**2. Imbibition**

The main study of imbibition is through experiments. The spontaneous imbibition experimental setup is indicated in Figure 1. There is no extra pressure applied during the spontaneous imbibition. Figure 2 shows the forced imbibition experimental setup, which can apply injection pressure on a sample.

**Figure 1.** Two typical spontaneous imbibition experiments (**a**) measuring sample weight change by hanging on the balance; (**b**) measuring fluid volume change in imbibition vessel.

**Figure 2.** Typical forced imbibition experiment [11].

According to the experimental results, the imbibition rate and volume are significantly affected by various factors including wettability, initial water saturation, temperature, flow direction, fluid and rock properties, and clay content, which are described respectively in the following subsections.

**Wettability.** Wettability is an important factor that can impact the imbibition process. The wettability indicates the ability of a fluid to adhere to the walls of a solid. The fluid includes gas and liquid phases. When the three phases (gas, liquid, and solid) interact, the contact angles between the gas–liquid interface and the solid–liquid interface can be used to indicate wetting and non-wetting states. In the reservoir, the rock with the smaller contact angle exhibits a faster imbibition rate for the wetting phase [12]. Therefore, adjustment of the contact angle is an effective way to control imbibition and is widely investigated [13–18]. Zhou et al. [5,6] designed experiments to compare imbibition rates in shale samples with various contact angles. The results showed that the imbibition rate was strongly influenced by changing contact angles.

Wettability alteration is one of the main mechanisms to mobilize residual fluid during water flooding. The alteration is dependent on fluid composition, rock surface mineralogy, system temperature, pressure, and saturation history [19–23]. Imbibition process can also alter the wettability of formation rocks. In previous studies, there are several situations of wettability alteration due to imbibition, including the imbibition fluids being acid, water with specific ionic content, and surfactant.

Dilute acid imbibition pre, post, or during hydraulic fracturing could improve the wettability of carbonate-rich shale formations and hence improve production [24–28]. The reaction between acid and rock can alter the wettability of formations by weakening the oil–rock surface bonds on the oil-wet thin layer. The alteration is to improve the pore connectivity; thereby, the trapped oil and gas are easier to be produced.

When the ionic content in water is changed, the wettability of reservoirs can be altered. This usually happens during low-salinity or salinity-modified waterflooding. These mechanisms of the wettability alteration include fines migration and rock dissolution [29–32]; PH increases [33–35]; multi-component ion exchange [36–40]; and surface charge changes or double-layer expansion [41–51].

The purpose of surfactant in imbibition fluid is to mobilize residual saturation [52–55]. Wettability alteration toward the hydrophilic state and a decrease in interfacial tension (IFT) are caused by surfactant during imbibition [55]. Cationic surfactant adsorption in negatively charged sandstone cores can decrease the performance to lower IFT and wettability alteration [56]. Alameri et al. [57] reported that surfactants in combination with low-salinity water flooding could be applied to circumvent the high salinity challenge and improve recovery in oil–wet carbonate reservoirs. Surfactants or a hybrid of surfactant with low-salinity water were observed to improve the wettability and IFT of formations at the laboratory scale [11,18,49,58–60]. Figure 3 shows the wettability alteration (through contact angle measurements) of carbonate formation, sandstone formation, and shale (Three Forks shale formation) comparisons when the bulk fluids are seawater, seawater + CO2, and low-salinity water + CO2 [11].

Contact angle measurements within the pore space are not realistic; thus, the spontaneous imbibition and zeta potential measurements can provide realistic indicators of wettability alteration in porous media, especially in unconventional shale reservoirs [49,51]. Nontheless, Mahani et al. [44] measured contact angle and zeta (ζ)-potential of the carbonate −brine interface on crushed carbonate fragments. Their experiments showed that at lower brine salinities, the ζ-potential of the limestone −brine interface become more negative, which is indicative of a weaker electrostatic adhesion of the rock −brine interfaces and implies a wettability alteration to a less oil-wet condition. Alvarez and Schechter [49] performed spontaneous imbibition, contact angle, and ζ-potential measurements on siliceous unconventional liquid-rich Permian basin reservoir cores using surfactants and fracturing brine. Alvarez and Schechter [49] experiments show anionic surfactants superior wettability alteration.

