Pore-scale imbibition comparisons between capillary and gravity forces reveal distinct drainage mechanisms and residual oil distributions

1. IntroductionThe imbibition of the wetting phase into porous media is a universalphenomenon in nature and is associated with many practical problems[1], such as water imbibition in soil [2], CO2 geo-sequestration [3], andproduction of crude oil [4]. In porous media, imbibition is the oil-waterdisplacement process driven by capillary or gravity force and is anessential enhanced oil recovery (EOR) approach for low-permeabilitypetroleum reservoirs [5,6]. Since gravity (density difference betweenoil and water) cannot be altered in actual oil field development, varioussurfactants that possess high interfacial activities were injected into theformation to enhance the imbibition effect by increasing capillary force[7,8] or crude oil [9]. Theoretically, the dynamics and associated resultsof capillary force-driven [10] and gravity-driven [11] imbibition areinherently different. Capillary force-driven imbibition primarily isdetermined by factors such as interface wettability [12,13], fluid property [14], porous media geometries [2,6] and liquid-solid interactions[15]. Gravity-driven imbibition mainly depends on the gravitationalforce [16] and liquid-liquid interface interactions [17]. In general, thedominant force of an imbibition system is usually determined by theinverse bond number and the oil drainage direction (cocurrent orcountercurrent imbibition) detected from the core imbibition experiment [18–20]. However, the mechanism, mode and contribution of thetwo imbibition driving forces remain unclear, which prevents imbibitionfrom being fully utilized in actual production and optimization.At present, there is still a lack of a fully quantitative assessmentmethod for the imbibition effects of the main driving forces. On the onehand, only a few reports have directly provided a comparison ofcocurrent and countercurrent imbibition experiments. The capillaryforce-driven imbibition rate was discovered to be greater in the primarystage [15], but it is inadequate to be a universal law. On the other hand,a reduced contact angle is also observed in gravity-driven systems,which prompts the speculation that the capillary force contributes toimbibition [21]. However, it remains unknown whether or how muchthe capillary force contributes to imbibition.In addition, previous studies provide insufficient information on themicro mechanism and residual oil distribution features at the pore-scale[22,23]. Microscopic studies on capillary forces are limited to the threephases gas, liquid and solid, which cannot represent the characteristicsof oil-water-rock phases in real reservoirs [24,25]. The gravity effect onimbibition has only been investigated through horizontally or verticallyplaced micromodels without a description of imbibition rate and residual oil distribution change [22,26]. It can be summarized that thedeficiency of macro quantitative comparisons and micro-mechanismunderstanding makes it difficult to accurately interpret the actions andeffects of capillary force and gravity during the imbibition process.In this paper, two different surfactants were used for comparativeexperiments, one of which leads to gravity-driven imbibition and theother to capillary force-driven imbibition. First, static core imbibitiontests were performed in imbibition cells to compare the oil recovery rateand imbibition rate. Then, microtube imbibition experiments weredesigned to investigate the micro mechanism and residual oil distribution features of the two imbibition systems. Finally, force-displacementcurves (F-D curves, measured by atomic force microscope (AFM)) wereemployed to analyze the formation mechanism of various solid-liquidinterface interactions. The objective of this study is to identify themicro-mechanism and residual oil distribution features of differentimbibition systems and provide a basis for production optimizationthrough imbibition.

