The permeability of shale exposed to supercritical carbon dioxide

Permeability is a critical parameter of tight reservoir rocks and one of the important parameters for characterizing fluid flow and production from reservoirs. It determines the feasibility of its commercial development. SC-CO2 has been used in shale gas exploitation for efficient fracturing and the added benefit of CO2 geo-storage. And SC-CO2 plays an important role in permeability evolution of shale gas reservoirs. In this paper, Firstly, the permeability characteristics of shale under CO2 injection are discussed. The experimental results show that the relationship between permeability and gas pressure is not a single exponential relationship, but there is an obvious segmentation phenomenon, which is particularly obvious when it is close to the supercritical state, and the overall trend is first decreased and then increased. Subsequently, other specimens were selected for SC-CO2 immersion, and nitrogen was used to calibrate and compare shale permeability before and after treatment to assess changes in shale permeability after SC-CO2 treatment at pressures from 7.5 to 11.5 MPa and X-ray diffraction (XRD) analysis and scanning electron microscopy (SEM) were used to analyze the raw and CO2-treated shale particle sample, respectively. Results indicate the permeability increases significantly after SC-CO2 treated, and permeability growth is a linear function of SC-CO2 pressure. According to (XRD) analysis and (SEM) analysis, SC-CO2 not only can act as a solvent and dissolve carbonate minerals and clay minerals, but also can complex chemical reactions with mineral components in shale, Further dissolution of carbonate minerals and clay minerals, widened gas seepage channels and enhancing the permeability.

, injection of CO 2 in shale formation can achieve the storage of CO 2 and further enhance shale gas production 12 .
The average buried depth of shale gas reservoirs in China is about 3000 m 13 . CO 2 is easy to reach supercritical state (critical temperature of 31.1℃ and critical pressure of 7.38 MPa) under the condition of high temperature and high pressure. Over the years, numerous studies have been conducted to investigate the impacts of CO 2 on shale. Thickened liquid carbon dioxide fracturing fluid, reflux better, less damage to the reservoir, and low adsorption performance, can more effectively penetrate into the reservoir and thickened liquid carbon dioxide fracturing fluid also prevents leakage of methane in the reservoir 14 , Adsorption of SC-CO 2 in shale specimens caused expansion 15 , which can break cross links between aromatic nuclei in coal 16 and lead to the reduction in permeability 17 . The interaction with SC-CO 2 caused the greater changes in mechanical properties compared with sub-CO 2 18 . Due to characteristics of high diffusion, low viscosity and surface tensile 19 , SC-CO 2 is able to alter structural properties of organic matters acting as solvent. For example, the interaction of CO 2 with coal induced the formation of new carbon structures 20 . Changes in surface characteristics have been investigated in various methods such as low-pressure N 2 adsorption (LP-N 2 A), FE-SEM, XRD and FTIR [21][22][23] . Some researchers performed the simulation to study CS-EGR 2,24-26 , while there are still many unsolved problems due to the weak maturity of the technique.
In summary, the interaction with SC-CO 2 is complex, including adsorption, seepage, and extraction, and most studies have been conducted in the macro-or micro-scale rather than multi-scale. Further, the permeability is a www.nature.com/scientificreports/ key parameter for reservoir estimation and exploitation, but less attention was paid on permeability variation of shale after exposed to SC-CO 2 at various pressures. Therefore, in this work, permeability tests were performed using N 2 before and after SC-CO 2 treatment to assess changes. Additionally, the changes of mineral composition, surface microstructure and elements in shale under supercritical carbon dioxide were studied by X-ray diffraction (XRD) analysis and scanning electron microscopy (SEM).

Materials and experimental methods
Materials. Shale blocks were obtained from an outcrop of Longmaxi Formation in Yanzi Village, Changning County, Yibin City, Sichuan province. The area is located in the west of Hubei and Chongqing, Structurally located in the eastern margin of the Sichuan Basin, according to Chinese system partition of oil and gas reservoirs. The sampling site is under the lower Cambrian single-source and single-source accumulation system in southern Sichuan-southeast Sichuan, It belongs to the shale of Lower Silurian Wufeng Formation-Longmaxi Formation series. Shale specimens and sampling location are shown in Fig. 1. After using the drilling machine to drill the cut rock sample, place the rock sample on the cap on the doublesided grindstone machine for both ends Polished, then remove residual moisture on the surface of the shale specimen after drilling and cutting, wrap with plastic wrap to keep it moist, finally packing for classification. Specimen parameters are shown in Table 1. A small specimen cut from the same block was prepared for XRD analysis and SEM analysis. Remove the particle sample from the remaining portion of each specimen and crush to a size less than 200 mesh (< 75 μm). Fully mix crushed samples to reduce non-uniformity for XRD analysis and SEM analysis.
