Investigation of Oil Saturation Development behind Spontaneous

Dec 16, 2016 - As the imbibition front constantly moves forward, the change of oil saturation behind the imbibition front ... For porous media of smal...
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Investigation of Oil Saturation Development behind Spontaneous Imbibition Front Using Nuclear Magnetic Resonance T2 Bin Liang,† Hanqiao Jiang,† Junjian Li,*,† Changcheng Gong,† Ruyi Jiang,‡ Shiyuan Qu,† Yanli Pei,† and Hanxu Yang† †

Key Laboratory for Petroleum Engineering of the Ministry of Education, China University of Petroleum, Beijing 102249, P. R. China Department of Science and Technology Management, China National Petroleum Corporation, Beijing 100007, P. R. China

‡

ABSTRACT: Spontaneous imbibition is a critical mechanism for the development of water-wet fractured reservoirs. In order to improve the ultimate oil recovery, it is important to understand the change of in situ oil saturation during the spontaneous imbibition process. In this study, spontaneous imbibition experiments of two ends open (TEO) are conducted using unconsolidated sand packs. The sand packs are filled with quartz sands of three different particle sizes respectively and are fully oil-saturated. Nuclear magnetic resonance (NMR) T2 is used to monitor the saturation development behind spontaneous imbibition front. For porous media of the same lithology, the imbibition speed and final oil recovery decline with the reduction of average pore size. As the imbibition front constantly moves forward, the change of oil saturation behind the imbibition front does exist, and the major decrease of oil saturation happens in the large pore space. In terms of a particular region behind the spontaneous imbibition front, with the progression of the front, the oil saturation gradient in the area declines. Specifically, the dramatic gradient descent occurs when the spontaneous imbibition front just passes by. The smaller the average pore size is (the larger the mesh of sand is), the more rapid the saturation changes behind imbibition front. For porous media of small pore size, even when the imbibition front has moved far away, oil saturation still changes a lot.

1. INTRODUCTION Spontaneous imbibition is an automatic process that the wetting phase is imbibed into porous media by the force of capillary pressure while the nonwetting phase is accordingly driven out.1 Spontaneous imbibition is powered by surface energy and counteracted by viscous forces. The spontaneous imbibition of wetting phase into porous media has always been of broad interest and is relevant to numerous practical problems.2,3 Spontaneous imbibition is an important phenomenon during various oil recovery processes and is a critical mechanism especially for the development of fractured reservoirs.4,5 In water-wetted fractured reservoirs, water is absorbed into matrix from the fracture surface and pushes the oil to fractures. Both co-current and counter-current spontaneous imbibition occur in different reservoir development stages,6,7 and they may coexist during water flooding in fractured reservoirs. Co-current flow means the two immiscible phases flow in the same direction, and counter-current flow means the two immiscible phases flow in the opposite direction.8,9 Understanding the mechanism of spontaneous imbibition is essential for the development of the fractured reservoirs.10 Researchers have done a lot of work in various aspects.2 Specific topics include the properties of the imbibition front,11 the capillary back pressure at an outlet face,12 the capillary pressure of the nonwetting phase at the imbibition front,13 sample shape and the boundary conditions,14 viscosity ratio,15 as well as counter-current and co-current flow.7 Among all of these scientific problems, boundary conditions and oil saturation development of the imbibition process still call for a large amount of attention. © XXXX American Chemical Society

There are several kinds of boundary conditions for spontaneous imbibition, (1) all faces open (AFO) condition, (2) two ends closed (TEC) condition, (3) two ends open (TEO) condition, and (4) one end open (OEO) condition. And boundary conditions have great impact on the imbibition performance.14 AFO is most commonly used because it is the easiest to conduct.16 However, the flow patterns of AFO boundary condition are complicated due to the existence of both co-current and counter-current flow. It is difficult to describe the imbibition process using the established mathematical models for the two-phase flow.2 Unlike the AFO case, OEO or TEO boundary condition is nominally linear. For incompressible liquids and the OEO boundary condition, the rate of uptake of wetting phase must be the same as the production rate of nonwetting phase at the open face.2 The flow pattern of the TEO boundary condition is even more complicated. In initial studies of spontaneous imbibition with TEO boundary condition, it was assumed that the process was counter-current imbibition. The imbibition process was equivalent to two back-to-back OEO imbibition models with a nonflowing boundary in the middle. Researchers have made effort to monitor the imbibition behaviors according to this boundary definition.17 However, further tests showed that the oil production of the two end faces was highly asymmetric, even though the water invasion from the two faces was essentially symmetric.18 This phenomenon was mainly caused by the difference in pore size distribution both along the core and at the end face, and the pore size variation of the latter could lead Received: November 4, 2016 Revised: December 4, 2016 Published: December 16, 2016 A

