Unconventional oil and gas resources are rich in China^[1]. Fracturing stimulation is always used to development in low permeability, tight and shale oil and gas reservoirs. Fracture network is formed in the reservoirs through fracturing construction, so that the well-controlled reserves can be increased and flow capacity is improved. Imbibition and oil discharge play a very important role in the flow of unconventional oil reservoirs and is an important factor affecting the production rate and efficiency.

Scholars across the world have carried out a large number of studies on imbibition mechanism ^[2⇓⇓-5], imbibition effect and influencing factors ^[6⇓⇓-9]. Cai et al. studied the imbibition mechanism by using the fractal theory^[10-11]. Yang et al. developed a physical simulation method for imbibition in different scales of cores, and investigated the influencing factors on the imbibition process in tight reservoirs, and constructed a quantitative evaluation method for imbibition in water flooding ^[12]. Aghabarari et al. ^[13] confirmed the significant effect of re- infiltration on naturally fractured reservoirs, and pro-posed a governing equation for oil discharge in a matrix block during the re-infiltration process. Andersen et al. ^[14] established an imbibition flow model for the interaction between water, oil and rock, and discussed the influence of viscosity on imbibition. Viscous coupling is beneficial to dynamic imbibition, but it is not beneficial to spontaneous imbibition. Qin et al. ^[15] developed a dynamic pore-network model, and analyzed complex pore with triangular, square, and circular cross-section shapes on imbibition efficiency and imbibition rate. Wang et al.^[16] established an imbibition model for fractured reservoirs, and found that oil saturation was low in the lower part of the core and near-fracture surface zone, but it was the highest at the two horizontal ends perpendicular to the fracture during dynamic imbibition. Cheng et al. ^[17] and Wang et al.^[18] studied the spontaneous imbibition of dual-porosity oil reservoirs and gas reservoirs by using the inclined capillary model, and obtained the maximum displacement and migration time of liquid imbibition by considering factors such as gravity, dynamic contact angle and fracture width.

A large number of experiments showed that surfactants can reduce interfacial tension and improve efficiency of imbibition and oil discharge (the percentage of oil discharged from a core to the total oil content) ^[5,19]. However, the imbibition driving force gradually changes from capillary force to gravity as the surface tension decreases and the capillary force decreases, which is not conducive to imbibition. Schechter et al. ^[20] proposed that the inverse Bond number should be used as the basis for steering judgment. If the inverse Bond number is greater than 5, capillary force is the dominant factor. If the inverse Bond number is less than 1, gravity is dominant. When the inverse Bond number ranges from 1 to 5 ^[20], both forces take into effect.

Nanofluids have been an important target in recent years for improving the effect of imbibition and oil discharge ^[3,21]. Compared with a surfactant system, a nanofluid complex system has a synergistic effect of wettability switch and reducing surface tension ^[3]. Xu et al. ^[3] compared the efficiency of imbibition and oil discharge of a non-ionic surfactant, a nano-SiO₂ fluid and a compound nanofluid of them. After the imbibition of salt water-based liquid, the core imbibition rate and oil removal rate in three systems are further increased by 2%-4%.

NMR imaging technology can directly reflect the dynamic characteristics of imbibition and oil discharge in nanofluids. Zhao et al. ^[7] tested the NMR image of imbibition of carbon nanofluid and found that the efficiency of oil discharge in nanofluid increased with time. In comparison, the imbibition efficiency in fresh water remained almost unchanged after reached a certain degree. Zhou et al. ^[22] recorded the imbibition process of nanofluid and salt water in tight sandstone cores by using NMR imaging, and the results showed that core imbibition of nanofluid can continuously advance to the core center, while the imbibition of salt water can’t.

NMR imaging is an important method to detect the distribution characteristics of crude oil during imbibition. Its results are more intuitive and reliable, but there are few studies on related mechanisms. This article aims at the problems existing in the core imbibition and shifting nuclear magnetic resonance (NMR) imaging experiment, such as the loss of surface oil phase and the adsorbing of air. The experiment was improved, which contains design of the in-situ imbibition NMR method. Using the method, sandstone core imbibition experiments are carried out in nanofluids, and the entire process of oil migrating image is recorded. At the same time, the imbibition characteristics of sandstone cores with different permeabilities in nanofluids are analyzed based on the physical properties of sandstone cores and the changes of driving force during imbibition.

