Experimental Study on the Influence of Effective Stress on the Adsorption–Desorption Behavior of Tectonically Deformed Coal Compared with Primary Undeformed Coal in Huainan Coalfield, China

Abstract

In order to explore the influences of effective stress change on gas adsorption–desorption behaviors, primary undeformed coal (PUC) and tectonically deformed coal (TDC) from the same coal seam were used for adsorption–desorption experiments under different effective stress conditions. Experimental results showed that gas adsorption and desorption behaviors were controlled by the coal core structure and the pore-fissure connectivity under effective stress. The coal matrixes and fissures were compressed together under effective stress to reduce connectivity, and it was difficult for gas to absorb and desorb as the stress increased in primary undeformed coal. The loose structure of tectonically deformed coal cores can help gas to fully contact with the coal matrix, resulting in higher adsorption gas volumes. The support of coal particles in tectonically deformed coal cores weakens the compression of intergranular pores when effective stress increases, which in this study manifested in the fact that while the volumetric strain of the coal matrix change rapidly under low effective stress, but the adsorbed gas volume did not decrease significantly. The reduction in effective stress induced the rapid elastic recovery of the coal matrix and the expansion of cracks, and increased desorption gas volumes. The stress reduction significantly increased the initial gas volume of the tectonically deformed coal, while promoting slow and continuous gas desorption in primary undeformed coal. Therefore, the promotion effect of the reservoir pressure reduction on gas desorption and coal connectivity enhancement can help to improve coalbed methane recovery in primary undeformed coal and tectonically deformed coal reservoirs.

1. Introduction

Tectonically deformed coal (TDC) can be formed due to brittle-, shear/transitional-, and ductile deformations caused by tectonic stress in primary undeformed coal (PUC), which occurs extensively in actual geology processes [1,2]. TDCs are widely distributed in China [3], and the main characteristics of low permeability, low strength and weak cohesiveness make the conventional reservoir stimulation methods, such as fracturing and drainage decompression, not suitable for CBM extraction [3,4,5,6]. Relief-mining, permeability-enhancement and coalbed methane-extraction technologies have been successfully applied in parts of the TDC reservoir, such as Huainan coalfield and Tiefa coalfield [7,8,9,10]. However, there is still a lack of in-depth research on key issues, such as the physical properties response of coal reservoirs and the migration law of coalbed methane (CBM) after stress release.

The extraction process of CBM includes three consecutive stages of desorption, diffusion and seepage, which is a continuous physical process under the coupling effect of stress field, temperature field and seepage field [11,12]. The adsorption–desorption is the prerequisite for CBM production [13]. CBM with a content of more than 90% exists in the micropores in an adsorbed state [14]. The adsorption behavior of CBM on the surface of the coal body can be described by Langmuir equation, multi-molecular layer adsorption theory, and adsorption potential theory [15], and is affected by many factors, such as coal properties (coal rank, pore structure and composition), gas type, moisture and temperature [16,17,18,19]. Desorption is the reverse process of adsorption. CBM begins to desorb when the reservoir pressure drops below the critical desorption pressure, and the volume of desorption gas increases as the reservoir pressure continues to decrease. During the CBM migration, the coal body is deformed as the reservoir pressure decreases, which promotes the expansion and extension of the pore-fissures in the coal body and results in a more complex diffusion and seepage process. Therefore, reservoir stress is an important factor affecting the adsorption–desorption, diffusion, seepage and production of CBM in the coal reservoir [20,21,22].

Previous studies have mainly focused on the effect of reservoir stress on the porosity and permeability of the coal body. Zhao et al. (2004) discussed the influence of coal matrix deformation on gas seepage in coal under triaxial stress [23]; Xie et al. (2013) established four theoretical models for the permeability enhancement during co-mining of coal and CBM [24]; Xu et al. (2016) believe that permeability shows an approximate negative exponential function with the change of effective stress [25]; Liang et al. (2019) and Xiao et al. (2019) conducted fractal studies of porosity and permeability of porous media [26,27]. However, there are few research reports on adsorption–desorption behavior under reservoir stress, especially for TDC reservoirs.

In fact, reservoir stress has a strong impact on the adsorption–desorption behavior of TDC. During the TDC formation, violent tectonic stress changes the macromolecular structure of TDC and forms sub- and ultra-micropores, increasing the surface areas available for gas adsorption [1]. Wang et al. (2019) believed that TDC has a faster gas-desorption rate and more powerful gas-release energy in the initial gas desorption in comparison to PUC [2]. Under in situ conditions, the reservoir stress compresses the coal matrix and pore-fissures [28,29]. Tang et al. (2007) found that the desorption gas volume increased and the desorption time decreased as the axial pressure decreased [30]; He et al. (2010) thought that the opening and closing of pore-fissures in coal under external stress could change the migration direction of adsorbed gas [31]; Li et al. (2013) and Hol et al. (2011) found that effective stress reduces the adsorption capacity of methane and carbon dioxide in the coal matrix [12,32]. In addition, the gas adsorption weakens the van der Waals forces on the surface of the coal matrix [33] and makes the coal matrix develop swelling deformation. The adsorption-swelling under the limitation of reservoir stress conversely compresses the internal pore-fissures [34] and makes the broken TDC matrix more compact. This contributes to a rapid response of TDC to stress changes when the coal body is exposed, reflected in the rapid desorption and migration of gas, and coal body breakage and even outburst [4,35,36].

