Mathematical Model of Imbibition Replacement and Optimization of Soaking Time for Massively Fractured Tight Oil Reservoirs

Due to the small pore throat characteristics of tight oil reservoirs, their strong capillary pressure makes imbibition replacement an effective development method. Field data has indicated that only a little fracture fluid can flow back and that there is an enhancement in oil recovery with shut-in periods after volume fracturing. A large number of scholars have carried out core-scale experiments on imbibition characteristics, but there has been limited research on the quantitative characterization of the differential pressure and imbibition replacement during counter-current imbibition. At the same time, there was also controversy on the calculation method of the optimal soaking time. In this paper, a mathematical model of oil-water two-phase flow is first established. Then, a mathematical model representing differential pressure and imbibition replacement in tight reservoirs is derived with a diversion function. Based on the saturation equation, Corey relative-permeability curve, and J function, the model is simplified to a mathematical model of spontaneous imbibition in the shut-in periods after volume fracturing. Second, based on the finite difference method, a dynamic solution method for the flow field considering the dynamic capillary force was established, and the variation law of the pressure field and the water saturation field during the soaking time was revealed. The simulation results show that imbibition characteristics are the core of flow field reconstruction, and the differential pressure action can ensure the advancing distance of the fracturing fluid; both of them are not a linear superposition on tight oil development but complement each other and promote each other. Third, according to the growth rate of the imbibition replacement between fractures and the matrix during the soaking time, the calculation method of optimal soaking time was established. Taking the development parameters of the volume fracturing development case in the Ordos Basin into account, a reasonable soaking time was optimized. Finally, we analyzed the optimal soaking time under different conditions, and a chart of optimal soaking time for different initializations was plotted. Such a chart has profound reference significance for engineers, and they can make quick and accurate decisions regarding development and adjustment.