Impact of Pressure and Brine Salinity on Capillary Pressure-Water Saturation Relations in Geological CO

Capillary pressure-water saturation relations are required to explore the CO 2 /brine flows in deep saline aquifers including storage capacity, relative permeability of CO 2 /brine, and change to stiffness and volume. The study on capillary pressure-water saturation curves has been conducted through experimentation and theoretical models. The results show that as the pressure increases up to 12MPa, (1) capillary pressure-water saturation curves shift to lower values at given water saturation, (2) after the drainage process, residual water saturation decreases, and (3) after the imbibition process, capillary CO 2 trapping increases. Capillary pressure-water saturation curves above 12MPa appear to be similar because of relatively constant contact angle and interfacial tension. Also, as brine salinity increases from 1M to 3M NaCl, (1) capillary pressure-water saturation curves shift to lower capillary pressure, (2) residual water saturation decreases, and (3) capillary CO 2 trapping increases. The results show that pressure and brine salinity have an influence on the capillary pressure-water saturation curves. Also, the scaled capillary CO 2 entry pressure considering contact angle and interfacial tension is inconsistent with atmospheric conditions due to the lack of wettability information. Better exploration of wettability alteration is required to predict capillary pressure-water saturation curves at various conditions that are relevant to geological CO 2 sequestration.


Introduction
The demands for carbon-producing fossil fuels that have served the dominant energy resources for decades have been on the rise [1,2]. A growing discharge of carbon dioxide (CO 2 ) to atmosphere is anticipated. In order to reduce CO 2 emission into the atmosphere, geological carbon sequestration (GCS) is required to store a large amount of CO 2 in places such as depleted oil or gas reservoirs, coal seams, deep ocean sediments, and deep saline aquifers [3][4][5]. Among them, deep saline aquifers are the most promising area because of their large capacity reaching roughly 1,000 to 10,000 Gt of CO 2 , which accounts for 99% of potential storage capacity in the world [6,7]. CO 2 flow and CO 2 -water displacement in deep saline aquifers depend on relation between capillary pressure ( ) and water saturation ( ) under reservoir conditions [8][9][10][11]. This -relationship is usually termed as capillary pressure-water saturation curve or soil-water characteristic curve which has relationships with soil properties such as storage capacity [12], relative permeability of CO 2 /brine [13][14][15][16][17], strength of soils [18][19][20], and changes to stiffness of soils [21][22][23].
Capillary pressure ( ) has been expressed as a function of relative water saturation ( ) using two most popular equations suggested by Brooks and Corey [24] (1) and van Genuchten [25] (2): Advances in Condensed Matter Physics where is the water saturation, is the residual water saturation, is the capillary pressure, is the capillary air (or gas) entry pressure, and and are fitting parameters. With -and -values, both Brooks and Corey [24] and van Genuchten [25] models can be used to estimate the relative permeability of the fluids.