Considerable research has laid a theoretical foundation for gas adsorption and desorption mechanism [16,17,18,19]. However, the sample specification used in conventional adsorption–desorption experiments is a coal particle with a size of 0.18–0.25 mm. The preparation of coal particle samples destroys the original fracture structure of the coal matrix [37], which makes it impossible to characterize the effect of reservoir stress on adsorption–desorption behavior. With the increase in the mining depth and CBM extraction in the TDC reservoir, reservoir stress has gradually become an important factor affecting CBM extraction. In this study, PUC and TDC cores from the same coal seam were used for adsorption–desorption experiments under stress loading–unloading conditions, focusing on the changes in adsorption–desorption gas volumes, stress–strain of the coal matrix, and pore-fissure gas pressures under various effective stress, to explore the response of coal matrix structure to stress changes and its promotional influence on gas adsorption–desorption behaviors. The experimental results not only offset the inadequate understanding of adsorption–desorption process under reservoir stress, but also provide some clarifications for the theoretical research and engineering implementation of reservoir depressurization and CBM extraction engineering in TDC reservoirs.

2. Experimental Methods

2.1. Sample Collection and Preparation

2.1.1. Sample Information

The coal samples were all collected from the same coal seam, that is, the coal seam No. 11-2 of Shihezi Formation in the Permian, at Zhangji coal mine in Huainan coalfield, Anhui province, China (Figure 1). A tectonic event has a significant influence on coal matrix deformation [38]. As shown in Figure 1, different parts of the same coal seam formed various structures affected by faults and interstratified glide, i.e., coal bodies near the roof and floor were broken to form fissures but retained the original structure due to shear failure; while the coal body in the middle of the seam underwent ductile deformation and even rheological deformation because of structural compression or interlayer gliding.

Depending on their mechanical genesis, morphology and structure [39], these coal samples were divided into primary undeformed coal (PUC, blocky, complete and hard), brittle deformed coal (BDC, broken and loose) and ductile deformed coal (DDC, loose, weak and easily crushed into powder). As shown in

Table 1. Basic information of coal samples.

Coal Type	Sample ID	Deep /m	Maximum Reflectance of Vitrinite (%)	True Density (g/cm3)	Moisture (%)	Ash (wt, %)	Volatile (wt, %)	Fixed Carbon (wt, %)
Primary undeformed coal	PUC	−680	0.8	1.46	1.49	19.43	34.01	45.07
Tectonically deformed coal	BDC	−681	0.81	1.47	1.54	20.51	35.47	42.49
	DDC	−681	0.83	1.43	1.41	26.1	38.3	34.19

, DDC had a similar chemical composition and properties to PUC. Due to strong ductile deformation, the composition and coalification of BDC were slightly different from those of PUC.

2.1.2. Coal Core Preparations

Since the effect of stress on the coal sample was considered in this study, according to the requirements of the experimental equipment, the coal sample needed to be processed into a standard core with a diameter of 50 and a length of 100. As shown in Figure 2, the large PUC blocks were carefully cut into standard cores in the vertical stratification direction using a coring machine at the China University of Mining and Technology (CUMT), and a grinder was used to manufacture reasonable parallelism and smoothness of the natural samples in accordance with the standards of ISRM [40].

However, TDCs is difficult to cut into standard cores due to the loose structure, and reconstituted coal cores have served as substitutes for natural coal samples in previous investigations [17,41,42,43]. The TDC mass was sieved using a milling machine and weighed according to its original particle diameters, as shown in

Table 2. Mass ratio of particle diameter in TDC samples.

Sample ID	Particle Diameter (mm)
	>20	20–4	5–0.2	0.2–0.180	0.180–0.076	<0.076
BDC	35.89%	14.33%	16.55%	30.45%	2.2%	0.58%
DDC	26.06%	19.86%	20.31%	31.48%	1.64%	0.64%

. These particles were mixed with some water and packaged with breathable gauze, then compacted by a specially designed steel mold 50 mm in diameter, and 25 MPa of axial model pressure was applied with a standing state for 168 h. During core preparation, model pressure was monitored and adjusted every 12 h. Finally, the sample was extruded from the steel mold, a diamond cutter was used to cut the two ends of the sample to achieve the height of 100 mm, and then the coal cores were wrapped with breathable tape carefully to prevent breakage.

The TDC and PUC cores were vacuum dried at 30 °C for 24 h before the tests to eliminate moisture effects. These cores had the almost coherent appearance size and scale and were used to conduct contrast experiments.

