Permeability Characteristics of Coal after Supercritical CO2 Adsorption at Different Temperatures

CO2 storage in coal seams has become one effective method to reduce CO2 emission and help exploit coalbed methane (CBM). The permeability is a key parameter for CBM extraction. In deep coal seams (>800m), CO2 exists in the supercritical state. In the present work, permeability tests were performed on briquettes before and after supercritical CO2 (SC-CO2) adsorption at various temperatures to investigate the effects of SC-CO2 adsorption on the permeability. Experimental results show that SCCO2 adsorption leads to volumetric expansion and permeability augment. The permeability enhancement decreases continuously at 35°C, while it initially increases and reduces at pressures exceeding 9 or 10MPa at 45 or 55°C, respectively. Besides, the permeability enhancement ratio shows a linear increase with the expansion. The research provides a basis for further research on the enhanced coalbed methane (ECBM) recovery.


Introduction
The emission of CO 2 has been increasing over the years, and carbon capture and storage (CCS) has been considered to mitigate greenhouse effects [1]. Among various storage options (oil reservoirs, saline aquifers, and coal seams), storage in coal seams is promising because of advantages: firstly, there are plenty of unmineable coal resources because of limited recovery, and potential reserves of CBM in China ranks third in the world [2]; secondly, due to greater affinity of CO 2 to coal than CH 4 , it contributes to ECBM recovery. Researchers from America, Japan, and China have performed pilot experiments for ECBM feasibility [3][4][5]. Specifically, when the temperatures and pore pressures are above the critical point (31.06°C, 7.38 MPa), CO 2 exists in a supercritical state in coal seams with a depth under 800 m [6]. SC-CO 2 has the characteristics of strong diffusion, low viscosity, and surface tension.
Research has been carried out on ECBM through experiments and numerical simulations [7][8][9][10]. When CO 2 is pressurized into coal seams, gas transport mainly includes diffusion, seepage, and competitive adsorption [11]. Adsorption of CO 2 has been investigated from the subcritical state to the supercritical state [12,13], and various adsorption models have been assessed, such as Langmuir, Dubinin-Astakhov (D-A), and Dubinin-Radushkevich (D-R) models [14]. The adsorption could induce swelling [15,16] and change the pore distribution, surface area, and function groups of coal [17,18], leading to the variation in the seepage characteristics and mechanical properties [19,20]. Pores are classified as micropores (<2 nm) for adsorption, mesopores (2-50 nm), and macropores (>50 nm) for seepage, and changes in pore structures have been investigated to reveal the mechanism. Sampath et al. compared the effects of short-term and long-term CO 2 interaction on pore structures [21]. Considered the existence of water in coal seams, Ni et al. [22] and Liu et al. [23] investigated the interaction with SC-CO 2 and water, indicating that the chemical reaction also influences pore structures.
The permeability is a key parameter for gas exploitation, and it is influenced by the effective stress and CO 2 adsorption, occasionally along with extraction and dissolution. Although previous studies have focused on permeability variation, however, the specific influence of each factor is uncertain, especially in the supercritical state. In the present work, a series of permeability tests were performed before and after SC-CO 2 adsorption under nonconfining conditions at different temperatures. The effect of CO 2 adsorption on the permeability is investigated, and porosity differences between specimens are reduced by using briquettes. Results can provide a basis for further field application of ECBM.

Experimental Specimens and Apparatus
2.1. Specimens. The porosity of specimens drilled from the same block may be different, and this difference can influence the permeability characteristics and adsorption capacity. Therefore, the briquettes are selected as the specimens because of homogeneity and controllable porosity.
Blocks are extracted from Xinqiu Mine, Fuxin, Liaoning Province. The blocks are crushed and sieved until the diameter is below 0.25 mm. 255 g pulverized coal and 5 g rosin are put together into a cylinder with a thick wall, and a briquette is shaped in the cylinder with a loading of 460 kN as shown in Figure 1. The diameter and length are 50 mm and 100 mm, respectively. All specimens are dried at the temperature of 105°C for 24 hours. The average porosity is 0.31 by comparing the apparent density of specimens and the true density of powdered coal, and it can be considered that there is no difference between specimens.