A capillary CO 2 entry pressure ( ) between two phases (CO 2 and water) in porous media is important for both caprock system and reservoir, which are related to CO 2 leakage from the underlying storage reservoir and CO 2 injection to reservoir, respectively [26,27]. A capillary CO 2 entry pressure can be calculated using the following Young-Laplace equation: where CO 2 is injected CO 2 pressure, water is the water pressure in reservoir, is interfacial tension between CO 2 and water, is water contact angle on mineral surface in water-CO 2 -mineral system, and is pore radius in porous media. Capillary CO 2 entry pressure is estimated using the contact angle and the interfacial tension at various pressure-temperature conditions relating to geological CO 2 sequestration (GCS) [26,[28][29][30][31][32][33][34][35][36][37]. Interfacial tension only varies within a small range of about 20-35 mN/m at the GCS relevant conditions [29,33,35], which has an influence slightly on the capillary CO 2 entry pressure. Contact angle shows relatively huge changes within the range of 7-10 MPa pressure [28][29][30][31]38], which has been explained through influential factors such as (1) the presence of the change of adsorbed water film thickness on mineral surface [39][40][41], (2) specific density of the function groups (silanol and silicic acid groups) on the mineral surface that influences the water film thickness or the hydrophilicity [42], and (3) CO 2 reaction with hydroxyl groups on the mineral surface via hydrogen bonding [43]. For example, Jung and Wan [31] show that equilibrium contact angles on silica surface increase up to 17.6 ∘ ± 2.0 ∘ along with increased pressure by reactions with supercritical CO 2 (scCO 2 ). Also, contact angles increase with brine salinity almost linearly with a net increase by 19.6 ∘ ± 2.1 ∘ from deionized water to 5.0 M NaCl [31]. However, most of published contact angle results have shown significant discrepancies [27,30,36,38,[44][45][46][47][48][49][50][51]. Thus, the role of surface reactions with scCO 2 and the extent of their impact on mineral wettability remain elusive, making it difficult to estimate the capillary CO 2 entry pressure using (3). Instead of (3), capillary pressure-water saturation curves for GCS have been determined during drainage and imbibition processes through laboratory experimentation that consider reservoir pressure and temperature conditions [46,[52][53][54][55][56][57]. The results in published data show the discrepancies due to the difficulties in accomplishing a full CO 2 -water saturation, controls of slight change to capillary pressure under a high-pressure system, and measurement of water saturation [46,[52][53][54][55]57]. Recently, Tokunaga et al. [56] developed the experimental system to measure the capillary pressure-water saturation using hanging water column method at GCS relevant pressure and temperature conditions [56]. However, established capillary pressure curve is not able to cover a broad range of pressure, temperature, and chemical conditions including brine salinity effects which are relevant to GCS conditions. Thus, exploration of the capillary pressure curves at various pressure-temperature and brine salinity conditions relevant to geological CO 2 sequestration (GCS) was conducted in this study.

Experimental Study
2.1. Materials. Uniformly round Ottawa sand 40/60 (number 40-60 mesh) as the representative of silica materials of which grain size was distributed between 250 m and 355 m was sieved. While Ottawa sand 40/60 used in this study has higher porosity than core samples in GCS sites, many contact angle data have been published for Ottawa sand 40/60 [31] that can be used to estimate the capillary CO 2 entry pressure using (3) [please note that contact angle and interfacial tension effects on capillary pressure-water saturation curves were emphasized in this study; thus, contact angle and interfacial tension data are required]. The sand was wet-packed to a full saturation at = 0.381 in a chamber. Hydraulic conductivity with a separate sample of the sand (packed to the same porosity, = 0.381, and pore volume = 80.7 cm 3 ) was = 3.96 × 10 −4 m/s (2.1 darcies) based on the constant head test. 1.0 M and 3.0 M NaCl solutions were prepared for the aqueous phases to explore the brine salinity effects on capillary pressure-water saturation curves. Air and CO 2 (Airgas, 99.99% purity) were used as nonaqueous phases.

Experimental Setup.
Experimental system including a high-pressure chamber (inner diameter, ID = 8.21 cm and height = 4 cm) was designed for capillary pressure-water saturation tests (Figure 1). A stainless steel porous plate with 1 m pore size (3.0 mm thick and 79.7 mm diameter, Mott Corp.) was placed at the bottom in chamber and fully saturated-Ottawa sand pack was placed on porous plate in chamber. Another porous plate with a 50 m pore size (3.0 mm thick and 79.7 mm diameter, Mott Corp.) was placed on top of the sand pack. Fully saturated-sand was packed in chamber using wetting method. One-fifth of the chamber was filled with water and soils were dumped into the water, which was repeated five times to prepare for a fully saturated-sand pack. Figure 1 shows the experimental setup for capillary pressure-( -) water saturation ( ) relation test. The hanging water column method was used [60,61]. The chamber was connected to vertically oriented transparent capillary pressure regulator. When capillary pressure regulator was moved downward, the capillary pressure ( ) was induced by head difference between the top and bottom of sand pack, which caused the water to flow out from the sand pack. Also, the transparent capillary pressure regulator served as a reservoir for measuring the outflow from the sand pack (volumes interpolated to 0.2 mL). The top of the chamber and the upper end of the capillary pressure regulator were connected using a high-pressure tube, which maintained a closed system ( Figure 1).
