In this study, six shales were obtained from the Longmaxi formation, Sichuan Basin. The shales of S1, S3, S5, and S6 were collected from the bottom to upper-middle Longmaxi formation at the Chongqing Blackwater Section (Figure 1). In comparison, the S2 and S4 were gathered from the bottom Longmaxi formation located at Qiliao and Pengshui Sections, respectively (Figure 1). The detailed petro-physical, organic geochemical, and mineralogical information parameters are presented in Table 1. The TOC of the selected shales in the range of 1.44%–4.97%, estimated by the CS-800 Carbon sulfur analyzer. The R _o (vitrinite reflectance equivalent) of the selected shales averaged at ∼2.41%, classifying to the over-mature stage. The XRD experimental results are listed in Table 1 and shown in Figure 2. Results indicated that the quartz content contributes the most significant mineral proportion of shales, ranging from 48.77% to 54.04%. The SEM results are displayed in Figure 3, the shale pore types include dissolved pore (Figure 3B), intergranular pore (Figures 3C,D), organic pore (Figure 3F), and microfracture (Figures 3A,E).

In this study, the low-temperature N₂ gas adsorption (LT-N₂GA) measurements were performed to investigate the pore structure properties of shales, following the Chinese standard of SY/T6154-1995. For the sample preparation, the large-sized shales were crushed to 60–80 mesh, then dried in an oven to remove impurity gas and internal bound-water. The LT-N₂GA procedures can be summarized as: 1) Subject a certain amount of powder shales to vacuum degassing. 2) Obtaining the N₂ adsorption/desorption properties under constant experimental conditions. 3) Estimating the pore structure parameters (e.g., specific surface area, pore volume). based on the BJH and BET models (Yao et al., 2008).

CO₂ adsorption isotherm measurements were performed by the volumetric-based method (Figure 4). The principle of this method depends on the pressure changes in the sample and reference cells during CO₂ adsorption process. CO₂ adsorption isotherm experimental procedures were summarized as: 1) Grind the bulk shale into 60–80 mesh (0.02–0.03 cm) using a ball-mill instrument and then represent dry treatment for 72-h at a given temperature of 110°C to remove the moisture inside the sample. 2) Transfer the powder sample in to sample cell and then present vacuum treatment by a vacuum pump. 3) Calculate the free space volume based on the mass balance parameters before/after helium injection. 3) Inject the designed pressure of CO₂ into the sample cell for CO₂ adsorption. e) Estimate the CO₂ adsorption capacity on the basis of the ideal-gas equation.

Table 2 shows the pore structure parameters of the selected shales identified by the LT-N₂GA measurement. Results indicated that the BJH pore volume of shales range from 0.0117 to 0.0163 cm³/g, the volume of micropores (pore radius <2 nm), mesopores (pore radius 2–50 nm), and macropores (pore radius >50 nm) contribute the total proportion as ∼41.75%, ∼41.05%, and ∼17.2%, respectively. While the BET specific surface area in the range of 7.94–66.02 m²/g, the specific surface area of micropores, mesopores and macropores contribute the total proportion as ∼75.75%, ∼23.75%, and ∼0.5%. The low percentage of macropores in BET specific surface area is mainly because the LT-N₂GA testing principle–limiting characterizes the pore size larger than 200 nm. As shown in Figure 5, the pore size distributions (PSD) of some shales (S6 and S5) emerge two significantly different peaks; from left to right, the peak locates at 2–3 and 10–20 nm, respectively. For the remaining shale samples, the PSD is characterized by a unimodal size distribution with a peak at approximately 8–20 nm.

Based on the LT-N₂GA experimental data and Frenkel-Halsey-Hil (FHH) model, the complexity and heterogeneity of shale were quantitatively characterized (He et al., 2021; Liu K et al., 2021). The greater fractal dimension is indicative of more heterogeneity pore structure. FHH fractal dimension calculation method was expressed as follows: ln V V 0 = K ln ln P 0 P + C (1) where V means the nitrogen adsorption volume under pressure P, mmol/g; P means the experimental equilibrium pressure, MPa; V ₀ means the monolayer coverage volume, mmol/g; K and C are constant, dimensionless; P ₀ is the nitrogen saturation pressure, MPa. According to Eq. 1, the slope of lnV vs. ln (ln (P ₀/P)) plots equals the constant C. While the fractal dimension D equals “C+3” value. Theoretically, fractal dimension D in the range of 2–3, the closest value to two indicates the more regular the pore space structures, and the closest value to three means the more complex and heterogeneity pore structures.