Experimental apparatus and methods. Experimental apparatus. The device diagram is shown in Fig. 2. Mainly divided into three parts, included as pressure control system, temperature control system and main device. Pressure control system included high pressure vessels, air compressor, booster pump, etc. Temperature control system is water bath (the upper limit is 100 ℃ and the accuracy is 0.01 ℃). Main device included core holder (the ultimate pressure is 60 MPa), pressure sensor (with an accuracy of 0.01%, the ultimate pressure is 100 MPa), upstream and downstream chambers, pipes, valves, etc.
Experimental methods. Carbon dioxide permeation experiment. Vacuum and volume correction of experimental device before experiment 7,27 . Flow behavior of CO 2 in shale under injection pressure ranging from 5.5 to 11.5 MPa was measured by pressure pulse permeability experiment method. The experimental program is shown in Table 2.
Carbon Dioxide infiltration experiment. Firstly, N 2 permeability tests were performed with the pore pressure from 2 to 8 MPa, and subsequently, specimens were subjected to SC-CO 2 with pore pressures of 7.5-11.5 MPa respectively under confining pressure of 12 MPa for 48 h. Finally, N 2 was passed through the treated specimen again and permeability changes were estimated in each scheme. The SC-CO 2 treatment scheme shown in Table 3.   XRD. The mineral composition of the shale crushed samples before and after SC-CO 2 treatment was determined using an x-ray diffractometer. Determination of mineral changes caused by SC-CO 2 injection into shale by XRD analysis.
SEM. Surface microstructure characterization of shale crushed samples before and after SC-CO 2 treatment using a scanning electron microscope equipped with an energy dispersive X-ray spectrometer (EDS).
Permeability theory. In the mathematical model of traditional pressure pulse permeability experiment 28 .
The governing equation, boundary conditions and initial conditions are:     www.nature.com/scientificreports/ p (x,t) in Eq. (1) is the pressure inside the shale sample. p 1 and p 2 are the upstream and downstream pressure. The pressure (△p D ) between the upstream and downstream chambers is expressed as: The general dimensionless solution can be expressed as 28 : θ is the the nth positive root of the Eq. (8).
The later solution can be simplified to 28,29 where f 0 is constant and s 1 is equal to: Finally, can get the permeability formula as: If the upstream and downstream volumes are equal, can get 28 .
Substitute it into the above equation: where V is the volume of both the upstream and the downstream chambers (m 3 ). F 1 can be expressed as: ω1 can be obtained by the Eqs. (16) Ethical statement. I certify that this manuscript is original and has not been published and will not be submitted elsewhere for publication. And the study is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time. No data have been fabricated or manipulated (including images) to support your conclusions. No data, text, or theories by others are presented as if they were our own. Te submission has been received explicitly from all co-authors. And authors whose names appear on the submission have contributed sufficiently to the scientific work and therefore share collective responsibility and accountability for the results.  Figure 4a shows CO 2 density changes with increasing fluid pressure for different phases.
