Characterization of the Dynamic Imbibition Displacement Mechanism in Tight Sandstone Reservoirs Using the NMR Technique

School of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, China Engineering Research Center of Development and Management for Low to Ultra-Low Permeability Oil & Gas Reservoirs in West China, Ministry of Education, Xi’an 710065, China State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4 CNPC Greatwall Drilling Company, Chaoyang, Beijing 100101, China


Introduction
Tight oil is a key area of global unconventional oil development [1]. Unconventional tight oil and gas resources in China are widely distributed and have great development potential [2,3]. Tight oil and gas resources are found in the Triassic strata of the Ordos basin, Permian strata of the Junggar basin, Cretaceous strata of the Songliao basin, Paleogene strata of the Bohai-Bay basin, and other strata, which have broad prospects of exploration and development [4]. The tight oil in the Ordos basin is a typical representative of the tight oil resources of continental sedimentation in China. However, compared with the marine tight oil in North America [5][6][7], there are various types of pores and throats in the tight sandstone reservoir of the Ordos basin. Moreover, the pores and throats are small and widely distributed, with developed microcracks and strong heterogeneity [8]. This results in difficulties in water injection, serious water breakthrough and out, and low oil recovery in tight oil development. It is of great importance to take advantage of imbibition to improve waterflooding performance.
Imbibition, as an important displacement mechanism in ultralow-permeability reservoirs, has been widely investigated by a large number of scholars [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Extensive experimental and theoretical studies were carried out to investigate the effect of imbibition on oil recovery and establish classical imbibition models. Spontaneous imbibition experiments were conducted to investigate the ultimate oil recovery, pore structure, and relative permeability curve related to imbibition, further confirming the dominant parameters of imbibition. In addition, some scholars [24][25][26][27][28] have studied the effects of surfactants and other additives on imbibition displacement. With the development of shale oil, the study of imbibition displacement has been shifted from tight sandstone/carbonate reservoirs to shale oil reservoirs. Kuila et al. [29] found that water could be imbibed into almost all nanopores of shale. Later, some scholars [30][31][32][33][34] carried out experiments to study the imbibition displacement mechanism in shale oil reservoirs and analyzed its feasibility. They examined the effects of surfactant and pH value of suction liquid on spontaneous imbibition recovery.
Compared with static imbibition, dynamic imbibition considers the effect of fluid flow in the matrix and fracture on imbibition displacement in the tight reservoir development. Experimental studies on dynamic imbibition [35,36] have been carried out. They proved the existence of a critical flow rate in the process of imbibition displacement. When the flow rate is higher than the critical flow rate, water breakthrough tends to occur. A corresponding numerical model was developed to capture this phenomenon. Pooladi-Darvish and Firoozabadi [37] analyzed the difference of counter-current imbibition and cocurrent imbibition after water breakthrough in the cores with different permeabilities. Some scholars [28,[38][39][40][41][42] have studied the effects of core wettability, initial water saturation, interfacial tension (IFT), fluid viscosity ratio, soaking time, and permeability on dynamic imbibition. Hammond and Unsal [43] simulated and developed the correlation between the displacement pressure and the imbibition rate during the dynamic imbibition process. Sharma et al. [44] quantitatively evaluated the effects of the flow rate and viscosity ratio on dynamic imbibition displacement. They established a scaling model of dynamic imbibition with the consideration of both the capillary and viscous forces. Qiao et al. [45] and Andersen et al. [46] studied the effect of viscous coupling on the efficiency of dynamic imbibition displacement.
Previous studies mainly applied the conventional core flooding setup to investigate the effect of dynamic imbibition on oil recovery and displacement efficiency. However, the real-time oil-water distribution in different pore-throatfracture systems cannot be characterized quantitatively during the dynamic imbibition with conventional experiments. Although some scholars have studied the effect of the injection rate on dynamic imbibition, few studies have been done to investigate the relationship between the critical (optimal) injection rate and the core permeability. The total injection volume is very important for cost control and optimization of water injection. Previous studies on the effect of injection volume on the efficiency of dynamic imbibition displacement are also lacking. Moreover, the comparison of oil and water distribution in pore-throat-fracture systems between static and dynamic imbibition has not been reported. The field application conditions of imbibition recovery in tight reservoirs are still not clear.
In this work, an experimental technique is developed to investigate the real-time distribution of oil and water in pore-throat-fracture systems using tight sandstone cores with various permeabilities in the Ordos basin. The effect of the displacement rate and volume on oil-water distribution in the core microstructure is well clarified. A correlation is developed to represent the relationship between the displacement rate, displacement volume, and core permeability. In addition, the differences between static and dynamic imbibition on imbibition displacement are quantitatively evaluated. This study provides a theoretical foundation for enhancing oil recovery in tight sandstone reservoirs.

