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. 2020 Jul 30;5(31):19606–19614. doi: 10.1021/acsomega.0c02118

Swelling of Shales by Supercritical Carbon Dioxide and Its Relationship to Sorption

Xiang Ao †,‡,*, Zhilin Qi †,‡, Zuping Xiang †,‡, Zhiqiang Li †,‡, Hai Qu †,‡,*, Ziyi Wang †,‡
PMCID: PMC7424733  PMID: 32803055

Abstract

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Shale gas is a promising energy source offering additional energy security over concerns of fossil fuel depletion. Injecting CO2 into depleted shale gas reservoirs might provide a feasible solution for CO2 storage and enhanced gas recovery. However, shale strain caused by the CO2 injection as well as CO2 sequestration in the reservoir needs to be considered during shale gas production. For this purpose, this paper examines the adsorption capacities, CO2-induced swelling, and He-induced strain of shales at 0–16 MPa and 35–75 °C. The maximum excess adsorption at different temperatures correlated with the bulk phase density: as the CO2 temperature increased, the maximum excess adsorption density decreased. The density of the adsorbed phase, obtained using the Dubinin–Radushkevich model, was used to fit the excess adsorption data. At low pressure, the CO2-induced strain on shale was caused by the gas adsorption, whereas at high pressure, it was caused by gas pressure. The absolute adsorption linearly correlated with the adsorption-induced strain.

1. Introduction

Because of the economic developments and standard of living improvements, natural gas demand is continuously increasing.1 Shale gas is considered a promising energy source capable of providing more energy security.2,3 The shale gas is extracted by hydraulic fracturing and horizontal drilling, both of which require large amounts of water, which, in turn, might cause damage, waste water resources, and pollute groundwater.4,5 In addition, because of the high clay content in shale gas formations in China,6 it is almost certain that drilling and hydraulic fracturing will be necessary. A related issue is the need to control swelling strain on clay-rich shale caused by adsorption of water. To avoid these issues, many researchers have focused on anhydrous fracturing,7−10 especially with carbon dioxide as fracturing fluid. Therefore, currently, CO2 injections into the shale formations to enhance the production of shale gas and CO2 sequestration are actively studied.11−15 Analysis of the CO2-induced swelling strain of shale is fundamental to select appropriate methods for methane seepage in shale pores as well as for shale gas diffusion and CO2 storage in shale formations.

A lot of current literature focuses on the swelling strain caused by the gases injected into coal formations or shales. For example, the maximum volumetric strain of Australian coals was 1.7–1.9%.16 The maximum volumetric strain of low-ranked coals caused by CO2 injection was 1.65%. In addition to experimental studies, a lot of works use theoretical modeling to describe CO2-induced swelling in coal.17 Shale expansion caused by other gases was also studied. For example, Chen et al. investigated the swelling strain on shale injected by CH4.18 Despite many articles reporting swelling strains caused by CO2 injections into the matrix, the adsorption of gases co-occurring with their injections was rarely reported.19−22

Typical temperatures and pore pressures of shales with high organic content shale formations are in the 370–550 K and 15–20 MPa ranges. Thus, the state of CO2 injected into shale formations under these conditions is, thus, supercritical. Supercritical gas adsorption on shale was reported previously.23 For example, the excess adsorption on shales was measured by volumetric and gravimetric methods.24 Chareonsuppanimit et al. measured shale adsorption of high-pressurized gas adsorption using the simplified local density model to fit the experimental data.25 Chalmers and Bustin reported that the storage capacity of CO2 in shale reservoirs based on the shale adsorption ability and that CO2 adsorption would reduce its surface energy.26 The tendency of the shale to restore this lost energy would lead to shale swelling,27 which might have severe consequences for CO2 storage or hydraulic fracturing, including shale structure damage, inducing fracture close, porosity, and permeability decrease.28−32 Therefore, the analysis of CO2-induced swelling of shale is fundamental.

This paper reports shale swelling strain caused by the injected CO2 at 0–16 MPa and 35–75 °C, and measurement of the pressure-induced strain using He. We also show the analysis of the absolute adsorption on shale as well as its relationship with the gas adsorption-induced strain.

2. Theories

2.1. CO2 Adsorption by Shale

Among a variety of different models capable to accurately describe CO2 adsorption by porous media, we chose the supercritical Dubinin–Radushkevich (SDR)33 model

2.1. 1

where ntex is the excess adsorption; nmax is regular and the maximum excess adsorption; D is a fitting parameter; and ρa and ρg are densities of the adsorbed phase and CO2, respectively.