The scatterplot of lnV vs. ln (ln (P ₀/P)) for six shales are displayed in Figure 6. It can be found that there are two distinct linear segments, one at the P/P ₀ intervals of 0–0.5 and the other one at the 0.5–1 region. In addition, these two linear segments show great linear relationships (R ²>0.95), indicating the different fractal characteristics. Here, the fractal dimension at P/P ₀ intervals 0–0.5 and 0.5–1 as D ₁ and D ₂, respectively. Moreover, D ₁ and D ₂ represent the pore surface fractal and the pore structure fractal, dominated by Van der Waals forces and capillary condensation actions, respectively (Yao et al., 2008). As shown in Table 3, The fractal dimension D ₁ of shales value as ∼2.29–2.75, average at 2.51. While the fractal dimension D ₂ ranges from 2.56 to 2.89, average at 2.70 (Table 3).

Figure 7 represents the CO₂ isothermal adsorption data with respect to different pressures for the selected shales. The excess CO₂ adsorption capacity rapidly increases with pressure at low-pressure intervals, and slowly increases at high-pressure intervals. Additionally, the CO₂ adsorption capacities vary from region to region. The experimental determined maximum excess CO₂ adsorption capacity of shale S1 is ∼2.02 cm³/g, the smallest value among all the samples (Figure 7). In comparison, the experimental determined maximum excess CO₂ adsorption capacity of S6 is valued as ∼5.41 cm³/g (Figure 7). These differences probably arise because of the complex solid and heterogeneity in shales–resulting in the variation in internal composition and pore structure–leading to the different CO₂ adsorption capacities in different shales.

Langmuir model is the commonly used adsorption characterization model in coals, which can be extended to investigate the CO₂ adsorption capacity for shales. The Langmuir model was based on the following assumptions (Perera et al., 2011; Dutka, 2019; Liu Y et al., 2022): 1) The adsorbent surface was characterized as uniform; 2) A dynamic adsorption equilibrium state between adsorbent and adsorbate; 3) The adsorption behavior was monolayer molecular adsorption; 4) No interaction force among the adsorbent gas molecules. The Langmuir model can be deduced as follows: V = V L P P + P L (2) where V means the experimental measured adsorption capacity, cm³/g; P means the experimental pressure, MPa. V _L means the Langmuir adsorption capacity, cm³/g; P _L means Langmuir adsorption pressure, MPa.

The CO₂ isothermal adsorption data fitting results are listed as Table 3, and the fitting curves are displayed in Figure 7. Results indicate that the Langmuir model fitting curves are consistent with experimental excess CO₂ adsorption capacity changes. The CO₂ adsorption capacity rapidly increases with increasing pressure before reaches to a critical pressure; after that, the fitting curves rise smoothly and tend to saturate. As shown in Table 3, the Langmuir volumes of the CO₂ isothermal adsorption in the shale in the range of 3.26–6.95 cm³/g (averaging ∼5.03 cm³/g). While, the Langmuir pressure of the CO₂ isothermal adsorption in the shale ranges from 0.99 MPa to 3.05 MPa (averaging ∼1.76 MPa). It can be concluded that the Langmuir model is used equally well to investigate the CO₂ sorption behavior for shales, as evident by the high correlation coefficients >0.9875.

Figure 8 shows the relationships between TOC content, R _o value and Langmuir CO₂ adsorption capacity. Results indicate a perfect positive linear correlation between TOC content and Langmuir CO₂ adsorption capacity, with a high correlation coefficient as ∼0.9169 (Figure 8A). The higher TOC content is indicative of greater CO₂ adsorption capacity. The above phenomenon can be attributed to the massive nanopore kerogen development in organic matter, which is the leading adsorption site of CO₂ in shales. In addition, the R _o presents a very weak negative correlation with the Langmuir CO₂ adsorption capacity (Figure 8B). Tang et al. (2016) investigated the adsorption behavior of the shales under the same conditions for organic matter and kerogen shale types, and found the adsorption capacities of over-mature shales were lower than these in high-maturity stages. The results presented in this section are consistent with the previous study (e.g., Chalmers and Bustin, 2008; Tang et al., 2016).