The basic method of core imbibition NMR imaging is to take out the core regularly in the imbibition process, and then put it into the core holder for imaging test. After the test, put the core into the liquid to continue the imbibition process, and thus operate repeatedly to complete the whole experiment. This method can obtain the changing core imbibition NMR images. However, the loss of oil phase on the surface and the adsorption of air will have a certain impact on the effect of oil discharge and the change of the driving force during imbibition after moving the core from original imbibition condition, and consequently affecting the accuracy of the experimental results. The experimental method is improved to solve this problem, and the in-situ visualization experiment method is designed. Namely during the whole experiment process, the core saturated with oil is immersed in the nanofluid all the time, and the NMR image is taken regularly without taking out the core. In other words, the imbibition process is kept going on during the whole experiment, so there is no loss of oil phase and air adsorption phenomenon. Therefore, it will not affect the effect of oil imbibition and the change of driving force in the imbibition process. The specific experimental process is as follows: (1) Put an oil-saturated core into an imbibition bottle. (2) Pour the prepared SNFQ nanofluid (self-made nanofluid by Shanghai University Petroleum Center) into the imbibition bottle. (3) Put the imbibition bottle into the coil of the NMR instrument, and start the software to automatically and regularly collect T₂ (transverse relaxation time) spectra and imaging data. The volume of discharged oil can be directly read on the glass tube scale on the upper part of the imbibition bottle (precision at 0.05 mL).

Equipment: MesoMR12-060V-I nuclear magnetic resonance apparatus, BH-Ⅱ vacuum pressurized saturation apparatus, SL-2 core porosity and permeability measurement unit and several glass imbibition bottles. In the experiment, the opening of the NMR instrument is upward to facilitate the placement of the imbibition bottle.

Liquid materials: (1) Prepared SNFQ nanofluid using ordinary water, used for testing the concentration of nanofluid. (2) Nanofluid prepared with deuterium oxide for imbibition nuclear magnetic experiment. The deuterium oxide is produced by Beijing Bellingwei Technology Co., LTD. The nano-powder is NP hydrophilic powder (produced by Nanocentre of Shanghai University) with particle sizes of 10-20 nm. Add the nano-powder into the deuterium oxide and stir evenly to prepare the nanofluid with a mass concentration of 0.15%-0.30%. Finally, the nanofluids is dispersed by ultrasonic wave for 15 min. (3) The oil sample is made of diesel oil and crude oil from Xinjiang Karamay Oilfield at a ratio of 4 to 1, with a density of 0.835 mg/L.

Experimental cores: (1) Heterogeneous two-layer cores provided by Beijing Shida Rongzhi Technology. (2) Artificial sandstone cores are non-magnetic cores made in laboratory. (3) Natural cores are from Kramay Oilfield. All the cores are hydrophilic or weakly hydrophilic, with porosity ranging from 10.20% to 36.20% and gas permeability of (0.013-1663)×10^-3 μm² (Table 1).

According to the core permeability, set different experimental environment and experimental procedures, three permeability experiments have been carried out: (1) At room temperature (20 °C), No. Y3-Y5 cores were selected to carry out core imbibition experiment in nanofluids prepared by ordinary water, focusing on the influence of nanofluid mass concentration on imbibition and oil drainage, and determining the appropriate nanofluid mass concentration. (2) Cores Y1-Y2 and Y7-Y12 were soaked in deuterium oxide-based nanofluids for 15 h at room temperature (20 °C), and then soaked at 80 °C for 5 h. Oil discharge, core in-situ NMR image and T₂ spectrum were collected at different time periods. (3) Core Y6 was used to soak in nanofluids prepared with deuterium oxide for 8 d continuously, and data of NMR image and T₂ spectrum were collected at an interval of 4 h.

Cores Y3-Y5 are weak hydrophilic with permeability of (1100-1250)×10^-3 μm². After saturated with crude oil, core Y4 was soaked in fresh water for 16 h, and then immersed in nanofluids with mass concentration of 0.5% for nearly 8 h. Cores Y3 and Y5 were immersed in nanofluids with mass concentration of 0.2% and 0.3%, respectively for 16 h, and the results of efficiency of imbibition and oil discharge were shown in Table 2.

