Capillary-Sealing Efficiency of Mica-Proxy Caprock for CO₂/H₂ Geologic Storage in the Presence of Organic Acids and Nanofluids

Due to the rapid increase in world population, the global demand for energy has increased gradually over the past century and is anticipated to rise by 40% by 2040 (Rahbari et al. 2019; Ali et al. 2022a,Ali et al. 2021b; Aslannezhad et al. 2023). This energy demand is primarily fulfilled by fossil fuels, such as oil, natural gas, and coal (Speight 2011; Bavel 2013; Peterson 2017; Hogerwaard et al. 2020). Moreover, fossil fuels are expected to continue as the primary source of energy for the next 30 years (Wogan et al. 2019). However, the consumption of fossil fuels is causing high emissions of greenhouse gases (GHGs), especially CO₂, into the atmosphere, thus having a negative effect on the Earth’s climate (Bui et al. 2018; Vahrenkamp et al. 2021; Shar et al. 2022). According to a mutual report from the National Aeronautics and Space Administration and the National Oceanic and Atmospheric Administration, the average temperature of the Earth increased by 0.99°C (1.78°F) in 2016 compared with that observed in the mid-twentieth century (Potter et al. 2017). Therefore, governments worldwide are committed to adopting strict environmental regulations and decarbonization strategies to curb the excessive emissions of GHGs by building a diversified low-carbon-based economy (Masson-Delmotte et al. 2019; Mohanty et al. 2021).

The existing plans for decarbonization rely on improving industrial technology to enhance the efficiency of carbon capturing and sequestration and promote clean energy conversion from renewable resources such as solar, wind, and geothermal (International Energy Agency 2018; Masson-Delmotte et al. 2019; Mikunda et al. 2021). Hydrogen is presently emerging as a promising clean fuel that can support the decarbonization process by converting energy from fossil fuels into a more environmentally friendly form (referred to as blue hydrogen) and effectively storing clean energy from renewables (referred to as green hydrogen) to overcome their intermittent supply issues (Cuce et al. 2016; Edelenbosch et al. 2017; Lazarou et al. 2018; McPherson et al. 2018; Hordeski 2020; Moustakas et al. 2020; Alanazi et al. 2022d). Hydrogen (H₂) can be produced via processes such as electrolysis (Shiva Kumar and Himabindu 2019; Dawood et al. 2020; Alanazi et al. 2022b), bi-methane reformation (Chen et al. 2020; Mohanty et al. 2021), and biomass gasification (Shayan et al. 2018; Cao et al. 2020). However, wide-scale implementation of an H₂-based economy requires a medium with a large storage capacity, which can be theoretically offered by geological formations such as deep saline aquifers, depleted oil and gas reservoirs, and salt caverns (Heinemann et al. 2021; Zivar et al. 2021). Although the geological formations can serve as a feasible storage medium, their storage efficiency is greatly impacted by underground conditions, rock type, and trapping mechanisms (Tarkowski 2019).

The geostorage of CO₂ for sequestration is well exploited and recognized in the industry, while underground H₂ storage is still under investigation (Heinemann et al. 2018; Hassanpouryouzband et al. 2021; Krevor et al. 2023). While CO₂ for disposal is typically injected in its supercritical form (as no withdrawal is required), underground H₂ storage involves cycles of injection and reproduction for periods of peak demand, with the requirement of a cushion gas to maintain a safe hydrostatic pressure (Ma et al. 2019; Zivar et al. 2021). In the latter case, the captured CO₂ can be used as the cushion gas to support H₂ withdrawal (Oldenburg 2003; Oldenburg and Pan 2013; Alanazi et al. 2023a, 2023b). The trapping mechanisms for both gases in the geological formations are relatively similar and include structural trapping, residual trapping, dissolution trapping, and mineral trapping (Al-Khdheeawi et al. 2020, 2021; Amarasinghe et al. 2021; Yekeen et al. 2021). Among these, structural trapping and residual trapping are the main trapping mechanisms and are dictated by the capillary forces of the fluids within a rock and the interfacial forces between the fluids and formation rocks (Iglauer et al. 2015; Ali et al. 2020a, 2023; Abdulelah et al. 2021; Al-Yaseri et al. 2021; Alanazi et al. 2022a). When a gas is injected for storage, it displaces the wetting phases (typically formation fluids) within the rock pores depending on the receding contact angle, such that capillary leakage can occur at $θr$ > 90° (Broseta et al. 2012; Iglauer et al. 2015; Alanazi et al. 2022c). Thereafter, a free gas plume begins to move upward due to buoyancy, accumulates under an overlaying formation layer of poorly permeable rocks (i.e., caprock), and is trapped by the high capillary pressure exerted by the gas column against the buoyancy pressure (Wu et al. 2020; Hosseini et al. 2022; Zhang and Wang 2022). Furthermore, when the gas injection is stopped, the wetting phase column exerts a backpressure on the nonwetting phase, and the gas resides as clusters in a process called residual trapping; this is related to the advancing contact angle, whereby the wettability does not affect the primary drainage when $θa$ < 50° (Chiquet et al. 2007; Al-Menhali and Krevor 2016; Rahman et al. 2016). Thus, typical geological storage formations are characterized by an overlying layer of very low-permeability caprocks, which are often formed from shale, anhydrite evaporates, or salt of very low permeabilities ranging from 10^–23 to 10^–19 m² (Armitage et al. 2011; Haldar and Tišljar 2014). The caprock permeability typically decreases with porosity and pore throat radius and increases with clay mineral content (Rezaeyan et al. 2015; Hosseini et al. 2022). The capillary entry pressure of a caprock affects the sealing efficiency of the geologically stored gases (i.e., CO₂, CH₄, and H₂) (Espinoza and Santamarina 2017) and nuclear waste (Mallants et al. 2001). It also affects gas migration from unconventional source rocks (Yu et al. 2018; Wu et al. 2020).