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tell whether and how the oil/water saturation would change behind the imbibition front. The motivation of this article is to investigate the in situ oil saturation development behavior behind the spontaneous imbibition front using NMR scanning which can reflect pore size distributions and fluid saturations during oil recovery process.34 In order to study saturation changes without interference, we use specifically designed quartz sand packed columns to ensure the co-current spontaneous imbibition and visualization of imbibition front. The article focuses on the in situ oil saturation changes within a specific area behind imbibition front as the imbibition front constantly moves forward. Meanwhile, we also study the effect of particle sizes on the imbibition speed, saturation development, and ultimate recovery.

to the differences in bubble pressure which is the threshold pressure to produce the oil from core end face.2 In addition, oil would flow across the hypothetical no-flow boundary in the middle of a core.19 A possible way to make co-current imbibition possible for TEO imbibition is to expose one end face to water (W) and the other end face to oil (O), while this configuration can allow the core to imbibe water from one face (W) and produce oil from the other face (O).20,21 We usually call this kind of boundary condition as TEO (WO). At the initial imbibition stage of TEO (WO) imbibition, almost all the oil is produced by counter-current imbibition from W face. When the oil phase pressure at the W face is less than the bubble pressure, the imbibition becomes purely co-current.2 Yet the counter-current imbibition of TEO (WO) could be prohibited by putting a slice of low-permeability core at the W face.22,23 NMR, as a nondestructive technique, together with the information obtained from Micro-CT X-ray images, has been applied to monitor spontaneous imbibition of distilled water in shale, sandstone, and volcanic rocks.24 It deepens the study of petrophysical properties in both conventional and unconventional reservoirs. Yang et al.25 put forward a characterizing method in evaluating fracturing fluid intake on water imbibition characteristics in tight reservoirs. Meng et al.24 focused on the appearance of preferential and non-preferential pores (micropores) during spontaneous imbibition in different rocks. The NMR peak was investigated by Gannaway 26 for the quantification of effective inorganic and organic porosity in gas shales. Odusina et al.27 presented a research of shale wettability with NMR to monitor sequential imbibition of brine and oil, finding the volume of oil imbibed is influenced by a combination of total organic carbon, thermal maturity, and organic pore volume. On the estimation of fluid saturation in spontaneous imbibition, using 2D NMR in organic shales, Nicot et al.28 gave experimental evidence of an NMR contrast between oil and water in organic shales and explored the cause of high T1/ T2 ratio. A methodology proposed from Ding et al.29 evaluated the mechanisms of water imbibition in sandstone gas reservoirs by using NMR to measure the amount of imbibed water and the gas saturation. Freedman et al.30 took advantage of two advances in NMR well logging, from which gained the brine and oil T2 distributions to compute saturation and oil viscosity values. Specifically, a critical issue in discussing dynamic saturation is saturation development. Baldwin monitored the in situ saturation development of AEO using magnetic resonance imaging (MRI) during spontaneous imbibition.31 Due to the co-current and counter-current spontaneous imbibition coexisted during AEO imbibition, it is controversial to conclude whether the oil saturation would unceasingly change after the imbibition front passed by. Wickramathilaka and Fernø et al. investigated the development of imbibition front using MRI.32,33 The MRI can effectively describe the movement of the imbibition front, however, it cannot accurately detect the saturation changes behind imbibition front. Mason et al.18 studied the water saturation profiles changes during TEO imbibition by NMR T2. Their work could precisely tell the change of water saturation profiles with continuous TEO imbibition. But the influence of backwash oil on water saturation cannot be distinguished considering the existence of counter-current imbibition. Therefore, they could not exactly

2. EXPERIMENTAL SECTION 2.1. Quartz Sand and Fluids. Quartz sand of different mesh sizes is used in this study. Same composition of quartz sand ensures the same interface properties. The chemical property of quartz sand is stable and will not react with fluids employed in our work. As wettability has a strong effect on spontaneous imbibition,35,36 contact angle tests are used to test the wettability of quart sand (Figure 1).

