Deformation-Failure Characteristics of Coal with Liquid CO₂ Cryogenic-Freezing Process: An Experimental and Digital Study

Abstract

The aim of this paper is to analyze the deformation-failure degree and microstructure variations in coal under the cryogenic-freezing effect of liquid CO₂. In this paper, X-ray CT scanning technology is adopted to measure the microscopic-morphological parameters of coal. Drawing support from the image processing and three-dimensional (3D) visualization functions of Avizo software, 3D spatial structure variation rules, as well as the deformation and permeability parameters, are quantitatively calculated. Under the effect of LCO₂ cryogenic freezing, the macroscopic mechanical properties and deformation-failure degree of coal are thoroughly analyzed. The results show that fracture-scale parameters of treated coal are significantly increased, resulting in spatial structure parameters including the coal plug total volume (V_t), fracture network volume (V₀), and proportion of fracture network (μ₀) to increase by 17.11%, 56.57%, and 55.59%, respectively. A comparison analysis indicates that the coverage area of a single value function from the percolation theoretical model for treated coal plugs becomes larger, and its percolation curves are more intensive; the quantitative coal permeability coefficients are increased to more than 40% on average, which further proves that the permeability of coal by using LCO₂ cryogenic freezing is significantly improved. Under the same uniaxial stress loading rate, the peak stress threshold value required by treated coal in the compaction and elastoplastic deformation stage is decreased. The corresponding output acoustic emission energy is apparently increased, owing to the increased brittleness of coal, and deformation failure of coal occurs more easily. Simultaneously, the fracture network and matrix surface of treated coal are more complex, and the corresponding fractal characteristic is obvious. It could be thus concluded that the coal plugs have deformation-failure changes under cryogenic freezing by using LCO₂, increasing the proportion of coal microstructure and enhancing coal permeability. Therefore, the capability of gas migration through the coal microstructure becomes easier, which is favorable for coalbed methane recovery.

1. Introduction

Coalbed methane (CBM) is regarded as a clean resource. The efficient extraction and utilization of CBM can not only avoid energy waste but can also prevent coal and gas outburst disasters in coal mines [1,2,3,4]. In China, the deep-well mining method is generally adopted to exploit coal resources [5], due to the coalbed being deeply buried, huge crustal stress, and other factors, which cause the permeability of the coal seam to be lower than 0.1 mD [6,7,8], resulting in the relatively weaker efficiency and economic benefit of CBM extraction. Therefore, new techniques must be taken into consideration to improve coal permeability and CBM recovery [9,10]. Liquid CO₂ (LCO₂) as a fluid has been proposed as a viable option to improve coal permeability and enhance CBM recovery owing to its cryogenic-freezing effect, low viscosity, easy diffusion, and strong-adsorption capability [11,12,13].

Previous studies revealed that coal’s permeability is closely related to the properties of its own microstructure (pore, fracture, and coal matrix); among them, the impact of the fracture structure on permeability is significant [14,15,16,17]. For LCO₂-ECBM, in particular, scholars are devoted to researching the deformation and failure mechanism of the coal microstructure under its frost-heaving force and artificial stress [13,18,19]. They mainly focused on coalbed permeability variations caused by the coal microstructure under multi-stress failure, inducing the morphology in terms of extension for original fractures and the formation of new cleats used to qualitatively describe the evolution of coal permeability [20,21]. However, the detailed deformation and failure characteristics of the coal microstructure before and after LCO₂ cryogenic freezing adopted the methods that include software analysis and mathematical theory model are still poorly understood, owing to the limited theoretical understanding of the coal microscale mechanical performance. Thus, it is of vital importance to use effective ways to further study the mechanical evolutions in coal micro-fractures, so that advanced ECBM techniques can be developed by the corresponding theoretical support.