In this work, the theoretical capillary sealing efficiency and CO₂/H₂ storage capacity of a proxy caprock (mica) are investigated for the first time as a function of pressure, temperature, and organic acid content. An extensive laboratory measurement was carried out to study CO₂ and H₂ wettability using mica samples under various storage conditions (i.e., pressures and temperatures of up to 25 MPa and 343 K), published by Arif et al. (2016), Ali et al. (2021c), and Ali et al. (2022b). The analysis framework discussed in this paper demonstrates the impact of key parameters on the capillary sealing efficiency and CO₂/H₂ storage capacity in the presence of organic acids and nanofluids. The calculations assess the effectiveness of injecting alumina oxide nanoparticles before CO₂ storage in altering the mica wettability and mitigating the effects of high concentrations of organic acid, thereby improving the sealing efficiency of the caprock (Ali et al. 2021a). In the current work , the aim is to provide a fundamental analytical approach for understanding the wetting characteristics and sealing efficiency of a caprock, along with the potential containment security issues and potential mitigation techniques, as applied to H₂ and CO₂ wettability, which are essential for the success of carbon capture and sequestration and underground H₂ storage operations.

Wettability is defined as a measure of the interaction between a fluid (usually a liquid, e.g., water or brine) and a solid surface (e.g., a rock) in the presence of another fluid (usually a gas) and is represented by the contact angle (θ) (Adamson and Klerer 1977). One type of θ is the dynamic contact angle, which is measured either during imbibition (the wetting phase displacing the nonwetting phase) or during drainage (the nonwetting phase displacing the wetting phase) when it is correlated with the advancing contact angle (⁠$θa$⁠) and the receding contact angle (⁠$θr$⁠), respectively, as shown in Fig. 1a . While the dynamic contact angle is a technique to measure the three-phase contact line under dynamic conditions, the static contact angle is measured when the interface between the two fluids is not in motion, as shown in Fig. 1b .

In the literature, Ali et al. (2021c) measured the dynamic contact angles for mica/H₂/brine and Arif et al. (2016) measured the same for mica/CO₂/brine, under geological storage conditions (5 MPa, 10 MPa, 15 MPa, and 20 MPa; 308 K, 323 K, and 343 K) at a brine salinity of 10 wt% NaCl for pure mica substrates. The measurements were acquired using the tilted-plate method (Lander et al. 1993), described next in Procedure for Contact-Angle Measurements Using the Tilted-Plate Method, for organic-aged mica substrates. Other techniques have been applied to measure the dynamic contact angles for H₂ and CO₂ such as the captive bubble method and a microfluidic-based method. van Rooijen et al. (2022) measured the dynamic contact angles at room temperature and 10 bar pressure using microfluidics. The obtained measurements by van Rooijen et al. were found to be comparable with the experimental measurements provided by Hashemi et al. (2021), who used the captive bubble method in experiments. To provide a theoretical and fundamental analysis using the wettability measurement, we applied Laplace’s equation (Derrell A. 1966) to calculate the capillary entry pressure (⁠$pce$⁠) and the maximum height of the gas column (⁠$hgmax$⁠) using interfacial tension (IFT) data between liquid and gas (⁠$γlg$⁠), density difference, and an effective pore throat radii (⁠$r)$ = 5 nm and 10 nm, detailed in Procedure for Contact-Angle Measurements Using the Tilted-Plate Method).