The effect of shale mineral composition on its CO₂ adsorption capacity is mainly reflected in the clay and brittle minerals. In this study, the relationships between clay content, brittle mineral content and Langmuir CO₂ adsorption capacity in shales are displayed in Figure 9. It can be found that there exists a positive correlation between the clay content and Langmuir CO₂ adsorption capacity (Figure 9A). While, the brittle mineral content was negative related with the Langmuir CO₂ adsorption capacity (Figure 9B), properly because the increase in brittle mineral content in the shale leads to relative decreases both in the clay and TOC content. The correlation coefficient of clay content and Langmuir CO₂ adsorption capacity was more significant than that with brittle mineral content, indicating clay content is the significant control factor on CO₂ adsorption.

Figure 10 presents the correlations between pore structure parameters (obtained from the LT-N₂GA measurements) and CO₂ adsorption capacity of shales. Results illustrate that both the specific surface area and pore volume positively affect the CO₂ adsorption capacity. The correlation coefficient of CO₂ adsorption capacity and specific surface area was greater than that with pore volume, indicating that the specific surface area is the most direct factor affecting the CO₂ adsorption of shale. The behavior of CO₂ adsorbing in shale pore surface is attributed to the physical adsorption of Vander Waals force. The larger specific surface area is indicative of more adsorption sites–more conducive to the CO₂ adsorption in shales.

The shale pore structures were characterized by heterogeneity (as discussed in Section 3.1), and the influence of these fractal characteristics on CO₂ adsorption behavior cannot be ignored. Generally, there are two conventional definitions for describing fractal characteristics of porous materials: the surface fractal dimension (D ₁) and the pore structure fractal dimension (D ₂). Thus, it is necessary to quantitatively investigate the effect of pore fractal characteristics on the adsorption and storage capacity. As shown in Figure 11, the two fractal dimensions have different influences on the CO₂ adsorption capacity of shales. Results show that the fractal dimension D ₁ positively correlated with the Langmuir CO₂ adsorption capacity (Figure 11A). Because the higher fractal dimension D ₁ values represent more rough surfaces of shales that offer more adsorption sites for CO₂ and lead to the higher adsorption capacity of shales. Additionally, there were no significant relationships between the fractal dimension D ₂ and Langmuir CO₂ adsorption capacity (Figure 11B).

Shale reservoirs have considerable potential for large-scale CO₂ sequestration, and the sequestration mechanisms are mainly controlled by adsorption and mineralization reactions. CO₂-ESGR technology opens up a new way for the green and efficient development of domestic unconventional oil and gas and geothermal resources. It is conducive to realizing the strategic goal of “Carbon Peak” in 2030 and “Carbon Neutrality” in 2060 in China. In 2020, the shale gas proved geological reserves reached ∼2 × 10¹² m³, providing a good application prospect in CO₂ geological storage. There are two classic methods to estimate the CO₂ geological storage potential in shales; one is the CSLF (Carbon Sequestration Leaders Forum) method (as described in Eq. 3), and the other one is the DOE (United States Department of Energy) method (as described in Eq. 4). M co 2 = P P G I × ρ g × R e (3) where M _CO2 is the CO₂ geological storage volume in shales, m³; ρ _g is the density of CO₂, kg/m³; P _PGI is the available shale gas production, kg; R _e is replacement volume ration between CO₂ and CH₄, dimensionless. M co 2 = A s h a l e × ρ g × h × V a + V f × E (4) where M _CO2 is the CO₂ geological storage volume in shales, m³; A _shale is the target shale gas reservoir area, m²; ρ _g is the density of CO₂, kg/m³; h is the thickness of target shale gas reservoir, m; V _a is the CO₂ adsorption capacity, m³/kg; V _f is the free phase CO₂ content, m³/kg; E is the effective factor of shale CO₂ geological storage, which is influenced by the CO₂ adsorption capacity, buoyancy characteristics, and transport capacity. Based on the combination of CO₂ adsorption capacity and above parameters in Eq. 3 or Eq. 4, it is straightforward to calculate the CO₂ geological storage potential in shales.