Displacement pressure is a key factor in the dynamic imbibition process. Foreign studies have shown that the displacement is considered unstable when the displacement pressure is greater than the critical value, leading to a low recovery, and it is stable when the displacement pressure is less than the critical value, corresponding to a high recovery ^[26]. Z1, Z2, and Z3 samples in Table 1 were selected for dynamic imbibition experiments at different displacement pressures. As shown in Fig. 7, the T₂ spectrum peak decreases with the displacement time, indicating that the crude oil in the core can be effectively produced under a certain pressure difference. The permeability levels of Z1, Z2, and Z3 samples are basically the same. The recovery of Z1 at 3 MPa, Z2 at 10 MPa, and Z3 at 15 MPa is 34.68%, 40.47%, and 36.35%, respectively (Table 3). With the increase of the displacement pressure, the recovery increases and then decreases, indicating that a higher displacement pressure is not certainly better in the dynamic imbibition experiment, and there is an optimal value range. It can be seen from Fig. 8 that the imbibition recovery decreases from 29.92% to 6.82% with the increase of the displacement pressure, while the displacement recovery increases and then decreases slowly with the increase of the displacement pressure. When the displacement pressure is small, the viscous force is small, the core imbibition process is close to a spontaneous imbibition, and the water can slowly spread to the small pores in the matrix. The imbibition process occurs in the area with balanced capillary pressure and viscous force. In this period, the main oil drainage mechanism is the imbibition at capillary pressure in small pores. However, the low pressure makes the viscous force difficult to overcome the capillary pressure of most small pore throats, leading to an invalid displacement. Moreover, the volume of water injected in the same time period is limited, which cannot guarantee the high efficiency of imbibition, resulting in a lower total recovery. When the displacement pressure rises to 10 MPa, the viscous force increases with the rising displacement pressure. Under the action of imbibition at capillary pressure and displacement at viscous force, the crude oil imbibed into large pores or fractures can be quickly displaced by the viscous force, thus resulting in a high total recovery. When the displacement pressure further rises to 15 MPa, the viscous force becomes dominant in oil drainage. However, the water in the fracture is discharged before it undergoes imbibition and exchange with the crude oil in the matrix. The matrix imbibition is limited and the imbibition effect is poor. Meanwhile, the displacement pressure is high and the viscous force is large. When the viscous force is greater than the capillary pressure, a fingering phenomenon occurs, the breakthrough time reduces sharply, and the oil-water front becomes unstable, which may cause serious water channeling, resulting in a low recovery at high injection pressure.

Therefore, the displacement pressure in field water flooding should be selected with two considerations. First, the displacement pressure should be higher than the lower limit of displacement pressure in efficient and stable displacement, that is, the viscous force is ensured to effectively overcome the capillary pressure of most small pore throats, allowing it to enter the small pores to replace the crude oil therein, so that the oil production rate is maintained and the recovery from matrix is improved effectively. Second, the displacement pressure should be lower than the upper limit of displacement pressure in efficient and stable displacement, so that the displacement effect can be maximized, the oil-water sweep area and imbibition efficiency be improved, and the recovery from fractures and large pores be enhanced, while water channeling be avoided. Furthermore, the field injection pressure should be determined properly depending on reservoir physical properties, fracture development, and fluid properties.

The permeability of tight/shale oil reservoirs is low, and the permeability has a great impact on dynamic imbibition. Fig. 9 compares the NMR T₂ spectra of Z5 (permeability 0.271×10^-3 μm²) and Z4 (permeability 0.145×10^-3 μm²). It can be seen that the signal amplitude of crude oil in small pores, large pores and fractures of Z5 decreases more than that of Z4. As shown in Table 3, the imbibition recovery and displacement recovery of Z5 are 24.91% and 20.29% respectively, 4.67 and 3.17 percentage points more than that of Z4. The ultimate recovery of Z4 and Z5 is 45.20% and 37.36%, respectively, indicating that the displacement recovery and imbibition recovery increase with the increase of permeability. This is believed to be controlled by the microscopic mechanical mechanism and physical properties of the reservoir.

The dynamic imbibition during water flooding mainly includes two processes:

(1) The injected water is imbibed into the core. This process is determined by the capillary pressure of the reservoir. At the same wettability level, the lower the permeability, the smaller the capillary radius is. In this case, a higher capillary pressure can bring a larger imbibition distance.

(2) The crude oil is displaced and discharged. This process is mainly controlled by the single-phase oil start- up pressure induced by the viscous resistance on the pore wall and the relative seepage resistance between the oil and water phases. These resistances are mainly related to permeability. The higher the permeability, the larger the pore throat radius and the better the pore throat connectivity, which can effectively reduce the probability of sticking and breaking during oil droplet displacement, and the smaller the resistance to injected water entering small pores and the resistance to oil discharge, so that the crude oil in pore throats of various scales can be produced to a higher degree. In addition, Fig. 10 shows that the lower the core permeability, the longer the imbibition equilibrium time required, the lower the recovery, and that the higher the permeability, the higher the imbibition efficiency and the recovery.