Experimental Section
2.1. Core Samples and Fluids. The cores used in the experiments are from tight sandstone formations of the Yanchang group in the Ordos basin. The porosity and permeability are low, but microcracks are well developed. Based on the FE-SEM (FEI Quanta200F) and thin section petrography (TSP) technique tests for four samples shown in Figure 1, it is found that types of pores of tight sandstone in the Yanchang group are mainly intergranular pores, followed by feldspar dissolved pores and debris dissolved pores. The core properties are shown in Table 1. The porosity ranges from 8.29% to 12.36%, and the permeability ranges from 0.138 to 2.451 mD. Synthetic formation water in the target reservoir is used in the experiments. The water used in the experiments is the synthetic formation water in the target reservoir block (water type is CaCl 2 , salinity is about 18000 mg/l, and viscosity and density at 50°C are 0.523 mPa·s and 1.02 g/cm 3 , respectively). The fluorocarbon oil is used in the experiments (viscosity and density at 50°C are 3.67 mPa·s and 0.82 g/cm 3 , respectively). The viscosity and density are almost equivalent to the formation crude oil. Fluorocarbon oil is able to shield the signal of crude oil in NMR because it does not contain hydrogen. The measured IFT between synthetic formation water and fluorocarbon oil is 12.15 mN/m using an interface tensiometer. In addition, the contact angles of different cores in oil/water/core systems were measured.

Experimental Setups.
In this experiment, a constant rate and constant pressure pump (ISCO-500D, USA) is used to control the displacement rate and pressure. The confining pressure can be controlled by injecting fluorocarbon oil with a manual pump, and the maximum confining pressure can reach 20 MPa. The test temperature is controlled by the incubator to maintain the formation temperature. The NMR setup (Niumag Corporation, China) is used to measure the T 2 spectrum of synthetic formation water at various experimental conditions. In addition, the experimental setups also include transfer cylinders in which the brine is injected into 2 Geofluids core samples and a core holder which is made of PEEK materials with no hydrogen. The NMR instrument includes a magnetic body, radiofrequency emitter, and data collection system. The basic parameters of NMR measurements are set. The waiting time and echo time are 5 s and 0.25 ms, respectively. The scanning number and echo number are 16 and 1024, respectively. It was noted that fluorocarbon oil without hydrogen signals does not affect the NMR response. As a result, there is no effect on the measurement of the NMR T 2 spectrum for brine. Figure 2 presents the schematic diagram of the dynamic imbibition displacement experiment using the low-field NMR technique. The test temperature is 50°C. The experimental procedures are summarized as follows:

Experimental Procedures.
(1) Place the core in an extraction vessel with a volume ratio of benzene to alcohol of 1 : 3 to wash the oil.
Heat the core to 105°C in an incubator after washing oil and maintain the temperature for 48 h. Then, take out the core and measure the dry weight and dimensions of the core (2) Due to the small pore radius of the tight reservoir, conventional vacuum saturation cannot make the core pore completely saturated with water. So, the core is placed into the core holder, and a highpressure displacement device is used to inject synthetic formation water into the core. When the produced liquid is about 5 PV, the NMR spectrum is measured for the first time. The injection is continued until the production reaches 10 PV. The NMR spectrum is measured again. When there is no significant difference between the two NMR spectra, it can be concluded that the core pore is completely saturated with formation water    (3) Displace fluorocarbon oil at a low rate using the highpressure displacement system. The core is considered to be saturated with fluorocarbon oil when the liquid production is 5 PV, and measure the T 2 spectrum of the core (4) Displace the synthetic formation water at a constant rate using the high-pressure displacement system, and measure its T 2 relaxation time spectrum (5) Change the experimental conditions (displacement rate, displacement volume, etc.) and repeat the experimental procedures (1)-(4). It should be noted that injection pressure can be adjusted timely to maintain the constant displacement rate 2.4. Low-Field Nuclear Magnetic Resonance (NMR). The decay rate of the NMR signal can be described by the longitudinal relaxation time T 1 and transverse relaxation time T 2 . Because the measurement speed of T 2 is fast, the T 2 measurement method is often used in NMR measurement. The collision between the hydrogen nucleus and the pore wall occurs when the hydrogen nucleus is in transverse relaxation motion, which results in the energy loss of the hydrogen nucleus. The more frequent the collisions, the faster the energy loss of the hydrogen nucleus, thus accelerating the transverse relaxation process of the hydrogen nucleus. The frequency of collision between the hydrogen nucleus and the pore wall is determined by pore size. The larger the pore, the smaller probability the hydrogen nucleus collides with the pore wall, and vice versa. The pore size is inversely proportional to the relaxation rate of hydrogen nuclei, which is the theoretical foundation to investigate pore structure using the NMR spectrum (or T 2 spectrum) [47]. T 2 is calculated using the following formula: where T 2B is the relaxation contribution from the fluid itself (i.e., bulk relaxation) with the unit of ms; T 2D is the relaxation contribution from the magnetic gradient diffusion (i.e., diffusion relaxation) with the unit of ms; and T 2S is the relaxation contribution from the rock surface (i.e., surface relaxation) with the unit of ms. When NMR technology is applied to the analysis of tight sandstone cores, the diffusion relaxation can be ignored because it is too small. Therefore, the T 2 relaxation time mainly comes from surface relaxation, followed by bulk relaxation. Surface relaxation is closely related to the specific surface area of tight sandstone cores. The specific surface area of rock refers to the ratio of the pore surface area to the pore volume in rock. The larger the specific surface area, the larger the surface relaxation, the smaller the T 2 relaxation time, and vice versa. Therefore, the T 2 relaxation time of the core can be expressed as where ρ is the relaxation rate in μm/ms and S/V is the specific surface area in 1/μm. Because T 2B is much larger than T 2 , 1/T 2B can be neglected. The relaxation time is mainly from surface relaxation.
where F S is the shape factor of the single pore (dimensionless) and r c is the pore radius in μm. By combining Equation (3), Equation (2) can be simplified as Using C = ρF S , Equation (3) can be transferred as It is obvious that the relaxation time T 2 is theoretically a linear function of pore radius r c . Therefore, the distribution

Results and Discussion
3.1. Effect of Injection Volume on Dynamic Imbibition. In order to quantitatively evaluate the effect of the injection volume and rate on the dynamic displacement efficiency in tight sandstone, the coefficient a is given to characterize the increment amplitude of displacement by dynamic imbibition at different injection volumes and rates of formation water, which is the relative displacement efficiency of dynamic imbibition under different injection volumes.
where V 0 is the area of the T 2 spectrum peak of irreducible water in the core and V i is the area of the T 2 spectrum peak of formation water under different injection volumes and rates.
The displacement experiments are carried out using synthetic formation water with a 0.1 ml/min displacement rate at different injection volumes. The effects of different injection volumes on the dynamic imbibition displacement of the reservoir core in the target block are evaluated, respectively, as shown in Figures 3-6 and Table 2.
As shown in Figures 3-6 and Table 2, the relative displacement efficiency of core dynamic imbibition increases gradually with the increase of injection volume of synthetic formation water. But the increased amplitude decreases obviously. With the same injection volume, the relative displacement efficiency of core dynamic imbibition increases with the increase of core permeability, especially for core samples No. Figures 3 and 6, respectively. T 2 spectrums present bimodal distribution. For the cores with high permeability, it contains more large pores (including microcracks), and the displacement of dynamic imbibition exhibits the best results at the same injection volume.