Coal, a porous organic material, consists of a coal matrix, minerals, and a spatial composition (pore structure and fracture network) [22,23,24]. Many studies show that by injecting LCO₂ into a coalbed with low or medium pressure, the cryogenic-freezing and phase-transformation forces give a tensile-shear failure of coal, inducing coal-matrix shrinkage and causing the original fractures to generate new tensile-shear fractures, thus forming some new fractures along the direction of its weakness areas within the coal matrix [11,25]. Moreover, it has been verified that coal permeability also changed under the multi-forces by using LCO₂ [26,27,28]. However, in accordance with the process of coal-fracture networks damaged by the LCO₂ cryogenic-freezing effect, relatively little research has been carried out on the quantitative description of coal micro-fracture parameters, such as the scale (length, width, etc.) and variation ratio of its surface or internal area, especially coal permeability and mechanical characteristic response. Additionally, deep analysis using mathematical models or software to comparatively investigate the evolution laws of coal microstructures and permeability coefficients that are quantitatively described by a three-dimensional (3D) visualization method is still required [29,30]; even the visualization and meticulous quantification of the deformation-failure characteristics of coal microstructures before and after LCO₂ cryogenic freezing has become one of the hotspots in related research fields [31,32].

In this paper, the X-ray computed tomography (X-ray CT) method is utilized to observe the morphological images of the coal microstructure before and after LCO₂ cryogenic freezing [32,33]. Then, we used digital software to reconstruct the 3D visualization and percolation theoretical models to investigate the variations in basic structural parameters (scale parameters and permeability) among the different metamorphic degree coal samples, Furthermore, the macro-mechanical and fractal properties are analyzed to further describe the damaged degree of coal under the corresponding experimental conditions. Therefore, the deformation-failure characteristics of coal during the LCO₂ cryogenic-freezing process are deeply revealed.

2. Experiment and Methodology

2.1. Coal Samples

Three coal blocks with different metamorphic degrees are cut from the fresh-exposed coalbeds at an average depth of 670 m from Chinese mining areas, the collecting areas of three types of coal samples are all less affected by mining, and their deformation and damage degree is relatively weaker, according to the international standard ISO 7404–2: 1985 [34]. Then, the standard cylindrical coal plugs (50.0 mm diameter and 100 mm length) are obtained from the fresh coal blocks, as shown in Figure 1.

Samples of anthracite coal were obtained from the Yangquan mining area (named YQ), Shanxi Province; gas-fat coal from the Lv-Shuidong mining area (named LSD), Sichuan Province; and long-flame coal from the Liu-Huanggou mining area (named LHG), Xinjiang Province. The selected sites for coal samples from the three mining areas are all high-gas and low-permeability coalbeds. In accordance with Chinese National Standards GB/T 6948–1998 [35] and GB/T 212–2008 [28,36], the basic physical properties of experimental coal samples are shown in

Table 1. Physical parameters of experimental coal samples.

Sample No.	Proximate Analysis (%)				fx	ρ (g/cm3)	Φ (%)	Metamorphic Grade
	Mad (%)	Vdaf (%)	Aad (%)	FCad (%)
YQ	1.91	13.72	14.22	70.15	0.74	1.62	2.34	Anthracite coal
LSD	4.06	30.97	7.75	57.22	0.65	1.68	6.37	Gas-fat coal
LHG	4.58	39.79	18.86	36.82	2.51	1.74	5.38	Long-flame coal

Notes: M_ad is the moisture content; V_daf is the volatile matter; A_ad is the ash yield; FC_ad is the fixed carbon content; f_x is the firmness coefficient; ρ is the density; and Φ is the porosity.

.

2.2. Experimental System and Procedures

As shown in Figure 2, the experimental system consists of a self-developed device that is used to process coal sample cryogenic freezing, a vacuum-drying system, an X-ray CT scanning system, an automatic data and image processing system, and some other apparatus. Specifically, the experimental test procedures are as follows:

(1) Constant temperature drying: To stop the moisture content from affecting experimental accuracy, we placed coal samples into a thermostatic drier box at a constant temperature of 30 °C for 48 h until the mass variation was <0.2% [11,37].