After saturating the sand pack, the water level in the capillary pressure regulator was equilibrated on surface of   the sand pack in chamber that allows equilibration to zero capillary pressure ( = 0). Drainage curves were obtained by moving the water-CO 2 interface in the capillary pressure regulator successively downward to lower depth, ℎ, which is the elevation head difference between the surface of the sand pack and water-CO 2 interface in the capillary pressure regulator. The outflow volumes from sand pack were measured using the capillary pressure regulator [61]. After obtaining the drainage curves, rewetting (or imbibition) curves were obtained by moving water-CO 2 interface in the capillary pressure regulator successively upward [61]. As the elevation head difference, ℎ, decreased during imbibition process, inflow water volume into the sand pack was measured using transparent capillary pressure regulator [note: the elevation head difference in this study can be controlled up to ∼2 m, which implies that the capillary pressure can be up to ∼ 15 kPa when temperature and pressure are 45 ∘ C and 8 MPa, resp.; thus, this method is adapted only to high permeable sand]. The capillary pressure induced by the regulator can be calculated using the following equation: = (Δ ) × ℎ × , where Δ is the density difference between CO 2 and brine (Table 1), ℎ is the elevation head difference, and is the gravitational acceleration.
Experimental system was connected to the high-pressure pump (Teledyne ISCO, 500HP) so as to control the constant pressure of the closing system ( Figure 1). The chamber was instrumented with a pressure transducer (OMEGA PX309) and a thermocouple (T-type, copper-constantan). Heating tapes surrounding the chamber with heat gun and heatinglight were used to maintain the chamber temperature (∼45 ∘ C) with PID (proportional-integral-derivative) controller (Cole Parmer, EW-89000-10). The entire system was located in an insulating box. The variables tested in this study were pressure (0.1 to 15 MPa) and brine salinity (1 and 3 M NaCl), while constant temperature was maintained (∼45 ∘ C) ( Table 1). Figure 2 shows the capillary pressure-water saturation curve in air-brine displacement at 0.1 MPa air pressure that shows the consistency with the published data [56]. It implies that our experimental system is valid to measure the capillary pressure-( -) water saturation ( ) curve. Figures 3 and 4 show all experimental results obtained from this study using 1 M and 3 M NaCl brine, respectively. CO 2 pressure has the range of 5 MPa to 15 MPa.   involved in the control of the capillary pressure ( ) using the capillary pressure regulator. Uncertainties in average capillary pressure ( ) and water saturation ( ) of the sample are ∼10 Pa and ∼0.015, respectively, considering the resolution of capillary pressure regulator. In both Figures 3 and 4  residual brine saturation ( ) decreases after the drainage process; and (4) residual CO 2 saturation ( ,CO 2 ) increases after completing the imbibition process. However, capillary pressure-water saturation curves between 12 MPa and 15 MPa CO 2 pressures relatively appeared similar.