The experimental results show that the imbibition and oil discharge effect of core Y4 in fresh water is very poor, with only a small amount of oil spout, and the efficiency of imbibition and oil discharge (EIOD) is only 1.0%. After the core was put into the nanofluid with 0.5% mass concentration, the EIOD was greatly increased to 61.1%. The EIOD of core Y3 in the nanofluid with lower concentration is 6.8%. The EIOD of Y5 in the nanofluid with higher concentration is better, up to 51.4%.

The main reason why nanofluids can greatly improve the effect of imbibition and oil discharge is that it can greatly reduce the interfacial tension of oil-water phase and the resistance of imbibition and oil discharge. Fig. 1 shows the relationship between interfacial tension of oil-water phase and nanofluids with different mass concentrations. The higher the concentration is, the lower the interfacial tension is. However, when the mass concentration exceeds 0.3%, the interfacial tension decreases slowly with the concentration. After comprehensively considering imbibition efficiency and experiment time, the mass concentration of 0.3% is taken as an optimal value and used in the rest experiments.

The cores of Y1-Y2 and Y7-Y12 were soaked for 15 h in nanofluid with mass concentration of 0.3% at room temperature (20 °C), and then soaked for 5 h at 80 °C. Fig. 2 shows the relationship between EIOD and imbibition time of five cores. It can be seen that: (1) When the experimental temperature is 20 °C and the imbibition time is 0-15 h, the EIOD curve increases rapidly in the initial period (0-4 h) and then increases slowly; (2) The higher the permeability is, the larger the pore diameter is, the smaller the flow resistance is, and the earlier the initial time of imbibition and oil discharge is. According to the experimental observation record, oil discharge started after 0.5 h in core Y1 with permeability of 1663×10^-3 μm². The oil discharge started after about 1.0 h in core Y8 with permeability of 16.5×10^-3 μm². In Y9 with permeability of 8.15×10^-3 μm² and Y11 with 0.08×10^-3 μm², oil discharge was slow and started at 2.0 and 3.0 h respectively. The initial oil discharge time is negatively correlated with the permeability. (3) When the experimental temperature is 80 °C and imbibition for 15-20 h, it can be seen that the EIOD of all cores were significantly increased because both the viscosity resistance and the interfacial tension decrease with the increase of temperature. The increase of temperature is beneficial for imbibition and oil discharge.

The EIOD per unit time is defined as imbibition rate. Fig. 3 shows the correlation curve of imbibition rate and imbibition time. (1) When the experimental temperature is 20 °C and the imbibition time is 0-15 h, the change of imbibition rate is different from that of EIOD. The higher the core permeability, the shorter the time of imbibition rate increase is. After 2.0 h of imbibition, the imbibition rate of cores Y1 and Y7 began to decrease. For the other cores, the time of imbibition rate beginning to decline was about 4 h. The specific reason is that Y1 and Y7 have high permeability, low resistance and fast oil discharge rate, and reach the peak of oil discharge earlier. However, other cores have low permeability, high imbibition resistance, low discharge speed and late starting point, so they need long time to reach peak oil discharge; (2) When the experiment temperature is 80 °C at 15 h to 20 h of imbibition, similarly, the imbibition rate increased firstly and then decreased. Because viscous resistance and interfacial tension reduced at high temperature, and the force balance between oil and water was broken at certain time, and promoted the discharge of oil. But the force tended to reach balance again with time, so the imbibition rate decreased.

Fig. 4 shows the T₂ spectrum curves of cores Y1, Y8 and Y11 at different imbibition time in nanofluid with mass concentration of 0.3% at room temperature. The area enveloped by the curve and horizontal axis represents the oil content in the core, while the relaxation time axis represents the pore size. The longer the relaxation time, the larger the pore size is. The figure shows that: (1) The right peak of the T₂ spectrum curve of core Y1 is the highest, the corresponding relaxation time is 117 ms, and the core storing space is dominated by large seized pore- throat. With the extension of imbibition time, only the right peak of the T₂ spectrum curve decreases significantly, indicating that the imbibition process is mainly in large pores and throats. The left peak of the curve almost does not change, indicating that oil in small pores and throats is difficult to discharge. (2) The relaxation time of the T₂ spectrum of core Y8 is 72 ms corresponding to the highest peak, the core storing space is mainly medium- sized pores and throats. With the extension of imbibition time, the peak of the T₂ spectrum curve drops sharply, and the left peak also declines to some extent, indicating that imbibition and oil drainage process is mainly carried out in medium pores and throats, while oil in small pores is also released with limited contribution. (3) The left peak of the T₂ spectrum curve of core Y11 is the highest, corresponding relaxation time is 0.9 ms. The core space is dominated by small pores and throats. With the extension of imbibition time, only the left peak of the T₂ spectrum curve decreases significantly, and the imbibition and oil discharge process is mainly carried out in small pores and throats. There is only a slight change in the right peak of the curve, indicating that oil discharge occurs in smaller pores and throats, while larger pores are not the main site but as main flowing channels.