2.2. Experimental Setup

An “adjustable confining pressure adsorption–desorption and stress–strain monitoring platform” (Figure 3) was used in this study, following the requirements of the national standards of China (MT/T 752-1997). This experimental platform can monitor the adsorption–desorption gas volumes, stress–strain of coal matrix, and gas pressures in the coal body under various temperature and pressure conditions (T = 0–80 °C; P = 0–35 MPa).

At the beginning, two strain gauges were adhered to the coal core surface and wrapped to measure axial strains and radial strains, placed 90° apart as recommended by the International Society for Rock Mechanics (ISRM). The wires of the strain gauge were carefully filled across the gap between the coal core and the rubber sleeve and the grooves on the inner surface of the plug. Then a predetermined confining pressure and temperature was set using the confining pressure tracking pump and heating jacket.

According to the in situ condition, the experimental temperature was set to 32 °C. The effective stresses were set to 15 MPa, 13 MPa, 10 MPa, 8 MPa, 5 MPa and 1.5 MPa. This experiment could not simulate a situation in which the effective stress was 0 MPa because the minimum pressure of the rubber sleeve should be at least 1.5 MPa greater than the gas pressure for tightness.

The gas pressure levels in the pipeline, reference cell and sample holder were reduced to −0.1 MPa for 30 min using a vacuum pump to ensure tightness according to China standard (NB/T 47013.8-2012). The unadsorbed helium was injected into the reference cell, pipelines and sample holder, respectively, to calculate the volume of pipelines and intergranular pores in coal as blank controls. Then helium was pumped out, and nitrogen was injected into the reference cell instead of methane for safety reasons. Nitrogen and methane have similar adsorption–desorption properties in coal [44]. After the gas pressure stabilized, the valve between the reference cell and the sample holder was opened, and the coal sample began to adsorb. The confining pressure tracking pump automatically adjusted the confining pressure based on the gas pressure in the cores to maintain a constant effective stress. The gas adsorption time exceeded 15 h, and the gas pressure changes in the reference cell were expected to be less than 0.01 MPa in 2 h at the end of the adsorption process.

Then the valve of the sample holder was closed and the confining pressures were adjusted to simulate the effective stress changes. The pore gas pressure levels in the coal cores were recorded simultaneously. Once the confining pressure stabilized, the outlet valve was opened and the coal cores began to desorb. The desorption time was set to 7 h and the gas pressure was recorded in the gas collector. The above data are available when the changes in temperature and gas pressure were less than 0.1 °C and 0.1 kPa, respectively.

2.3. Test Method

2.3.1. Adsorption Gas Volume

The measured adsorption capacity of coal core under constraint conditions is defined as excess adsorption capacity (or Gibbs adsorption capacity). Some of the injected gas was absorbed in pores, and the remainder existed in the equilibrium bulk gas phase in the sample holder and free space of coal. Based on the mass conservation equation [45], the adsorbed capacity was calculated as follows.

$$\Delta n_{rec}=n_{pipe}+n_{abs}^{Gibbs}+n_{unabs}^{clam}$$

(1)

where n is the quantity (mol) of gas; the subscript rec, pipe, ads and unads represent the reference cell, pipelines, adsorption and unadsorption.

Since the reference cell and the sample holder formed a closed system, the gas volume could be calculated by the ideal gas state equation:

$$PV=nZRT$$

(2)

where n, P, V and T are the quantity (mol), pressure (MPa), volume (mL) and Kelvin temperature (K) of gas, respectively; R is the ideal gas constant, equal to 8.3144 J/(mol·K); and Z is the compressibility factor, which can be obtained from the National Institute of Standards and Technology (NIST).

2.3.2. Strain Measurements

The coal core strains were expressed by the relative changes in the electrical resistance of the strain gauges (called piezoresistive response) [46], as shown in Equation (3). The strain gauge had a resistance value of 1002 ± 0.1 Ω with a sensitivity coefficient of 2.0 ± 0.01%. The electrical resistance was measured at intervals of 10 s using a DH3821 electrometer, and the resistance values of the strain gauges did not exceed ± 0.5%.

$$\epsilon =K\frac{\Delta R}{R_0}=K\frac{R_{\epsilon }-R_0}{R_0}$$

(3)

where ε is strain, K is coefficient, ΔR is the resistance difference, R_ε is the resistance of the specimen for the applied strain ε and R₀ is the resistance of the unstrained specimen.

2.3.3. Pore Characterization

An AutoPore IV 9500 Mercury injection Apparatus, made by Micromeritics Instrument, USA, was used for the pore volume and connectivity testing in this study according to the international standard (ISO 15901-2:2005). The coal samples were pulverized to 1–3 mm and the injected pressures of mercury ranged from 0.012 to 226.70 MPa, corresponding to a tested pore sizes of 4.33 nm to 174.06 µm based on the Washburn equation:

$$P=-\frac{2\sigma \cos \theta }{r}$$

(4)

where P is applied mercury pressure, MPa; r is the pore radius, μm; σ is the surface tension of mercury, 0.48 N/m; and θ is the contact angle between the coal and mercury, 130°.

