① Shale oil reservoir is composed of shale matrix, secondary hydraulic fractures, and main fractures. Also, the liquid can flow among triple media.

The governing equation of oil phase flow is as follows: ∂ ∂ t ( ∇ S o ρ o ϕ ) + ∇ ( ρ o v o ) + ρ o k k r o h η o Δ p o = 0 , (1) where S _o is the oil saturation; ρ _o is the oil viscosity (mPa·s); φ is the porosity of matrix; k _ro is the relative permeability of oil; η _o is the mobility of oil; Δp _o is the pressure difference of oil in different media.

The governing equation of water phase flow is as follows: ∂ ∂ t ( ∇ S w ρ w ϕ ) + ∇ ( ρ w v w ) + ρ w k k w o h η w Δ p w = 0 , where S _w is the water saturation; ρ _w is water viscosity (mPa·s); φ is the porosity of matrix; k _rw is the relative permeability of water (mD); η _w is the mobility of oil; and Δp _w is the pressure difference of water in different media. S o + S w = 1 , p c = p o − p w , where S _o is the oil saturation; S _w is the water saturation; and P _c is the capillary pressure (Pa).

Various models are constructed by fully exploiting the functions of the commercial reservoir simulation software (CMG IMEX) based on the assumptions and equations. The reservoir consists of triple media: main hydraulic fracture (HF), second hydraulic fracture (SF), and matrix(M). The models show single-porosity, while the fracture system is set up by adopting logarithmic local grid refinement. Due to the great differences in reservoir properties and oiliness in different sweet spots in Jimsar, the upper and lower sweet spot of fracture element grid models are established. As shown in Figure 2, the horizontal wellbore is along the x-axis direction and the hydraulic fracture is along the y-axis direction. Diverse color represents different permeability. The red region represents the main hydraulic fracture with high conductivity, and the blue region represents the secondary hydraulic fracture with low conductivity. The whole numerical simulation process is divided into two stages: the fracturing fluid injection stage and the well shut-in stage. Through the numerical simulation of the fracturing fluid injection stage, the real distribution of different medium (HF, SF, and M) pressure and fluid saturation after fracture of formation is simulated.

An upper sweet spot model based on J1 (a horizontal well in the upper sweet spot, Jimsar) and a lower sweet spot model based on Y1 (a horizontal well in the lower sweet spot, Jimsar) are established to explore the law of fracturing fluid imbibition and oil replacement during the shut-in time. The parameters of the reservoir, fracture, and engineering are obtained through field data (Wang et al., 2020; Zhang et al., 2021). The PVT properties of the oil are acquired from the indoor experiment (Liao et al., 2019). Relevant known model parameters are summarized in Table 1 and Table 2 (the data are obtained from Xinjiang Oilfield).

The reservoir capillary pressure is high because of the characteristics of low porosity, ultra-low permeability, and widely developed microscale pores (Zhang et al., 2021). Capillary pressure, as the main power for slickwater to enter the matrix, affects the distribution of fracturing fluid and crude oil in the matrix and fracture system (Li et al., 2007). From the experiment test, the capillary pressure curve and two-phase relative permeability curve used in models are assigned as presented in Figures 3A,B respectively. The two-phase relative permeability of the fracture system uses the classical relative permeability setting (Zhang et al., 2017).

The oil and water transfer between different media and the pressure of these media are difficult to monitor in reality because the techniques are limited. Therefore, the well bottom-hole pressure falloff at the shut-in period and water cut at flowback time could be used to validate the model.

This work verifies the model by well bottom-hole pressure of J1 and Y1 and water cut of J1, J2, J3, Y1, Y2, and Y3 using actual monitoring data. The validations are shown in Figures 4A,B. As shown in Figure 4, the simulated pressure change, water cut and the actual well pressure change, water cut fit well, which verifies the accuracy of the model.