The contact-angle measurement system is shown schematically in Fig. 2 . The dynamic advancing (⁠$θa$⁠) and receding (⁠$θr$⁠) contact angles were measured using a high-pressure, high-temperature (HPHT) cell and a tilted-plate sample container (Al-Anssari et al. 2016; Ali et al. 2020b; Alanazi et al. 2023b). The HPHT cell was composed of Hastelloy to withstand temperatures and pressures of up to 423 K and 60 MPa. The sample plate was tilted at angles of 15–17° (Al-Yaseri et al. 2022a). The HPHT cell was connected to two high-precision ISCO syringe pumps (supplied by Teledyne ISCO D-260) with a pressure accuracy of 0.01%. The brine was pumped into the cell, followed by injection of the gas (CO₂ or H₂). The mica sample was then placed on the sample holder at a tilt angle of 17°, the HPHT cell was isolated and sealed, and the gas was injected at a steady rate until the required testing pressure and temperature were reached. The temperature was controlled by heating the fluid in ISCO pumps using Model 900 F heating baths (Julabo), while the cell temperature was controlled using a strip heating tape (HTC101-002; Omega Company) (Ali et al. 2022d). Once the HPHT cell was filled with the gas, the pressure was equalized to the desired testing pressure by using two ISCO pumps. Then, a needle was used to introduce a droplet of brine (5.4 µL ± 0.77 µL) onto the surface of the tilted mica substrate via a third ISCO pump. Once the brine droplet touched the substrate surface, the two dynamic contact angles (⁠$θa$ and $θr$⁠) appeared at the two tails of the droplet and were recorded using a high-speed camera (Fujinon CCTV lens, Basler scA 640–70 fm; HF35HA-1B; frame rate = 71 fps; 1:1.6/35 mm, pixel size = 7.4 μm) (Arif et al. 2016; Al-Yaseri et al. 2017; Yekeen et al. 2021). ImageJ software was used to determine the contact angles by analyzing the droplet images. The measurement was repeated three times for all the desired testing conditions, and the mean values showed an overall standard deviation of ±5° at 25 MPa and ±3° at 0.1 and 15 MPa (Ali et al. 2020a, 2021a).

In this study, the equilibrium contact angle (⁠$θe$⁠) was calculated as a function of $θr$ and $θa$ from the measurements of Ali et al. (2021c) and Arif et al. (2016) by using the empirical approach described by Tadmor (2004) based on Young’s equation and Neumann’s equation of state (Li and Neumann 1992; Kwok and Neumann 1999), given here as Eq. 1:

where $ℵa$ and $ℵr$ were calculated using Eqs. 2 and 3:

The gas/liquid/solid capillary pressure (⁠$pc$⁠) has many definitions depending on the pore throat interface and hydrodynamic situation (Iglauer et al. 2015; Zhang and Wang 2022). The most basic definition treats the capillary pressure as the difference between the nonwetting phase (e.g., $pg$ for a gas) and wetting phase (e.g., $pl$ for a liquid), as shown in Eq. 4 (Derrell A. 1966):

A nonwetting phase (i.e., CO₂ and H₂) cannot invade the caprock until the pressure drop exceeds a certain threshold, known as the capillary entry pressure $(pce)$⁠. The capillary entry pressure can be approximated by the Laplace equation, as shown in Eq. 5:

where $γlg$ is the brine/gas IFT, $θr$ is the receding contact angle, and $r$ is the effective pore throat radius of the caprock.

The capillary sealing pressure works against the buoyancy pressure exerted by the gas column height, and, when the buoyancy pressure exceeds the $pce$⁠, the generated negative suction force will cause the invasion of gas into the caprock. If the pressure holds, however, the gas will be trapped structurally beneath the caprock (Zhang and Wang 2022). In connected reservoirs where the pressure gradient (⁠$∆p$⁠) across the caprock is equal to the buoyancy pressure gradient (⁠$Δpbuoy$⁠) (Fig. 3), the maximum stable storage column of gas (⁠$hgmax$⁠) is equal to the hydrostatic trapping equilibrium, as given in Eq. 6:

where $g$ is the gravitational acceleration, and $ρl$ and $ρg$ are the densities of the liquid and gas phases, respectively. In this work, the capillary sealing efficiency of the caprock was assessed by using the $pce$ and $hgmax$ values calculated from Eqs. 4 and 5 using the contact angle data sets for the caprock/gas/brine systems provided by Ali et al. (2021a, 2021c, 2022c) and Arif et al. (2016) to comprehend the efficiency, safety, and structural trapping capacity.