In addition, a Sigma 500 environment scanning electron microscopy (ESEM) was used to observe the microstructure of pore-fissure structure in coal, whose magnification could reach 1 million times. The special coal blocks were cut into lumps (1 × 1 × 0.5 cm³) with a relatively flat surface and sputtered with a thin gold coating to get better observation results.

3. Experimental Results and Analysis

3.1. Pore Distribution

The pore volume distribution and connectivity of coal samples were tested by mercury intrusion porosimetry. It can be seen from Figure 4 that the brittle deformed coal (BDC) had a similar pore distribution compared to the primary undeformed coal (PUC), but had greater pore volume. The ductile deformed coal (DDC) had a high mesopore and macropore volume, while its transition pore volume was even smaller than that of PUC. Cai et al. (2013) believed that the micropores smaller than 10 nm accounted for more than 90% of the space for gas adsorption [47]. The micropore volumes in PUC, BDC and DDC increased sequentially, indicating that tectonic deformation helps to improve the gas adsorption capacity of coal.

Part of the mercury vapor is retained inside the semi-connected “ink bottle-shaped” or “narrow-neck bottle” pores during mercury ejection, and thus forms a hysteresis loop of mercury intrusion–ejection [48]. The hysteresis loop can characterize the pores’ connectivity, and the higher the curve fit degree, the better the connectivity. It can be seen from Figure 4b that the connectivity of BDC was slightly higher than that of PUC due to a closer mercury intrusion–ejection loop, while the DDC formed a larger mercury intrusion–ejection loop at the micropores and transitional pores due to the poor pore connectivity.

The pore-fissure morphology observed by SEM (Figure 5) shows that the connected shear fissures in BDC broke the coal matrix, by contrast with PUC. The shear cracks reduced the influences of strain energy on the molecular structures and helped to retain the basic structural unit (BSU). Under continuous tectonic stress effects, aromatic networks grow preferentially in the parallel stress direction and overlap in the vertical stress direction [1,49]. Due to the differences between the locally oriented and nearby non-oriented aromatic layers, as well as aromatic nucleus dislocations and aromatic layer slips [47], a large number of micropores and sub-micropores were formed between aromatic nuclei and aromatic layer sheets, causing a sequential increase in the micropore volumes in PUC, BDC and DDC (Figure 4a). Meanwhile, a number of narrow-necked bottle pores formed between BSU, reducing coal connectivity and resulting in a large hysteresis loop in DDC (Figure 4b). In addition, the long-term tectonic stress effects led to the destruction and reconstruction of the BSU. The ductile deformed coals gradually condensed partially degraded small molecules into aromatic rings during the slow deformation process [50] and improved coalification (Table 1).

3.2. Adsorption Process

The “adjustable confining pressure adsorption–desorption and stress–strain monitoring platform” (Figure 3) was used for the adsorption–desorption experiments under effective stress of the PUC and TDC cores. The free gas volume, adsorption gas volume and strain changes of these coal cores under different effective stresses were recorded during the 15 h adsorption experiment. Seidle and Huitt (1995) found that a complete adsorption equilibrium needs nearly 3 months with small polished coal (about 1.5 inch) [51]. It can be speculated that the coal core (50 mm × 100 mm) needed much more time to achieve complete adsorption equilibrium in this study. However, the experimental processes showed that the gas pressures in the reference cell and pore-fissures of the coal cores changed slightly in the later stage, and the matrix strains of the core samples tended to stabilize. Therefore, these experimental data enabled analysis of the gas adsorption process under effective stress to a certain extent, and the adsorption capacities of coal cores were evaluated based on the adsorption gas volumes at the same time, rather than the final equilibrium adsorption gas volumes.

3.2.1. Adsorption Gas Volume

The varied adsorption behaviors of TDC and PUC cores originate from their inherent matrix composition and core structure. Natural coal is generally characterized by a dual pore-fissure structure; that is, the pore systems deemed as adsorption sites and the fissure systems treated as seepage paths [34,52]. The gas storage capacity of coal is positively correlated with the pore volume and specific surface areas. It can be seen in

Table 3. The adsorption parameters of coal core samples under effective stresses.