2. Experimental section2.1. MaterialsTwo surfactants, surfactin (a biosurfactant produced by Bacillussubtilis in the laboratory, MW=1036) and an anionic gemini surfactant(AG, Xylene di-C14/C16-sulfonate, Oil Chem, MW=746), were used inthis study (Fig. 1).The simulated oils for the experiments were crude oil (density is0.93 g/cm3 , viscosity is 76 mPa⋅s, from Shengli Oil Field) and kerosene(density is 0.80 g/cm3 , viscosity is 0.79 mPa⋅s, from Sigma-Aldrich)mixed at a volume ratio of 1:5 and having a density of 0.91 g/cm3 andviscosity of 13 mPa⋅s. These properties were tested at 65 ◦C.The artificial brine used in this study contained NaCl (2900 mg/L),MgCl2⋅6H2O (100 mg/L), and CaCl2 (200 mg/L) at pH 7.0. brine wasused to prepare surfactant solutions with surfactin (0.2 wt%) and AG(0.35 wt%). Additionally, the interfacial tensions (at 65 ◦C) between theaqueous phase, namely, brine, surfactin and AG solutions, and thesimulated oil phase were 15 mN/m, 6.9 mN/m and 0.0065 mN/m,respectively. Low-permeability natural cores were obtained fromShengli Oil Field, China (Table 1).2.2. Experimental methods2.2.1. Imbibition cell experimentThe cores were saturated with the simulated oil. The original oilsaturation (so) is shown in Table 1. Then, the cores were aged in oil at65 ◦C for 30 days. The aged cores were placed in imbibition cells filledwith the aqueous phase, namely, brine, surfactin and AG solutions. Thetiming was started when cores were immersed. Then, the oil recoveryand imbibition rate were calculated after recording the oil productionregularly.2.2.2. Visualized pore-scale imbibition experimentThe pore-scale imbibition system is depicted schematically in Fig. 2.The apparatus comprises four primary systems: a microtube model, asyringe pump, a temperature controlling device and an imaging system.The syringe pump was used to inject the aqueous phase into themicromodel. The temperature controlling device was utilized to maintain a constant internal temperature (65 ◦C) in the model. An imagingsystem consisting of a high-resolution microscope and a high-resolutioncamera was used to capture and record the imbibition process.The micromodel was formed by bonding and sintering an etchedglass plate and another glass cover plate (40 × 40 mm2 ) [27,28]. Thesetup included fluid transport channels and imbibition microtubes (inthe black box of Fig. 2). Transport channels I and II (depth 20–25 µm anddiameter 200 µm) were saturated with oil and aqueous phases, respectively. To inject fluids, inlets (a and d) and outlets (b and c) weredesigned in transport channels I and II, respectively. Three microtubes(diameters of 20 µm, 40 µm, and 60 µm) connecting transport channels Iand II were the observation regions for pore-scale imbibition.The experimental procedures were as follows:(a) Oil saturation stage. The micromodel was vacuumed and oilsaturated with 30 days of aging.(b) Primary water flooding stage. After closing a and b, the aqueousphase was slowly injected from c with a flow rate of 0.05 μL/min.However, the imbibition liquid still could not avoid flooding intothe microtubule and affecting the crude oil interface.(c) Imbibition stage. The inlets and outlets of the micromodel wereopen. The morphology and motion of the oil-water interface inthe microtubes were observed. In addition, transport channel Iwas on top when the micromodel was oriented vertically.2.2.3. Contact angle measurementPreparation of the oil-SiO2 substrate. First, the substrate (SiO2,1.5 ×1.5 cm2 , JGS2 Material) was ultrasonically cleaned sequentially inacetone, anhydrous ethanol, and deionized water for 10 min and driedby using high purity nitrogen (99.99%, Beijing Malti Technology Co.,China). Second, the oil evenly covered the clean substrate by using anHAD-A280 spin coater (6000 rpm, Beijing Hengold Instrument Co., Ltd.,China). Third, the oil-SiO2 substrate was placed in a clean environmentQ. Ma et al. Colloids and Surfaces A: Physicochemical and Engineering Aspects 653 (2022) 129981 3 and aged for 30 days at 65 ◦C.The contact angle between the oil droplet (volume of 2 μL) and oilSiO2 substrate (OCA20 meter, Dataphysics, Germany) was measured byutilizing the captive bubble method in solution.2.2.4. AFM measurementA ContAl-G (BudgetSensors, Bulgaria) probe with an elastic coefficient of 0.2 N/m and resonant frequency of 13 kHz was installed in‍ ‍‍‍FM-NanoviewOp-AFM (Suzhou Feisman Precision Instruments Co., China)‍‍‍‍.The morphology (5 ×5 ×0.1 µm3 ) of the oil-SiO2 substrate in differentsolutions was scanned. Then, the F-D curve between the probe and oilSiO2 substrate was obtained through F-D mode within a complete cycle(T = 80 ms). Furthermore, the substrate should be tested not less than 3times at a fixed location to ensure the repeatability of the results.