Experimental
System. The experiments include two parts, permeability tests and adsorption experiments. Based on Darcy's law, transient and steady-state methods are frequently used to determine permeability [24][25][26]. In the present work, the latter method is used because of the relatively high permeability of briquettes. The experimental system for permeability tests consists of the injection part (N 2 cylinder), a seepage and reference cell, a pump with a regulator, and a flow meter as shown in Figure 2. After being vacuumed, confining pressures are applied by the pump firstly. N 2 is pressured into the reference cell, and once the pressure is stable, N 2 is injected into the seepage cell to start the test. The flow meter is used to measure the flow rate of N 2 , and the permeability is determined by [27] k = 2μP 2 LQ where μ is the viscosity of N 2 , Q is the flow rate. P 1 and P 2 are the upstream and downstream pressures, respectively, and L and A are the length and cross-sectional area, respectively. The main parts of the experimental system for adsorption are the reference cell and adsorption cell. The adsorption amount is measured by the volumetric method, and the void volume is estimated by injecting He according to the national standard. The diameter and length of a specimen at several positions are measured with a vernier caliper to calculate the volume before and after the experiment, and volumetric expansion can be determined by where S is volumetric swelling and V 0 and V are the initial and final volume of the specimen, respectively. According to the measurement in Wu et al. [13], the adsorption amount can be determined by where n is the excessive adsorption amount per unit of a specimen. m is the weight of a specimen. R, the universal gas constant, is 8.314 J/(g·mol·K). T is the equilibrium temperature. V R and V A are the void volumes of reference and adsorption cells, and P R and P A are respective pressures of two cells. Subscripts 1 and 2 refer to the initial and final state, respectively. Z R1 , Z R2 , Z A1 , and Z A2 are compressibility factors corresponding to P R1 , P R2 , P A1 , and P A2 , respectively, at the temperature of T.

Experimental Procedures.
The experimental procedures cover three stages, determining the permeability, CO 2 adsorption, and measuring the permeability after CO 2 desorption. Stage one: a series of permeability tests are performed on a briquette placed in the seepage cell using N 2 with the injection pressure of 2 MPa and confining pressure of 12 MPa at 35°C Stage two: the specimen is taken out from the seepage cell and placed in the adsorption cell. Experiments of CO 2 adsorption are conducted without confinement at the pressure of 8 MPa and temperature of 35°C. The experiment lasts for 24 hours according to the national standard, and the pressure reduction and deformation are recorded Stage three: after desorption for 12 hours, permeability tests are repeated three times to investigate the variation and determine the effect of adsorption on the permeability.
A new specimen is replaced in the adsorption cell, and the second and third stages are repeated at CO 2 pressures of 9, 10, 11, 12, and 13 MPa. Subsequently, the temperature is increased to 45 or 55°C; this series of experiments are repeated.

Experimental Results and Discussion
3.1. Permeability Characteristics before and after SC-CO 2 Adsorption. Figure 3 shows that the permeability enhances remarkably after SC-CO 2 adsorption at different temperatures. After the adsorption, the permeability decreases by 0.4 mD with pressures ranging from 8 MPa to 9 MPa, and it reduces by approximately 0.7 mD at pressures increasing from 9 MPa to 13 MPa at 35°C. Nevertheless, the permeability after CO 2 adsorption increases slightly initially and subsequently decreases moderately with the increase of CO 2 pressures at 45 and 55°C, and peaks are observed obviously at the pressures of 9 MPa at 45°C. Compared with the initial permeability, the permeability enhancement ratio, η, can be determined by where k 0 and k are permeability values before and after CO 2 adsorption, respectively. To reveal the variation of η with temperatures, the ratio is replotted as shown in Figure 4. The ratio decreases by approximately 13% at the pressure of 8 MPa, while it increases by 10% before decreasing at 9 MPa. When pressures are in the range of 10-13 MPa, the proportion increases slightly with temperatures ranging from 35 to 45°C, and it continues rising moderately with the increase of temperatures to 55°C. Figure 5 demonstrates that CO 2 adsorption induces various swelling at different pressures and temperatures. The volumetric swelling reduces by 4% at 35°C, while the expansion increases slightly before 9 MPa and subsequently decreases by 3.5% and 1.2% at 45 and 55°C, respectively. When pressures exceed 10 MPa, the expansion at 55°C is greater than that at other temperatures.

