Effect of CO₂ Injection on the Multiphase Flow Properties of Reservoir Rock

Abstract

Geologic carbon storage (GCS) has recently been drawing attention as an effective and sustainable method to reduce CO₂ emissions to the atmosphere. The injection of CO₂ is mainly conducted into brine-saturated reservoir formations, and assessment of the multiphase flow properties becomes essential to evaluate the injectivity and storage capacity for carbon storage. Characterization of the CO₂/water flow system requires comprehensive knowledge of host rock’s relative permeability, capillary pressure, and wettability that are related to each other. Moreover, chemical reactions between the mineral grains and acidic mixture of CO₂ and water may significantly affect the flow properties. In this study, a comprehensive experimental approach to characterize the chemical effect on the multiphase flow of CO₂ in water-saturated reservoir rock is presented. One silica-rich formation—Berea sandstone, and two calcite-rich formations—Apulian and Indiana limestones, are selected to represent the reservoir materials. Robust experimental techniques for measurements of the relative permeability and degree of saturation based on the changes in poroelastic response are introduced. The relative permeability curves are determined, as it is shown that the curvatures and maximum degree of CO₂ saturation change after CO₂ treatment, especially for the limestones. In addition, the apparent contact angle increases and surface roughness decreases due to the chemical effect of CO₂ injection on limestones. Finally, the advantages and limitations of the presented measurements are discussed and reported flow properties are compared to those predicted from the pore-scale analyses.

1 Introduction

Climate change is argued to be accelerated by CO₂ among different greenhouse gases, highlighting the importance of mitigating its atmospheric emission (IPCC 2021). As part of the solution, geologic carbon storage (GCS) has been widely recognized as a sustainable and effective method to reduce the discharge of CO₂, aiming to collecting it from stationary sources and injecting into subsurface formations for permanent sequestration (IPCC 2005). The injection is generally conducted into brine-filled porous reservoir rocks with potentially large storage capacities, mainly comprising of sandstones and limestones located at depths of at least 800 m (Orr 2004; US DOE 2010).

As CO₂ is injected into the reservoir, the distribution of the aqueous fluid is rearranged laterally, followed by the shift of CO₂ upward due to its density being smaller than the one of water (Johnson et al. 2005). It was observed that CO₂ injected into Utsira sandstone in the North Sea propagated laterally over an area of ~ 10 km², while the plume was also rising due to buoyancy (Chadwick et al. 2006). This transposition of the fluid can be described by understanding the hydraulic behavior of participating rock—one of the most important factors in assessing the formation’s suitability for most geo-energy projects. However, as CO₂ injection is generally conducted into brine-saturated reservoir formations, the concept of permeability for single-phase flow cannot be directly applied for the multiphase fluid system (Fig. 1). Therefore, the relative permeability needs to be evaluated considering the interaction between the wetting and non-wetting fluids (Kopp et al. 2009; Bachu 2013). Characterization of the multiphase flow response for GCS projects involves assessment of viscous and capillary forces at the pore scale and the interfacial and wetting properties of the involved fluids (Fulcher et al. 1985). Moreover, as the injection of high-pressure CO₂ introduces poromechanical deformation and chemical reaction, proper description of relative CO₂ permeability in reservoir rock requires comprehensive understanding of the multiphysical processes (Rutqvist 2012; Rohmer et al. 2016; Vilarrasa et al. 2019).

Fig. 1

Schematic illustration of the multiphase flow processes during CO₂ injection for geologic carbon storage (GCS)

The significance of accurately assessing the two-phase flow behavior has been highlighted by many laboratory-scale experiments, where the relative permeabilities were measured through various methods. Civan and Donaldson (1989) suggested a semianalytic approach to calculate the relative permeability for the immiscible displacement of two incompressible fluids based on the fractional-flow equation and an integro-differential equation (Donaldson et al. 1988; Bennion and Bachu 2005; Bachu and Bennion 2008), and Bachu and Bennion (2008) reported a series of core-scale experiments to evaluate the two-phase flow characteristics of brine and CO₂ for various rock types, using the mass balance method to determine the degree of saturation and the relative permeability curve. Krevor et al. (2012; 2015) conducted tests on reservoir rock to measure the relative permeability under in situ conditions. The X-ray computed tomography (CT) method was utilized to determine the degree of saturation by scanning the fluid distribution in the pores, as other studies have also adopted this method (Perrin et al. 2009; Pini et al. 2012).

A different approach to evaluating the degree of CO₂ saturation is based on accurate measurements of the ultrasonic wave velocities during the multiphase flow experiments (Shi et al. 2007; Falcon-Suarez 2020). In general, the changes in velocities and wave attenuation are shown to be correlated with the degree of non-wetting fluid saturation (Winkler and Plona 1982; Amalokwu et al. 2014). Akbarabadi and Piri (2013) conducted unsteady- and steady-state flow tests and determined the relative permeability curves, while the effect of hysteresis on capillary trapping was also examined for both supercritical and gaseous CO₂. The integrated workflow to measure the relative permeability from unsteady-state flow was introduced by Berg et al. (2013, 2021). Permeability and capillary pressure curves could be iteratively extracted by history matching through the inverse modeling, but the solutions might not be unique due to some instability issues.

Despite the existing number of studies focused on measuring the CO₂ relative permeability in porous rock, the experimental data remain to be dependent on the experimental setup and interpretation (Müller 2011; Chen et al. 2014; Pini and Krevor 2019). Many numerical simulations have also been conducted to predict the multiphase flow during CO₂ injection (Chen et al. 1994; Juanes et al. 2006; Martinez et al. 2013). Pruess et al. 1999 introduced a multiphase fluid and heat flow code TOUGH2 and presented simulations of CO₂ flow in brine aquifer considering the losses through fault discharge (Pruess and Garcia 2002). As TOUGH2 could not consider the effect of chemical reactions and mechanical stress, the code was expanded to include a nonisothermal reactive geochemical transport relationship and became TOUGHREACT (Xu and Press 2001; Xu et al. 2006). The analytical relationship between relative permeability and saturation were proposed by Brooks and Corey (1964), van Genuchten (1980), Burdine (1953), and Mualem (1976). However, comparing their prediction for CO₂ relative permeability, saturation, and capillary pressure, significant discrepancies have been reported, thus experimental validation is needed (Oostrom et al. 2016).

CO₂ injection causes the non-wetting fluid (CO₂) to displace the wetting fluid (brine or water), so understanding the wettabilities of the participating fluids is extremely important since it affects the capillary pressure and degree of saturation (Anderson 1986). Wettability is the preference of a solid to be in contact with one fluid than the other, and depending on the fluid’s contact angle to the surface, the material can be classified as water/CO₂/intermediate-wet (Abdallah et al. 1986). Different approaches to measuring the wettability of the multi-fluid system have been reported, as both the quantitative (contact angle measurement, Amott method, and USBM method) and qualitative methods (imbibition rates, relative permeability curves, microscope examination, and capillary pressure curves) have been introduced (Amott 1959; Craig 1971; Donaldson et al. 1969; Ionescu and Maini 1983). Among the suggested techniques, measurements of the contact angle can be selected as one of the most consistent for reporting the wettability since it is not affected by surfactants or other compounds and is determined by the balance of the interfacial forces of the multi-fluid system and the surface (Anderson 1986). Thus, many different approaches such as the tilting plate method, sessile drop and bubble method, vertical rod method, and cylinder method have been proposed to perform accurate contact angle measurements (Adamson and Gast 1967; Johnson 1969; Good 1979; Neumann and Good 1979; Drelich et al. 1996). These techniques have been already implemented to report the contact angles for the water/brine–CO₂–mineral system at high pressure (Espinoza and Santamarina 2010) and even inside the rock pores using micro-CT images (Tudek et al. 2017).