It is known that the Bond number, as it is defined (the ratio of gravity to capillary pressure), increases with the increase of permeability. The larger the Bond number is, the stronger the gravity effect is, and the greater the imbibition oil production power is. However, when the permeability increases to a certain level, the change of the seepage resistance is smaller, and the increase of the imbibition power is also smaller, resulting in the slow increase of recovery under high permeability ^[14]. Fig. 10 also shows that the recovery increase of cores with different permeabilities during dynamic imbibition is steep and then slows down, that is, the recovery rate declines gradually in the late stage of imbibition. Accordingly, the dynamic imbibition process of cores with different permeabilities can be divided into high-speed imbibition and low-speed imbibition stages. For high-permeability cores, oil is mainly discharged in the high-speed imbibition stage, while the oil yield in the low-speed imbibition stage is very small and appears earlier. The analysis shows that the seepage resistance of high-permeability samples is small: in the early stage of imbibition, the capillary pressure is high to provide a large imbibition power, leading to a high recovery; in the late stage of imbibition, the capillary pressure declines rapidly with the increase of the matrix water saturation, resulting in an early onset of the low-speed imbibition stage. In contrast, low-permeability cores require a longer imbibition time to obtain higher recovery. Therefore, the permeability-increasing treatments such as fracturing are adopted practically to greatly improve the seepage capacity of the reservoirs, and water flooding is believed to enhance the development performance significantly.

Tight/shale oil reservoirs are mostly developed by horizontal well staged fracturing to create complex fractures, which have a great influence on dynamic imbibition. Fig. 11 shows the NMR T₂ spectra of two cores (Y1, a tight matrix-type core with a permeability of 0.121×10^-3 μm², and Y2, a fracture-type core with a permeability of 0.657×10^-3 μm², as shown in Table 1). It can be seen that the T₂ spectrum of the matrix-type core is mainly monomodal, reflecting the prevalence of nano-scale small pores, with some large pores, and the T₂ spectrum of the fracture-type core is trimodal, with the T₂ spectral peak appearing at the pore size greater than 13 μm, in addition to the spectral peaks of small pores and large pores, and also the signal amplitude decreasing with the dynamic imbibition time. Thus, the pores with sizes greater than 13 μm are defined as fractures. For the fracture-type core, at the displacement time of 0.2 h, the T₂ spectrum line at the fracture falls significantly, and the T₂ spectrum line at the small pores of the matrix moves down slightly. With the displacement time, the T₂ spectrum lines at the matrix and the large pores lower gradually and shift to the right, indicating that the crude oil in the matrix gradually migrates to the fracture under the action of water, and the matrix supplies oil to the fracture. In Table 3, the imbibition recovery and displacement recovery are 8.42% and 29.76%, respectively, for the fracture-type core, and 25.95% and 8.11%, respectively, for the matrix-type core. The ultimate total recoveries of the two cores are 38.18% and 34.06%, respectively, indicating that the core after fracturing enables water to more easily enter the micro- to nano-scale small pores of the matrix to replace the crude oil therein, thus leading to a high total recovery.

In essence, the internal seepage capacity of the core after fracturing is better. In the early stage of water injection, the crude oil in the fractures and the large pores around the fractures can be produced by displacement. In the late stage, the fractures can not only increase the imbibition contact area between the matrix and water, but also reduce the oil-water seepage resistance and promote the oil-water exchange between the matrix fractures. These features finally contribute the high total recovery. In field practices, the reservoir stimulation treatments such as large-scale volume fracturing and the mechanism of oil drainage by dynamic imbibition between matrix fractures can be combined to effectively improve the recovery.

Fig. 12 shows the NMR T₂ spectrum of Z6 in the fracturing stage, which reflects the migration of fluid in different pores after the fracturing fluid enters the core. It can be seen that the T₂ spectrum line of the core with oil saturated is obviously trimodal, with the three peaks corresponding to small pores, large pores and fractures, from left to right, respectively. Due to the artificial fractures, the third peak reflects a poor continuity with the first and second peaks. After the fracturing fluid enters the core, the signal amplitude at the fractures on the right decreases, and the signal amplitudes at the small pores and large pores on the left increase slightly, indicating different microscopic migration characteristics of crude oil in the pores. The migration trend of crude oil in pores (black arrow line in Fig. 12) can be obtained by fitting the top point of the spectrum peak. Clearly, with the progress of fracturing, the trend line of small pores and large pores has a left-leaning inclination, that is, the spectrum peak tends to shift leftward. It is considered that the fracturing fluid in the core sweeps the oil phase as the front advances. Under the action of pressure gradient, the high-pressure fracturing fluid first sweeps the fractures with small seepage resistance. In this case, minor crude oil in the fractures is discharged, leading to a reduction in single amplitude. Meanwhile, due to the displacement and imbibition effects, the fracturing fluid drives the crude oil in the fractures to migrate slightly towards the pores with smaller sizes, leading to the left leaning of the NMR T₂ spectrum.