Figure 1. Contact angle of quart sand. The 100−200 mesh quartz sand is compressed to rock slices under the pressure of 30 MPa, and we soak the rock slices in the kerosene where a water droplet drips afterward. According to the contact angle, we conclude that the quartz sand is strongly water-wet. The specifications of the quartz sand are listed in Table 1.

Table 1. Parameters of Quartz Sand sequence number

mesh

particle size(um)

1 2 3

50−60 100−120 100−200

300−250 150−125 150−75

Two types of fluids are used in our experiments. Kerosene is used as the nonwetting phase. The density of kerosene is 0.8 g/cm3, and the viscosity of kerosene is 2.8 mPa·s. The wetting phase is synthetic brine of 100g/L MnCl2. Much higher than normal formation water salinity, this concentration of MnCl2 is able to block the signal of water during NMR T2 scanning. Thus, we can focus on the signal development of kerosene during the spontaneous imbibition process. 2.2. Spontaneous Imbibition Apparatus. Meng et al. previously came up with an experiment setup for spontaneous imbibition.23 Based on their work; we develop our apparatus as follows. Quartz sand is B

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Energy & Fuels filled into a transparent glass column with inner diameter of 10 mm. We select quartz column mainly for its resistant property and little impact on the experimental results. The schematic of the apparatus is shown in Figure 2. Both ends of the column are processed by mantle

in oil so that the relaxation time of the oil will keep unchanged and NMR T2 tests can serve as an indicator of oil saturation change.38 Relaxation time shows in the transverse coordinate of NMR T2 spectrum. The magnitude of relaxation time reflects the force that the fluid is subjected to. Under the condition that the properties of rock surface and fluid are the same, the magnitude of relaxation time reflects the pore size. Generally, the longer the relaxation time is, the larger the pore size is. There are some equations that describe the relationship between the pore size and relaxation time. For example:39

r= Figure 2. Experimental apparatus for spontaneous imbibition.

0.735T2 C

(1)

Where r is pore size, μm; T2 is relaxation time, ms; C is conversion factor, which can be obtained by pressure mercury curve-fitting. From the equation above we can conclude that the relaxation time and pore radius are positively correlated. In our experiments, what we concern is not the exact value of pore size but the oil saturation change, so we take the relaxation time roughly as the pore size. Figure 4 shows the NMR T2 spectra of three unconsolidated sand packs. After saturated with kerosene, the sample was scanned for the first time. As mentioned before, the longer the relaxation time is, the larger the average pore size is and the larger the signal amplitude is, the larger the free liquid volume is. Diagram reveals that the signal amplitude of quartz sand-filled tube with 50−60 mesh is the greatest; accordingly, its free fluid volume of the same pore size is the largest. In the case of 100−120 mesh when the relaxation time exceeds 100, the signal amplitude becomes smaller than that of 50−60 mesh case. This phenomenon is consistent with our general cognition that the 50−60 mesh quartz sand-filled tube possesses more large pores. We compare the T2 spectra of 100−200 mesh case with 100−120 mesh case, discovering that the former has higher maximum signal amplitude, while the corresponding pore sizes are almost the same. The 100−200 mesh quartz sand can be regarded as 100−120 mesh sand added with 120−200 mesh sand. Some large pores of 100−200 sand are filled with smaller particles so that the free flow space in large pores shrinks, whereas the maximum pore size is not heavily affected. Laboratory core analysis indicates that the NMR T2 spectrum of saturated water sandstone is typically bimodal where the right peak corresponds to the movable fluid and the left peak corresponds to the irreducible fluid; the T2 cutoff value of the movable fluid is usually near concave points between the two peaks.35 In our work, the T2 cutoff value is approximately 30 ms. 2.4. Experimental Procedure. The first part of the experimental system is the constant pressure maintenance system (Figure 5). ISCO pump40,41 continues to inject water into the water holder with a speed of 1 mL/min far faster than the speed of spontaneous imbibition, which keeps the container full to maintain a constant level of liquid. The second part is the imbibition experimental device. The constant pressure system provides a constant liquid level that is as the same height as the glass column. This ensures that capillary force is the driving force of the spontaneous imbibition and offsets the influence of gravity. We can observe the speed of the imbibition front through the ruler placed over the glass column. The outlet end is connected with weighing scales to record oil production. The third part is nuclear magnetic resonance system. The effective range of the magnetic field probe is 10 cm; therefore our major research area lies in the first 10 cm of the column. As the imbibition front moves forward by 10 cm each time, we will put the glass tube into the NMR system for T2 spectrum scanning. Since the quartz tube is 44 cm long, the whole process of the experiment needs to be scanned for four times. The glass column is processed with T2 spectrum scanning when the imbibition front distance is 10, 20, 30, 40 cm.