Adsorption and Deformation.
Although the Langmuir model is generally applied to estimate the adsorption amount and deformation, however, it is poorly applied to adsorption at pressures exceeding 6 MPa mainly due to the assumption of monolayer adsorp-tion. Alternatives such as the modified D-R model have been found more suitable to fit with the adsorption amount and swelling [28,29]. In this model, gas densities replace the pressures and adsorbed densities replace the saturated vapor pressures, which avoids the limitation of saturated vapor pressure in the supercritical state, as shown in where S max is the maximum swelling. For adsorption amount, D is related to the adsorption heat and affinity of the gas to the sorbent, while for swelling it is possibly regarded as an empirical parameter. ρ, CO 2 density, varies with temperatures and pressures and is obtained from the website of the US National Institute of Standards and Technology (NIST), as shown in Figure 6. ρ a , the density of the adsorbed phase, is considered as 1000 kg/m 3 [28,29]. The deformations of specimens at three temperatures are fitted with the modified D-R model with a great determination as shown in Figure 7 and Table 1. S max decreases by 13% with temperatures ranging from 35 to 55°C, while it does not vary significantly with the temperatures in the previous study [29]. This difference is mainly because the briquette structure is loose, while the structure of raw coal specimens is dense. The adsorbed density of CO 2 is approximately close to liquid CO 2 density, revealing that the adsorbed CO 2 requires less volume than gaseous CO 2 . The a term is related to CO 2 solubility, and this term can be used to describe the compression at great pressures. Figure 8 demonstrates that the swelling of specimens decreases linearly by 1.5% with the increase of adsorption amount by 1 mmol/g, which is shown in the previous study [13]. Studies reported an increase in deformation with the augment of absolute adsorption, along with a stable trend at CO 2 pressures approaching 10 MPa [15,29]. The process of CO 2 adsorption and specimen deformation is from the disequilibrium state to the dynamic equilibrium state. With CO 2 injection, CO 2 diffuses due to pressure differences and it is absorbed by the matrix. CO 2 acts as the 3 Geofluids plasticizer and enables coal structure rearrangement, reducing the softening temperatures [30]. CO 2 adsorption can reduce the surface energy of the coal and weak mechanical properties. These are the main reasons that matrix swells significantly after adsorption. High-pressure CO 2 can constrain matrix swelling and the expansion shows a downward trend when CO 2 pressures exceed 10 MPa.