Wettability is an essential parameter that drives the ability of any gas to dispense into geological rocks, determining the flow pattern, gas injection, and withdrawal behavior, along with the thermodynamics, storage potential, and storage safety (Yekeen et al. 2021; Zeng et al. 2022). In this background, the sealing potential against upward movement of any gas (CO₂, CH₄, and H₂) for permanent or temporary immobilization in the reservoir formation is provided by a top layer of impermeable rock (caprock) (Iglauer 2022). Thus, it is critical to measure the sealing efficiency of the caprock for the successful structural storage of respective gases (Al-Bazali et al. 2005; Cranganu and Soleymani 2015; Espinoza and Santamarina 2017). Actual geostorage formations are anoxic and reductive due to the presence of organic acids (Lundegard and Kharaka 1994; Akob et al. 2015). Therefore, the effects of various geological conditions such as pressure, temperature, organic acid concentration, and alkyl chain length on the wettability and capillary sealing efficiency of a proxy caprock are identified herein based on the experimental results of previous studies. In the present work, the capillary sealing efficiency was computed for caprocks with two typical pore throat radii of 5 nm and 10 nm by using data from Watson et al. (2005), Armitage et al. (2011), and Hosseini et al. (2022). Similarly, the $γlg$ data for H₂/brine and CO₂/brine were taken from Ali et al. (2022b), Chow et al. (2018), and Pan et al. (2021b), while the H₂ and CO₂ wettability data were obtained from Ali et al. (2021c) and Arif et al. (2016), respectively.

The temperature and pressure of a formation increase with depth (Pan et al. 2021a). Hence, the conditions in the experiments by Ali et al. (2021c) and Arif et al. (2016) were selected based on typical reservoir conditions (5–20 MPa; 308–343 K). The reported receding (⁠$θr$⁠) and advancing (⁠$θa$⁠) contact angles for H₂ and CO₂ in the pure mica/gas/brine systems are plotted in Fig. 4 , which clearly indicates that the contact angles increase as the pressure increases and the temperature decreases. This is attributed to the increase in the intermolecular forces between the gas and solid substrate (in the case of pressure change) and the decrease in the interfacial energy between the gas and the solid substrate (in the case of temperature change) (Zeng et al. 2022). Furthermore, the effects of pressure and temperature on H₂/brine wettability are less pronounced than those on the CO₂/brine wettability due to the high difference in density between H₂ and CO₂ (Heinemann et al. 2018). For instance, at 308 K and 20 MPa, the advancing contact angle (⁠$θa$⁠) reaches 65° for the mica/H₂/brine system compared with 110° for the mica/CO₂/brine system, with the latter representing a very weak water-wet condition (i.e., a CO₂-wet condition).

The calculated equilibrium contact angles (⁠$θe$⁠) for H₂ and CO₂ are plotted in Fig. 5  and listed in Table A-1  of the  appendix. Here, similar trends to those of the advancing and receding contact angles shown in Fig. 4  are observed. This is consistent with the literature (Sarmadivaleh et al. 2015; Al-Yaseri and Jha 2021; Ali et al. 2021b, 2022c; Hashemi et al. 2021; Hosseini et al. 2022). These investigations have shown that the wettability of rock becomes very weak (intermediate water-wet to gas-wet) at high pressures for rock/gas/brine systems. Previous studies have also shown that higher $θr$⁠, $θa$⁠, and $θe$ values are measured at high pressures for various rocks (Arif et al. 2021; Al-Yaseri et al. 2022b).