Pressure Effect on Capillary Pressure-Water Saturation
Published data show that contact angle steeply increases in line with pressure from 7 MPa to 10 MPa and remains relatively constant until 25 MPa [31]. Also, contact angle increases with brine salinity up to 5 M NaCl [31]. However, interfacial tension decreases in line with increased CO 2 pressure and varies only within a small range of 20-35 mN/m at GCS relevant pressure and temperature conditions [29,33,35]. Table 1 shows the published data of contact angle and interfacial tension at various pressure and temperature conditions used in this study. Thus, as CO 2 pressure increases from 5 MPa to 12 MPa, contact angle increases and interfacial tension decreases, which causes the capillary CO 2 entry pressure to decrease and capillary pressure-water saturation curves to shift to lower values at any given water saturation. Also, minor changes of contact angle and interfacial tension in the range of 12 MPa to 15 MPa have influence on relatively similar capillary pressure-water saturation curves in Figures  3 and 4. It implies that the different capillary pressurewater saturation curves in GCS conditions depend on the variation of contact angle and interfacial tension according to increased pressure. Also, published data show that contact angle and interfacial tension remain constant when pressure is more than 10 MPa [29,31,33,35]. Thus, capillary pressurewater saturation curves at 10 MPa CO 2 pressure conditions or higher are expected to be similar to the results at 12 MPa in this study.   Figure 4 shows that general trend of capillary pressure-water saturation curves at 3 M NaCl is similar to 1 M NaCl in Figure 3. Figure 5 shows the capillary CO 2 entry pressure changes at 1 M and 3 M NaCl brine salinity resulting from increased pressure. The results show that (1) all capillary (3) capillary CO 2 entry pressure is lower at 3 M NaCl than 1 M NaCl. Generally, as the brine salinity increases, contact angle increases up to 5 M NaCl [31], while interfacial tension decreases [29,33,35]. Table 1 includes all contact angle and interfacial tension at the various pressure and temperature conditions used in this study. For example, at the pressure 5 MPa, as brine salinity increases from 1 M to 3 M NaCl and contact angle increases from 36 ∘ to 44 ∘ , while interfacial tension decreases from 51 mN/m to 47 mN/m (Table 1). Also, in the range of 8 MPa to 15 MPa, increased contact angle and decreased interfacial tension are observed with increased brine salinity from 1 M to 3 M NaCl, which causes the capillary CO 2 entry pressure to decrease in Figure 5 [note that increased contact angle and decreased interfacial tension are not significant from 8 MPa to 15 MPa]. Jung and Wan [31] showed that the contact angle increased with brine salinity almost linearly, with a net increase of 19.6 ∘ ± 2.1 ∘ from 0 M to 5.0 M NaCl with CO 2 pressure range of 0.1 MPa to 20 MPa at 45 ∘ C. It implies that more capillary CO 2 entry pressure decrease is expected with the increased brine salinity unitl 5 M NaCl. Figure 6(a) shows the residual water saturation ( ) with increased pressure at 1 M and 3 M NaCl brine salinity. The results show that (1) the residual water saturation ( ) value in air-water measurement is ∼0.16 at 1 M NaCl which is consistent with the range in published data (0.14 ≤ ≤ 0.16, Gittins et al. [62]; Schroth et al. [63]), which verifies our experimental system; (2) residual water saturation values ( ) after completing the drainage process generally decrease due to increased CO 2 pressure from 5 MPa to 12 MPa and remain constant until 15 MPa. Contact angle increases steeply as pressure increases from 7 MPa to 10 MPa and remains relatively constant until 25 MPa [31]. Table 1 includes the contact angle used in this study. It implies that sand pack becomes more hydrophobic under the higher CO 2 pressure within the range of 5 MPa to 12 MPa, which has an influence on less residual water saturation in sand pack with increased pressure up to 12 MPa in Figure 6(a). Also, similar contact angles in the range of 12 MPa to 15 MPa CO 2 pressure (i.e., 56 ∘ -57 ∘ at 1 M NaCl) cause the residual water saturation to remain relatively constant with the range of 12 MPa to 15 MPa, and (3) residual water saturation values ( ) decrease with brine salinity from 1 M to 3 M NaCl. Increased contact angle with brine salinity from 1 M to 3 M NaCl in Table 1 implies that sand pack also becomes more hydrophobic under higher brine salinity, which causes the residual water saturation to decrease with increased brine salinity from 1 M to 3 M NaCl in the range of 5 MPa to 12 MPa. However, small variation of contact angles at 12∼15 