fiber and are sealed with austenitic 316 screw caps. Austenitic 316 is a kind of nonmagnetic material that guarantees the caps will not disturb magnetic field during the NMR scanning process. The apparatus can withstand a pressure gradient of up to 900 kPa. At the beginning of TEO imbibition, because the nonwetting phase pressure ahead of the imbibition front is stronger than the bubble pressure at the inlet, the nonwetting phase will be driven countercurrently. This phenomenon could be eliminated by placing a slice of strongly water-wet sandstone at the inlet side.22,23 In this study, the slice is cut off from an cylindrical core with a permeability of 2.3 um2 to nitrogen. The slice should be controlled within 1 mm and as thin as possible. A wire mesh is set at the left side of the slice to keep the sand flat and prevent the sand from being loose. 2.3. NMR T2 Test.37 In the NMR T2 test, “nuclear” refers to hydrogen nuclei (1H), which has a magnetic moment (tiny bar magnet). “Magnetic” means the instrument provides the magnetic field. Under certain conditions, a strong interaction between the hydrogen atom and magnetic field will be generated. This characteristic is “nuclear magnetic resonance”. It is known that water and oil are rich in 1H and the 1H will display different distribution patterns under different conditions, just as shown in Figure 3.

Figure 3. Schematic diagram of nuclear magnetic resonance. When a core sample, saturated with oil or water, is placed under natural conditions, the tiny bar magnets of hydrogen nuclei will show a random distribution. And the sample has no magnetic property. However, if the sample is placed in static magnetic field, the tiny bar magnets will head to the same orientation. The magnetic moment synthesis of each hydrogen nucleus is presented as a macroscopic magnetization vector. The magnitude of the magnetization vector is proportional to the number of the hydrogen nuclei, which is proportional to the volume of the fluid. In the NMR T2 spectrum, the signal amplitude is a representative of the macroscopic magnetization vector. Therefore, the larger the signal amplitude is, the larger the free fluid volume is. Since both oil and water contain hydrogen nuclei, it is difficult to separate them with the magnetic signal. However, if the core is soaked in MnCl2 solution for enough time, paramagnetic ions Mn2+ will diffuse into the water, therefore the relaxation time of water is reduced under the limit of instrument detection. Moreover, Mn2+ is insoluble

3. RESULTS AND DISCUSSIONS 3.1. Oil Recovery During Spontaneous Imbibition. Figure 6 describes the oil recovery process of different unconsolidated sand packs. The imbibition speed decreases with the reduction of particle size. The imbibition oil recovery C

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Figure 4. Schematic diagram of nuclear magnetic resonance.

Figure 5. Apparatus schematic of NMR T2 scanning for spontaneous imbibition experiments.

nonwetting is approximate; therefore, oil recovery did not vary linearly with square of imbibition time. The difference in imbibition speed can be roughly explained by the following equation. The permeability of a quartz sandfilled tube is

of 50−60 mesh quartz sand reached 80% at about 500 min, while the 100−120 mesh sand was only 63% at 1000 min. For the sand pack of 100−200 mesh, it needed around 2800 min to achieve a steady state, which was much longer than that of sand pack of 100−120 mesh. However, the final recovery of these two sand packs were almost the same. The plots of oil recovery versus the square root of imbibition time are shown in Figure 7. It was shown that the oil recovery was not proportional to the square root of imbibition time. This is not surprising. For linearly pure counter-current imbibition, it has been proven that the oil recovery is proportional to square root of imbibition time by numerical and experimental method.2,22,42−44 However, for co-current imbibition, the oil recovery varies linearly with square root of imbibition only when the viscosity of nonwetting phase is much smaller than the wetting.2 In this article, the viscosity of wetting phase and

K=

ϕ × r2 8τ 2

(2)

where K is the permeability of tube, ϕ is porosity, r is the average radius of macrospore, and τ is pore throat curvature. The capillary pressure can be written as45 pc =

2σwocos θwo r

(3)

where pc is capillary force, σwo is the interfacial tension which mainly depends on the nature of oil−water, θwo is contact angle D

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Figure 8. Developments of spontaneous imbibition fronts.