The red arrows indicate the sharp increase in CO 2 density at the phase transition. Figure 4b shows CO 2 phase diagram. Figure 4c-e shows CO 2 permeability in shale at different confining pressures, 10 MPa, 11 MPa, and 12 MPa. When approaching the supercritical state, there is an obvious segmentation phenomenon, and there is a more obvious trend of sudden drop. The curve of permeability of shale injected with CO 2 versus pore pressure is appro -ximately W-shaped. In the early stage, the permeability shows a downward trend with the increase of pore pressure, and the decline begins to slow down when the phase state changes, and after the critical pressure is exceeded, the downward trend began to be obvious again, but the overall trend showed a downward and then upward trend. For example, compared with gaseous CO 2 , the SC-CO 2 stage permeability is reduced by nearly 40%, at the confining pressure of 12 MPa, CO 2 permeability decreased from 3.91 × 10 −4 μD to 2.45 × 10 −4 μD with upstream pressures increasing from 5.5 to 9.5 MPa, while it increases by 1.26 × 10 −4 μD with the increase of pressures from 9.5 to 11.5 MPa. The permeability curve can be divided into four stages, a: when the pore pressure is low, permeability decrea -ses gradually, Ranathunga et al. 30 thought the reduction of CO 2 permeability is a result of matrix swelling. In the present work, we infer the reduction is the result of Klinkenberg effect and swelling. Rather than only the swelling; b: as the pressure of the universe increases, the Klinkenberg effect weakens but expansion still exists, the effect of effective stress is greater than adsorption expansion, the downward trend of permeability slows down; c: corresponding to the CO 2 density curve, when approaching the phase change, the density increases sharply and the carbon dioxide adsorption capacity increases, decrease in penetration rate increases, SC-CO 2 has the characteristics of high viscosity and density like the liquid, and this may cause a decrease of the flow rate. However, SC-CO 2 also has high solubility, the increase of carbon dioxide density will lead to the increase of SC-CO 2 solubility and generates carbonic acid with water in shale specimens, it will broaden the pores in shale and increase pore connectivity, with the increase of pore pressures, the density curve tends to be flat when it is close to 9.5 Mpa, at this time the permeability drop of the corresponding seepage curve tends to be flat; d: With the increase of pore pressures, at this time, the effect of effective stress on permeability is dominant, the effective stress reduces and the permeability shows an augment. This confirms that SC-CO 2 can significantly change the permeability of shale. www.nature.com/scientificreports/ Comparison in N 2 permeability before and after shale exposure to SC-CO 2 . Figure 5a summarizes the original permeability plotted with pore pressures. For the sample T2101, at the confining pressures of 10 MPa, the permeability declines by 0.41 × 10 −4 μD with N 2 pressure increasing from 2 to 3 MPa, while it increases by 1.33 × 10 −4 μD with the increase of N 2 pressures from 3 to 8 MPa. The overall trend showed a downward and then upward trend. Figure 5b-f depicts the permeability enhancement after SC-CO 2 treated at pressures of 7.5-11.5 MPa. Can be clearly found, the permeability of shale after CO 2 treatment is significantly higher www.nature.com/scientificreports/ than that before treatment. And the relationship between shale permeability and pore pressure is approximately exponential. Figure 6a shows that differences in the permeability vary with N 2 pressures after SC-CO 2 treated. The permeability growth, ΔK i, can be calculated based on original permeability, K 0 , and final permeability, K i , after exposure to SC-CO 2 at pressures, i. After exposed to SC-CO 2 at the same pressure, ΔK with injecting 2 MPa N 2 is much lower than others, and ΔK with injecting 3 MPa N 2 is observed the greatest. We calculate ΔK at various Figure 6. (a) permeability growth after exposed to SC-CO 2 at different pressures (b-h) permeability growth of N 2 permeability after exposed to SC-CO 2 . www.nature.com/scientificreports/ N 2 pressures. The relationship between SC-CO 2 treatment pressure and differences in permeability and porosity are listed in Table 4. Figure 6b-h shows ΔK is a linear function of SC-CO 2 pressures with great determination, indicating that high pressure CO 2 has a positive effect on permeability enhancement. The permeability variation is expressed as: In the transient pressure pulse test, part of the gas will be adsorbed by the matrix, causing the final equilibrium pressure of the system to drop. Therefore, according to the initial equilibrium pressure and final equilibrium pressure of the system, it can be calculated by Boyle's law Determine the porosity.
where z can be obtained by Eq. (19) 31 Due to the small pulse pressure, the pores of the shale test parts can be regarded as approximately unchanged, which is ϕ p 0 = ϕ p f .
where C and D can be obtained by Eq. (20) and Eq. (21) where , R is Gas Universal Constant, T c is critical temperature, P c is critical pressure. The porosity variation is expressed as: In the Eq. (18), z is the gas compression factor,p f is the final equilibrium pressure, A is the cross-sectional area of the rock sample, and L is the length of the rock sample. It can be seen that there is only an unknown quantity of Φ, and the porosity can be calculated. Figure 7a-e shows that differences in the porosity vary with N 2 pressures after SC-CO 2 treated, it can be seen from Fig. 7f that the average growth rate of porosity is proportional to CO 2 pressure and to be linear.
