynamic contact angle effect increases; there is a critical value for the influence of interfacial tension on the imbibition dynamics. In improving oil recovery by imbibition in tight oil reservoir, interfacial tension too low cannot achieve good imbibition effect, and the best interfacial tension needs to be obtained through optimization.