(2) Micro-CT scanning of raw specimens: To investigate the original microstructure of coal, an X-ray CT system is used to scan the distributions of microfracture inside and on the surface of original coal samples. The spatial resolution of the micro-CT system is 15 μm, and the X-ray scanning power in micro-CT is 225 kV/300–320 kV [38]. Automatic data and image processing systems are adopted to discern and process the inhomogeneous variation of micro-fractures into coal samples, simultaneously cutting a 3D scanning stereogram of the coal cylinder into uniform coal slices in accordance with the set parameters [39].

(3) Coal samples cryogenic-freezing process: After the drying treatment of the tested specimens, we first put the marked coal samples into a self-developed device and then vacuumed the device simultaneously. Secondly, the self-pressurization capability of a Dewar bottle constantly transported LCO₂ into the device along the direction of a uniaxial load that was maintained at a low temperature of around –30.0 °C to treat the coal samples for 12 h [28,40].

(4) Micro-CT scanning of treated coal samples: When the cryogenic-freezing treatment process of coal samples is finished, we utilize an X-ray CT system to scan the fracture network distributions once again according to the preset experimental conditions. Finally, we reconstruct the 3D models and qualitatively investigate the failure mechanism of coal samples with LCO₂ cryogenic freezing.

2.3. Three-Dimensional Visualization and Quantitative Description of Coal Microstructure

Three-dimensional reconstruction is a frequently-used method to obtain the identification and fine-quantitative characterization of some solid microstructures by adopting a computer language. Avizo system software 2019 is widely used in the fields of medicine, biology, geology, industrial manufacturing, and rock mechanics, owing to its high simulation and quantitative-characterization functions. Thus, it has gradually become extensively utilized software in 3D reconstruction, fine characterization, and the simulation of CT scanning images of coal and rock mass [41]. This paper focuses on the key scientific problems of the coal microstructure and its permeability evolution laws under the damaging effect on LCO₂ cryogenic freezing; Avizo system software 2019 is used to conduct 3D visualization and coal-permeability simulated calculations based on the CT scanning coal slices. The detailed procedures are shown in Figure 3.

(1) CT scanning slice pretreatment: Based on the image processing function of the Avizo system software 2019, the gray level of CT scanning slice images is adjusted among three different metamorphic coal samples before and after LCO₂ cryogenic freezing. Then, according to the difference in the gray value of images, the coal matrix (gray), fractures (dark black), mineral composition (white), and other substances are identified. To eliminate the influence of spots in the CT scanning images of coal samples on the processing results, the median-filter method is used to operate the image.

(2) Threshold segmentation of CT slice image: The wind-water ridge algorithm in the Avizo system software 2019 is preferred to segment the CT scanning slice image with the local threshold, obtaining the structural components of the coal-fracture network. It should be noted that the core idea of the wind-water ridge algorithm is to find the continuous closed-region recognition from images according to the different pixel sizes and to obtain the critical value of the “converging watershed limitation value region” to realize the purpose of image threshold segmentation [42]. The specific algorithm can be expressed as shown:

$$\mathrm{g}(x,y)=grad[f(x,y)]={\{[f(x,y)-f(x-1,y)]\times 2[f(x,y)-f(x,y-1)]\times 2\}}^{\frac{1}{2}}$$

(1)

$$\mathrm{g}(x,y)=max(grad(f(x,y)),g\theta )$$

(2)

where f(x,y) represents the original image; grad{·} represents the gradient operation; and g^θ represents the threshold.

(3) Image 3D visualization modeling: To truly realize the fine characteristics of the 3D morphology and internal microstructure of tested coal samples, using the visual-imaging principle of the VRT algorithm in the Avizo system software 2019, and carrying out the 3D reconstruction method to calculate the spatial geometry distribution and scale developing effect of the coal matrix, fracture network, and mineral composition before and after coal cryogenic freezing by using LCO₂, the purpose of 3D visualization and quantitative representation is achieved.

(4) Data extraction and analysis: Firstly, the algorithm module of the Avizo system software 2019 is used to describe the representative volume units (REV) with a 3D reconstruction model of coal samples. Then, with the help of the maximum spherical algorithm in the Avizo system software 2019 [43], the topological calculation of chain filling is adopted for the coal microstructure within the 3D reconstruction digital core model during LCO₂ cryogenic-freezing treatment, and the 3D visualization geometric parameters of the coal-fracture network are obtained, realizing the quantitative characterization with the spatial distribution properties of coal microstructure.