**Figure 3.** Contact angle of carbonate (top row), sandstone (middle row), shale (bottom row) core samples after they were soaked in seawater (SW), carbonated seawater (SW+CO2), and carbonated low salinity water (LS1+CO2). The volume of oil droplets ranges from 4 to 15 μL [11].

> **Initial Water Saturation.** It is difficult to determine the effect of initial water saturation on imbibition through experiments due to several reasons. When the formation has higher initial water saturation, the amount volume of imbibition can be smaller or larger. The smaller imbibition amount was indicated by Blair [61] and Li et al. [62]. The larger imbibition volume was pointed out by Cil et al. [63], Zhou et al. [64], and Morrow et al. [65]. Bennion and Thomas [66] discussed the existence of the state of noncapillary equilibrium in a low-permeability gas reservoir with abnormally low initial water saturation, and the undersaturated matrix will imbibe a significant amount of water during drilling and completion, resulting in phase trap damage to the formation. In addition, some studies indicated there was little effect from the initial water saturation on imbibition [62,67,68]. The reason for the contradictory conclusions is that the capillary pressure and effective permeability both depend on water saturation. The capillary pressure has an inverse correlation to the water saturation, while the effective permeability of water has a positive correlation to the water saturation. Thus, when the initial water saturation is high, the capillary pressure is normally low, but the effective permeability of water is high. The imbibition volume is controlled by the opposite effects from low capillary pressure but high permeability. Therefore, Morrow and Mason [69] said that the influence of initial water saturation should be investigated specific to a formation. Zhou et al. [70] found that in shale, the lower initial water saturation could cause a faster imbibition rate and higher volume of the imbibition. This is due to the very small pore size of the shale, which causes

the capillary pressure to dominate the imbibition process when the initial water saturation is low.

**Temperature.** Temperature impacts imbibition because wettability and fluid properties change under various temperatures. Handy [71], Pooladi-Darvish, and Firoozabadi [72] indicated that higher temperature caused a faster imbibition rate. Peng and Kovscek [73] proved this conclusion through the forced imbibition experiment system with temperature control. Elevated temperature may result in formation damage due to fine migrations [74].

**Flow Direction.** The process of same flow direction for wetting and non-wetting phases is called co-current imbibition, which usually happens during the water flooding operation [75]. The opposite flow direction, which is regarded as counter-current imbibition, mainly occurs in unconventional formations and fractured water-wet reservoirs [75,76]. Qin [77] pointed out that the direction of the flow was determined through the wettability of the formation rock, fracture and boundary condition in the reservoir, and injection rate during operation. In the studies of Bourbiaux and Kalaydjian [78], Kantzas et al. [79], Pow et al. [80], and Li and Horne [81], it is found that co-current imbibition can cause a faster rate of recovery than counter-current imbibition.

**Fluid and Rock Properties.** Fluid viscosity, rock permeability, and pore size can impact the imbibition rate. When water displaces oil and gas in the reservoir, the imbibition rate increases as water viscosity increases [82].

Rock permeability is also a factor to influence the imbibition rate. The higher permeability is expected to have a higher imbibition rate [83,84]. However, Graham and Richardson [12] found that the high permeability ratio of fracture to matrix was difficult to relate to imbibition rate.

Pore size indirectly affects imbibition rate. The small size of pores can cause a high capillary pressure that is one of the driving forces of imbibition. Thus, the imbibition rate would be higher in the small size of pores. However, Egermann et al. [85] indicated that in unconventional formations, the pore size is small, while the permeability is also low. Hence, the imbibition could be still slow in unconventional formation.

**Clay Content.** In clay-rich formations, such as shale, imbibition is strongly affected by clay mineral [86]. Zhou et al. [6] analyzed the relationship between clay content and imbibition. In shale, the sample with higher clay content could imbibe more volume and at a faster rate than the sample with lower clay content. This was later confirmed in other experimental measurements, such as NMR [87], and the excessive imbibed water beyond capillary-driven water remains as irreducible water in the clay of shale. In addition, the imbibition of fluid with additives was also different in various clay content shale samples. In the high clay content sample, the fluid with 0.07% friction reducer has a greater imbibed volume than the fluid with KCl or KCl substitute (choline chloride, magnesium chloride, and tetramethyl ammonium chloride). However, the fluid with the 2% KCl was imbibed more than other fluids in the shale with less than 10% clay content.