Wettability explains the distribution of multiphase fluids in the pore space but does not directly describe the saturation state and needs to be considered along with the hydromechanical behavior of the system (Marsden 1965; Falode and Manuel 2014). Moreover, several factors such as the pore geometry, surface roughness, and heterogeneity can increase the complexity of assessing the wettability of the porous rock, as previous studies reported a wide range of contact angles for various materials (Drelich et al. 1996; Sarmadivaleh et al. 2015). Particularly, since reservoir formations are composed of micro-sized and rough mineral grains, the surface roughness should also be analyzed to accurately determine the wettability (Morrow 1990; Amirfazli et al. 1998; Baldacchini et al. 2006). Kaveh et al. (2014) performed laboratory experiments at representative reservoir conditions to establish a relationship between the surface roughness and contact angle, where it was found that the CO₂ injection did not significantly affect the surface roughness, although its increase caused the contact angles to become slightly larger. Haeri et al. (2020) proposed that the contact angle increased with the surface roughness based on a series of tests with various sandstones. In contrast to the previous results, Al-Yaseri (2016) reported that for the CO₂/brine/quartz system, the contact angles decreased with increase in the surface roughness in accordance with the Wenzel theory (1936) which can also be inferred from the measurements on the solid surfaces (Wang et al. 2013). To investigate these discrepancies, the effect of CO₂ injection on the surface roughness and its relationship with the wettability requires further experimental assessment.

Another important factor to be considered is the chemical reaction caused by CO₂ injection, as it alters the pore structure and directly affects mechanical and flow characteristics of the reservoir rock (Mazumder and Wolf 2008; Luquot and Gouze 2009; Grombacher et al. 2012; Su et al. 2019; Tarokh et al. 2020). Due to the challenges with direct experimental measurements, only a few recent studies have been focused on the chemical effect on the multiphase flow behavior, reporting the change in relative permeability curves due to dissolution of calcite in limestones (Kim et al. 2018; Niu and Krevor 2020).

In this study, we present the experimental work to assess the multiphase flow characteristics of reservoir formations during CO₂ injection. Berea sandstone, Apulian limestone, and Indiana limestone are selected as representative materials, and the properties of pristine- and CO₂-treated specimens are compared. The relative permeability curves are determined by adopting a novel technique, where the poroelastic measurements are utilized to calculate the degree of saturation. Maximum and residual degree of saturation and the entry pressure for CO₂ are evaluated, and the chemical effect of CO₂ treatment is observed. The relative permeability curve measurements are compared with the predictions based on the application of the mercury intrusion porosimetry (MIP). In addition, microscopic measurements are conducted for the wettability and surface roughness, and further discussions on the potential implications for CO₂ storage are provided.

2 Methods

In this section, the detailed information on the materials selected for this study is introduced. Then, the methods for the relative permeability measurement, CO₂ treatment, and calculation of the degree of saturation from the poroelastic measurements are elaborated. In addition, the devices utilized to assess the microscopic properties—mercury intrusion porosimetry, microgoniometer, and profilometer, are explained.

2.1 Materials

Three isotropic and homogeneous porous materials—Berea sandstone, Apulian limestone, and Indiana limestone, are selected for this study. Berea sandstone is a sedimentary formation that overlies the Bedford and Ohio shale and underlies Sunbury shale, also known as Berea grit (Newberry 1874). It was formed in the late Devonian period and primarily consists of fine to medium-sized grains, being studied as the host rock for oil and natural gas (Collins 1979). The gray-colored sandstone dominantly consists of quartz (around 90% by mass), with minor inclusions of kaolinite, K-feldspar, and muscovite. The porosity φ is measured to be 0.22.

Apulian limestone is a glauconitic fossiliferous carbonate rock, formed in the mid-Cretaceous era, and originated from the Apulia region in Southern Italy. This formation mainly comprises calcite (more than 95%) with a small portion of plagioclase, glauconite, and iron oxide, representing the soft calcite-rich rock for this study. The matrix of Apulian limestone is constructed with 0.05–1 mm size fragmental calcitic foraminifera, which are calcitic mud (micrite) cementations with allochems. For this soft limestone, the porosity is measured to be the largest among the tested rock: φ = 0.37.

Indiana limestone is versatile for buildings and public structures, as it is widely recognized for its durability and stability (Shaffer 2020). It is formed with uniform carbonate grainstones during the Mississippian Subperiod of the Carboniferous and is composed mainly of calcite (more than 97%), with inclusions of quartz, aluminum oxide, and sulfur. This light-gray to bluish-gray rock has the porosity equal to 0.13.

For this study, deionized water is selected as the pore fluid instead of brine. Thus, we neglect the influence of salinity and solely focus on the chemical effect of the acidic mixture of CO₂ and water on the rock minerals and pore structure. All the selected materials contain less than 1% of clay minerals (by mass) to minimize the chemical interaction of pore fluids with clays, and repeatability of the test data confirms that swelling and alteration processes can be neglected. CO₂ is injected and maintained in the liquid state throughout all the tests to disregard any phase transitions and associated thermal effects on the rock properties. In addition, injection of liquid CO₂ is energetically more efficient comparing to the supercritical fluid and should be investigated for near-wellbore multiphase flow (Rayward-Smith and Woods 2011; Vilarrasa et al. 2013). The capillary pressure–saturation curves and porosities for all materials are measured using the mercury intrusion porosimetry (MIP) method, with mercury being a non-wetting fluid in air-saturated samples (Fig. 2). The dominant pore sizes are determined as 20 μm, 2 μm, and 1 μm for Berea sandstone, Apulian limestone, and Indiana limestone, respectively. At least three samples are tested for each material to confirm the consistency of obtained results.

Fig. 2

Capillary pressure (mercury)–saturation curves for Berea sandstone, Apulian limestone, and Indiana limestone measured using mercury intrusion porosimetry

2.2 Multiphase Flow Test

The multiphase flow is defined as the simultaneous flow of more than one fluid through a porous media, as it becomes the case for CO₂ injection in water-saturated rock in geologic carbon storage (Fig. 3). Although multiple fluids exist, characterization of the multiphase flow behavior triggers from defining the concept of intrinsic permeability. Permeability describes the capacity of the interconnected porous medium to allow fluid to penetrate and can be introduced based on the law of conservation of mass. If it is written in Darcy’s form for laminar and steady-state conditions, the flow rate q can be expressed as a function of viscosity of the fluid µ_f and the differential pressure dp^f along the differential distance x_i.

$${q_i}= - \frac{k}{{{\mu _f}}}\frac{{\partial {p^f}}}{{\partial {x_i}}}$$

(1)

The parameter k in this equation can be measured when a constant differential pressure Δp^f between the upstream and downstream sides of a specimen is applied: p^f_up–p^f_down = Δp^f. The flow rate is calculated as the volume of the fluid ΔV exiting the specimen over time Δt. If the viscosity of the fluid is known (µ^f = 0.001 Pa·s for pure deionized water at 22 °C), L is the length of the specimen, and A is the cross-sectional area perpendicular to the flow, then permeability can be calculated as

$$k=\frac{{{\mu ^f} \cdot L \cdot \Delta V}}{{A \cdot \Delta t \cdot \Delta {p^f}}}$$