Fig. 13 shows the NMR T₂ spectrum of Z6 in the soaking stage. At 12 h of soaking, the signal amplitude of small pores at the left peak moves down, the signal amplitude of large pores at the middle peak increases slightly, and the signal amplitude of fractures at the right peak changes little. After fitting, the dip angle of the trend line of the top point of the left peak is 90°, indicating a linear decline of oil content in the small pores. At 24 h, the signal amplitude of large pores continues to rise, while the signal amplitudes of small pores and fractures continue to decrease, indicating that the crude oil in small pores and fractures continues to migrate to large pores. Fig. 14 shows the change in oil recovery in pores at different development stages. It can be seen that at the end of soaking, the oil content in small pores of tight glutenite and shale cores decreases by 9.90 and 0.16 percentage points, respectively, the oil content in fractures decreases by 2.67 and 2.48 percentage points, respectively, while the oil content in large pores increases by 2.17 and 1.90 percentage points, respectively. Therefore, due to the pressure difference between the matrix's small pores and the fractures during soaking, some fracturing fluid enters the matrix's small pores under the action of pressure and capillary force, and the crude oil in some small pores of the matrix flows into the larger-scale pores and finally migrates to the outlet end through the large pores and fractures. This process leads to the negative recovery from large pores in Fig. 14.

Fig. 15 shows the NMR T₂ spectrum of Z6 in the flowback stage. When the flowback pressure is 10 MPa, the T₂ spectrum lines of large pores and fractures are significantly lower than those at the end of soaking, indicating that the crude oil in fractures and large pores is first carried out of the core. The oil contents in the fractures of tight glutenite and shale samples decrease by 4.87 and 4.79 percentage points, respectively. When the flowback pressure is reduced further to 5 MPa, the T₂ spectrum line of small pores moves down greatly, indicating that the crude oil in the small pores of the matrix is produced. In contrast, the T₂ spectrum line of large pores and fractures does not move down obviously, indicating that the small pores are the main oil supplier at this time. When the flowback pressure decreases to 0 MPa, the T₂ spectrum line of small pores falls slightly, while the T₂ spectrum lines of large pores and fractures descends greatly, indicating that the oil supply capacity of small pores is weakened, and large pores and fractures are the main oil suppliers. The top points of the three peaks of the T₂ spectrum all show a downward right shift, indicating that all crude oils in small pores, large pores, and fractures of the matrix are produced. In the flowback stage, the oil recoveries of small pores, large pores, and fractures in the tight glutenite core are 0.84%, 3.48%, and 6.03%, respectively, and those in the shale core are -0.33%, 4.06%, and 6.34%, respectively. The total recoveries of the glutenite and shale cores increase by 10.34 and 9.91 percentage points, respectively (Fig. 14). The recovery of small pores in the shale core is negative, which is a result of the failure to continuous oil supply from small pores in the shale core which is tighter and less connected than the glutenite core, and also the reverse imbibition caused by the “return” of crude oil in large pores and fractures to small pores.

Fig. 16 shows the NMR T₂ spectrum of Z6 in the production stage. In the early stage (2-12 h), the T₂ spectrum peak at fractures and large pores decrease significantly, indicating that the injected water first displaces the crude oil in the fractures and large pores, while the crude oil in the matrix remains unemployed. In the middle stage (24-48 h), with the increase of water volume, the water phase enters the matrix under the action of imbibition and displacement to gradually displace the crude oil in the matrix. Compared to the end of flowback stage, the oil recoveries of small pores, large pores, and fractures are 8.21%, -0.26%, and 5.52%, respectively, for the tight glutenite core, and 13.69%, 1.90%, and 8.36%, respectively, for the shale core (Fig. 14). Obviously, the large pores exhibit a small recovery, but mainly play the role of “bridge” between small pores and fractures of matrix during oil discharge. In the late stage (48-96 h), the signal amplitude of T₂ spectrum of fractures almost drops to 0, and the signal amplitude of T₂ spectrum of small pores decreases and tends to shift leftwards, indicating that the core matrix supplies oil from fractures to production. At this stage, the oil-water exchange between matrix and fractures is mainly controlled by: (1) the driving of pressure difference between matrix and fractures, and (2) the imbibition and replacement under the action of capillary pressure. In this process, the water phase can be imbibed into the pores inside the matrix. At the end of production (96-144 h), the T₂ spectrum lines of large pores and fractures almost no longer change, while the T₂ spectrum lines of small pores remain a certain decline, indicating that the small pores can continuously produce oil under the action of imbibition in this stage. At the end of water flooding (144 h), the recoveries of small pores in the tight glutenite and shale cores increase by 10.71 and 2.56 percentage points, respectively, suggesting that the crude oil in the matrix is effectively employed. At the end of the experiment, the imbibition recovery, displacement recovery and total recovery of the tight glutenite core are 29.65%, 16.26% and 45.91%, respectively, and the percentages of the shale core are 11.94%, 22.79% and 34.73%, respectively (Fig. 17). Compared with tight glutenite, shale has a matrix with small pore size, poor pore throat connectivity, slow supply of crude oil, low imbibition recovery and low total recovery.