Fig. 5 shows the appearance photos of cores Y10 and Y3 in nanofluid with mass concentration of 0.3% at room temperature. The permeability of core Y10 is 0.71×10^-3 μm², and the permeability of Y3 is 1250×10^-3 μm². On these photos, after soaking for 0.5 h, oil droplets appeared on the top of both cores, but no oil on the sides. After soaking for 80 s more, the oil droplets on core Y3 leaked out and appeared necking and breaking phenomenon, while the droplets of Y10 core didn’t show obvious change. After soaking for 128 s more, the oil droplets of core Y10 became a little larger but still not drained away, while more oil droplets of core Y3 were discharged at the original position. It shows that the higher the core permeability, the stronger the driving force of oil discharge is, and the smaller the resistance is. Discharging channels have occurred and forming forward imbibition. When core permeability is low, the driving force is weak and the resistance is large, and it will take longer time to form oil discharge channels.

Fig. 6 shows the NMR images of cores Y1, Y6, Y8 and Y10 after different imbibition hours in nanofluid with mass concentration of 0.3% at room temperature. The nanofluid was prepared with deuterium oxide and has no nuclear magnetic signal, as shown in blue. The nuclear magnetic signal of crude oil is shown in red. The darker the color, the higher the oil content and the stronger the signal is. The color changing from red to green, from light blue to dark blue represents the signals from strong to weak, and also represents the oil content from high to low.

The permeability of core Y1 is 1663×10^-3 μm², and that of core Y6 is 527×10^-3 μm². It can be seen that the image changes of the two cores have similar characteristics. The overall image signal weakens at the beginning of imbibition, and then weakens faster at the bottom of the cores, slower in the middle and upper edges, indicating that the crude oil in the bottom is discharged faster than that in the middle and upper edges. The bottom signal of core Y1 began to weaken significantly at 1 h and presented an inverted triangular image 20 h later. The bottom signal of core Y6 began to weaken slightly at 4 h and presented a fingerlike image 20 h later. This phenomenon is more likely to occur in cores with higher permeability. This is because the higher the core permeability, the larger the pore size is. Especially for a hydrophilic core, oil adhesion is weak and friction resistance on the pore-throat wall is small, so oil is driven upward by buoyancy and capillary force, which can overcome the influence of gravity and friction on the pore wall.

The permeability of core Y8 is 16.50×10^-3 μm², and that of core Y10 is 0.71×10^-3 μm², the changing characteristic is different from that of cores Y1 and Y6. It shows that the nuclear magnetic signal around the core weakens quickly, and then the trending gradually extends inward, indicating that the crude oil around the core is discharged first during imbibition. Then the internal crude oil diffuses and is discharged (the bright bar at the bottom of core Y10 means the residual gelatine in the process of placing the core by the oil discharge instrument, which does not affect the experimental results). Pores in the core with low permeability are small, so the capillary force is relatively large, the friction on the pore wall is large. As a result, the buoyancy and capillary force on oil is not enough to overcome the impact of pore wall friction and gravity, and it is difficult to drive oil moving upward. The oil is discharged mainly by capillary force along the nearest core wall.

When a core is immersed in the same liquid environment, the force type acted on oil droplets in different pore channels is consistent, but the magnitudes of the forces are different, and the characteristics of imbibition are different. In order to ensure the exact same imbibition environment, the double-layer heterogeneous artificial sandstone core (Y7) was selected for the imbibition experiment. The two layers of the core were prepared by quartz sand with different particle sizes under the same condition, and their wettability is completely identical. The left part has permeability of 300×10^-3 μm², and the right has 1500×10^-3 μm².