The $pce$ and $hgmax$ values were calculated for this study using the typical $r$ values of 5 nm and 10 nm (Arif et al. 2016), and the results are plotted in Figs. 6 and 7 . These indicate an overall decrease in both $pce$ and $hgmax$ with the increase in pressure at a constant temperature, which is attributed to the decrease in the interfacial forces (i.e., $γsg$⁠, $γlg$⁠, and $γsl$⁠), the density difference (⁠$ρl-ρg$⁠), and the water wettability (i.e., $θr$⁠) of the mica surface. Because $r$ is proportionally related to both $pce$ and $hgmax$ (Eqs. 8 and 9), the results typically demonstrate lower values at higher $r$ for both the mica/H₂ and mica/CO₂ systems. This implies a decrease in the capillary sealing efficiency and storage capacity of the mica samples with the increase in pressure. However, the variations in the $pce$ and $hgmax$ values according to pore size (⁠$r$⁠) are seen to be higher for the mica/H₂ system than for the mica/CO₂ system. In detail, the mica/CO₂ wettability shows larger overall decreases in $pce$ and $hgmax$ with the increase in temperature and pressure. At a fixed temperature of 308 K, the $pce$ and $hgmax$ values of the pure mica/CO₂/brine system exhibit their maximum declines (to become close to zero) when the pressure is increased from 5 MPa to 20 MPa. A negative suction flow of the CO₂ into the mica pores can occur due to the capillary forces of the strongly CO₂-wet mica at pressures of 20 MPa and above, which can lead to leakage of the CO₂. By contrast, the $pce$ and $hgmax$ values of the pure mica/H₂ system decline less significantly with the increase in pressure and temperature, thus indicating better sealing conditions (⁠$pce$⁠) and higher storage capacity (⁠$hgmax$⁠) than the mica/CO₂ system. For instance, the average $pce$ and $hgmax$ values of the mica/H₂/brine system at r = 5 nm, T = 308 K, and P = 10 MPa are calculated to be 23 MPa and 2300 m, respectively, compared with 7 MPa and 700 m for the mica/CO₂/brine system. These differences between the sealing efficiencies and storage capacities of the mica/H₂ and mica/CO₂ systems are mainly attributed to the significant difference in the densities of H₂ and CO₂ (Heinemann et al. 2021; Zivar et al. 2021). The previous results were obtained from pure mica/gas/brine systems. However, this is not the case for real geological formations, where organic molecules in anoxic conditions exist, which affect the sealing efficiency significantly as highlighted by Akob et al. (2015) and Lundegard and Kharaka (1994). The effect of organic molecules on capillary sealing efficiency is examined in the following subsection.

The presence of organic matter in the subsurface formation has a significant impact on the rock/gas/brine interfacial properties (Ali et al. 2021c). Several investigators have studied the effects of contamination and adsorption of organic acids on the wettability of the rock surface under reservoir conditions (Mallants et al. 2001; Bui et al. 2018; Ali et al. 2022b). A small concentration of organic matter adsorbed on rock surfaces can change their rock wettability from water-wet to gas-wet. Hence, the mica substrates used as proxy caprocks can be aged with organic acids to achieve more realistic conditions, comparable with those of actual underground reservoirs (Lundegard and Kharaka 1994; Akob et al. 2015). Organic acids generally contain between 2 and 26 carbon atoms (Ali et al. 2020b), as summarized in Table 1 . The synthetic organic acids used for contact angle measurements in previous studies cover the same overall range (Mallants et al. 2001; Oldenburg and Pan 2013). In those studies, the mica substrates were aged in various concentrations of the selected organic acids for 7 days, and the $θa$ and $θr$ values were then measured at 15 MPa and 323 K for both the mica/H₂ (Ali et al. 2021c) and mica/CO₂ (Arif et al. 2016) systems. The previously reported measurements are plotted in Fig. 8 , and the newly-calculated equilibrium contact angles at the various concentrations of each acid are plotted in Fig. 9 . Here, the wettability exhibits a strong shift from water-wet to gas-wet for both H₂ and CO₂ as the organic acid concentration is increased from $10-2$ to $10-9$ mol/L. As observed above in the absence of organic acid, the shift in mica wettability toward gas-wet conditions is more significant in the CO₂/brine system than in the H₂/brine system due to the very low density of H₂ compared with that of CO₂. In addition, lignoceric acid, having the longest alkyl chain (largest number of carbon atoms), is seen to have the greatest effect on the sealing efficiency and storage capacity among all the tested organic acids.

The calculated $pce$ and $hgmax$ values are plotted against the negative log of organic acid concentration at pore sizes (⁠$r$⁠) of 5 nm and 10 nm for the mica/H₂ system in Figs. 10 and 11  and for the mica/CO₂ system in Figs. 12 and 13 . Thus, both the $pce$ and $hgmax$ values are seen to reach close to zero for the mica/H₂ system with $10-2$ mol/L lignoceric acid, while negative values are observed for the mica/CO₂ system, particularly when $r$ = 10 nm. In general, these results suggest that a lower pore size provides better sealing efficiency and a higher gas column height in both systems.