Figure 6. Oil recovery of different sand packs.

Figure 9. Change of average oil saturation behind imbibition front.

Figure 7. Oil recovery of different sand packs.

which depends on the oil−water and surface properties of rock, and r is the radius of macrospore. The Darcy’s law is

behind the imbibition front, and Swr is the irreducible water saturation. In our experiments, the sand packs are fully saturated with kerosene without irreducible water saturation, thus Swr = 0. It can be seen that all the average oil saturation curves present a declining trend. The average oil saturation of 50−60 mesh sand-filled tube is the lowest, with an average of 0.2, and the average oil saturation of 100−120 one is 0.42. The highest average oil saturation is 100−200 mesh sand filled tube which has the lowest sweep efficiency. 3.2. Saturation Development behind Imbibition Front. It is concluded from Figure 9 that all the average oil saturation curves show a declining trend. Why could this phenomenon happen? For a specific region behind the spontaneous imbibition front, does the oil saturation change as the imbibition front constantly moves forward? In this section, we try to explain this phenomenon using the NMR T2 scanning on the specific area within the first 10 cm near the inlet. The scanning procedure is described as Figure 10. Since the length of effective magnetic body is 10 cm, we choose the first 10 cm of the glass column as the study object. The glass column is scanned for the first time when the imbibition front arrives at 10 cm. Then we repeat the above step separately as the imbibition front arrives at 20, 30, and 40 cm. Figure 11 is the NMR T2 spectra of 50−60 mesh sand-filled sand pack at different imbibition periods. We have recognized

Aσwocos θwo kAΔP A ϕ × r 2 2σwocos θwo = · · = 2 r μL μL 8τ μL ϕr · 2 (4) 4τ

Q=

For the porous media of the same lithology and same fluids, the interfacial tension σwo and the contact angle θwo are the same. Therefore, it is true that the average pore size r and production speed Q are positively correlated, which approximately explains Figure 5. Figure 8 displays the development of imbibition fronts. We find that the larger the mesh size is, the slower the front development speed is. For the sand pack with 50−60 mesh quartz sands, it only takes 150 min to touch the end, while it requires 550 min for the 100−120 case and 1150 min for the 100−200 case. The average oil saturation in Figure 9 can be calculated by the following equation: Sor = 1 − Wo/Vfront − Swr

(5)

Where Sor is the average oil saturation behind the imbibition front, Wo is the oil production which depends on the development of the imbibition front. Vfront is the bulk volume E

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Figure 10. Apparatus schematic of the NMR T2 scanning sequences.

Figure 11. NMR T2 spectra of 50−60 mesh sand-filled tube at different imbibition periods.

that the relaxation time has positive relation with pore size and the signal amplitude is proportional to the volume of free fluid, hence we can regard the signal amplitude as the equivalent of oil saturation. There was a sharp decrease in oil saturation in large pores when the imbibition front just arrived at 10 cm. The signal amplitude was 0.27 times as much as the initial signal amplitude. And after the imbibition front reached 20 cm, large pores still presented an apparent drop in oil saturation (shown by the red arrow). Yet there was no significant change in oil saturation as the imbibition front continued moving ahead, indicating that the decline of oil saturation primarily happens in large pores. Figure 12 is the oil saturation of different throat size intervals at different imbibition periods. Obviously, most of the oil was stored in large pores while little existed in small and medium pores. For large pores, when the imbibition front arrived at 10 cm, the average oil saturation surprisingly plunged to 0.23. As

Figure 12. Oil saturation of different throat size intervals at different imbibition periods (50−60 mesh).