MPa has an influence on relatively constant residual water saturation (i.e., 56 ∘ -57 ∘ at 1 M NaCl and 57 ∘ -58 ∘ at 3 M NaCl) which implies that residual water saturation at 12 MPa or higher is not affected by brine salinity due to similar contact angles. Tokunaga et al. [56], showed that silica surface became more hydrophobic according to increased CO 2 exposure time. Also, Wan et al. [49] observed that contact angle on silica surface increases with exposure time to CO 2 . Even though the results by Wan et al. [49] Advances in Condensed Matter Physics and Tokunaga et al. [56], were obtained from the short-term laboratory tests, it is expected that residual water saturation can be increased with a long-term in situ CO 2 injection into the field because the increased CO 2 exposure time causes the mineral surface to be more hydrophobic. Figure 6(b) shows the residual CO 2 saturation in pores after imbibition process, which can be considered as capillary CO 2 trapping capacity in geological CO 2 storage. Capillary trapping is the result of hysteresis by drainage and imbibition process during/after CO 2 injection in the porous medium. CO 2 injection in geological CO 2 storage generates the drainage process that displaces the resident brine with injected CO 2 in pores. After CO 2 injection is completed, the brine returns to the storage site, which generates an imbibition process and causes a certain amount of CO 2 to be trapped by capillary pressure [64,65]. For imbibition curves, while residual brine saturation in the air-brine displacement returns back to 95% at zero capillary pressure, residual CO 2 saturation increases in the CO 2 -brine displacement with increased CO 2 pressure, which is consistent with the previous results by Tokunaga et al. [56] [note that it is not consistent with the trends of residual oil saturation during the desaturation; residual oil saturation decreases when the wettability becomes less [66]]. For example, 5% residual CO 2 saturation at 0.1 MPa air-brine system with 1 M NaCl increases up to 31% at 15 MPa CO 2 pressure and 1 M NaCl, indicating that more capillary CO 2 trapping can be expected in geological CO 2 storage after the completion of imbibition process than the estimate from the air-brine displacement tests. General trends in Figure 6(b) show that (1) capillary CO 2 trapping increases with CO 2 pressure and (2) more capillary CO 2 trapping is observed with 3 M NaCl than 1 M NaCl, which implies that higher capillary CO 2 trapping in the long-term period field tests can be expected compared to the results from the laboratory test. Figure 7 presents the capillary pressure-water saturation curves using theoretical models such as both van Genuchten [25] and Brooks and Corey [24] models, which have a good consistency with experimental results. Capillary CO 2 entry pressure obtained from theoretical models decreases with increased pressure the same as experimental results and the curve slope decreases slightly in CO 2 -brine displacement comparing to the air-brine displacement, which cause -and -values to decrease with increased pressure up to 8 MPa (Table 2). -value in the airbrine displacement is 0.96 in this study, which is consistent with published data ( = 0.90 for hygiene sandstone, van Genuchten [25]) [note that hygiene sandstone is one of the sandstone types in the north-northwestern area in USA].value reflects the sensitivity of capillarity increase over the change of water saturation Δ /Δ , which decreases in a CO 2 -brine displacement with the increased pressure up to 8 MPa and remains relatively constant in the range of 8 MPa to 15 MPa. It implies that the capillarity increases slower as brine drainage progresses in sediments with higher pressures. For example, at 5 MPa CO 2 pressure and 1.0 M NaCl, when capillary pressure is ∼1.86 kPa that is only ∼0.36 kPa higher than capillary CO 2 entry pressure (i.e., ∼1.5 kPa), brine less than 9% (i.e., < ∼0.09) only remains in pores. As the CO 2 pressure increases, the residual brine saturation decreases with the low increase of capillary pressure after CO 2 injection ( Figure 7). Besides, the results show that -values decrease with increased pressure (Table 2). It also implies that the capillary pressure increases less as brine drainage processes in sediments with higher pressures, which is consistent withvalues. -value in the air-brine displacement is ∼12.5, which is within the range of published data ( = 3.42 for hydrophilic sand with 0 ∘ contact angle and = 20.0 for hydrophobic sand with 88 ∘ contact angle, Shokri et al. [67]; Brooks and Corey [24]). Viewing the contact angle ∼38 ∘ on silica sand in this study, -value is considered reasonable.