2.2. Absolute Adsorption

Absolute adsorption (nab) was calculated using the excess adsorption (nex) by the equation shown below34

2.2. 2

where ρa and ρg are the densities of the adsorbed phase and CO2, respectively.

2.3. CO2-Induced Strain

According to the research by Sakurovs,35 in relation to swelling, the modified SDR model is shown in eq 3

2.3. 3

where Smax is the maximum swelling of the shale, ρa and ρg are densities of the adsorbed phase and gas, respectively, k is a constant related to the solubility of CO2, and E is a constant depending on adsorption heat and affinity of the gas to the adsorbent. For the swelling data, E acts as an empirical curve-fitting parameter.

2.4. Density of the Adsorption Phase

Because the density of the adsorbed phase cannot be experimentally obtained, it was assumed to be equal to the density of liquid CO2, which is independent of temperature, pressure, and the adsorbent type.36 However, in many research, it is incorrect for the adsorbed phase density as a constant. The adsorbed phase density can be determined by fitting adsorption isotherms with models such as the Dubinin–Radushkevich (DR) model.37 Therefore, we determined the adsorbed phase density from the adsorption isotherms fitted using the DR model.

2.5. Effective Stress

The effective stress was calculated as shown below38

2.5. 4

where σeff and σ are the effective and total stresses, respectively; pc is pore pressure; and α is the Biot coefficient, which is specific for a given rock and is typically independent of stress and pore pressure.39−41 However, Ma and Zoback42 reported that the Biot coefficient was dependent on the pore pressure.

3. Materials and Methods

3.1. Characteristics of Shale

The subject of this work was shale from an outcrop of the Longmaxi Formation of the lower Silurian near Yibin City, Sichuan Province, in the Sichuan Basin. The total organic carbon content (TOC) and the vitrinite reflectance (R0) values (which were equal to 7.88 and 2.85%) were optimal (TOC ≥ 2%, 3% ≥ R0 ≥ 1%)43 for the shale gas occurrence of shale gas. The major phases of the shale, determined using powder X-ray diffraction (XRD) performed by the Siemens D5000 instrument, were quartz (40.2%), calcite (11.7%), and clay (15.1%) (see Table 1). XRD was performed in the 2–45° 2θ range at 0.02° step and 2 s dwell time.

Table 1. Phase Composition (Determined by XRD) of Shale Samples Collected from the Longmaxi Formation of the Lower Silurian Near Yibin City, Sichuan Province, in the Sichuan Basin, China.

mineral name content, wt %
quartz 40.2
clay 15.1
calcite 11.7
plagioclase 3.8
iron pyrites 2.7
barite 1.0
K-feldspar 0.8
karsten itebarite 0.41
clay 15.1
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The shale matrix pores range from micro- to nano-meters and relatively large surface area (SA), which were determined using mercury porosimeter and by recording N2 adsorption/desorption isotherms at 77 K using a Micromeritics ASAP2020. The SA was calculated at P/P0 N2 pressure equal to 0.14. Pore size distribution was obtained using a Barrett–Joyner–Halenda (BJH) model.

3.2. Experiments

3.2.1. Shale Samples

Shale samples were collected using a cylindrical core 100 mm long and 50 mm in diameter inserted perpendicular to the shale. Precautions were taken to avoid cracks and external contamination to ensure sample contents and properties to be as close to each other as possible. The sample surfaces were polished using (consequently) 60, 120, 200, 600, 2000, and 3000 mesh sandpaper, after which the samples were rinsed and dried at 110 °C for 24 h.44 Altogether, 15 samples were used in this study, and every temperature condition used three samples. Because of the CO2 isotherm adsorption curve always using the crushing sample, in this work, sample 1 was crushed to the powder after the test of adsorption-strain. The crushing sample was used to measure the CO2 isotherm adsorption curve at 35 °C (Figure 1).

Figure 1.

Figure 1

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N2 adsorption/desorption isotherms of the shale samples.

3.2.2. Experimental Setup and Procedures

We used a high-pressure and high-temperature adsorption deformation setup described by Ao et al.45 to measure the gas-induced shale strain and the excess CO2 adsorption (see Figure 2).

Figure 2.

Figure 2

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A) Instrumental setup used in this work to measure the shale strain; (B) Diagram of the strain gage setup; (C) Diagram of the sample cell.