3. Results3.1. Imbibition cell experimentImbibition cell experiments were performed with different solutions(Fig. 3). In brine and AG solutions, the oil drained mainly from the top ofthe cores, conforming to the characteristics of cocurrent imbibition.However, in surfactin solution, countercurrent imbibition occurredbecause the oil drainage was distributed over all the surfaces of the core.The ratio between capillary and gravity forces was defined by Du Prey(1972) as the inverse bond number, which is used to determine thedominant force of an imbibition system and the oil drainage direction(cocurrent or countercurrent imbibition) detected from the core imbibition experiment [11,29]. According to the inverse bond number theory [30], gravity is the dominant force in brine and AG solutions,whereas capillary force dominates in surfactin solution.The oil recovery measured in AG and surfactin solution was 4.7%and 5.3% greater than that in brine (Fig. 4). Compared with the brine,the imbibition rate of AG and surfactin solution increased by nearly 3times. Within the first 50 min of the experiment, the maximum imbibition rate of surfactin solution (7.9 μL/min) was significantly higherthan that of AG solution (4.4 μL/min).3.2. Microscopic interface behavior of two effective imbibition systems inmicrotubesThe imbibition process in a horizontally placed microtube is depicted(Fig. 5). The results show that no significant oil-water migrationoccurred during the whole process of imbibition in brine and AG solution, and a residual oil film adhered to the wall. However, the surfactinsolution pushed the oil phase (maximum rate was 12.5 µm/min) andpeeled the oil film, leading to the appearance of a clear three-phase (oilwater-solid) interface. The orientation of this concave interface wasconsistent with the direction of migration. Because of differentdiameters of microtubules, the oil-water interface cannot be guaranteedto be at same horizontal position. The green line marks the initial position of imbibition, as shown in Fig. 5b. The results showed the imbibition rate of a small-radius microtube (20 µm) markedly exceeded thatof a larger-radius microtube (40 µm or 60 µm), proving that the capillaryforce was the dominant driving force (Fig. 5b).In surfactin imbibition, the meniscus in the smaller tubes advancedfaster than that in the larger tubes (Fig. 6). As shown in the Table 2, Thecapillary force (driven-force) is much larger than the viscous force (dragforce). Therefore, the effect of viscous force on imbibition process wasignored. In addition, gravity can be ignored in the imbibition process inhorizontal microtubes.Pc = 2σcosθ r (1)Fvis = 8μvL r2 (2)where Pc is capillary force, Pa; σ is interfacial tension, mN/m; θ is contactangle, ◦; r is microtube radius, mm, Fvis is viscous force, Pa; μ is oil viscosity, v is imbibition rate, mm/s, L is imbibition distance, mm.Fig. 7 shows the microtube test in the vertical direction, wheretransport channel I was filled with AG solution and was located at theupper end. The oil migrated upward along the wall (maximum rate is11.2 µm/min) and entered channel I after 90 min, which indicated thatgravity was dominant. The microtube was oil-wet, with a clear residualoil film on the wall.3.3. Analysis of interfacial features of oil-SiO2 substrates in threesolutions3.3.1. Contact angleThe contact angle of oil against the oil-SiO2 substrate was measuredin brine and surfactant solution (Fig. 8). The brine system wasintermediate-wet with a contact angle of 102◦ but became water-wet insurfactin (35◦) and AG (26◦) solutions.3.3.2. Surface roughnessThe variations in the surface morphology of the oil-SiO2 substrate were depicted by AFM (Fig. 9). When immersed in brine, a few smallpeaks appeared on the substrate, of which the mean roughness was3.11 nm. The mean roughness of the substrate surrounded by surfactinsolution was 0.29 nm with a nearly smooth surface. The mean roughnesssignificantly increased in the AG solution and reached 2.36 nm.3.3.3. Solid-liquid interfacial forceThe solid-liquid interfacial force between the probe tip and oil-SiO2substrate was obtained by AFM (F-D mode) in different solutions(Fig. 10). The distinct adhesion force existed in AG solution (14.6 nN)and brine (11.3 nN) and notably had a ‘hysteresis section’ within the Drange of 9.5–17.6 nm in brine. However, the solid–liquid interfacialforce was much lower in surfactin solution (0.44 nN).