Wettability modifiers are often recommended for improving the wettability of reservoir rocks and caprocks before gas injection for storage (Ali et al. 2021a). Therefore, recent studies have investigated the addition of various concentrations of nanofluids to rock surfaces to enhance the wettabilities of high organic-content rocks (Akob et al. 2015; Ali et al. 2022b). The advancing and receding contact angle measurements that were obtained in the previous study by Ali et al. (2021a) are reproduced here in Fig. 14a . For this work, the equilibrium contact angles were also calculated for the various organic acids, and the results are presented in Fig. 14b . These results indicate that the aging with alumina nanofluid at concentrations of 0.05–0.75 wt% is very effective in reversing the hydrophobic conditions caused by the presence of organic acids, thus making the substrate more hydrophilic. However, while all of the nanofluid concentrations lead to a decrease in wettability, the maximum degree of change is observed at 0.25 wt% (Fig. 14a).

In this work, the effects of alumina oxide (Al₂O₃) nanoparticles on the sealing efficiencies of the mica substrates are further evaluated by using the above numerical results of Ali et al. (2021a) to calculate the $pce$ and $hgmax$ values at 15 MPa and 323 K for assumed $r$ values of 5 nm and 10 nm. As shown in Figs. 15 and 16 , the organic-aged mica substrates exhibit enhanced sealing efficiencies and storage capacities in the presence of the nanofluids. For instance, in the case of lignoceric acid at a concentration of $10-2$ mol/L, the capillary sealing efficiency (⁠$pce$⁠) increases significantly from approximately –2 to 3.5 MPa as the concentration of nanoalumina is increased from 0.05 to 0.25 wt% (Fig. 15). At the same time, the $hgmax$ increases from –250 m to about 350 m (Fig. 16), thereby preventing the potential negative suction of the stored CO₂.

An analysis of the capillary sealing efficiency and storage capacity of caprock is crucial for determining the potential for the structural entrapment and underground storage of H₂ and CO₂ (Iglauer et al. 2015; Espinoza and Santamarina 2017). Therefore, previously published contact angle measurements on the proxy caprock mica (Arif et al. 2016; Ali et al. 2020a, 2021c, 2022c) were used herein to calculate the capillary entry pressure (⁠$pce$⁠) and static column height of the gas (⁠$hgmax$⁠). In addition, the effects of key parameters such as pressure, temperature, and pore size (using typical values of $r$ = 5 nm and 10 nm) were demonstrated, along with those of organic acids and alumina nanofluids, on the wettability, capillary sealing efficiency, and static column height of the gas. The present results indicated that the sealing efficiency and storage capacity for H₂ and CO₂ decrease with the increase in pressure and surface concentration of organic acid but increase with increasing temperature. The analysis demonstrated a theoretical inverse relationship between the capillary entry pressure and the pore throat radius. Thus, the smaller the pore size, the more suitable the conditions are for sealing and storage capacity. Furthermore, the wettability and sealing efficiency of the organic-aged mica/CO₂ system were improved by the addition of nanoalumina, with an optimal nanofluid concentration of 0.25 wt%. In brief, this work has provided a detailed theoretical workflow for assessing the influence of various parameters on the wettability, sealing efficiency, and storage capacity of mica substrates (as a proxy caprock) for the safe and secure geological storage of H₂ and CO₂.

 
• g

  gravitational acceleration, m/s²

 
• $hgmax$

  maximum height of the gas column, m

 
• p_ce

  capillary entry pressure, MPa

 
• p_g

  gas pressure, MPa

 
• p_l

  liquid pressure, MPa

 
• r

  effective pore throat radius, m

 
• γ_lg

  IFT between gas and liquid, mN/m

 
• γ_sg

  IFT between solid and gas, mN/m

 
• γ_sl

  IFT between gas and liquid, mN/m

 
• ΔP_buoy

  pressure difference exerted by buoyancy, MPa

 
• θ_a

  advancing contact angle, degrees

 
• θ_e

  equilibrium contact angle, degrees

 
• θ_r

  receding contact angle, degrees

 
• ρ_g

  gas density, g/cm³

 
• ρ_l

  liquid density, g/cm³

 
• $ℵa$

  Tadmore advancing correlation parameter

 
• _$ℵr$

  Tadmore receding correlation parameter

The authors would like to acknowledge King Abdullah University for Science and Technology (KAUST) for supporting this work by the Research Funding Office under Award No. 4357.

Original SPE manuscript received for review 6 February 2023. Revised manuscript received for review 5 May 2023. Paper (SPE 217471) peer approved 4 September 2023.