Coal Type	Samples ID	Es /MPa	VFG /mL	VPS /cm3	P %	VG /mL	VA /mL	VApg /mL·g−1
PUC	PUC-1	1.5	68.72	2.06	1.01	525.76	457.04	1.63
	PUC-2	5	53.2	1.57	0.78	362.7	309.5	1.08
	PUC-3	8	45.23	1.32	0.68	201.95	156.72	0.57
	PUC-4	10	36.9	1.06	0.53	133.7	96.8	0.35
	PUC-5	13	35.42	1.02	0.53	92.02	56.6	0.2
	PUC-6	15	35.6	1.02	0.5	89.1	53.5	0.19
BDC	BDC-1	1.5	318.33	9.87	5.11	798.34	480.01	1.83
	BDC-2	5	309.3	9.59	4.48	757.5	448.2	1.58
	BDC-3	8	300.7	9.32	4.46	739.16	438.46	1.57
	BDC-4	10	307.7	9.54	4.44	735.5	427.8	1.46
	BDC-5	13	301.58	9.35	4.39	709.41	423.32	1.46
	BDC-6	15	302.3	9.37	4.35	712.9	410.6	1.39
DDC	DDC-1	1.5	288.64	8.94	4.3	759.19	495.37	1.82
	DDC-2	5	288.7	8.94	4.26	745.99	435.1	1.55
	DDC-3	8	276.4	8.56	4.22	656.41	399.28	1.48
	DDC-4	10	272.6	8.44	4.13	645.1	372.5	1.25
	DDC-5	13	247.95	7.67	3.51	604.47	356.51	1.23
	DDC-6	15	240.9	7.45	3.33	601.9	361	1.22

Note: Es is the effective stress; D, L and W are the diameter, length and weight of core, respectively; V_FG is free gas volume, STP; V_PS is pore-fissure volume; P is the porosity of core; V_G is change gas volume in the reference cell; V_Apg is adsorption gas volume per gram.

that the TDC samples had stronger adsorption capacity than the PUC samples due to their larger micropore volume (Figure 4). Meanwhile, the primary cleat system was damaged and replaced by substantial intergranular pores in the reconstituted TDC cores. These intergranular pores provided a number of free gas spaces (V_FG) to improve coal connectivity and promote sufficient contact between gas and coal matrix.

In addition, the pore connectivity within the coal particles in the reconstituted TDC cores affected the adsorption behavior. In general, the smaller coal particle can provide greater specific surface area and more adsorption sites. The DDC cores had smaller particle size (Table 2) and more micropore volumes (Figure 4a) than BDC, but their adsorption gas volume was relatively small (Table 3). This was because the gas pressure tended to reach equilibrium in the fractures of coal core quickly, and then the gas gradually entered the coal matrix. Here, the gas pressure difference between the fracture and inside of coal matrix was mainly affected by the gas diffusion ability in the matrix, rather than the gas seepage characteristics in the fracture [53,54]. The low proportion of transition pores (Figure 4a) and many semi-connected pores (Figure 4b) in DDC hinder the gas entry into the coal matrix, resulting in a smaller adsorption gas volume.

3.2.2. Effective Stress

The effective normal stress in the coal skeleton was equal to the total stress minus pore pressure, which can be expressed as:

$${\sigma }_{ij}^{\prime }={\sigma }_{ij}-\alpha p{\delta }_{ij}$$

(5)

where ${\sigma }_{ij}^{\prime }$ is the effective stress of the coal skeleton (MPa); ${\sigma }_{ij}$ is the total stress of the coal skeleton (MPa); ${\sigma }_{ij}$ is the coefficient related to the coal body; p is the pore pressure (MPa) of the coal skeleton, and ${\delta }_{ij}$ is the Kronecker symbol.

This paper focuses on the relationship between the effective stress of coal and the adsorption–desorption of CBM under stress change conditions. The effective stress was defined as the difference between the confining pressure and the pore gas pressure of coal cores. Coal matrix is a macromolecular structure with elastoplasticity [55]. As shown in Figure 6, the increase in effective stress squeezed the coal cores and increased the volumetric strain of the coal matrix. It can be seen from Figure 6a that the changes in volume strain in TDC cores (BDC and DDC) were more obvious than those in PUC due to their looser structures under the same effective stress increases.

The increased effective stress reduced the free space volume inside the coal cores and narrowed the gas adsorption path, leading to a decrease in the adsorption gas volume. The coal matrix and cracks were compressed in the PUC cores simultaneously to effective stress, resulting in a rapid decrease in adsorption gas volume with the increase in effective stress (Figure 6c), even though the free space volume changed a little (Figure 6b). However, the mutual support of coal particles in the reconstituted TDC cores weakened the compression of intergranular pores by effective stress, and thus their volumetric strain decreased rapidly under low stress conditions (Figure 6a), but the free space volume and adsorption gas volumes did not decrease significantly when stress increased (Figure 6b,c). In addition, the DDC particles were easily compressed, which led to a larger decrease in free space volume and gas adsorption volume under effective stress than for BDC.

3.2.3. Adsorption Swelling

During the gas adsorption process, the coal matrix undergoes a slow strain change due to adsorption swelling [56]. The adsorption-induced swelling strain can be obtained by subtracting the poroelasticity-caused strain, which is obtained from the helium strain results and the total measured strain [34]. In previous studies, significant swelling anisotropy was generally observed in natural coal, but it disappeared in reconstituted TDC cores [37,57]. Therefore, the volumetric swellings in this study were calculated, and are shown in Figure 7.