4. Discussion4.1. Analysis of the dominant forces of imbibition and residual oildistribution featuresThe results of imbibition cell tests showed that the AG and surfactinsystems led to cocurrent and countercurrent flow, respectively. Moreover, inverse bond number theory demonstrated that the two systemswere dominated by gravity and capillary force [12,31]. For furtherconfirmation, the morphology and dynamics of the oil-water interfacewere observed in microtubes. The results showed that capillary forceplays a role in surfactin solution, while the AG system could only rely ongravity. Similar to AG system, studies on other surfactants (ultralowinterfacial tension) reported that the imbibition period can be significantly compressed by utilizing gravity (30 days when horizontallyplaced, only 4.5 h when vertically placed) [22]. Therefore, both the coreand microtube tests verified that the dominant driving forces of surfactinand AG solutions were capillary force and gravity, respectively.Compared with gravity, the imbibition rate driven by capillary forcewas higher in the primary stage, which was consistent with the results ofprevious core tests [31]. Therefore, to understand the real reasons forthe difference, further microtube tests were conducted in this paper. Theresults showed that gravity only promotes longitudinal motion andcauses oil to flow out of the top of the core (current imbibition). However, the capillary force can push oil along the horizontal direction (oildrainage from the core sidewall, countercurrent imbibition) so thatmore oil displacement channels (the core top and sidewall) are formedand contribute to a high imbibition rate.Moreover, dominant imbibition forces were also one of the controlling factors on residual oil distribution in microtube tests [21]. Thesystem driven by capillary force is generally considered to have the wallwettability altered from hydrophobic to hydrophilic during imbibition,and the residual oil coalesces into a “cluster” and distributes near theoutlet. For the system with gravity as the dominant force, after effusionof oil along the microtube wall caused by interfacial activity improvement, the residual oil forms films and stays away from the outlet.As discussed above, surfactant systems that are compatible withactual requirements (development rate, residual oil distribution, injection level, etc.) can be prepared and applied to improve the imbibitionoil recovery.4.2. Formation mechanism of different solid-liquid interface featuresThe solid-liquid interfacial interaction is critical in determining thewettability of certain surfactants [15,32,33]. Generally, as the contactangle decreases, the wall wettability can be converted from hydrophobicto hydrophilic [12,34]. Although some studies regard it as the criteria ofcapillary force driving the imbibition process [29], there is no directexperimental evidence of the contribution degree of capillary force. Inthis study, the microtube test results show that the contact angle of AGsolution decreased compared with that of brine, but the wall surface wasstill oil-wet (i.e., no capillary force). Therefore, the solid–liquid interface interaction cannot be singly distinguished by the value of the contactangle.To solve the above problem, further comparative analysis of thesolid-liquid interface interaction in the two systems was conducted byusing AFM. We believe that the bumps on the surface of the oil-SiO2substrate in the brine solution are small oil droplets. In comparison withthe other systems, we found that the surface bumps almost disappearedin the surfactin solution, but occurred in minor quantities with increasedroughness in the AG solution. It indicated that Surfactin can strip the oilfilm from the substrate surface and expose the original hydrophilicsurface, while AG only mixes with the crude oil and makes the oil filmthinner. This also gives a molecular explanation for surfactin solutionimbibed into the microtube by capillary force. The F-D results showedthat a strong adhesion force and “hysteresis section” appear when crudeoil (i.e., a hydrophobic, soft material) adheres to the oil-SiO2 substrate[35]. The SiO2 substrate is covered with an oil film with high adhesion,making the surface have similar mechanical properties to soft matterwhich causes the "hysteresis section" in F-D curve [36,37]. The surfactinsolution nearly eliminated the adhesion force, reflecting the disappearance of hydrophobic film on the surface. However, the adhesionforce in the AG solution showed the microscopic mechanical propertiesof a hydrophobic hard surface [38]. Although the contact angle of theAG solution showed strong hydrophilicity, a hydrophobic layer was stillpresent. This was consistent with the behavior of residual oil films inmicrotube tests.The considerable difference between the interface behaviors ofFig. 4. Imbibition oil recovery (a) and rate (b) with varying times in thethree solutions.Fig. 5. Imbibition process of brine (a), surfactin solution (b), an AG solution (c) in the horizontally placed microtube.Fig. 6. Imbibition rate of surfactin solution in horizontally placed microtubesof different radii with varying times.Table 2Calculation of imbibition driving force in surfactin solution for differentmicrotube radii.r (μm) Pc (Pa) Fvis (Pa) Pc - Fvis (Pa)20 565.11 27.04 538.0740 282.56 5.12 277.4460 188.37 1.15 187.22