The NMR imaging of core Y7 in nanofluid with mass concentration of 0.3% at room temperature is shown in Fig. 7. The right side of the core has high permeability, large pore space, high oil content and strong signals. In the process of soaking, the image signal changes from strong to weak from top to bottom, showing the characteristics of oil discharged from the top of the core. The permeability of the left side of the core is relatively low, the pore space is relatively small, and the oil content is relatively low, so the signal is relatively weak. In the process of soaking, the image signal gradually becomes stronger from the periphery to the interior, which shows the imbibition characteristics of the crude oil around the core is discharged first, and then the inner crude oil diffuses out to the periphery.

Fig. 8 shows the NMR images at different time of Y6 core soaked in nanofluid with mass concentration of 0.3% for 8 d at room temperature. The permeability of core Y6 is 527×10^-3 μm². It can be seen that: (1) At the initial stage of imbibition (1-3 h), the overall image signal of core is obviously weakened, the crude oil in the surrounding of the core discharges first, and then crude oil in the center of the core disperses towards outside. (2) In the middle stage of imbibition (3-96 h), the signals at the bottom begin to be weakened at 3-15 h compared to the top, and the image appeared "finger-like" characteristics at 24 h. At the same time, the signals of the core are weakened overall, but the phenomenon on the lower edge of core is more obvious, indicating some oil droplets migrated from bottom to top. (3) In the later stage of imbibition (after more than 96 h), the nuclear magnetic signals are weakened further, and the weakening degree in the bottom part is obviously greater than that in the upper part, and the oil droplet migration from bottom to top is more obvious. The imbibition characteristics of medium-permeability cores are similar to those of low-permeability cores in the early stage, and similar to those of high-permeability cores in the mid-late stage. This is because that medium-permeability core was immersed in nanofluids for a long time, so the core wettability was improved and the hydrophilicity was enhanced, at the same time oil-water interfacial tension was reduced. The influence of these effects will extend from core surface to the center with soaking time, and break the balance of three-phase interface of water-oil-core, and finally change the way of crude oil discharge.

The nanofluids have the ability to change an oil-wet core to a water-wet core, or enhance the hydrophilicity of a water-wet core. Also, nanofluids can reduce the surface tension and induce structural separation pressure to displace oil at the three-phase interface ^[23]. When a core is immersed in nanofluid, the oil, nanofluid and core gradually approach to a three-phase interface balance, then the nanofluid begins to displace the oil droplets while the three-phase contact line moves forward and temporarily forms a dynamic balance. Nanofluid can reduce oil-water interfacial tension and converts oil-wet pore wall to hydrophilic (or enhances hydrophilicity), so as to change the affecting direction of capillary force (or increase capillary force). Forced by the structural separation pressure from the three-phase interface where nanoparticles accumulate, the interface balance is broken, and the three-phase interface line moves forward. Finally, a new three-phase balance appears. Again and again, the oil is gradually drained out. Nanofluids can improve the effect of imbibition and oil discharge, which is a synergistic effect of the wettability reversal of an oil-wet core (or increasing the hydrophilicity of a water-wet core), the reduction of interfacial tension and the formation of structural separation pressure. Therefore, when a core is immersed in nanofluid or surfactant, the EIOD rises slowly with time. But in water, it is easy to reach imbibition equilibrium and the EIOD won’t rise any longer^[3].

Nanofluids can greatly reduce oil-water interfacial tension and improve the efficiency of imbibition and oil discharge (EIOD). The higher the concentration, the lower the interfacial tension, and the higher the EIOD will be. However, when the concentration reaches a certain value, the increase rate of EIOD tends to be slow. With the increase of temperature, the viscosity resistance and interfacial tension of crude oil reduce, and the EIOD increases.

For the core with high permeability, the oil at the bottom may migrate upward and be discharged during imbibition. The higher the core permeability is, the more obvious this phenomenon, which is manifested as oil discharged at the top of core. For the core with relatively low permeability, the crude oil around the core is discharged first, and then the crude oil in the center disperses outward, showing the characteristics of surrounding oil discharge. The characteristics of imbibition and oil discharge of a medium-permeability core are similar to those of a low-permeability core in the early stage, and tend to be similar to those of high-permeability core in the middle and late stages. After being soaked in nanofluid a long time, the hydrophilicity of the core may increase continuously, the oil-water interface tension may decrease continuously, and oil may be discharged at the top in the middle and late stages.