(5) Percolation theoretical model construction: To realize the quantitative calculation of coal permeability evolution before and after LCO₂ cryogenic freezing, based on the combination of porous media percolation theory, probability theory, and topology [44], using the dilation and erosion (D&E) algorithms from the multi ROI analysis module of the Avizo system software 2019, the percolation threshold of coal is determined by the average value on the volume proportion of the fracture network at each pixel and a 3D visualization percolation theoretical model of coal is established to accurately calculate the permeability coefficient and seepage described parameters [45].

2.4. Analytical Methods of Deformation Failure Characteristics in Coal

To realize the deformation-failure characteristics of coal during the process of LCO₂ cryogenic freezing, this paper focuses on comparatively analyzing key parameters, such as the basic mechanical and fractal properties. Then, the thermodynamics and structural mechanics are combined to clarify coal microstructure variations and their damage degree under the damaging effect of LCO₂ cryogenic freezing. The detailed procedures are as follows:

(1) Mechanical characteristic parameter test: The synchronous experimental platform of uniaxial compression and acoustic emission are used, investigating the basic mechanical properties of original and treated coal samples under a normal temperature (30 °C). In the uniaxial compression load, the displacement rate is 0.002 mm/s, the acoustic emission system loads are at an interval of 1 μs, and the sampling frequency is set as 1 MHz [46]. The experimental system will automatically record the relative parameters, such as displacement, stress, and strain, as well as acoustic emission signals during the coal deformation-failure process. By evaluating the variation laws of corresponding parameters, the damaging effect and macroscopic mechanical properties are comparatively discussed as the coal samples are cryogenically frozen by using LCO₂.

(2) Calculation of fractal box dimensions: To quantitatively describe the damage degree of coal caused by LCO₂, this paper introduces the “fractal box dimension” algorithm into the Avizo software to quantitatively clarify the fractal characteristics of coal samples. The logic of the fractal box dimension algorithm mainly refers to an arbitrary Rⁿ space with a fixed boundary, which assumes A as a box area in the space, if subset A is utilized to cover the area of Rⁿ in a certain geometric scale. Then, from the statistical point of view, the minimum number of n-dimensional cube boxes with the required side length of r is defined as N_r(A) [47]. Supposing there is a constant parameter D_i, when r → 0, there is:

$$N_r(A)\propto \frac{1}{r^{Di}}$$

(3)

Thus, defining D_i as a box dimension parameter with A, which existed as a constant parameter k between N_r(A) and r used to cover the space of Rⁿ, there is:

$$\underset{r\to 0}{\lim }\frac{N_r(A)}{1/r^{Di}}=k$$

(4)

Taking the logarithms on both sides of Formula (4), the following can be obtained:

$$D_i=\underset{r\to 0}{\lim }\frac{\lg k-\lg N_r(A)}{\lg r}=-\underset{r\to 0}{\lim }\frac{N_r(A)}{1/r^{Di}}=k$$

(5)

It notes that the fractal box dimensions D_i fitting a linear-function relationship, lg(r) named as an abscissa, and lgN_r(A) named as an ordinate to draw a corresponding scatter diagram in the specific solution process, fractal box dimensions of each image can be obtained by solving the absolute value of the slope k in fitting curves. Therefore, by comparing the value of fractal box dimensions of coal before and after treatment, the complexity and roughness of coal samples caused by the isotropic stresses with a cryogenic-freezing process of LCO₂ are obtained to measure its deformation-failure characteristics.