The dissolving capability of SC-CO 2 for matters in shale is related to the densities [32][33][34] . When the supercritical fluid pressure rises to the critical pressure, The solubility c * of solid solutes in supercritical fluid increases with the increase of supercritical fluid pressure 35 , The relationship between the solubility and relative density of the reference solid solute in SC-CO 2 is as follows 35 : Darrell, Okamoto Ikuo, Xiaoqiang et al. [35][36][37] suggested that Eq. (23) could reflect the relationship between the solubility of solid solute in SC-CO 2 and the relative density, where c * is the solubility, ρ r,1 is the relative density, ρ c,1 is the critical density(467.6 kg/m 3 ), T r is the relative temperature, T c,1 is the critical temperature(304.2 K), e 0 , e 1 and e 2 are formula parameters, α, β and γ are the molecular mass and enthalpy associated with the supercritical fluid. Figure 8 shows the relationship between the solubility of naphthalene in SC-CO 2 and the relative density of SC-CO 2 at 313.98 K. The formula parameters are given by Table 5, it can be found that with the increase of SC-CO 2 pressure, the solubility of naphthalene in SC-CO 2 increased. Through the analysis of Eqs. (23) and Fig. 8, in Fig. 7, SC-CO 2 pressure increased from 7.5 to 11.5 MPa, CO 2 density increased, caused an increase in the solubility of SC-CO 2 , increased porosity change rate of shale.
There is a power-law relationship between permeability and porosity, The most commonly used model can be defined as: k k 0 = ϕ ϕ 0 3 38,39 , Take ϕ ϕ 0 as the abscissa and Take k k 0 as the ordinate. The fitting result is shown www.nature.com/scientificreports/ in Fig. 9, it is found from the fitting results that the value of α is close to 3, but not equal to 3 or 6 38-40 , The internal pore distribution and seepage path of shale specimens treated with different pressures of SC-CO 2 and the value of α are different, The lower the SC-CO 2 pressure, the larger the α value. A larger α corresponds to a higher sensitivity of the permeability to the porosity 41 . www.nature.com/scientificreports/ XRD analysis. Table 6 lists the composition of shale samples before and after CO 2 treatment. XDR analysis shows that the mineral composition of shale samples before and after SC-CO 2 treatment changes significantly, mainly due to complex chemical reactions between SC-CO 2 and mineral components in shale [42][43][44][45] . As can be seen from Table 6, as the SC-CO 2 pressure increases, the proportion of quartz increases and the content of clay minerals and carbonate minerals decreases. Ao 49 .
In addition, SC-CO 2 pressure also affects the degree of dissolution of carbonate and clay minerals in shale 50 , the solubility of CO 2 in water increases with increasing pressure and is more pronounced above the critical state, high solubility will produce high concentration of hydrogen ions to accelerate the reflection of minerals and hydrogen ions(H + ), resulting in significant changes in mineral content after SC-CO 2 treatment.

SEM analysis.
The changes of shale microstructure before and after 11.5 MPa SC-CO 2 treatment were observed by SEM. As shown in Fig. 10, the shale surface is heterogeneous, and the original shale fragment samples are significantly different from those treated at 11.5 MPa. After SC-CO 2 treatment, many pores were generated on the surface of shale fragment samples, some of the material on the shale surface disappeared (Fig. 10, marked A), and generate some new substances (Fig. 10, marked B), which may be caused by mineral dissolution.  www.nature.com/scientificreports/ Yongdong Jiang et al. found that the average pore size of shale increases after SC-CO 2 treatment 51 . Therefore, the permeability is enhanced. Pores are defined as micropores (< 2 nm), mesopores (2-50 nm) and macropores (> 50 nm) based on the classification reported by the International Union of Pure and Applied Chemistry (IUPAC) 52 . Gas adsorption is related to the specific surface area of small pores, and larger mesopore and macropores are significant for the gas diffusion and seepage behaviors 34,53,54 . Previous literature 21,55 reported SC-CO 2 exposure can cause the reduction of micropores and mesopores, while the increase of macropores induced can promote the pore connection (Fig. 10, marked a and b) and enhance the permeability. EDS analysis. Element analysis was performed on eight spots (Fig. 10, marked 1-8) before and after SC-CO 2 treated at the pressure of 11.5 MPa, and the comparisons are listed in Table 7 EDS analysis was performed on the whole surface after SC-CO 2 treated at pressures of 7.5-11.5 MPa, and results are shown in Table 8. Si and Ca account for the great proportion, and C and Al account for the lowest proportion, it can be found from the proportion of elements, indicating clay minerals are the main components. Few variations in the portion of Si on the whole surface reveal SC-CO 2 has few effects on quartz (SiO 2 ). The portion of C increases slightly while portions of O, Ca and Mg decrease gradually with the increase of SC-CO 2 pressure. Figure 11 shows the trends of some elements in shale after different SC-CO 2 treatments, it can be found that the reduction rate of O, Ca, Mg increases with the increase of SC-CO 2 pressure, and the increasing trend is from gentle to increasing. Compared with Fig. 6, it can be seen that the change trend of O, Ca, Mg content with SC-CO 2 pressure is consistent with the change trend of SC-CO 2 solubility with pressure. The densities change markedly with the increase of pressures and therefore, the dissolving capability enhances. In general, at pressures lower than 10 MPa, SC-CO 2 can extract lipophilic, low boiling point components, and especially substances with molecular weights below 300 56 . Yin et al. observed that carbonate and clay minerals (montmorillonite, kaolinite, and calcite) reduced while quartz increases because of the dissolution of organic matter or other minerals by SC-CO 2 22 . The finding of Kutchko et al. indicated that dry SC-CO 2 did not alter coal properties to the same extent as with organic solvents 57 . The interaction with dry SC-CO 2 induces physical changes rather than chemical changes. However, when CO 2 is dissolved in formation water, a series of chemical reactions take place in a liquid medium, forming carbonic acid [43][44][45] . Therefore, mineral composition can undergo chemical and physical reactions in such environment.