The measurements were performed using the following steps:

  • 1.

    Strain gauges were attached to the samples, rinsed with absolute ethanol, using Omega SG496 glue (see Figure 2B).

  • 2.

    The sample was mounted inside the test cell to determine the void volume (composed of pore volume and free space inside a sample), which was performed using He.

  • 3.

    The system was then heated to the target temperature using a water bath. The setup was allowed to equilibrate to ensure that the temperature-induced expansion took place. The maximum swelling was assumed to be reached after the strain gauges showed no significant changes, after which the system was evacuated. Prior to the tests, the samples were degassed for 24 h, during which the samples shrank slightly. The adsorption measurements and data processing were conducted, as described by Chen et al. The amount of the Gibbs excess adsorption (Δniex) was obtained as shown below

3.2.2. 5

where m is the sample weight, VR is the volume of the reference cell Vvoid is the void volume of the system, and ρ is the density of CO2 (taken from the US National Institute of Standards and Technology Chemistry WebBook) (NIST, 2019).46 The indices “I,” “F,” and “Eq” refer to the initial, final, and equilibrium conditions, “R” and “S” refer to the reference and the sample cells, and “i” and “i – 1” refer to the corresponding experimental steps, respectively.

  • 4.

    The tests were performed at 35, 45, 55, 65, and 75 °C using 15 MPa pressure increments and equilibrated for 24 h before each measurement.47 The strain was recorded simultaneously with CO2 adsorption measurements.

  • 5.

    For comparison, strain induced by He was measured at 35 °C and 0–16 MPa.

  • 6.

    The step 3 and step 4 were used to measure the CO2 isotherm adsorption curve using the crushing sample.

4. Results and Discussion

4.1. CO2 Adsorption Isotherms

For each temperature, the amount of excess adsorbed CO2 was measured in eight pressure intervals: from 0.02 to 2, from 2 to 4, from 4 to 6, from 6 to 8, from 8 to 10, from 10 to 12, from 12 to 14, and from 14 to 16 MPa. The resulting isotherms were then used to calculate an equilibrium adsorption gas content for each pressure and temperature step using eq 5 (Figure 3).

Figure 3.

Figure 3

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Schematics showing the experimental step sequence to measure the amount of adsorbed CO2 and shale deformation.

Supercritical adsorption occurs when a gas is adsorbed above its critical temperature.48 Thus, because our adsorption experiments were performed above the supercritical temperature of CO2, the curves shown in Figure 4 can be considered supercritical adsorption isotherms. The adsorption isotherms belonged to type I. Below the critical CO2 pressure, the amount of excess adsorption increased as CO2 pressure increased. It indicates that the adsorption is a monolayer–molecular layer adsorption. The reaction of solid–fluid and fluid–fluid interfaces is van der Waals force. Therefore, the gas molecules can be adsorbed on the solid and can also be adsorbed on the molecules. In addition, the interaction between the solid surface and the adsorbed molecules is weak, whereas the force between the adsorbed molecules is strong. In the 6–9 MPa range, the bulk density increased as CO2 pressure increased. These changes are equal to changes in the density of the adsorbed phase. Therefore, the maximum excess adsorption is obtained, and thereafter, as the pressure further increases, the adsorption decreases. In addition, it was found that the adsorption amount tends to zero, and the packing density is close to that of the adsorbed phase.49 The excess CO2 adsorption decreased as temperature increased (see Figure 4). The temperature during the tests was above the CO2 critical temperature (which is equal to 31.13 °C), especially for the tests performed at 65 and 75 °C.

Figure 4.

Figure 4

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Excess CO2 adsorption by shale samples at different temperatures as a function of pressure.

Because of the CO2 isotherm adsorption curve always using the crushing sample, in this work, we compare the isotherm adsorption curves of the plunger sample and crush sample. From the Figure 5, the average standard deviation of the isotherm adsorption curve tested by the crushing sample and plunger was equal to 19.8% and the correlation coefficient was equal to 0.91. According to the research by Pan et al.,50 the sample sized 21 mm × 21 mm × 21 mm was determined the diffusive of shale. The result showed that the amount of gas into the shale approaches 80% at 100 min. It is indicated that most of the gas can enter the shale within a day. It indicates that gas diffusion into the shale through the plunger sample and crush sample has no obvious difference. To sum up, we believe that using the plunger sample to determine the adsorption and strain at the same time is reliable (Table 2).

