Horizontal wells with complicated fracture networks have become a key technical measure to improve the oil recovery of low-permeability and tight reservoirs in China. Spontaneous imbibition is regarded as the major oil recovery mechanism after fracturing. Due to the limitation of the observation scale, the traditional experimental methods cannot accurately describe multiphase fluid flow in the micro-/nanopore space of low-permeability and tight reservoirs, and the pore-scale oil recovery mechanism during spontaneous imbibition was not clearly understood. In this study, a novel mathematical model of oil replacement by spontaneous imbibition in fractured porous media is developed and then numerically solved using the phase-field method. By comparing the numerical results with the analytical solution of single-tube capillary-driven flow, which is widely described by the classical Lucas–Washburn equation, the accuracy of the proposed method is validated. The effects of rock wettability, oil–water viscosity ratio, interfacial tension, and fracture network on oil imbibition recovery are further explored. The results demonstrate that the pore-scale dynamic events of oil droplets including snap-off and coalescence can be well observed. The stronger the degree of water-wet and the lower the oil–water viscosity ratio, the higher the oil imbibition recovery. The oil–water interfacial tension exerts little impact on the oil imbibition recovery, while it can significantly affect the imbibition time. As the oil–water interfacial tension decreases, the imbibition time will become longer. The existence of a fracture network can enlarge the contact area of oil–water exchange, thus greatly improving the oil imbibition recovery during spontaneous imbibition. It is concluded that the pressure difference between fracture and matrix is of particular importance to achieve a high oil imbibition recovery in fractured porous media. The above understandings can provide a theoretical basis for the efficient development of similar reservoirs.

Tight oil reservoirs generally have no natural productivity due to the influence of micro/nano pore structure. The horizontal well volume fracturing technique is widely used to achieve effective development of this type of reservoirs. The remaining oil in matrix pores is mainly produced by spontaneous imbibition in the actual soaking and flowback process. Due to the great limitation of observation scale, the traditional experimental testing methods cannot accurately characterize the distribution and production of remaining oil at nano-scale in tight oil reservoirs, the microscopic mechanism of spontaneous imbibition has not been clearly explained. In order to resolve those issues, a two-dimensional geometric model is firstly established based on the raw images of typical tight rock sample obtained by a highresolution CT imaging device. A novel pore-scale mathematical model of spontaneous imbibition in tight porous media is developed from the Navier-Stokes equations, which is numerically solved by using the phase-field method. Compared with the analytical results of the single-pipe imbibition model, the reliability of the proposed method was fully validated. Based on the analysis of the spontaneous imbibition microscopic dynamic phenomena, the influences of wettability, oil-water interfacial tension, oil-water viscosity ratio and micro-fracture morphology on the remaining oil in micro/nano pores and spontaneous imbibition recovery are further explored. Results show that, the results obtained by the phase-field modeling of spontaneous imbibition are in good agreement with the analytical solution of the single-pipe imbibition model, and the front evolution process of oil-water interface during spontaneous imbibition is accurately described. The pore-scale dynamic events of oil droplets, snap-off, cross flow and coalescence are well characterized. The oil/water interfacial tension has little effect on spontaneous imbibition recovery, but significantly affects the imbibition time. The smaller the oil/water interfacial tension is, the longer the imbibition time is. Wettability and oil-water viscosity ratio can exert a significant effect on imbibition recovery. The existence of micro-fractures increases the imbibition contact area, improves the fluid flow capacity, and significantly improves the degree of remaining oil production and imbibition recovery. A novel methodology to study two-phase fluid flow during spontaneous imbibition in tight porous media is proposed using the phase-field method in this work, which can provide a theoretical basis for understanding the underlying fluid flow dynamics during fracturing, soaking and flowback process of tight oil reservoirs.