3. Results and Discussion

3.1. Characteristics of Coal-Fracture Networks by Using CT Scanning

(1) Qualitative analysis of coal fractures by using LCO₂ cryogenic freezing

Avizo software is utilized on the gray-scale recognition, median-filtering, and threshold segmentation processes of CT scanning of coal slices to obtain the microstructure distribution laws in the coal samples. Figure 4 shows the microstructure distribution diagram of the coal matrix, mineral component, and fracture network before and after LCO₂ cryogenic-freezing treatment. It shows that in the CT scanning coal-slice images in the original coal samples with three different metamorphic degrees in Figure 4a, the original fracture network distribution of YQ, LSD, and LHG is mainly composed of a single form with a full or semi-penetration in the coal plugs. In the weak surface area of the coal plug edge structure, there are some “T” shaped micro-fractures as a single form that vertically existed within the edge of the coal plug. Thereby, it reveals that the distributions of the overall fracture network in the original coal plugs are single, which is related to the generally low permeability of coal samples in the collected mining areas to a certain extent.

However, from Figure 4b, it can be analyzed that after the coal plugs are subjected to a cryogenic-freezing treatment by using LCO₂, the original single fracture obviously expands and extends in the whole coal plug, accompanied by new fracture networks penetrated along the main fracture of coal as well as the weak surface area of the coal matrix. Particularly, the newly formed fractures connected with each other as a “T” or near “S” type, inducing the fracture networks in the coal plugs to be more complex than that of the original coal samples. This is because once LCO₂ contacts the coal structural area, a convective heat transfer phenomenon will occur, and the external thermal stress generated will cause tensile stress damage to the original fracture into the coal plugs, forcing the original fracture to expand into weaker areas in the coal [27]. Furthermore, from the analysis of morphological characteristics of coal samples in this experimental test, the overall damage degree of coal plugs is relatively larger by the effect of LCO₂ cryogenic freezing; the coal matrix exfoliated at the edge of coal plugs, the number of internal new fractures and the extension scale effect of original fractures, and even the penetration degree of fractures is increased, eventually forming more complex fracture networks in the coal plug. Therefore, it can be summarized that the external load stress generated by using LCO₂ tended to induce mechanical damage to the coal microstructure and promote the secondary development of its fractures more clearly.

(2) Quantitative description of the damage effect of coal surface fractures

The above analysis is mainly based on qualitatively revealing the mechanical-damage effect of the coal microstructure and fracture distribution laws caused by LCO₂ cryogenic freezing, but the quantitative characteristics of coal fracture scale parameters have not been realized. Thus, this paper adopts the module algorithm of the Avizo software to perform binarization and threshold segmentation processing of coal CT slices, separating and extracting two-dimensional fractures and quantitatively calculating the fracture length (l₀), width (w₀), fracture surface area (S₀), fracture network proportion (μ₀), and other basic parameters in the CT scanning images; the results are shown in

Table 2. Quantitative calculation results of the coal fracture parameters.

Sample No.	Type	n0	l0	w0	S0	μ0
YQ-anthracite	Original	3.0	31.75	0.13	18.26	0.93 × 10−5
	Treated	26.0	32.22	0.24	198.12	9.46 × 10−5
LSD-gas fat	Original	2.0	26.37	0.14	13.08	0.67 × 10−5
	Treated	19.0	46.74	0.15	75.15	3.89 × 10−5
LHG-long flame	Original	1.0	26.20	0.14	3.69	0.18 × 10−5
	Treated	2.0	40.46	0.17	13.76	0.71 × 10−5

Notes: n₀ is the fracture number of coal slices, piece; l₀ is the fracture length of coal slice, μm; w₀ is the fracture width of coal slice, μm; S₀ is the fracture area in the coal slice, μm²; and μ₀ is the proportions of the coal fracture surface, %.

.

The results show that the increase rate of l₀, w₀, S₀, and μ₀ for YQ anthracite coal is 32.22%, 45.83%, 90.78%, and 90.17%, respectively; the increase rate of l₀, w₀, S₀, and μ₀ for LSD gas-fat coal is 43.58%, 6.67%, 82.59%, and 82.77%, respectively; and the increase rate of l₀, w₀, S₀, and μ₀ for LHG long-flame coal is 35.24%, 17.65%, 78.66%, and 74.64%, respectively. All of the above parameters show that the coal-fracture network evolution laws of YQ, LSD, and LHG specimens are mainly performed in the generation of larger amounts of new fractures and the extension of the original fracture after coal samples are treated with LCO₂. Additionally, from the analysis of the whole fracture network for the treated coal samples, the concentrated stress produced along the contacted weak area between LCO₂ and the coal matrix structure, such as cold shock and phase-transition pressure, has a more obvious effect on tensile failure for the fracture network of original coal, which is significantly promoted with the regeneration and secondary development of the coal-fracture network [48].