(2)

For the multiphase fluid flow, relative permeability k_ri = k_i / k is introduced to describe the flow capability of the i-th fluid. By extending Eq. (2), the relative permeability can be calculated from the knowledge of the viscosity µ_ι^f, as well as the flow rate ΔV_i/Δt and differential pressure Δp_i^f in the i-th fluid (Bear 1988).

$${k_{ri}}=\frac{{\mu _{i}^{f} \cdot L \cdot \Delta {V_i}}}{{k \cdot A \cdot \Delta t \cdot \Delta p_{i}^{f}}}$$

(3)

The two-phase flow test of water and CO₂ is conducted in the core flooding device with the high-pressure CO₂ injection setup, assuming that flow of the two fluids in the rock is steady-state and laminar. Right cylindrical specimens with diameter D = 50.8 mm and length L = 100–110 mm are inserted in the rubber viton membrane installed inside the device. The core holder allows imitation of high in situ stress conditions and is connected to four pressure controllers: the Stigma 500/700 controller (Sanchez Technologies, France, 70 MPa capacity) for the confining pressure, and three syringe pumps (Teledyne ISCO, USA, 25.9 MPa capacity) for the CO₂ upstream, water upstream, and downstream pressures. Accurate measurements of the pore pressure are performed via two pressure transducers (Honeywell, USA, capacity 34.5 MPa) installed at the upstream and downstream sides of the specimen. As two syringe pumps are connected to the upstream for CO₂ and water for the flow rate and pressure control, this setup allows two-phase flow experiments, while the CO₂ treatment test can also be conducted by only having the CO₂ syringe pump valve open (Kim and Makhnenko 2021).

The deformation of the specimen is assumed to be poroelastic, and the total mean stress P can be determined from calculating the induced axial stress σ_ax applied via the passive restraint installed in the axial direction. By knowing the applied confining pressure σ_lat and the pore pressure p^f, and measuring the Poisson’s ratio ν and Biot coefficient α from the mechanical tests, P can be calculated as (Kim and Makhnenko 2020a).

$$P=\frac{{{\sigma _{ax}}+2{\sigma _{lat}}}}{3}=\frac{{2\left( {1+\nu } \right)}}{3}{\sigma _{lat}} - \frac{{\left( {1 - 2\nu } \right)\alpha }}{3}{p^f}$$

(4)

Full saturation with water is achieved before each flow test by adopting the back pressure saturation method (Lowe and Johnson 1960; Makhnenko and Labuz 2016). Then, the pore water is exposed to liquid CO₂ for at least 4 h to guarantee that it becomes CO₂-rich under the testing conditions. In the flow test, the two upstream pumps for water and CO₂ are operated in the flow control regime with the prescribed rate of injection, while the downstream pump is maintained in constant pressure control. The ratio of the flow rates (water/CO₂) for the upstream pumps is prescribed to be 100:0%, 80:20%, 50:50%, 20:80%, and 0:100%. As the two fluids are injected from the upstream, the pressure in each pump fluctuates at the beginning, while it eventually reaches a constant value that allows calculation of the differential pressure Δp^f_i for each fluid (i = w for water and i = c for CO₂ in Eq. 3). The two-phase flow tests for reservoir rock are conducted for not more than an hour after reaching the steady-state flow condition to assure that the chemical reactions have minimal effect on the material properties. Moreover, as the relative permeability experiment starts from injection of water only and then increases the rate of CO₂ injection, it is to be noted that this study focuses solely on the drainage process. After treating the specimens with CO₂, it is completely removed from the pores by flushing the deionized water at low pressure before conducting any relative permeability measurements. Considering the pore size of the tested rock, and resaturating the treated specimens with water via the back pressure saturation technique, we affirm that the subsequent measurements of the mechanical and hydraulic properties are performed with presence of only the wetting fluid (Kim and Makhnenko 2021).

2.3 Saturation Calculation

In order to assess the storage efficiency for CO₂ injection projects, a proper understanding of the degree of saturation for the two fluids (water and CO₂) is required. In addition, as the pore compressibility can be affected due to CO₂ injection, the poromechanical response needs to be coupled with the multiphase flow. The materials selected for this study all represent monomineralic and isotropic rock (the sandstone is silica-rich and limestones consist mainly of calcite) allowing to adopt the poroelastic theory introduced by Biot (1941) for the description of their mechanical behavior. In this study, a novel method to determine the degree of saturation is introduced based on the measurements of the fluid-saturated rock compressibility during the CO₂ injection. After running a two-phase flow test and assuring that the total injected fluid volume of CO₂ and water exceeds five times the pore volume of the specimen, both the upstream and downstream valves are closed simultaneously, imposing the undrained boundary condition. Then, the Skempton’s B coefficient is directly measured as an increase in pore pressure Δp^f due to the application of the increment in the mean stress ΔP (Skempton 1954). At the same time, it can be expressed through other poroelastic parameters and the bulk modulus of the pore fluid that represents a mixture of water and CO₂ - K_{f, mix} (Detournay and Cheng 1993).

$$B={\left. {\frac{{\Delta {p^f}}}{{\Delta P}}} \right|_{\zeta =0}}=\frac{{\left( {1 - \frac{K}{{{K_s}^{\prime }}}} \right)}}{{\left( {1 - \frac{K}{{{K_s}^{\prime }}}} \right)+\phi K\left( {\frac{1}{{{K_{f,mix}}}} - \frac{1}{{{K_s}^{{\prime \prime }}}}} \right)}}$$

(5)

Here, K is the drained bulk modulus, K^′_s is the unjacketed bulk modulus, K^″_s is the unjacketed pore modulus, and φ is the interconnected porosity. The drained bulk modulus K (Eq. 6) and unjacketed bulk modulus K^′_s (Eq. 7) are measured using the hydrostatic compression device, with strain gauges installed on a prismatic specimen with a linear dimension of at least 30 mm in three perpendicular directions. The bulk deformation is monitored during the loading/unloading steps, as the slope for the pressure versus volume strain (ε_v = ε₁ + ε₂ + ε₃) is taken as the bulk modulus (Tarokh and Makhnenko 2019).

$$K={\left. {V\frac{{\Delta {p^f}}}{{\Delta V}}} \right|_{\Delta {p^f}=0}}$$

(6)

$${K_s}^{\prime }={\left. {V\frac{{\Delta {p^f}}}{{\Delta V}}} \right|_{\Delta {p^f}=\Delta P}}$$

(7)

The unjacketed pore modulus K^″_s is assumed to be equal to K^′_s for ideal porous media, so K^′_s = K^″_s is adopted in this study regarding the isotropy of the tested reservoir formations (Detournay and Cheng 1993). We acknowledge though that this assumption might be violated for Berea sandstone that has minor inclusions of other minerals (Makhnenko and Labuz 2016) and Apulian limestone that contains some non-connected pores (Tarokh and Makhnenko 2019).