F

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Figure 13. NMR T2 spectra of 100−120 mesh sand filled sand pack at different imbibition periods.

the imbibition front reached 20 cm, the average oil saturation further fell to 0.11. And the average oil saturation at 30, 40 cm, is 0.09, 0.08 separately. We figure out that the average oil saturation has the biggest drop of 0.77 when the imbibition front arrived at 10 cm for the first time. The oil saturation went down further with a drop of 0.12 when the imbibition front was at 20 cm. However, there was nearly no drop in oil saturation by further washing. The average oil saturation only declined by 0.03 with imbibition front moving forward for another 20 cm. The same applies to small and medium pores. Figure 13 is the NMR T2 spectra of 100−120 mesh sand filled sand pack at different imbibition periods. The oil saturation plummeted in large pores when the imbibition front reached 10 cm for the first time. The signal amplitude was 0.49 times as much as the initial signal amplitude. And there was still a big fall in oil saturation when the imbibition front arrived at 20 cm. Unlike the 50−60 mesh case, we could also see a noticeable drop in signal amplitude when the imbibition front arrived at 30 cm. Figure 14 is the corresponding oil saturation of different throat size intervals in different imbibition periods. In terms of large pores, the average oil saturation decreased to 0.51 when the imbibition front arrived at 10 cm, and the average oil saturation of the scanned area further declined to 0.39 when the imbibition front arrived at 20 cm. When the front arrived at 30 cm, the average oil saturation fell to 0.31, and when the front reached 40 cm, the average oil saturation decreased to 0.26. The results show that the average oil saturation has the biggest drop when the imbibition front just arrives at 10 cm. However, the descent speed here is larger than that of 50−60 case during further imbibition process. Unlike the 50−60 mesh sand-filled case, the average oil saturation descended by 0.13 with imbibition front moving forward for another 20 cm. Meanwhile, the decrease gradient change of oil saturation gradually slowed down with the imbibition front moving ahead. As for the small and medium pores, the oil they bear was so little that the

Figure 14. Oil saturation of different throat size intervals at different imbibition periods (100−120 mesh).

average oil saturation was negligible during the whole spontaneous imbibition process. Figure 15 demonstrates the NMR T2 spectra of 100−200 mesh sand-filled tube at different imbibition periods. Results show that the oil saturation also had a drop in large pores when the imbibition front arrived at 10 cm. The signal amplitude was half as much as initial signal amplitude and the oil saturation was still at a relatively high level. The oil saturation also fell in large pores when the imbibition front arrived at 20 cm, 30 cm. As the imbibition front moved forward, the declining speed of oil saturation slowed. Figure 16 is the corresponding oil saturation of different throat size intervals at different imbibition periods. Similarly, the average oil saturation in large pores went down when the imbibition front reached 10 cm, although not as sharp as the 100−120 mesh; as the imbibition front moved forward per 10 cm, the average oil saturation dropped by 0.1. Compared to the 100−120 mesh case, the gradient change of oil saturation decrease was not notable (approximate linear), even when the imbibition front arrived at 40 cm, the value could still be up to G

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Figure 15. NMR T2 spectra of 100−200 mesh sand filled sand pack at different imbibition periods.

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Figure 16. Oil saturation of different throat size intervals at different imbibition periods (100−200 mesh).

small and medium pores bear little oil. The biggest drop in oil saturation occurs right as the imbibition passes the studied area. • The oil saturation development performance behind the imbibition front changes with different average pore size of porous media. The smaller the average pore size is (the larger the mesh of sand is), the faster the saturation changes behind the imbibition front. Even after the imbibition front is gone, its influence can still make the oil saturation change in porous media with small pore size.

AUTHOR INFORMATION

Corresponding Author

*[email protected]. Notes

0.1. On the side of small and medium pores, they held much more oil than the previous two cases and the average oil saturation declined gradually. We tend to attribute this result to the much greater quantity of small pores in the 100−200 mesh sand-filled tube.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support from the National Natural Science Foundation of China (Grant 51404280) is acknowledged.

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4. CONCLUSIONS • NMR T2 can objectively reflect the pore size and fluid distribution in porous media, and it is an effective means to study the saturation change during spontaneous imbibition. The longer the relaxation time is, the larger the average pore size is, the larger the signal amplitude is, and the larger the free liquid volume is. • As the average pore size reduces, the imbibition time increases while the ultimate recovery declines in porous media of the same lithology; oil saturation behind the imbibition front does change as the imbibition front constantly moves ahead. • For a specific region behind the spontaneous imbibition front, the descent gradient of oil saturation reduces in large pores when the imbibition front is moving forward;

REFERENCES

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DOI: 10.1021/acs.energyfuels.6b02903 Energy Fuels XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.energyfuels.6b02903 Energy Fuels XXXX, XXX, XXX−XXX