Figure 5 displays the pressure distribution diagram in the different sweet spots at different shut-in times. Figure 6 displays the statistical diagram of pressure distribution at different distances from HF. From Figures 4A,B, it can be seen that at the end of pumping, the pressure in the center of the main hydraulic fracture is 66.5 MPa; the pressure of the matrix 5 m and above from the fracture is the initial reservoir pressure (38 MPa). After 200 days of well shut-in, the pressure in the center of the main hydraulic fracture decreases to 43 MPa, and the pressure of the matrix 5 m and above from the fracture increases to 40 MPa. Figures 4C,D displays that the pressure in the center of the main hydraulic fracture is 71.5 MPa; the pressure of the matrix 5 m and above from the fracture is initial reservoir pressure (44 MPa). After 200 days of well shut-in, the pressure in the center of the main hydraulic fracture decreases to 46.3 MPa, and the pressure of the matrix 5 m and above from the fracture increases to 45 MPa. Combined with the weak hydrophilic characteristic of the upper sweet spot reservoir and the weak lipophilic characteristic of the lower sweet spot reservoir (Zhang et al., 2021). It can be concluded that during the shut-in period, the main fracture fluid pressure in the upper sweet spot is continuously diffused to the secondary hydraulic fractures and matrix under the capillary force. The capillary force as the main power promotes the imbibition and replacement between the fracture system and matrix. As it can be seen from the pressure distribution diagram, the reservoir pressure distribution is relatively average after 200 days of well shut-in, while the main fracture fluid pressure in the lower sweet spot is continuously diffused to the secondary hydraulic fracture. As a repulsive force, the capillary force hinders the imbibition and replacement. A small amount of fracturing fluid retained in the fracture system enters the matrix under differential pressure. After 200 days of a well shut-in, an obvious “high-pressure zone” is formed near the fracture system. The matrix pressure at the far fracture increases by 2%. The pressure changes from beginning to end are small.

Figure 7 displays the water distribution diagram in different sweet spots at different shut-in times. Figure 8 displays the statistical result. As shown in Figure 7A, at the end of pumping, 20.3% of the fracturing fluid is distributed in the HF, and 41.2% of the fracturing fluid is distributed in the RF. 38.5% of the fracturing fluid is filtered and imbibed into the near fracture matrix; As shown in Figure 7B, after 200 days of well shut-in, 3.2% of the fracturing fluid is distributed in the HF, 5.9% of the fracturing fluid is distributed in the SF, and 90.9% of the fracturing fluid is filtered and imbibed into the near fracture matrix. The water saturation of the fracture system is close to 0, and almost all the fracturing fluid is imbibed into the matrix. The long-term well shut-in helps to promote the oil-water exchange of the upper sweet spot reservoir (the fracturing fluid in the fracture i imbibed into the near fracture matrix, and the crude oil in the matrix is replaced in the fracture system), which is consistent with the conclusion by A. Almulhim. That work shows that the fracture water saturation in the fracture can be reduced from 100% to irreducible water saturation in a strong hydrophilic reservoir (Almulhim, et al., 2014). As shown in Figure 7C at the end of pumping, 28.1% of the fracturing fluid is distributed in the HF, and 40.2% of the fracturing fluid is distributed in the RF. 31.7% of the fracturing fluid is filtered and imbibed into the near fracture matrix; As shown in Figure 7D, after 200 days of well shut-in, 21.9% of the fracturing fluid is distributed in the HF, 27.9% of the fracturing fluid is distributed in the SF, 50.2% of the fracturing fluid is filtered, and imbibed into the near fracture matrix. The water saturation of the fracture system is 0.6–0.9. The water saturation still holds high water content. Long-term well shut-in has little impact on the oil-water exchange of the lower sweet spot reservoir.

In this article, the oil-water changes among triple medium: HF, SF, and M are collected by setting different sectors. The oil-water replacement law during well shut-in is analyzed. It is defined that when the flow is less than 0.1 m³/d, the imbibition equilibrium is reached. During the well shut-in time, the oil is continuously replaced from the matrix to the fracture system in the upper sweet spot reservoir, as shown in Figure 9. The imbibition equilibrium is attained in about 65 days. When reaching the imbibition equilibrium, the cumulative oil volume replaced in sector SF is 161.2 m³, sector SF is 47 m³. A small amount of oil enters the fracture system in the lower sweet spot, as shown in Figure 9. The cumulative oil volume replaced in sector SF is higher than that of SF, reaching the imbibition equilibrium in about 14 days. The cumulative oil volume replaced in sector SF is 45.87 m³ and cumulative oil volume replaced into sector SF is 22.77 m³.

By counting the cumulative oil inflow of the fracture system, the simulation results of the two models are shown in Figure 10A. Combined with the fact that the SF density is low during the stimulation of the upper sweet spot reservoir, the complexity of the fracture system is low. In Figure 11, the initial oil saturation of the SF of the upper desserts is low. But the upper sweet desserts reservoir is hydrophilic with the capillary force as a power for imbibition. With the increase in shut-in time, the cumulative oil inflow changes gradually until the equilibrium state.

Because the density of SF is high during stimulation of the lower sweet spot reservoir. The complexity of the fracture system is high. In Figure 11B, the initial oil saturation of the SF is high, but the lower sweet spot reservoir is lipophilic. The capillary force is used as a resistance in the imbibition. The oil replacement is carried out only by the action of differential pressure between different media. The cumulative oil replacement hardly changes with the increase in well shut-in time.