With the knowledge of the poroelastic properties, the bulk modulus for the mixture of two fluids (water and CO₂) - K_{f, mix} can be calculated from Eq. 5. Then, from the Wood’s (1930) formula, the degree of saturation for each fluid can be determined, while the bulk modulus of CO₂ is calculated to be K_c = 0.07 GPa at the testing conditions (6.9 MPa and 22 °C) (Achenbach 1973) and bulk modulus of pure water K_w = 2.24 GPa.

$$\frac{1}{{{K_{f,mix}}}}=\frac{{{S_w}}}{{{K_w}}}+\frac{{1 - {S_w}}}{{{K_c}}}$$

(8)

The procedure to determine the saturation of the two fluids are repeated for each flow rate of H₂O/CO₂, where the relative permeabilities of the wetting and non-wetting fluids are measured. The relative permeability curve can be obtained by plotting the measured values of k_rw and k_rCO2 versus the degree of saturation for each of the fluids. This approach overcomes the limitations of other methods, such as the X-ray CT scanning, regarding the resolution, discretization effect, and testing conditions (Cnudde and Boone 2013) and can be used with the materials where pore sizes fall below the imaging resolution (e.g., shales).

For the discrete data points obtained from the multiphase flow measurements, the fitting is performed using the analytical relationships. The Brooks and Corey (1964) power law model is adopted, where the effective saturation parameter S_e is introduced. Then, with the fitting exponent parameters for water and CO₂, N_w and N_c, the relative permeabilities can be expressed as:

$${k_{rw}}={({S_e})^{{N_w}}}{\text{ }}{k_{rc}}={(1 - {S_e})^{{N_c}}}$$

(9)

The parameter S_e can be calculated from the knowledge of liquid saturation S_l, the residual liquid saturation S_rl, and the maximum liquid saturation S_max, that is equal to 1 for the case of full water saturation.

$${S_e}=\frac{{{S_l} - {S_{rl}}}}{{{S_{\hbox{max} }} - {S_{rl}}}}=\frac{{{S_l} - {S_{rl}}}}{{1 - {S_{rl}}}}$$

(10)

The effective saturation parameter S_e allows estimation of the capillary pressure P_c through Brooks–Corey fitting parameters: CO₂ entry pressure P_e and pore size distribution index λ (Dullien 1992).

$${P_c}={P_e} \cdot {S_e}^{{ - \frac{1}{\lambda }}}$$

(11)

Although the Brooks–Corey model provides intuitive fitting of the relative permeability curves and information on the CO₂ entry pressure, it cannot be directly connected to the saturation characteristics of a porous material. Therefore, van Genuchten model (1980) is used, since it adopts the same fitting parameters α, m, and n, for both capillary pressure and relative permeability curves.

$${S_e}=\frac{1}{{{{\left( {1+{{\left( {\alpha {P_c}} \right)}^n}} \right)}^m}}}$$

(12)

$${k_r}\left( {{S_e}} \right)={S_e}^{{\frac{1}{2}}} \cdot {\left[ {1 - {{\left( {1 - {S_e}^{{\frac{1}{m}}}} \right)}^m}} \right]^2}$$

(13)

Use of this model enables validation of the two different methods presented in this study—relative permeability and capillary pressure measurements. For van Genuchten model, certain restrictions can be imposed on the fitting parameters based on Mualem’s (1976) approach, where m can be expressed in terms of n as m = 1–1/n, while it should stay in the range of 0 < m < 1. However, for this study, we utilize three parameters independently to obtain a more accurate fitting.

2.4 CO₂ Treatment

The effect of CO₂ treatment on the multiphase flow behavior is explored by comparing the characteristics of the pristine and treated rock specimens. After reaching full saturation with deionized water, the pressure conditions are controlled to maintain 4.5 MPa effective mean stress and 6.9 MPa pore pressure. Then, liquid CO₂ is injected from the upstream side at 7 MPa with the downstream valve closed. The upstream valve is being closed after injecting 40–50 mL of liquid CO₂ to maintain an undrained condition, and the pore pressures at the upstream and downstream sides of the specimen are monitored. The readings on the pressure transducers indicated that the pore pressure slowly decreases to 6.2 MPa—the boundary value between liquid and gaseous CO₂. Therefore, additional liquid CO₂ is injected daily at the pressure of 7 MPa once the decrease in the pore pressure is observed.

Previous works reported that the duration time of CO₂ treatment correlates with the degree of the change in the material properties (Kim and Makhnenko 2022; Shi et al. 2019). For this study, 21 days are selected as the treatment period, as we intend not to introduce any macroscopic damage to the materials (Tarokh et al. 2020). Furthermore, since Apulian limestone is recognized as a softer material that highly reacts with the acidic mixture of water and CO₂, the treatment period is reduced to 3 days (Luquot and Gouze 2009; Kim et al. 2018).

2.5 Mercury Intrusion Porosimetry

The capillary pressure P_c for the CO₂–water–rock system can be determined by utilizing mercury intrusion porosimetry (MIP) to measure the porosity and pore size distribution. Quantachrome Poremaster 60 from Anton Paar© is used to inject mercury in the pores of dry reservoir rock samples with a mass of approximately 1 gram. As liquid mercury has a high cohesive force, its volume can be accurately measured, while it is forced to intrude the pores by increasing the pressure up to 413.7 MPa. After reaching full saturation with mercury, the weight of the sample cell is accurately measured to calculate the bulk density of the rock sample. Then, with the knowledge of the density (ρ = 13.54 g/cm³), contact angle (θ = 140°), and surface tension (γ = 480.0 erg/cm²) of mercury, the pore size distribution can be determined as the function of the pore throat diameter d using Young–Laplace equation.

$${P_c}= - \frac{{4\gamma \cos \theta }}{d}$$

(14)

The degree of saturation for each corresponding pressure is calculated as the ratio of the injected mercury to the total interconnected pore volume. Finally, the capillary pressure curve can be obtained by plotting the capillary pressure vs. the degree of saturation. Application of the capillary pressure curves for CO₂ injection requires converting the MIP data from the mercury/air/rock system to the CO₂/water/rock system. The abbreviation n/w describes the non-wetting/wetting system for CO₂/water, while m/a represents the mercury–air system. As a result, the capillary pressure for the CO₂–water–rock system can be calculated as:

$${P_{c,n/w}}={P_{c,m/a}}\frac{{{\sigma _{n/w}}\cos {\theta _{n/w}}}}{{{\sigma _{m/a}}\cos {\theta _{m/a}}}}$$

(15)

We employ the findings of Espinoza and Santamarina (2010), where the average interfacial tension and contact angle for CO₂/water are measured as 32 mN/m and 20° for silica-rich materials and 32 mN/m and 40° for calcite-rich materials, respectively. Although some previous studies reported different contact angles for porous rock to that of its composing mineral (Lv et al. 2017; Scanziani et al. 2017; Tudek et al. 2017), we presume that the contact angle and interfacial tension of the tested rocks follow their dominant composing minerals. Nevertheless, based on the direct measurements of the apparent contact angle, further discussion regarding the effect of CO₂ injection on wettability is presented.

2.6 Wettability

The wettability of the system can be assessed by measuring the contact angle θ, which is formed at an equilibrium state of the interfacial forces in the multiphase fluid system. Although in situ measurements of the wettability may differ from those at ambient conditions (Lv et al. 2017; Tudek et al. 2017), a robust method to evaluate the effect of CO₂ treatment on the contact angle is adopted by taking high resolution images with a microgoniometer MCA-3 (Kyowa, Japan). The device is capable of accurately controlling the size of the microscopic droplets to be as small as 100 μm and can detect the droplet from both the top and the side for its movement and wettability. A high magnification lens is installed with the ability to monitor the droplet in a 12-fold zoom that allows a field of view from 75 × 56  to 910 × 680 μm, with a fast image capture system for accurate measurements. The drop deposition can be automatically recognized with the FAMAS software, and the apparent contact angle can be measured in the range of 0.1–80° with 0.01° resolution.