Figure 5.

Figure 5

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CO2 isotherm adsorption curve at 35 °C using the plunger sample and crush sample.

Table 2. Mesopore and Micropore Characteristics of the Shale Samples.

  sample 1 sample 2 sample 3 sample 4 AAD %
BET SA, m2/g 18.3 17.0 18.4 17.3 3.38
Langmuir SA, m2/g 25.2 23.9 26.3 24.9 3.41
BJH SA, m2/g 10.0 9.8 10.0 9.4 2.40
BJH volume, m3/g 0.016 0.016 0.015 0.016 2.49
average mesopore size, nm 6.2 6.4 6.0 6.2 2.27
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Error analysis for the data shown in Figure 6 was necessary because even though the sample contents and properties were close to each other, they were not identical. The average values obtained using eq 1 at pressures equal to 2, 4, 6, 8, 10, 12, 14, and 16 MPa, and their corresponding errors are shown in Figure 6. The corresponding fitting parameters are listed in Table 3. The standard deviations were equal to 6.62, 3.71, 2.90, 4.27, and 5.19% for the data collected at 35, 45, 55, 65, and 75 °C, respectively. Relatively low experimental errors confirmed the similarity between our shale samples as well as experimental data reliability. Therefore, only one test was performed at rest conditions.

Figure 6.

Figure 6

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Excess CO2 adsorption by the shale sample as a function of the CO2 density and temperature.

Table 3. Experimental Data-Fitting Parameters Obtained Using the DR Model.

    nmax
 D
 ρa
  
    date average date average date average R2
35 °C 1 2.71 2.51 0.126 0.109 1460.25 1527.77 0.95
  2 2.26   0.104   1541.24   0.93
  3 2.57   0.097   1581.80   0.94
45 °C 4 2.26 2.38 0.097 0.103 1584.22 1513.20 0.99
  5 2.37   0.110   1456.77   0.97
  6 2.50   0.101   1498.62   0.98
55 °C 7 2.16 2.32 0.098 0.105 1489.06 1409.17 0.99
  8 2.37   0.103   1389.82   0.98
  9 2.44   0.114   1348.62   0.99
65 °C 10 2.17 2.25 0.105 0.102 1321.32 1330.85 0.99
  11 2.37   0.098   1347.73   0.98
  12 2.22   0.101   1323.50   0.97
75 °C 13 2.16 2.25 0.110 0.104 1229.50 1275.39 0.98
  14 2.37   0.100   1268.63   0.98
  15 2.21   0.103   1328.03   0.97
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The maximum amounts of adsorbed CO2 were obtained at similar density values, which were equal to 361 kg/m3 at 7.88 MPa and 35 °C, 349 kg/m3 at 9.08 MPa and 45 °C, 327 kg/m3 at 10.02 MPa and 55 °C, 304 kg/m3 at 10.71 MPa and 65 °C, and 295 kg/m3 at 11.49 MPa and 75 °C (see Figure 6). These results demonstrate that bulk CO2 density is the most significant variable during CO2 adsorption at high pressure.

The adsorbed phase density values, calculated using the SDR model, shown in Table 3, were used to calculated CO2 absolute adsorption using eq 2. The results, shown in Figure 7, indicated that the CO2 uptake increased significantly as CO2 pressure was increased (below the critical CO2 pressure). However, the adsorption rate decreased as CO2 pressure was increased (see Figure 7).

Figure 7.

Figure 7

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Total CO2 adsorbed at different temperatures as a function of CO2 pressure.

4.2. CO2-Induced Strain

Positive strain values were used to represent swelling. Prior to each strain test, the system was allowed to reach thermal equilibrium at the target temperature, based on heating in the water bath, ensuring that any temperature-induced expansion took place. Thus, the strain observed in our shale samples at different temperatures was caused by gas behavior. The experimental data were recalculated using eq 3, and the average values (calculated based on the results for four samples) were plotted as a function of the pressure (see Figure 8). The relative standard deviations of the data points were 7.19, 4.07, 3.77, 5.11, and 5.76% at 35, 45, 55, 65, and 75 °C, respectively. Relatively small deviations indicate minimum variations among samples and reliability of the experimental data. Therefore, only one test was performed at rest conditions (Figure 9).

Figure 8.

Figure 8

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Volumetric strain the shale samples upon CO2 injection as a function of CO2 pressure and temperature.

Figure 9.