Analysis of the Permeability Changes Induced by CO 2 .
The permeability ratio shows a linear augment with the volumetric swelling as shown in Figure 9. It is noted that the proportion at 55°C is slightly lower than that at other temperatures. The adsorption-induced swelling indicates greater porosity and wider seepage channels, and therefore, permeability is enhanced. This reveals that the permeability enhancement under nonconfinement is influenced mostly by the adsorption.
For CO 2 geological storage in deep coal seams, where strata pressures restrict the swelling, the permeability variation after CO 2 interaction is a coupled result of CO 2 adsorption and effective stresses, along with extraction or dissolution. For CO 2 adsorption in the confined stress, due to gas injection, both the reduction in effective stresses and CO 2 adsorption induce matrix expansion (equations (6) and (7)). Under the   4 Geofluids great confinement, the coal matrix expands inward and cleats narrow, leading to permeability reduction. Ranathunga et al. observed shrinkage in macropores with the help of scanning electron microscopy (SEM) [31]. All microcleats, the main channels of gas seepage, can be observed closely by micro-CT scanning after SC-CO 2 injection, and permeability decreases drastically by 2 orders of magnitude [32]. After CO 2 adsorption under a constraint pressure, the permeability reduction ratio augments linearly with the increase of swelling [33].
where ε is the total deformation induced by effective stresses and adsorption. ε e is the volumetric deformation caused by effective stresses, namely, σ − P, and K is the bulk modulus.
In equation (7), the minus indicates compression. As a solvent, SC-CO 2 can extract organic minerals and alter the pore surface, tarnishing the surface. Li et al. observed permeability augment after CO 2 cycling adsorption and desorption under a constraint pressure, along with the expansion in macro-and mesopores but few changes in micropores [34]. Because of noticeable fractures on the surface, the extraction is attributed to the remarkable permeability improvement. The solubility varies with CO 2 density, and therefore, it is difficult to quantify the effects of extraction.
Another influencing factor is the chemical reaction. Water exists in coal seams, and the interaction of CO 2 and water can dissolve the carbonate minerals. CO 2 could dissolve in water forming an acid solution, in which calcite is dissolved. The interaction of water and SC-CO 2 causes an increment in pores, and the permeability is improved [23]. Nevertheless, some silicate minerals could form precipitation and block pore connections, reducing the permeability [22].
3.5. Discussion for CO 2 -ECBM. CO 2 -ECBM is injecting CO 2 through wells into deep coal seams at a certain injection pressure. The permeability is the key factor during gas production. Although the permeability becomes greater at high pressures without considering the Klinkenberg effect [7], however, increasing CO 2 pressures cannot be effective for improving exploitation efficiency according to the previous analysis. Among the four factors, the effect of extraction and solution on permeability is limited and estimated difficultly. Swelling decreases gradually with the increase of CO 2 pressure. Besides, injecting high-pressure CO 2 is liable  to induce disasters and weaken the mechanical properties. Therefore, the permeability could be not enhanced significantly by only increasing CO 2 pressures. According to the national standard, numerous adsorption experiments last for 24 hours, after which the surface area decreases, while the surface area augments remarkably after 7 days and 14 days [21]. Kutchko et al. summarized no significant variations in macropores after 104 days considering the offset [35]. Due to limited observation, SEM images cannot reflect total surface changes, while those changes can be estimated in other methods such as CT and nuclear magnetic resonance (NMR) [36,37]. The interaction time should be taken into consideration, and further studies are required to investigate the long-term changes and mechanical behavior for coal of different ranks.

Conclusions
Permeability characteristics were investigated on briquettes before and after SC-CO 2 adsorption under nonconfinement. The main results are as follows: (1) Permeability enhances significantly after CO 2 adsorption in briquettes. The permeability enhancement reduces continuously with the increase of CO 2 pressure at 35°C, while it augments slightly before decreasing moderately at 45 and 55°C (2) CO 2 adsorption could cause volumetric swelling, and expansion is fitted well with the modified D-R model at the considering temperatures

Geofluids
Notations k: Permeability, mD μ: Viscosity, μPa•s Q: Flow rate, cm 3 /s P 1 : Upstream pressure, MPa P 2 : Downstream pressure, MPa L: Length, cm A: Cross-sectional area, cm 2 S: Volumetric expansion V: Initial volume of the specimen, cm 3 V 0 : Final volume of the specimen, cm 3 n: Adsorption amount per unit of a specimen, mol/g m: Weight, g T: Equilibrium temperature, K V R : Volume of the reference cell, cm 3 P R1 : Initial pressure of the reference cell, MPa P R2 : of the reference cell, MPa Z R1 : Compressibility factor corresponding to P R1 Z R2 : Compressibility factor corresponding to P R2 V A1 : Initial void volume of the adsorption cell, cm 3 V A2 : Final void volume of the adsorption cell, cm 3 P A1 : Initial pressure of adsorption cell, MPa P A2 : Final presures of adsorption cell, MPa Z A1 : Compressibility factor corresponding to P A1 Z A2 : Compressibility factor corresponding to P A2 η: Permeability enhancement ratio k 0 : Permeability before CO 2 adsorption, mD S max : Maximum swelling D: Empirical parameter ρ a : density of adsorbed CO 2 , kg/m 3 ρ: CO 2 density, kg/m 3 a: Empirical parameter ε: Total deformation of a specimen ε e : Volumetric deformation caused by effective stresses σ: Volume stress, MPa P: Pore pressure, MPa K: Bulk modulus, MPa.

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.