The specimens are prepared by cutting slices from rock cores with a 1–2 cm length and width and 0.5 cm depth, and then polishing their surface to maintain a uniform roughness. After washing it with deionized water, the rock is being completely dried before the contact angle measurements. The sessile drop method is used for this study as the microscopic droplets are applied to the flat and polished surface (McCaffery et al. 1970; Anderson 1986), after which the contact angles are measured using the microgoniometer. Dependence of the contact angle from the applied pressure, temperature, and salinity limits the understanding of the wettability. Thus, the effect of CO₂ treatment on wettability is qualitatively investigated by measuring the apparent contact angles at room temperature, atmospheric pressure, and zero salinity. Moreover, the reported contact angles are related to the wettability of the air–water–rock system, as it is expected to be different to the results of the CO₂–brine system. Additionally, at the microscopic scale, the advancing and receding contact angles are expected to be observed in the pores during multiphase flow and their values are, in general, pressure and temperature dependent (Tudek et al. 2017). However, due to the uncertainties associated with measuring the advancing/receding apparent contact angles in non-equilibrium state, such as wicking occurred during the movement and tilting of the rock surfaces, only the apparent contact angles at equilibrium are reported (Anderson 1986). Therefore, this assessment is mainly aimed at addressing the qualitative differences between the wettability of treated and untreated rock surfaces.

2.7 Surface Roughness

Characterization of the wettability is crucial for understanding the multiphase flow in porous rock, while the contact angle could also depend on the surface roughness (Wenzel 1949; Tamai and Aratani 1972; Morrow 1975). A qualitative approach to evaluate the effect of CO₂ treatment on rock’s surface roughness is adopted, where the Sloan Dektak3ST Profilometer provides repeatable and accurate measurements of the height and 2D profile of the surface, ranging from a few nanometers to 100 microns. With a 2.5-micron radius diamond-tipped conical stylus, the contact technique is utilized to measure the surface topography without any damage, as it scans across the surface of the specimen. All specimens are precisely ground to take a shape of a disk with 2 cm in diameter and 1 cm thickness. Each measurement is conducted by scanning 1000 μm along the specimen surface, with N = 2000 data points collected per scan. Then, 12 scans are performed per specimen to obtain average representative data by selecting different starting positions for the stylus. The profilometer is set to the highest scanning resolution with 12 s scanning time duration for each measurement. The root-mean-square (RMS) method is utilized to calculate the surface roughness, where Z_i is the measured height value and Z_avg is the arithmetic mean for all height values.

$$RMS={\left[ {\frac{1}{N}\sum\limits_{{i=1}}^{N} {{{\left| {{Z_i} - {Z_{avg}}} \right|}^2}} } \right]^{1/2}}$$

(16)

Fig. 3

Summary of the experimental methods utilized to characterize the multiphase flow behavior of reservoir rock upon CO₂ injection

3 Results

3.1 Poroelastic Properties

The knowledge on the poroelastic properties of reservoir rock is needed to calculate the degree of saturation with CO₂ and report the relative permeability curve. Pristine- and CO₂-treated specimens are tested in the hydrostatic compression cell under the jacketed and unjacketed conditions to calculate the corresponding bulk moduli measured during the unloading stage (Fig. 4). For the jacketed test on Apulian limestone, the pressure is increased up to 30 MPa, since preceding studies reported pore collapse of this material around 39 MPa (Tarokh and Makhnenko 2019). For the other two materials, the jacketed compression test is conducted up to 50 MPa. The results for all materials show that the drained bulk moduli increase gradually to reach a constant value, indicating that all the microcracks and oblique pores at the early compression stage are being closed. For Berea sandstone, the drained bulk modulus decreases from 12.1 to 10.3 GPa. For Apulian limestone, the jacketed bulk modulus K decreases (e.g., from 6.3 to 5.0 GPa at P = 30 MPa), meaning the material is getting more compressible due to the treatment process. The measurements for Indiana limestone show a similar result to Apulian limestone in terms of CO₂ treatment—the decrease in drained bulk modulus by 20%, from 29.5 to 23.1 GPa (at P = 30 MPa pressure). It is to be noted that for Berea sandstone and Indiana limestone, the bulk moduli of the pristine- and CO₂-treated specimens are almost identical at low mean stress values (0–4 MPa), while for Apulian limestone, the effect of CO₂ treatment can already be observed from the low mean stress indicating high compressibility of the material (Kim and Makhnenko 2022).

Accurate measurements of the unjacketed bulk modulus K^′_s are also required to calculate the degree of saturation, and the results of unjacketed experiments are reported in Kim and Makhnenko (2021). All the unjacketed moduli are measured to be constant during the loading and unloading stages. K^′_s for Berea sandstone remained the same after CO₂ treatment, being equal to 30 GPa. For Apulian limestone, the unjacketed bulk modulus decreased from 42.7 to 34.2 GPa, and for Indiana limestone, K^′_s also decreased by 20%, from 65.9 to 54.9 GPa (Table 1). The decrease in the unjacketed moduli of limestones is explained by the observed dissolution and precipitation of calcite caused by the chemical reaction with the acidic mixture of water and CO₂. However, it is to be noted that apparent precipitation may be related to the particle migration and rearrangement of calcite particles, which can be suggested as another reason for the creation of the new non-connected pores (Mangane et al. 2013). It appears that CO₂ treatment causes increases in the total porosity, as well as in the non-connected porosity in calcite-rich rock, making the overall solid matrix response more compliant (Kim and Makhnenko 2021).

Fig. 4

Drained bulk modulus K measurements for pristine- and CO₂-treated a Berea sandstone, b Apulian limestone, and c Indiana limestone

For this study, the measurements of the Skempton’s B coefficient are utilized to calculate the degree of saturation for the relative permeability curves. The B values are measured for the pristine- and CO₂-treated reservoir rock specimens at P′ = 4.5 MPa and are reported as functions of the degree of saturation, that is calculated from Eq. (5). The Skempton’s B coefficient for Berea sandstone decreases after the treatment from 0.77 to 0.67, while it increases from 0.47 to 0.53 for Apulian limestone and 0.32 to 0.40 for Indiana limestone. For limestones, calcite dissolution has been reported as the main reason for the increase in the B values, since the porosity increases and rock becomes more compliant (Kim and Makhnenko 2021). On the other hand, for Berea sandstone, the reduction in the undrained bulk modulus K_u along with the drained bulk modulus K is observed, and explained by the stress corrosion cracking, hence B= (K_u−K)/(1−Κ/Κ^′_s)/K_u can decrease (Tarokh et al. 2020).

3.2 Relative Permeability

Understanding the flow properties of reservoir rock in the water/CO₂ system is crucial for CO₂ injection, as it is closely related to the injectivity and storage efficiency. For the multiphase flow behavior, the capillary pressure and relative permeability are essential factors that describe the two-phase fluid displacement in the pore space. This section examines the effect of CO₂ treatment on the multiphase characteristic curves of the reservoir rock. The relative permeability is measured using the core flooding apparatus via the novel method that allows assessing the CO₂ saturation from changes in the undrained compressibility of rock upon CO₂ injection.