Pan and Connell (2011) suggested that the volumetric strains are linearly proportional to adsorbed gas volumes [58], which was similar to this experimental result (Figure 7a). It can be seen in Figure 7b that the adsorption swelling strain of coal matrix decreases with the increase in effective stresses. On the one hand, the increase in effective stresses compresses the coal matrix and fractures, which helps to reduce the adsorption gas volume. On the other hand, the coal matrix swelling extends toward the inside when effective stress is high enough to resist the resultant gas pressure and swelling stress [34]. The particles in TDC cores can support each other to swell outwards [59] and provide more space than PUC for internal swelling to form a denser internal structure after adsorption.

3.3. Desorption Process

The gas desorption experiments were carried out under constant effective stress and effective stress reduction. The stress–strain, pore gas pressures in the coal cores and desorption gas pressure in the gas collector were monitored during the experiments.

3.3.1. Desorption under Constant Effective Stress

Based on the gas pressure changes in the gas collector, the desorption gas volumes of the coal core samples were calculated, and are shown in Figure 8. The variation trend of the desorbed gas volume with time approximately satisfied the Langmuir-type equation, and increased rapidly at the initial stage with great gas-release energy [2], and then increased slowly and stabilized gradually. Tang et al. (2006) believed that desorption gas volume and desorption time have a negative exponential decreasing relationship with effective stress, a conclusion similar to this experimental result [60]. Moreover, the desorption gas volumes of the coal cores at low effective stresses were greater than those of high stress. Under the same effective stresses, the desorption gas volume of TDC samples (BDC and DDC) is generally higher than that of PUC sample at the same time.

Based on Figure 6c and Figure 8, the difference between the desorption and adsorption gas volumes of the coal samples under different effective stresses is shown in Figure 9, and represents the gas volumes trapped in the coal matrix. The PUC cores were hard and complete, and the increase in effective stress compressed the pore-fracture structure in the coal matrix and made it difficult for gas to enter and desorb from the pores. The difference in the relative decrease in adsorption and desorption as effective stress increased led to a decrease in the trapped gas volumes in PUC cores. The adsorption gas volumes of TDC cores did not decrease significantly when stress increased (Figure 6). However, the increase in effective stress compressed the coal particles and squeezed or even closed the semi-connected pores and the fissures, making it difficult for the gas to desorb quickly once it entered the pores. The volume of gas trapped in the TDC cores increased with the increase in effective stress.

3.3.2. Desorption under Effective Stress Reduction

• Desorption gas volume

Since the gas in the TDC reservoir was difficult to desorb under the high effective stress (Figure 9), reducing the effective stress of the TDC reservoir was an effective way to promote gas desorption and improve CBM recovery [7,9]. Accordingly, the samples were adsorbed at high pressure (15 MPa) and then subjected to decompression gas desorption experiments. It can be seen in Figure 10 that the reduction in effective stress was helpful to increase the desorption gas volume in the coal samples, and the greater stress drop led to a larger desorption gas volume. Under the stress reduction conditions, the desorption gas volume of the TDC samples changed faster than that of the PUC samples.

In order to exclude the influence of free gas in the initial desorption stage, the desorption proportion (D_p) was introduced in this work, defined as the percentage of the desorbed gas volumes in different times to the total desorption gas volumes:

$$D_p=Q_t/Q\times 100\%$$

(6)

where Q_t is the desorption gas volumes in different times, and Q is the total desorption gas volumes.

The changes in D_p in the initial desorption stage (first 30 min) are shown in Figure 11. When the effective stress decreased, the D_p of PUC in the first 5 min changed slightly, but it increased significantly at the 30th min, while the changes in D_p in the TDC samples (BDC and DDC) were reversed. When the stress was reduced from 15 MPa to 1.5 MPa, the increase in D_p based on constant stress desorption (15 MPa) at the 5th min in the PUC, BDC and DDC samples were 1.0%, 8.0% and 10.9%, respectively, but this increased by 18.6%, 1.0% and 2.5% at the 30th min. It can be considered that the effective stress reduction increases the desorption gas volumes of TDC cores at the initial stage, while it promotes the gas desorption of PUC during the whole process continuously and slowly.

2.

Strain and pore-fissure changes

The response of the gas desorption process to effective stress reduction is affected by the mechanical properties and pore-fissure structure of coal cores. During the effective stress reduction, the elastic recovery and fissure expansion of the coal matrix were beneficial in increasing desorption gas volumes. It can be seen in Figure 12a that the volumetric strain of TDC (BDC and DDC) was much higher than PUC. On the one hand, effective stress reduction led to elastic recovery of the coal matrix. On the other hand, TDC cores had much greater adsorption swelling strain than PUC, and the reduction in effective stress weakened the restriction on the adsorption swelling of coal matrix. The decrease in volumetric strains in PUC and BDC showed an approximately linear relationship with the effective stress reduction due to the elastic recovery of the intact matrix. The volumetric strain of DDC did not change much in the beginning of stress reduction, while it decreased significantly with the effective stress reduction, which may be related to the coal body instability [61]. When the effective stress dropped to 1.5 Mpa, the strains of PUC and BDC were closed, but the DDC sample still had some residual strain.