Figure 9

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Volumetric swelling of the shale samples induced by CO2 injection at different temperatures.

The shale samples became swollen as the CO2 pressure increased. The change in surface potential energy of the shale upon CO2 adsorption was equal to the elastic energy variation.51 The swelling strain of the samples increased as the CO2 pressure increased (at values below the critical pressure) because of the increased amounts of adsorbed CO2 (see Figure 4). The adsorption capacity reached its maximum level at this period. The maximum strain values at 35, 45, 55, 65, and 75 °C were 1.55, 1.29, 1.22, 1.08, and 1.03‰, respectively. Because of the adsorption ability decrease, the maximum swelling of the shale gradually decreased as the CO2 temperature was increased.

However, as the CO2 pressure was increased, the shale swelling decreased in two regions. In one instance, as the pressure was increased, the shale adsorption capacity decreased (see Figure 7), and as a result, CO2-induced swelling decreased. In addition, gradually increased CO2 pressure increased the effective stress. At 16 MPa, the strain values at 35, 45, 55, 65, and 75 °C were equal to 1.28, 1.19, 1.08, 1.03, and 0.91‰, respectively. These stain values correspond to 82.2, 92.5, 88.9, 95.65, and 88.4% of the maximum swelling, respectively. These results agree to those reported by Pan and Connell,19 who also reported sample shrinkage decrease as the gas pressure increased.

The maximum swelling strain decreased as the temperature was increased, which can be explained by two phenomena. First is sample swelling strain dependence on its adsorption ability. At the highest adsorbed CO2 amount, the maximum strain resulting from adsorption at high temperatures was lower than at low temperatures (see Figure 7). Second is similar values of the confinement pressures on the shale samples at high and low temperatures. The gas pressure- and adsorption-induced strains are discussed in Sections 4.4 and 4.3, respectively.

4.3. Gas Pressure-Induced Strain

Figure 10 shows the average values of the linear strain induced by He injection for the three shale samples as well as the error bars. The relative standard deviations of the perpendicular and parallel data were 7.5 and 9.6%, respectively, indicating the high reliability of the data. Because helium has no adsorption ability, there is no creep without deviator stress.52 Thus, the measured deformation was caused only by the pressure caused by the injected He gas.

Figure 10.

Figure 10

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Strain induced by gas injected at different pressures.

The shale samples exhibited compressive deformation affected by the gas pressure (Figure 10). Below 8 MPa, compressive strain increased linearly with pressure. At the same time, a significant shrink strain nonlinear increase was also observed. According to Ma and Zoback,42 the Biot coefficient does not significantly increase at low pore pressure. As the pore pressure increases, the Biot coefficient decreases. Thus, as He pressure increased, the effective stress would also increase linearly at low pressure, whereas at high pressures, the stress would increase nonlinearly. Experimental data fitting showed a linear relationship between the gas pressure and the linear strain of the shale. The perpendicular and parallel strain slopes were 0.02465 and 0.0172, respectively (see Figure 10). By comparing the Hooke equation to the fitting curve,53 one can see that the slope is inversely proportional to the shale bulk modulus. The vertical and radial elastic moduli obtained from the fitting were equal to 40 and 58 GPa, respectively.

4.4. Strain Caused by Gas Adsorption

A model used to describe coal formation swelling showed that the strain was proportional to the amount of CO2 absorbed by coal.19 The shale strain caused by CO2 injection (ε) is a sum of the strains caused by gas pressure (εp) and the adsorption-induced swelling (εa) effects

4.4. 6

The swelling strain caused by the adsorption increased with pressure (see Figure 11). Adsorption-induced strain was similar to the strain induced by CO2 injection in the 0–4 MPa range. At this pressure range, CO2 was slowly adsorbed, and the sample volume increased as the surface layer thickness increased during CO2 penetration into the pores and cracks. In this region, the pressure effect on the shale strain was not noticeable. The ratio between the adsorption-induced strain and CO2-induced strain was equal to 1.27‰ at 2 MPa. However, the difference between the adsorption-induced strain and the CO2-induced strain was evident as the pressure was increased. In this region, the strain effect caused by pressure was visible, and the ratio between the average strain caused by gas adsorption and CO2-induced strain was 1.79‰ at 16 MPa. Additionally, at higher pressures, the CO2-induced strain became negative because of the pressure effect, which agrees with the results shown by Pan and Connell19 using the coal (Tables 4 and 5).