The relative permeability curves are determined before and after CO₂ treatment. Prior to conducting the multiphase flow experiments, the intrinsic permeabilities for pristine- and CO₂-treated specimens are accurately measured at P′ = 4.5 MPa. For Berea sandstone, the intrinsic permeability is 1.9 × 10^− 13 m² for the pristine state, and it increases slightly to 2.1 × 10^− 13 m² after the CO₂ treatment. The permeability of pristine Apulian limestone is measured to be 7.5 × 10^− 15 m², changing to 8.2 × 10^− 15 m² for the treated specimen. Similarly, for Indiana limestone, the intrinsic permeability increases from 8.0 × 10^− 14 to 8.4 × 10^− 14 m² after the treatment. For all tested materials, the intrinsic permeability slightly increases due to the CO₂ treatment, while an interpretation is different for the sandstone and limestones. For the limestones, calcite dissolution appears to increase the porosity, and hence the permeability—similar results are reported in a number of studies (Bennion and Bachu 2008; Luquot and Gouze 2009; Kim and Makhnenko 2021). For Berea sandstone, the stress corrosion cracking is assumed to be the main mechanism affecting the permeability without any significant increase in porosity (Tarokh et al. 2020).

The values of Skempton’s B coefficient are measured during the two-phase flow experiments at each injection rate (10:0, 8:2, 5:5, 2:8, 0:10 for H₂O/CO₂), and the degree of CO₂ saturation is calculated from Eq. 5. The pristine- and CO₂-treated poroelastic properties measured at the same effective mean stress (P^′ = 4.5 GPa) are adopted in the calculations for each corresponding material. At the same time, we assume that the poroelastic parameters (K, K^′_s, and φ) remain constant at different flow rates. Calculated Skempton’s B coefficients decrease significantly right after starting CO₂ injection, also being different for the pristine- and CO₂-treated rock (Table 2). Then, the intrinsic permeability value is taken for each pristine- and CO₂-treated material to calculate the relative permeability from Eq. 3. Finally, with the degree of saturation calculated from the measurements of the poroelastic parameters and changes in Skempton’s B values (Eqs. 5 and 8), the relative permeability curves are reported (Figs. 5, 6 and 7). The results are fitted to the power law functions in terms of the degree of saturation, similar to the Brooks–Corey model. The fitting parameter N_w is determined using the least-squares method for all materials. The additional fitting is provided for van Genuchten model (Eqs. 12 and 13), where the set of fitting parameters (α, n, and m) is reported in Table 1.

For Berea sandstone, CO₂ treatment does not seem to significantly affect the relative permeability curves, with the exponent N_w remaining constant at 2.9 and slight increase in the maximum degree of CO₂ saturation from 0.70 to 0.73 (Fig. 5). For Apulian limestone, the maximum degree of CO₂ saturation increases from 0.68 to 0.80, while the exponent N_w decreases from 3.8 to 1.3, indicating that the shape of the relative permeability curve turned from a power law to a quasi-linear function (Fig. 6). The relative permeability curves for Indiana limestone are presented in Fig. 7, showing N_w decreasing from 6.3 to 5.2 and the maximum degree of CO₂ saturation increasing from 0.69 to 0.75 after the treatment. The values of S_w are reported with 5% accuracy where the main error comes from the determination of the Skempton’s B coefficient within the core flooding apparatus at high degree of CO₂ saturation (Kim and Makhnenko 2021). Each experiment is duplicated and the variation between the measured parameters appears to be less than 3%, while the average results are provided in the figures and tables. This study suggests that the multiphase flow response for sandstones is not affected by CO₂ injection, while for limestones, the exponent parameter N_w decreases as the maximum degree of saturation for CO₂ increases.

In addition to the Brooks–Corey model, van Genuchten model is applied for fitting the relative permeability curves for all materials. The α values are reported to increase due to CO₂ injection, as they are mostly related to the CO₂ entry pressure. Although, when the relative permeability vs. saturation relationship becomes approximately linear after the CO₂ treatment of Apulian limestone (Fig. 6b), van Genuchten model fails to provide a good fit, unlike the Brooks–Corey model.

Fig. 5

Relative permeability curves for a pristine- and b CO₂-treated Berea sandstone

Fig. 6

Relative permeability curves for a pristine- and b CO₂-treated Apulian limestone

Fig. 7

Relative permeability curves for a pristine- and b CO₂-treated Indiana limestone

CO₂ treatment appears to cause an increase in the maximum degree of CO₂ saturation for all tested materials, although it requires more detailed analyses on the elements that may affect the capillary pressure, such as the wettability and the surface roughness. Further investigations and validation of the measured relative permeability curves are presented in the discussion section, where the capillary pressure curves are coupled with the relative permeability measurements.

Table 1 Summary of the results for the porosity (φ), poroelastic properties: K (drained bulk modulus), K^′_s (unjacketed bulk modulus), and multiphase flow parameters: k (intrinsic permeability), N_w (Brooks–Corey exponent), α/n/m (van Genuchten fitting parameters), and S_CO2 (maximum degree of water saturation). The stress-independent values of the drained bulk modulus are reported (for P^′ > 25 MPa), and the intrinsic permeability is measured at P^′ = 4.5 MPa.

Table 2 Summary of the Skempton’s B coefficient measurements during the multiphase flow test at different flow rates of H₂O and CO₂ (P^′ = 4.5 MPa).

4 Microscopic Measurements

Characterization of the multiphase flow in rock oftentimes relies on the assumption that the microscale properties generally remain constant after CO₂ treatment. However, a number of studies have reported the chemical effect of CO₂ at a microscale (Farokhpoor et al. 2013; Al-Anssari et al. 2017). Thus, the parameters that directly affect the relative permeability–wettability and surface roughness have to be measured before and after CO₂ treatment (Kaveh et al. 2014; Haeri et al. 2020).

4.1 Wettability

Experiments are conducted to assess the effect of CO₂ treatment on the wettability of reservoir rock, as it is directly related to the changes in capillary pressure and relative permeability. For reservoir formations, pores on the surface may affect the contact angle measurements as they can be considered as defects or surface rugosity. By using the microgoniometer, the apparent contact angles for the air/water system are measured for the pristine- and CO₂-treated reservoir rock (Fig. 8). More than twenty measurements are taken for each sample at different locations, and the average values are reported in this study with the overall variations being within ± 5° for each material. For Berea sandstone, the CO₂ treatment causes a slight increase in the contact angle from 31 to 34°, so the effect is minor staying within the accuracy range. However, the contact angle increases from 52 to 75° for Apulian limestone and from 55 to 83° for Indiana limestone, revealing a significant effect of CO₂ treatment. It is to be noted that the measured contact angles are apparent angles that are based on the average plane of the surface for air/water system, as it does not quantitatively characterize the true contact angle in the microscale pores for the CO₂–water–rock system. However, it can be argued that these measurements provide a qualitative understanding of the effect of CO₂ treatment on the wettability of the reservoir rock.