Capillary-Scaled Capillary Pressure-Water Saturation
Curves. Capillary scaling factor, which is a dimensionless number, has been used to predict the capillary pressure-water saturation curves in porous media considering contact angle and interfacial tension [60,[68][69][70]. Capillary scaling factor Π based on Young-Laplace equation (3) is as follows [56] [note that pore radius is relatively similar in all sand packs due to same particles size distribution and porosity; thus, it was disregarded in capillary scaling factor]: (4) Figure 8 shows the scaled capillary CO 2 entry pressure that is estimated considering the capillary scaling factor and capillary entry pressure (Table 1) (i.e., scaled capillary CO 2 entry pressure [1/mm] = 0 × Π ). While the scaled capillary CO 2 entry pressure in a CO 2 -brine displacement shows relatively similar values, the scaled value in the air-brine displacement is much higher than CO 2 -brine displacement. This inconsistency can be considered as (1) the uncertainty of wettability alteration in GCS. While it is clear that contact angle increases at pressure-temperature conditions relevant to GCS, the extents of wettability alteration have not been fully understood and show the inconsistency among the published data [28][29][30][31], which has an influence on the distinct scaled capillary CO 2 entry pressure; (2) the published data show a wide range of contact angle in pores compared to the constant contact angle on a flat surface [32]. Kim et al. [32] observed that contact angles in pores using twodimensional microfluidic model have a wide range of contact angle in GCS, which can hinder the scaled capillary CO 2  entry pressure to become identical; and (3) receding-contact angles are considered for the scaled capillary CO 2 entry pressure, which is usually less than equilibrium contact angle [71]. In case of air-brine displacement, all receding-contact angles are constant. Thus, the impacts of contact angle on the scaled capillary CO 2 entry pressure may be disregarded [60,[68][69][70]. However, a wide range of receding-contact angles in GCS should be strictly considered in the scaled capillary CO 2 entry pressure. Thus, the difference between equilibrium-and receding-contact angles has an influence on inconsistency of scaled capillary CO 2 entry pressure in this study (Figure 8).

Conclusions
The capillary pressure-water saturation curves in a homogeneous silica sand pack are examined at various pressure and brine salinity conditions relevant to GCS, which are then compared with the values obtained from two theoretical models such as Brooks-Corey and van Genuchten models. The capillary pressure-water saturation curves using the theoretical models such as Brooks-Corey and van Genuchten models show a good consistency with experimental results, which provide the information on sensitivity of capillarity.
Generally, the results show that as the CO 2 pressure in geological CO 2 storage increases, (1) capillary CO 2 entry pressure decreases; (2) capillary pressure-water saturation curves shift to lower values at the given water saturation ; (3) after completing the drainage process, residual water saturation decreases; (4) after imbibition process, capillary CO 2 trapping ,CO 2 (or residual CO 2 saturation) increases; (5) the sensitivity of capillarity increase over the change of water saturation decreases; and (6) fitting parameters in theoretical models, -and -values, are decreased slightly.
Also, as brine salinity increases from 1 M to 3 M NaCl, (1) capillary pressure-water saturation shifts to lower values at given water saturation , and capillary CO 2 entry pressure Advances in Condensed Matter Physics 9 decreases due to increased contact angle and decreased interfacial tension and (2) residual water saturation decreases, but capillary CO 2 trapping increases because silica surface becomes more hydrophobic because of the reaction with injected CO 2 .
The results show that CO 2 pressure and brine salinity in GCS have an influence on the capillary pressure-water saturation curves due to varying contact angle and interfacial tension. Thus, capillary scaling factor is considered to predict the capillary pressure-water saturation curves. However, the results show that the scaled capillary CO 2 entry pressure in geological CO 2 sequestration is inconsistent with atmospheric conditions due to the lack of wettability information. Further exploration of wettability alteration in GCS is required to predict the capillary pressure-water saturation curves at various conditions which are relevant to geological CO 2 sequestration.