Figure 11.

Figure 11

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Shale strain as a function of CO2 pressure and temperature. Data points represent the adsorption-induced strain, while the curves represent the CO2-induced strain.

Table 4. Parameters Obtained Using the SDR Fitting Model.

    Smax
 E
 k
  
temperature test number data average data average data average R2
35 °C 1 2.21 2.00 0.056 0.055 1.27 × 10–3 0.000867 0.99
  2 2.02   0.046   8.52 × 10–4   0.99
  3 1.78   0.064   4.79 × 10–4   0.98
45 °C 4 1.63 1.63 0.074 0.078 5.99 × 10–5 7.45 × 10–5 0.98
  5 1.50   0.077   6.49 × 10–5   0.98
  6 1.78   0.083   9.88 × 10–5   0.97
55 °C 7 1.54 1.63 0.082 0.084 1.04 × 10–4 0.000107 0.98
  8 1.66   0.080   1.09 × 10–4   0.98
  9 1.68   0.090   1.08 × 10–4   0.98
65 °C 10 1.21 1.38 0.075 0.077 2.14 × 10–4 0.000142 0.98
  11 1.53   0.082   1.11 × 10–4   0.99
  12 1.41   0.075   9.99 × 10–5   0.99
75 °C 13 1.40 1.73 0.101 0.123 2.78 × 10–4 0.000268 0.99
  14 2.39   0.177   3.88 × 10–4   0.99
  15 1.41   0.090   1.38 × 10–4   0.06
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Table 5. Fitting Parameters for the Amount of Adsorbed CO2 and Adsorption-Induced Strain.

temperature (°C) intercept slope R2
35 0.55 0.69 0.80
45 0.23 0.84 0.97
55 0.25 0.83 0.94
65 0.12 0.89 0.98
75 0.03 0.90 0.98
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To assess practical applications of this approach, we plotted volumetric strain data as a function of the amount of adsorbed CO2 (see Figure 12). According to the results shown by Day et al.,22 the volumetric strain caused by adsorption in coal linearly correlated with the amount of adsorbed gas. Therefore, we also fitted our data using linear approximation (see Figure 12).

Figure 12.

Figure 12

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Adsorption-induced shale strain as a function of the adsorbed gas. Data points represent the test data, while the curves represent the fitting.

The volumetric strain caused by the shale adsorption of CO2 indeed linearly correlated with the amount of adsorbed CO2 (see Figure 12). However, the correlation coefficients for the data collected at 35 and 55 °C were somewhat low (0.80 and 0.94, respectively), which might indicate that the strain and CO2 adsorption amounts might not be in a linear relationship at these temperatures. The first explanation is that the value of the adsorbed phase density was constant and independent of the temperature. However, in some cases, the test temperature was above the critical temperature of CO2; thus, the liquid CO2 could not evaporate. Thus, if the density of the adsorbed phase was different at different pressures and temperatures, at this time, it cannot be taken into account because of insufficient data currently available. The second explanation is that even though different shale samples showed similar pressure-induced strain data, the samples might still have different mechanical properties.

5. Conclusions

Strains of shale samples collected from the Longmaxi Formation of lower Silurian in Yibin City, Sichuan Province, in the Sichuan Basin were studied. The adsorption capacities of shale samples, as well as their CO2-induced swelling and He-induced strain, were analyzed at 35–75 °C and 0–16 MPa. The following conclusions were made based on the experimental results collected in this work:

  • 1.The maximum excess adsorption at different temperatures correlated with the bulk phase density: as the CO2 temperature increased, the density of the maximum adsorption of CO2 excess decreased.

  • 2.The density of the adsorbed phase was obtained by fitting the excess CO2 adsorption data by the DR model.

  • 3.At low pressure, the shale strain caused by injected CO2 was mostly related to the adsorbed CO2, whereas at high CO2 pressures, the shale strain was caused by CO2 pressure.

  • 4.The amount of uptake adsorbed CO2 linearly correlated with the adsorption-induced strain.

Acknowledgments

This study was funded by the National Natural Science Foundation of China (NSFC) (no. 5180040902), the Natural Science Foundation of Chongqing (no. cstc2019jcyj-msxmX0507), the Natural Science Foundation of Chongqing (no. cstc2019jcyj-zdxmX0024), and the Natural Science Foundation of Chongqing (no. cstc2019jcyj-zdxmX0032).

The authors declare no competing financial interest.

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