Additionally, as the tested materials in this study are mainly composed of quartz or calcite, the contact angles of the pristine- and CO₂-treated mineral crystals are measured (Fig. 9). The contact angle for pristine quartz is 40°, and it increases to 42° after the treatment. For calcite, the contact angle changes from 78 to 83°, indicating that the effect of CO₂ treatment on the contact angle of minerals is significantly smaller than that for the porous rock that is composed of these minerals. This implies that the change in the contact angle for reservoir rock cannot result only from that of the minerals but can also be attributed to the changes in the surface roughness. The measured apparent contact angles of deionized water on mineral crystals also showed to be within the range of the reported values from other studies, where the contact angles for quartz were reported to be 26–50° (Lamb and Furlong 1982; Janczuk and Zdziennicka 1994; Drelich et al. 1996; Kowalczyk et al. 1996; Deng et al. 2018). For calcite, the contact angles are between 50 and 85°—larger than those of quartz (Okayama et al. 1997; Kowalczuk et al. 2017; Alnoush et al. 2021). Detailed procedures for the CO₂ treatment of crystal minerals are elaborated in Kim and Makhnenko (2021).

Fig. 8

Apparent contact angle measurements for a pristine- and b CO₂-treated Berea sandstone, c pristine- and d CO₂-treated Apulian limestone, and e pristine- and f CO₂-treated Indiana limestone. All measurements are conducted for the air/water/rock interface at ambient room temperature (22 °C) and pressure

Fig. 9

Apparent contact angle measurements of a pristine- and b CO₂-treated quartz, and c pristine- and d CO₂-treated calcite

4.2 Surface Roughness

One of the main reasons the apparent contact angle differs from the true contact angle is the surface roughness. Particularly, for porous rock formations, pores contribute to surface rugosity, which requires thorough investigation (Cassie and Baxter 1944). As the surface roughness is highly dependent on the specimen preparation, in this study, it is evaluated through the parameter R_q—the root-mean-square (RMS) average of the profile heights over the evaluation length of 1000 μm. Moreover, to investigate the effect of CO₂ treatment on the surface roughness, the ratio of the R_q values of the pristine- and CO₂-treated rock (R_{q, pris}/R_{q, CO2}) is reported. Ten to twelve scans are made for each specimen, and the average value of R_{q, pris}/R_{q, CO2} is calculated, while only the surface variation for a single measurement is presented in Fig. 10. R_{q, pris}/R_{q, CO2} values appear to be larger than 1 for all materials, indicating that CO₂ treatment smoothens the surface at the microscale. It appears that the chemical effect is more pronounced for the limestones, where the R_{q, pris}/R_{q, CO2} values are reported as 2.4 and 2.2 for Apulian and Indiana limestones, while the value for Berea sandstone is 1.1.

Wenzel’s relation predicts that a decrease in surface roughness would lead to a reduction in wettability, hence the increase in contact angle, as it is observed in this study for the CO₂-treated specimens (Wenzel 1936). Considering Young’s equation (Eq. 14), this effect can be intuitively verified, as the capillary pressure curve for water shifts down—toward smaller capillary pressure values, while the contact angle increases. Moreover, as the preceding study showed that the dominant pore sizes for the tested limestones increased after the CO₂ treatment (Kim and Makhnenko 2021), the surface roughness measurements are in agreement with the theory of Cassie and Baxter (1944), stating that the apparent contact angles for porous surfaces should increase with the pore size (Fig. 11).

In summary, the reported results align with the previous analyses on the wettability and surface roughness, indicating that the CO₂ treatment smoothens the rock surface, resulting in larger apparent contact angles for the wetting fluid. Therefore, this implies that the surface becomes more wet with respect to the non-wetting phase, which causes the increase in the maximum CO₂ saturation.

Fig. 10

Surface roughness measurements of pristine- and CO₂-treated: a Berea sandstone, b Apulian limestone, and c Indiana limestone

Fig. 11

Illustrative comparison between the Wenzel’s and Cassie–Baxter models for the apparent contact angles of pristine- and CO₂-treated specimens

5 Discussion

In the previous sections, the effect of CO₂ treatment on the poroelastic and multiphase flow response is experimentally determined, indicating that the compressibilities of limestones increase after the treatment, while for the sandstone the effect is less pronounced. The relative permeability measurements suggest that the maximum degree of CO₂ saturation increases for all materials. The evaluation of the fitting parameters for the relative permeability curves shows that the Brooks–Corey exponents decrease for limestones, implying that the CO₂ treatment increases the relative permeability of CO₂ at the same degree of saturation. In this section, further analyses on the capillary pressure–saturation curves are presented. The capillary pressure curves for pristine- and CO₂-treated specimens are reported by adopting the information on the residual water saturation that can be obtained from the relative permeability measurements.

5.1 Residual Water Saturation–Capillary Pressure Curve

Although accurate measurements from the MIP method allow characterizing the capillary pressure for the mercury/air system, it cannot be directly applied to the water/CO₂ system (Eq. 15), because the residual CO₂ saturation also needs to be considered (Bennion and Bachu 2005). The residual liquid saturation S_rl is the irreducible degree of saturation for the wetting phase, indicating the amount of the latter one that remains in the pores whichever are the pressure and flow rate of the non-wetting fluid. While the existing studies on CO₂ relative permeability and saturation mostly rely on X-ray computed tomography (Krevor et al. 2012, 2015; Akbarabadi and Piri 2013), this technique has a number of limitations in terms of the possibility to simulate the in situ stress conditions, as well as in terms of the available image resolution that neglects the presence of submicron-scale pores (Elkhoury et al. 2019). In this study, a robust method to estimate the residual saturation from the relative permeability curve is adopted. As the selected reservoir formations have relatively large pores and almost no inclusions of clay minerals, it is assumed that the effect of hysteresis is minor, which is confirmed by the experimental observations. Thus, the fitting curves for the discrete measurements of relative permeabilities are utilized to determine the residual saturation.

From the relative permeability measurements, the equation for the fitting curves can be obtained by the least-squares method, which allows the calculation of the effective saturation parameter S_e at zero relative permeability. Subsequently, the residual water saturation S_rl can be obtained using Eq. (10) for S_e. For Berea sandstone, S_rl is equal to 0.1 for pristine- and CO₂-treated specimens. The residual water saturation is calculated to be 0.08 and 0.07 for pristine Apulian limestone and Indiana limestone, respectively, and these values decrease to almost zero (≈ 0.01) after CO₂ treatment. These observations are in accordance with the previous studies, where the residual saturation is reported to be in the range of 0.05–0.11 for reservoir rock (Bennion and Bachu 2008; Krevor et al. 2012; Pini and Krevor 2019; Niu and Krevor 2020). The decrease in the S_rl values for limestones implies that higher CO₂ saturation can be achieved after the CO₂ treatment. As the residual liquid saturation values are obtained, the capillary pressure–saturation curves for the CO₂/water system can now be determined. By changing the minimum value of water saturation with respect to the measured residual saturation of CO₂, the capillary pressure–saturation curve can be proportionally reformed.

For Berea sandstone, the water saturation decreases at 0.004 MPa capillary pressure, and no significant effect of the CO₂ treatment is observed. The CO₂ entry pressure of Apulian limestone decreases due to the treatment from 0.04 to 0.01 MPa. This indicates that the non-wetting fluid (liquid CO₂ in this case) can more easily intrude into the pores. However, the effect is less pronounced for Indiana limestone, as its CO₂ entry pressure decreases only slightly from 0.009 to 0.008 MPa. Considering the microscopic measurements, the alteration of the residual water saturation–capillary pressure curve due to CO₂ treatment is in agreement with the wettability and surface roughness changes in limestones (Sect. 4.1 and 4.2). As the contact angles increase with the decreasing surface roughness, the limestones become more CO₂-wet, meaning that the CO₂ saturation becomes larger at the same capillary pressure after the treatment, with the CO₂ entry pressure decreasing (Table 3).