SC-CO 2 treatment time is an important factor. With the increase of treatment time from 1 to 5 days, both the specific surface area and porosity show slightly increasing trends 58  www.nature.com/scientificreports/ changes in pore areas after SC-CO 2 treatment in coal for 104 days possibly because of solubility factor of SC-CO 2 exceeding that of coal. Long-term geological storage of CO 2 has been revealed to reduce the compressive strength and elastic modulus 15,59 , and this loss becomes greater with the increase of time. The Brazilian splitting strength, splitting modulus and absorbed energy reduced by 46%, 22%, and 50% respectively after exposing to SC-CO 2 for 60 days 60 . The reduction in mechanical properties is risky in the engineering. Further studies are required to investigate changes in micro-, mecro-and macro-scale for CS-EGR.

Conclusion
In the present work, CO 2 flow behaviour is investigated at first and subsequently, shale permeability is compared before and after SC-CO 2 treatment using N 2 . Surface characteristics are studied with the help of XRD and SEM. Several conclusions are drawn in the paper. 1. The curve of permeability of shale injected with CO 2 versus pore pressure is appro -ximately W-shaped, and it is more obvious in the depressurization stage, the curve can be divided into four stages: a: when the pore pressure is low, permeability decrea -ses gradually under the combined action of Klinkenberg effect and CO 2 adsorption expansion; b: before the critical point, with the continuous increase of pore pressure, the slippage effect gradually weakens, and the adsorption tends to be saturated, the effect of effective stress is greater than adsorption expansion, the downward trend of penetration slows down; c: CO 2 undergoes a phase change,induced penetration rate dropped sharply again; d: with the further increase of pore pressure, the effective stress is further reduced, penetration increased. The overall trend showed a first decline and then an increase.
2. The permeability of shale increases significantly after SC-CO 2 treated at pressures of 7.5-11.5 MPa, and the permeability growth is a linear function of SC-CO 2 pressures, the porosity growth increases lineraly with the increase of SC-CO 2 pressures.
3. The α value of shale specimens treated with different pressures of SC-CO 2 are different, the lower the SC-CO 2 pressure, the larger the α value. A larger α corresponds to a higher sensitivity of the permeability to the porosity, it shows that with the increase of SC-CO 2 treatment pressure, the internal pore connectivity of shale specimens is better, the sensitivity to porosity is reduced, and the seepage path is more uniform.
4. Interaction between SC-CO 2 and shale causes physical and chemical changes. The XRD results showed that, significant changes in mineral composition of shale samples treated with SC-CO 2 , with the increase of SC-CO 2 treatment pressure, the percentage of quartz and some carbonate minerals increased, and the content of dolomite and clay minerals decreased sharply, description SC-CO 2 can dissolve mineral components in shale well.
5. The SEM results showed that, after SC-CO 2 treatment, the microstructure of shale changes obviously, and the primary pores and fissures in shale are corroded, Therefore, a new pore structure with enhanced connectivity is formed, which is beneficial to the seepage of gas in shale, which corresponds to the results of conclusion 3. The EDS results showed that, significant effect of SC-CO 2 treatment pressure on dissolution, dissolution leads to the reduction in proportions of Ca and Mg as well as the slight increase in the ratio of C. The change trend of O, Ca, Mg content with SC-CO 2 pressure is consistent with the change trend of SC-CO 2 solubility with pressure. Therefore, supercritical carbon dioxide injection can effectively increase the permeability of shale.

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.