3.2. Three-Dimensional Variations in Coal Microstructure by Using LCO₂ Cryogenic-Freezing

(1) Three-dimensional structural parameters of coal

The 3D visual modeling process is adopted as shown in Figure 3; the coal matrix, mineral composition, fracture network, and other components by using CT scanning slices based on the visual images, skeleton space, and 3D topological structure are reconstructed, establishing the 3D models of coal plugs, and the fracture network is identified and extracted. Then, based on the maximum spherical algorithm and percolation theory, the ball stick and grain structure models of a 3D visualized fracture network distribution layout were re-established, and the spatial structure parameters of coal before and after LCO₂ treatment, such as the total volume of coal plugs (V_t), total volume of coal-fracture network (V₀), and the proportion of spatial structure (μ₀) in the coal plug were quantitatively calculated. The results are shown in

Table 3. Geometric parameters of coal deformation in a 3D reconstruction.

Sample No.	YQ anthracite Coal			LSD Gas-Fat Coal			LHG Long-Flame Coal
	Vt/mm3	V0/mm3	μ0/%	Vt/mm3	V0/mm3	μ0/%	Vt/mm3	V0/mm3	μ0/%
Original	42,796.11	202.73	0.48	41,837.59	210.86	0.44	47,450.09	161.21	0.34
Treated	54,103.05	517.87	1.06	50,438.24	498.79	0.98	54,792.69	329.89	0.79

Notes: V_t is the total volume of the coal plug, mm³; V₀ is the fracture volume of coal, mm³; and μ₀ is the proportion of the fracture network in the coal plug, %.

and Figure 5a–c.

It was verified that the V_t of the three coal plugs with different metamorphic degrees (YQ anthracite coal, LSD gas-fat coal, and LHG long-flame coal) increased by 20.89%, 17.05%, and 13.40%, the V₀ increased by 60.85%, 57.73%, and 51.13%, and the μ₀ increased by 54.71%, 55.10%, and 56.96%, respectively, under the damaging effect on LCO₂ cryogenic freezing. Thus, by comparing the original coal plugs, the V_t and V₀ for the treated coal plugs are increased significantly, and the complexity of the coal microstructure spatial distribution is also enhanced. In summary, the above-analyzed variations in coal microspatial structure are obviously due to the fact that within the frost-heaving forces generated by contact with LCO₂, the coal structural plane is bigger than the mechanical-limit value of coal tensile failure, indicating that the coal microstructure is more prone to damage failure under stress loading, which will induce fracture network expansion and extension within the coal in a short time, a fracture channel that longitudinally contacts through the whole coal plugs as well as the development of a large number of new fractures [49,50]. Meanwhile, it can be concluded that the morphological properties and microstructures of coal (fracture-network components, ball-stick model, and grain structure) for the treated coal plugs are more complex to a certain extent, which further verifies that the damaging effect from LCO₂ cryogenic freezing on the coal microstructure is obvious.