In addition, as shown in Figure 12b, the reduction in effective stress expanded the fissure space in the coal core and reduced the free gas pressure at the initial desorption. The rapid decrease in free gas pressure promoted gas desorption from pores, and the increased internal pore connectivity of the coal matrix contributed to gas migration. Due to the loose internal structure and obvious strain recovery of the coal matrix, TDC (BDC and DDC) cores responded quickly to stress changes, resulting in a bigger drop in pore gas pressure than PUC and significant increases in the initial desorption gas volumes (Figure 11). Moreover, the DDC desorption gas volume increased rapidly from the effective stress reduction to 30%, which may be related to coal body instability during depressurization [8]. Although the volume strain and pore gas pressure of PUC did not show significant changes at the beginning due to the slow elastic recovery of the intact matrix as the effective stress reduction, it had a greater percentage increase in desorption gas volumes compared to TDCs (Figure 12c).

4. Discussion

4.1. Influence Mechanism of Effective Stress on Adsorption–Desorption

Theoretically, gas adsorption–desorption behavior on the inner surface of the coal matrix is a spontaneous process regardless of effective stress, which belongs to physical adsorption and can be described using the Langmuir equation and adsorption potential theory. Accordingly, the Langmuir equation for gas adsorption–desorption under effective stress can be expressed as [12]:

$$Q=\frac{a_{\sigma e}{b}_{\sigma e}P}{1+b_{\sigma e}P}$$

(7)

where $a_{\sigma e}$ and $b_{\sigma e}$ are the adsorption parameters under effective stress. $a_{\sigma e}$ represents the maximum adsorption capacity when all adsorption sites in coal are completely occupied by gas molecules. The effective stress compresses the coal matrix frameworks and pore-fissures, and even closes some of the micropores under long-term mechanochemical action under in situ conditions, thereby changing the internal surface area and adsorption sites. In this study, the tortuous pore-fissures were barely able to form an effective seepage channel under effective stress, and some trapped gas in semi-connected pores was difficult to desorb.

$b_{\sigma e}$ is the reciprocal value of P_L, which is related to the affinity of gas on the solid surface and the energy stored in the coal matrix. Therefore, $b_{\sigma e}$ can be explained using chemical potential difference (or partial molar Gibbs free energy) between coal and adsorbed gas under the influence of effective stress. The chemical potential of a single-component solid phase substance under stress can be expressed as [12]:

$${\mu }^{\alpha }=u^{\alpha }-T{s}^{\alpha }+P{v}^{\alpha }$$

(8)

where α is the solid phase; ${\mu }^{\alpha }$ is the chemical potential; $u^{\alpha }$ is the partial molar internal energy of the solid phase; $s^{\alpha }$ is the partial molar entropy of the solid phase; T is the thermodynamic temperature; P is the pressure on the solid phase; $v^{\alpha }$ the partial molar volume of the solid phase.

For the solid phase substance, the strain energy can be represented by the Helmholtz free energy ($f^{\alpha }$) [62], so that the Equation (5) can be rewritten as:

$${\mu }^{\alpha }=f^{\alpha }+P{v}^{\alpha }$$

(9)

The interaction of coal and gas forms a system under the stress, which undergoes matter and energy exchange driven by the chemical potential. The chemical potentials of solid matter and gas can be expressed as:

$${\mu }_s=f_s+{\sigma }_n{v}_s$$

(10)

$${\mu }_g=f_g+P{v}_g$$

(11)

where ${\mu }_s$ and ${\mu }_g$ are the chemical potentials of solid matter and gas; $f_s$ and $f_g$ are the Helmholtz free energy of solid matter and gas; $v_s$ and $v_g$ are the partial molar volume of solid matter and gas; ${\sigma }_n$ is the pressure applied on the rock surface; and P is the fluid pressure.

Therefore the chemical potential difference ($\Delta \mu$) of gas adsorption process on the coal matrix can be expressed as:

$$\Delta \mu ={\mu }_s-{\mu }_g=\underset{Elasticstrain}{\underbrace{\left(f_s-f_g\right)}}+\underset{Gaspressure}{\underbrace{P\left(v_s-v_g\right)}}+\underset{Effectivestress}{\underbrace{\left({\sigma }_n-P\right)v_s}}$$

(12)

Accordingly, the chemical potential difference of coal-adsorbed gas under stress is affected by three factors: elastic strain energy, gas pressure and effective stress. When the adsorption reached equilibrium, the chemical potential of adsorption gas phase was equal to the coal solid phase ($\Delta \mu =0$). The effective stress changes broke the original chemical potential balance, and hence affected the adsorption–desorption behavior and gas volumes ($b_{\sigma e}$).