surfactin and AG mainly resulted from their molecular structure(Fig. 11). Compared with surfactin, the hydrophobic group of the AGmolecule was closely arranged after insertion into the oil phase becauseof its small space occupation, and the hydrophilic groups were movedoutward to exhibit surface hydrophilicity [13]. However, the oil film onthe wall was not completely peeled. In comparison, the hydrophilicpeptide ring of surfactin possessed a large space occupation [39] andmultiple polar groups (two carboxyl groups, etc.). Therefore, the largehead group of the surfactin molecule can increase its contact probabilitywith the hydrophilic surface [40], and peel off the oil film on the solidsurface. Moreover, the scattered arranged hydrophobic groups of surfactin cannot provide a low-density hydrophobic region due to its largervolume [41]. Thus, there was no significant hydrophobic force, and theoil film was completely peeled, which contributed to the formation of astable hydrophilic surface and capillary force.In summary, the contact angle only reflects the character of theoutermost surface, while the wettability was determined by the distribution of surfactant molecules on the solid wall. Consequently, imbibition cell, microtube and AFM experiments are required to evaluate thetrue solid-liquid interface features and to determine whether the capillary force can be regarded as the dominant force.

5. ConclusionsIn practice, imbibition is an effective EOR method. Although abundant research findings on imbibition had been published [6,22,42,43],the pore-scale oil drainage mechanism, mode and contribution ofcapillary force and gravity remain unclear. In this study, the pore-scaleimbibition process and residual oil distribution features in differentimbibition systems were analyzed, and the research on surfactin EORand evaluation of reservoir adaptability may be instructive. Microtubeimbibition tests revealed differences in pore-scale mechanisms and residual oil distribution between the surfactin solution (capillaryforce-driven) and the AG solution (gravity-driven). Although the EORvalues were relatively close, surfactin and AG solutions exhibiteddifferent dominant forces, cocurrent imbibition and countercurrentimbibition. Besides, capillary forces cause the surfactin system to have afaster initial imbibition rate than the AG system. It was concluded thatdifferent imbibition driving forces act in different stages. In addition, aclear oil-water-solid interface is created by the surfactin solution in themicrotube, and the residual oil forms a "cluster" near the outlet. Imbibition of the AG solution results in the formation of residual oil coatingson the microtube walls. It can be seen that residual oil “clusters”distribute in large pores during capillary force driven imbibition process, whereas attach to the pore wall in gravity-driven imbibition system. Furthermore, AFM revealed that solid-liquid interface propertiesreveal that surfactin solution can peel off the oil films so that the hydrophilic wall is exposed, which makes capillaries promote the accumulation of clustered residual oil at the microtube exit. Compared tosurfactin, AG molecules adsorbed onto the oil layer, resulting in insignificant capillary force and residual oil films attached to the wall. Thereasons for different imbibition features and residual oil distributioncaused by capillary force and gravity were further revealed inpore-scale.CRediT authorship contribution statementQipeng Ma: Writing – original draft, Methodology, Visualization.Weiyao Zhu: Conceptualization, Resources, Supervision. Wengang Bu:Writing – language editing. Zhiyong Song: Writing – review & editing,Funding acquisition, Resources, Supervision. Hua Li: Methodology.Yajing Liu: Methodology.Declaration of Competing InterestThe authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influencethe work reported in this paper.Data AvailabilityData will be made available on request.AcknowledgmentsThis study was supported by the National Natural Science Foundation of China (51974013).References[1] K. Singh, M. Jung, M. Brinkmann, R. Seemann, Capillary-dominated fluiddisplacement in porous media, Annu. Rev. 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