(2) Coal permeability variations before and after treatment

From the analysis of inherent properties of the coal fracture structure, its permeability coefficient (k) is closely related to the development degree of its skeleton microfractures. k is one of the determining factors within the difficulty of gas seepage inside the coalbeds, which is an inherent property parameter of coal [51]. Some researchers have shown that coal is imposed on the external load stresses, leading to the deformation failure of its primary structure; the corresponding permeability coefficient will also be changed accordingly, which has been verified by the above analysis of coal microstructure variations. Therefore, this section is mainly based on the percolation theory of the Avizo software, which is used to calculate the variations in the coal permeability coefficient caused by the development of coal microstructures during LCO₂ cryogenic freezing. With the help of the multi-ROI analysis tools in the Avizo software, the cube modules are intercepted with an equal volume in the coal plugs, reconstructing 3D visualization models of coal permeability in accordance with the percolation theory. Then, the percolation curve models of the coal column unit block are divided and extracted, and the coal column permeability before and after treatment were quantitatively calculated, as shown in Figure 6. Comparing the model’s difference in permeability coefficient and percolation curves with the three original coal plugs indicates that the single-value function coverage area of the percolation model with LCO₂ cryogenic-freezing-treated coal plugs become larger, and the corresponding percolation curve models become more intensive. Additionally, quantitatively calculating the permeability coefficient of coal plug unit blocks showed increased permeability coefficient ratios of YQ, LSD, and LHG coal samples by 79.97%, 40.52%, and 65.83%, respectively. This indicates that the scale effect of the fracture network inside coal plugs damaged by LCO₂ is more obvious. It can be concluded that the penetrability of the coal matrix is highly enhanced. Especially, for LHG long-flame treated coal plugs, the coverage area of the coal permeability model and the complexity of the percolation curve are not obvious; the reason is that the fracture variation in LHG long-flame coal is relatively lower under the external load stress by using LCO₂, and expansion -extension only occurred for a single main fracture in the coal plug. However, compared with YQ and LSD coal plugs, the development degree with the fracture network is higher and the density of its percolation curves is also higher than that of original coal plugs, which further verifies that the fracture network development of coal is closely related to its permeability. The above analysis shows that under the damaging effect of LCO₂ cryogenic freezing, by enhancing the coal permeability, the difficulty of multi-gas seepage in the coalbed is reduced, which is conducive to coalbed methane extraction [52].

3.3. Mechanical Properties of Coal

A substantial number of studies indicate that the deformation, instability, and failure of coal under external stress are closely related to its own mechanical properties, and it is also one of the important factors affecting the difficulty of gas-solid coupling migration in coal. Thus, the variations in coal mechanical properties after LCO₂ cryogenic freezing are studied. Processing the feedback information of stress-strain parameters and acoustic emission signals in the stages of compaction, elastic and plastic deformation, as well as the variation laws of peak stress intensity, maximum compression deformation, and elastic modulus of coal plugs before and after treatment showed external load instability failure. It is further clarified that the macroscopic mechanical properties of coal change is based on the variations in microspatial structure, such as the evolution of coal pore and fracture structures, during the LCO₂ cryogenic-freezing process.

Figure 7a,b and

Table 4. Coal mechanical parameters by LCO₂ freezing-thawing.

Sample No.	Type	σmax/MPa	εmax/%	AEmax/ms × mV	E/GPa	fx
YQ	original	43.43	1.95	171,315.8	2.23	1.62
	treated	38.36	1.91	43,617.0	2.01	1.53
LSD	original	45.98	2.38	34,934.0	1.93	1.68
	treated	36.07	2.26	28,993.2	1.59	1.49
LHG	original	58.93	2.49	171,513.1	2.37	2.14
	treated	52.53	2.43	23,315.2	2.16	1.98

show the stress-strain and acoustic emission energy characteristic curves of YQ, LSD, and LHG coal plugs, respectively, which combine with the dividing methods of typical uniaxial compression deformation stages of coal or rock masses. It can be concluded that the variations in mechanical properties during coal deformation can be divided into four stages via comparative analysis: pore and fracture structure compaction (I), coal matrix elastic deformation (II), plastic deformation (III), and even instability failure (IV) of coal plug under the external load stresses. It is indicated from Figure 7a that the stress-strain curves of the original coal plug under the external load stress basically present a linear relationship, and the acoustic emission energy in these four stages is relatively monotonous in the compaction and elastoplastic deformation stages, which only presents a concentrated distribution of energy in the instability stage. It is revealed that for the original coal plugs, owing to the constant internal pore fracture structure space, if the external load stress cannot exceed the mechanical strength of the coal itself, there will be no slip or large-scale deformation failure, but the internal space will be squeezed and compacted. However, when the external loading stress exceeds the compressive strength of coal itself, the structure will incur instability in an instant and experience the brittle failure phenomenon, which will enhance the overall crushing space of coal plugs, and the detected spectral acoustic emission energy frequency will increase accordingly.