4.2. Response of Gas Absorption–Desorption to Stress Changes

Gas transport in coal reservoirs commonly includes two serial transport mechanisms: diffusion through the coal matrix and laminar flow in the cleat system [63]. The coal matrix skeleton and fracture fluids respond differently to stress changes, which is a function of effective stress through poroelasticity [64,65]. Meanwhile, differences in matrix mechanical properties and pore-fissure structures lead to various adsorption–desorption processes during stress reduction [34,39]. To interpret the differences between the adsorption and desorption processes of PUC and TDC samples, the adsorption models were proposed and presented in Figure 13. The original fissure structures were retained in BDC, and some intergranular pores replaced fissure networks in TDC samples.

The BDC sample had a similar pore distribution to PUC, but its developed macroscopic fissures (Figure 4) resulted in greater adsorption and desorption gas volumes under the same effective stress (Table 3). As seen in Figure 13, effective stress compressed the coal matrix and intergranular pores, and the adsorption swelling of the coal matrix narrowed the fissures [34,39]. The pore-fissures in PUC were more susceptible to squeezing due to complete matrixes. However, the coal particles in the TDC samples supported each other to swell outwards and reduced the intergranular pore compression when the stress increased. Although the TDC cores had greater strain (Figure 6a) under effective stress due to weaker mechanical strength and looser structure [66], the higher porosity (Figure 4) and developed fissures (Figure 5) enabled the gas to pass through the cores and fully contact with coal particles. The gas diffusion in the coal matrix was controlled by pore connectivity. The lesser transitional pores in DDC led to lesser adsorption gas volumes than BDC under the same effective stress (Table 3).

The influence of effective stress changes on the coal matrix is transferred from the surface to the interior. After effective stress released, the strain on the surface of PUC core changed immediately, but the elastic recovery and fracture expansion inside the coal matrix were relatively lagging, and the narrow desorption path in PUC also hindered the rapid release of coal matrix adsorption swelling. The coal particles in the TDC cores supported each other, and the effective stress reduction caused the rapid release of compression on coal particles and intercrystalline pores, resulting in coal matrix volume expansion and immediate fracture recovery. Therefore, the adsorption–desorption behavior of TDC was more sensitive to the effective stress changes compared to PUC, and a larger effective stress drop resulted in a greater increase in desorption gas volume.

4.3. Promotion of CBM Production

Experimental results showed that a large amount of gas can be trapped in the coal matrix under high effective stress (Figure 9). Compared with the desorption under constant effective stress, the reduction in effective stress helped to increase the desorption gas volume (Figure 10), which increased the desorption gas volumes of TDC cores at the initial stage and promoted the whole desorption process of PUC. Moreover, high effective stresses restrain the microcrack developments in the coal matrix [62], while the failure deformation formed in TDC reservoirs during stress release can help to expand fissures and enhance reservoir permeability [2,7,11], which facilitates gas migration to the wellbore. In the meantime, the reduction in gas pressure in the fissure can also promote gas desorption. Therefore, when the pore structure and the gas content of the TDC reservoir have been determined in the in situ condition, the reservoir pressure relief is a reasonable method to increase CBM recovery.

In addition, it is noteworthy that the effective stress changes simulated in this experiment have little effect on the main gas adsorption position of micropores because they are not violent enough to change the molecular structure compared to long-term geological evolution and tectonic movement. Therefore, the influence of effective stress on coal adsorption and desorption behaviors in this study was based on the compression of the pore-fissure structure and coal matrix, which was tortuous or even closed the gas transport channels into the micropores, thereby affecting the absorption and desorption of gas volumes at the same time. Meanwhile, due to coal anisotropy and the small number of coal samples in this study, the gas adsorption–desorption law under complex in situ stress relief conditions still needs further experiments and in-depth analysis.

5. Conclusions

In this study, primary undeformed coal (PUC), brittle deformed coal (BDC) and ductile deformed coal (DDC) from the same coal seam were used for adsorption–desorption experiments under different stress conditions. Based on changes in the adsorption–desorption gas volumes, stress–strain of the coal matrix, and pore-fissure gas pressures under various effective stress, the following conclusions can be drawn.

(1)

Differences in coal core structure and pore connectivity led to different adsorption–desorption behaviors between the TDC and PUC samples. The loose structure of the TDC cores helped the gas to fully contact with the coal matrix, and their adsorption gas volumes were much higher than those of the PUC cores under the same effective stress. When the gas penetrated the coal core, the adsorption gas volume was controlled by the pore connectivity of the coal matrix.

(2)

The effective stress affected the adsorption–desorption behavior and gas volumes. The adsorption gas volumes of PUC decreased rapidly with the increase in effective stress. The adsorption gas volumes of the TDC samples changed slightly with the effective stress, but high effective stress made it difficult for gas to desorb quickly after entering the pores, and a large amount of gas was trapped in the coal matrix.

(3)

The reservoir depressurization can help to improve the CBM recovery in coal reservoirs by increasing desorption gas volumes and pore-fracture connectivity. The reduction in effective stress can significantly increase the initial desorption gas volume of TDC cores and can promote slow and continuous gas desorption in PUC cores.