The van Genuchten parameters (α, m, and n) assessed from the relative permeability measurements (see Table 1) are utilized to validate the capillary pressure–saturation curves obtained from the MIP tests (Fig. 12). The two methods show an excellent agreement, so it can be argued that the introduced approach for reporting the relative permeability curve can provide reliable results. The only discrepancy is observed at low water saturation for Berea sandstone, which may be caused by a few factors. Firstly, it is the difference between specimen sizes for the core flooding (10 cm long) and MIP (< 1 cm linear dimension) tests. Berea sandstone contains grains with sizes 70–400 μm and pores and cracks with sizes up to 0.1 mm, while for the limestones they are an order of magnitude smaller. The small size of MIP specimens with relatively large pores and cracks on its surface may affect the saturation curve measurements (Churcher et al. 1991). Secondly, errors in determining the fitting curves can provide another explanation for the disagreement between the two methods. The relative permeability curve is highly sensitive to the value of the entry pressure of the non-wetting fluid, where a major decrease in the degree of saturation occurs. However, as few studies have reported, van Genuchten model has some limitations in accurately assessing the capillary pressure and saturation at low wetting fluid saturation conditions (Krevor et al. 2012; Pini and Krevor 2019). The pore distribution results obtained from MIP experiments cannot always be directly used to evaluate the relative permeability curves, and direct capillary pressure measurements at low saturation levels are suggested (Oostrom et al. 2016).

Fig. 12

Analysis for the capillary pressure versus water saturation for CO₂/water system of pristine- and CO₂-treated a Berea sandstone, b Apulian limestone, and c Indiana limestone

Table 3 Summary of the measurements of residual water saturation S_rl, breakthrough pressure, measured apparent contact angle, and ratio of the pristine- to CO₂-treated surface roughness

While the adopted testing approaches are different, it is important to note that the results obtained in this work are shown to be consistent with the existing studies for the pristine materials. For the relative permeability curves of sandstone and limestones, the Brooks–Corey exponents were reported to be within the range of 2.5–6 and the maximum degree of CO₂ saturation was 0.3 ± 0.1 (Perrin et al. 2009; Krevor et al. 2012; Akbarabadi and Piri 2013; Bachu 2013; Berg 2013; Oostrom et al. 2016). The results for the saturation–capillary pressure curves also match well with the previously reported studies.

5.2 Limitations of the Approach

In this study, a novel method is introduced to characterize the relative permeability curve by estimating the degree of saturation of the two fluids as the poromechanical responses are accurately measured. Although this method offers significant advantages, there are some limitations that need to be discussed.

The degree of saturation for the multiphase flow experiment is calculated by measuring the Skempton’s B coefficient, where it is assumed that the pore fluid is evenly distributed in the pores (Eq. 5). However, CO₂ saturation could be larger in the upstream and gradually decrease toward the downstream (Krevor et al. 2012; Berg et al. 2013; Chen et al. 2014). Although the undrained condition is maintained for a sufficient time (10 min) to redistribute the fluids before the measurements, this may affect the reported B values and cause errors in evaluating the degree of saturation of CO₂.

The novel method introduced in this study calculates the degree of water/CO₂ saturation by measuring the poroelastic properties, as the accuracy and validation of this technique need to be discussed. From the measurement of Skempton’s B coefficient, the bulk modulus of the mixed fluid consisting of CO₂ and water (K_{f, mix}) is calculated (Eq. 5). Since the B values significantly decrease as CO₂ is injected, the uncertainty in calculated K_{f, mix} values increases, resulting in larger errors for the reported degree of saturation. Also, for the non-wetting fluid saturation above 20%, the wetting fluid may not exist as a continuous phase in the pores, limiting the application of the Wood’s formula and potentially causing uneven pore pressure distribution (Dullien 1992). The applicability of this method for anisotropic materials that contain multiple minerals may also be an issue, as it provides uncertainty in calculating the applied mean stress (Eq. 4) and may violate the ideal porous media assumption of K^′_s=K^″_s increasing the errors in calculated Skempton’s B coefficients (Eq. 5).

By duplicating the experiments and considering the accuracy of the experimental devices, the relative errors in determining the material properties are calculated as follows: 3% for the porosity, 5% for permeability, 3% for Skempton’s B coefficient, 3% for the bulk moduli, and 10% for the degree of saturation. It is to be noted that the fitting parameters for the relative permeability curve (e.g., Brooks–Corey exponent) may differ by up to 50% due to the error range in the degree of saturation, so the average value is taken for comparison.

The hysteresis of the CO₂/water relative permeability curve for drainage and imbibition is another potential issue that has been reported in a few studies (Juanes et al. 2006; Bennion and Bachu 2007; 2008). This effect is argued to be minor for the tested reservoir rock, where we only concentrate on the drainage procedure (injection of the non-wetting fluid), assuming no hysteresis for the capillary pressure and relative permeability.

Lastly, the difference between the laboratory and the field scales needs to be considered. Despite accurate laboratory measurements of relative permeability and characterization of the microscopic properties, these findings cannot be directly applied to field-scale problems, as the preferential flow paths such as wormholes, cracks, and faults significantly affect the hydraulic behavior (Szymczak and Ladd 2009; Elkhoury et al. 2013). It is apparent that the uncertainty range increases with scale, and thus, the non-uniqueness and variation in relative permeability measurements must be taken into account, which can be determined through inverse modeling based on “history matching” for unsteady-state conditions (Berg et al. 2013, 2021). Moreover, as no direct measurements of relative permeability have been reported at the field scale, efforts to upscale the laboratory measurements have been introduced for the reservoir simulations (Crotti and Cobeñas 2001; Benson and Doughty 2006; Kamali and Hussain 2017), but further research needs to be conducted regarding validation of the proposed methods.

6 Conclusion

This study characterizes the effect of CO₂ treatment on the multiphase flow characteristics of reservoir rock by comprehensively considering various factors such as poroelastic deformation, capillary pressure, wettability, and surface roughness. By selecting one silica-rich and two calcite-rich porous rocks, the chemical effect on the type of the dominant mineral is examined. Different experimental methods—core flooding, mercury intrusion porosimetry, microgoniometry, and profilometry, are introduced to characterize the changes in relative permeability, capillary pressure, wettability, and surface roughness of reservoir formations during CO₂ injection. A robust technique is implemented to evaluate the relative permeability curve from the measurements of the changes in poroelastic response upon CO₂ flow in the rock, and the results are compared with independent evaluations based on the direct capillary pressure measurements. The capillary pressure curves are affected due to the chemical effect caused by CO₂ injection in water-saturated limestones, where the exponent values for the Brooks–Corey model decrease, implying that the relative CO₂ permeability increases with maximum CO₂ saturation. On the other hand, the exponent value is reported to remain constant for the sandstone, while its maximum CO₂ saturation slightly increases. A qualitative analysis of the contact angle and the surface roughness is conducted, showing that the CO₂ treatment smoothens the surface for limestones and increases their CO₂ wettability, while the effect is almost unnoticeable for the sandstone. This implies that CO₂ treatment may affect the relative permeability and wettability, highlighting the importance of adopting accurate multiphase flow parameters for reservoir models. In conclusion, this study thoroughly investigates the effect of CO₂ treatment on the multiphase flow characteristics of reservoir rock and suggests that the chemical effect can increase the CO₂ injectivity in calcite-rich formations.