H-3 and No. H-21, as seen in
For ultralow-permeability reservoirs (permeability lower than 1.0 mD), as shown in Figures 4 and 5 for core samples No. H-7 and No. H-15, when the injection volume is 1.0 PV, the increment amplitudes of relative displacement efficiency of dynamic imbibition reach the maximum values of 30.6% and 49.6%, respectively. When the injection volume increases from 1.0 PV to 1.5 PV, the increment amplitudes of relative displacement efficiency are 18.1% and 21.7%, respectively, with small reductions. When the injection volume increases from 1.5 PV to 2.0 PV, the increased amplitudes of relative displacement efficiency are only 10.5% and 11.3%, respectively, with obvious reductions. When the injection volume increases from 2.0 PV to 2.5 PV, the increment amplitudes of relative displacement efficiency reach the minimum values of only 5.0% and 4.9%, respectively. Therefore, for ultralow-permeability reservoirs with permeability less than 1.0 mD, it is recommended to select an injection volume of 1.5-2.0 PV in the field design of imbibition oil recovery to achieve a high oil recovery.
For conventional low-permeability reservoirs (permeability in the range of 1.0 to 10.0 mD), as shown in Figures 3 and 6, respectively, for core samples No. H-3 and No. H-21, when the injection volume is 1.0 PV, the increased amplitudes of relative displacement efficiency reach high values of 91.7% and 80.3%, respectively. When the injection volume increases from 1.0 PV to 1.5 PV, the increased amplitudes of relative displacement efficiency are only 9.6% and 18.0%, respectively, with obvious reductions. When the injection volume increases from 1.5 PV to 2.0 PV, the increased amplitudes of relative displacement efficiency are as low as only 3.0% and 8.6%, respectively. When the injection volume increases from 2.0 PV to 2.5 PV, the increased amplitudes of relative displacement efficiency are as low as only 1.9% and 3.6%, respectively. Therefore, for tight reservoirs with relatively high permeability, it is recommended to select an injection volume of 1.0-1.5 PV to appropriately reduce the injection volume, so as to minimize the construction cost to the most extent on the basis of ensuring the displacement efficiency of dynamic imbibition.

Effect of the Displacement Rate on Dynamic Imbibition.
The dynamic imbibition displacement experiments are carried out with 1.0 PV injection volume at different displacement rates. The effects of different displacement rates on the displacement efficiency of dynamic imbibition in the reservoir core of the target area are evaluated (Figures 7-10). The displacement efficiency under different displacement rates is plotted based on Equation (6), as shown in Figure 11. It can be seen from the experimental results that the relative displacement efficiency of core dynamic imbibition increases and then decreases with the increase of the displacement rate. There exists an optimal displacement rate that achieves the highest relative displacement efficiency of dynamic imbibition. The synergistic effect of capillary pressure and viscous force can achieve the highest displacement efficiency at an optimal displacement rate. When the displacement rate is lower than the optimal displacement rate, capillary pressure plays a dominant role, and crude oil in small pores is easier to be produced. Therefore, it can be seen from Figures 7-10 that the relative displacement efficiency of small pores (left part of the T 2 spectrum) at a low displacement rate is higher than that at a high displacement rate. When the displacement rate is higher than the optimal displacement rate, the differential pressure drive plays a dominant role, and the crude oil in large pores is easier to be produced. Therefore, there exists an optimal displacement rate to displace crude oil in the pores to the most extent. In addition, when the displacement rate is high, the time of the oil-water exchange in the pores is shortened, so that the water in the pores is displaced prematurely, resulting in the decrease of imbibition displacement efficiency. Therefore, it is necessary to select the appropriate injection rate to achieve the best displacement efficiency in the field construction design.
It can be seen from Figure 11 that core samples with high permeability (such as No. H-3 and No. H-21) have higher relative oil displacement efficiency of dynamic imbibition than core samples with low permeability (such as No. H-7 5 Geofluids And No. H-15). The high permeability of tight sandstone means that not only there are more large pores but also there might be more microcracks. These microcracks in the tight core can increase the surface area of the core for imbibition and provide more channels for the imbibition, effectively promoting the imbibition. Under the experimental condition of dynamic imbibition, the flowing formation water can timely displace the oil replaced by imbibition from the large pore, improving the imbibition to a certain extent.
It can be seen from Figure 12 that the optimal displacement rate almost linearly increases with the increase of core permeability. When the reservoir permeabilities are 0.138, 0.281, 1.213, and 2.451 mD, the optimal displacement rates are 0.05, 0.1, 0.2, and 0.4 ml/s, respectively, and the corresponding maximum displacement efficiency of imbibition is 142.2%, 149.6%, 210.2%, and 211.6%, respectively.
The linear correlation between optimal displacement velocity and permeability is regressed as follows:

Comparison of Static Imbibition and Dynamic
Displacement. From the results in Section 3.2, the relative displacement efficiency of imbibition in small pores is higher at the low displacement rate. Based on this conclusion, the core sample No. H-2 is used to compare and analyze the effects of static imbibition and dynamic imbibition on displacement efficiency in this section. Static imbibition is also referred to as spontaneous imbibition. A nonwetting phase is displaced by a wetting phase in the porous medium only by capillary pressure, without other pressure differences. The static imbibition experiment is performed with the same experimental equipment in Figure 2. After the synthetic   formation water is injected, the valves at the inlet and outlet ends of the core are closed. The core is soaked for a period of time, then the T 2 spectrum is measured. When the soaking time of static imbibition is 24 h, 48 h, and 96 h, the increments of the recovery factor are 172.1%, 206.2%, and 219.1%. The experimental results are shown in Figure 13, in which the experimental conditions of the dynamic imbibition T 2 spectrum are measured at the injection volume of 1 PV and injection rate of 0.2 ml/s. It can be seen from Figure 13 that the displacement efficiency of static imbibition in small pores is higher than that of dynamic imbibition. The displacement efficiency of static imbibition increases with the increase of soaking time, but the increased amplitude slows down obviously after reaching a certain time, so the static imbibition also has the optimal imbibition time. However, the displacement efficiency of dynamic imbibition in large pores or microcracks is significantly higher than that of static imbibition. In the process of imbibition, the small pores can provide more forces for imbibition because of the small capillary radius, while the large pores or microcracks can provide an effective channel for the oil replaced by dynamic displacement. It is possible   8 Geofluids to obtain the highest efficiency of imbibition recovery only when these two aspects are combined effectively. Therefore, in the actual field process of waterflooding imbibition recovery, the static imbibition and the dynamic imbibition can be combined to achieve a higher recovery efficiency of tight sandstone reservoirs. In field application, a relatively small injection rate is applied to avoid water channeling. The well is then shut in for a while. The shut-in period is determined by laboratory spontaneous imbibition core experiments. An optimal injection rate is carried out based on the conclusions in Section 3.2 to perform dynamic imbibition to improve the final recovery factor.

Conclusion
The microdisplacement mechanisms of dynamic imbibition are investigated based on the NMR technique. A set of experiments, including dynamic displacement, spontaneous imbibition, permeability measurements, and scanning electron microscopy, are performed to analyze the effect of displacement volume and displacement velocity on displacement efficiency. Furthermore, the comparison between static imbibition and dynamic imbibition on displacement efficiency is performed. The conclusion can be summarized based on experimental results: 10 Geofluids (1) The relative displacement efficiency of core dynamic imbibition increases with the increase of injection volume, but the increased amplitude decreases with the increase of injection volume. Under the same injection volume, the relative displacement efficiency of core dynamic imbibition increases significantly with the increase of core permeability. For ultralowpermeability reservoirs with permeability less than 1.0 mD, it is recommended to select an injection volume of 1.5-2.0 PV. For low-permeability reservoirs with permeability greater than 1.0 mD, it is recommended to select an injection volume of 1.0-1.5 PV (2) The displacement efficiency of core dynamic imbibition shows a trend of first rising and then declining with the gradual increase of the displacement rate.
There exists an optimal displacement rate, under which the synergistic effect of capillary pressure and viscous force can achieve the highest displacement efficiency of dynamic imbibition. The optimal displacement rate almost linearly increases with the increase of core permeability. At a low displacement rate, the relative displacement efficiency in small pores is higher (3) The displacement efficiency of static imbibition increases with the increase of soaking time, but the increased amplitude slows down obviously after reaching a certain time. The displacement efficiency of static imbibition in small pores is higher than that of dynamic imbibition. However, the displacement efficiency of dynamic imbibition in large pores or microcracks is significantly higher than that of static imbibition

Data Availability
All data, models, and code generated or used during the study appear in the article, and the authors are not restricted from sharing their data and materials.

Conflicts of Interest
The authors declare that they have no conflicts of interest.