Through the comparative analysis of Table 4 and Figure 7b, it can be concluded that after the treatment of coal plugs by LCO₂ cryogenic freezing under the same conditions, compared with original coal plugs, the slope of stress-strain curves among the three coal plugs is relatively reduced within a compression and elastoplastic deformation stage, and the peak stress-strain values are correspondingly decreased by 14.69% and 3.17% on average, respectively. Moreover, the acoustic emission signal conversion energy increased by 59.31% on average; these descriptions show that with the damaging effect on LCO₂ cryogenic freezing, the microstructure (pore and fracture) in the coal is developed, inducing the spatial structure in the coal to expand. Thus, the compressibility and acoustic signal penetration range are increased. Moreover, the results from the three treated coal plugs in the elastic and plastic deformation stage (II and III) by using the external loading stress action indicate that the limit load stress and strain value required for the coal deformation is reduced. The elastic and plastic deformation in the coal plug occurs easily at the same loading rate, which can be verified by instantaneous shaking within stress-strain curves in the process of elastic-plastic deformation stages. Simultaneously, the treated coal plug appears to defectively collapse, eventually experiencing instability failure under external loading stress conditions. In addition, the corresponding peak stress-strain with its limit value is also decreased. Furthermore, at the same acoustic emission loading rate, the energy tended to display a concentrated distribution, resulting in the elastic modulus of the three coal plugs decreasing by 12.12% on average, and its corresponding coal solidity coefficient reduced by 8.16% on average. These variations fully indicate that the brittleness of the coal skeleton and the limited strength value of the coal matrix itself are reduced during the convective heat-transfer process between the LCO₂ and coal matrix, and a damaging effect from LCO₂ cryogenic freezing on the coal plugs is generated [28]. Therefore, the cold energy impact has caused stress damage to the coal microstructure; it is manifested, on the one hand, in the coal deformation-failure process and, on the other hand, the development of the coal pore and fracture network, eventually leading to the enhancement of coal permeability [49].

3.4. Damage Degree of Coal Plug Measured by Fractal Box Dimension

To quantitatively describe the damage degree of coal caused by LCO₂ cryogenic freezing, the fractal box dimensions within a 3D fracture network space are utilized to measure the complexity and irregularity of coal plugs; the results are shown in Figure 8a,b. It can be revealed that the piecewise fitting curves of fractal box dimensions of the coal-fracture network show a linear relationship, resulting in the absolute value k_i ∈ [2,3] by the slope of the fitting curves, and the correlation coefficient is greater than 0.98, which clearly indicates the fractal characteristics of the coal-fracture network in this test. Especially for LHG long-flame coal, the fractal box dimension of the fracture network for the treated coal plug is greater than 3, which mainly due to the internal coal fracture is mainly manifesting in the expansion and extension under the damaging effect of LCO₂ cryogenic freezing, while the generation and complexity of the new fractures are not obvious, which has been verified in the previous analysis.

As shown in

Table 5. Fractal box dimensions of the coal samples.

Sample No.	YQ Anthracite Coal		LSD Gas-Fat Coal		LHG Long-Flame Coal
	D1	D2	D1	D2	D1	D2
Original	2.93	1.83	2.77	1.86	3.19	1.53
Treated	2.98	1.98	2.94	2.21	3.23	1.58

Notes: D₁ and D₂ is the fractal box dimension, respectively.

, by quantitatively calculating the fractal box dimension (D_i) of the coal-fracture network before and after LCO₂ treatment, the results show that the average D_i of fracture networks for the original coal plugs are 2.38, 2.32, and 2.25, respectively. For the treated coal plugs, the values of D_i of fracture networks are 2.48, 2.58, and 2.41, respectively. In contrast, the D_i for the treated coal plugs is significantly increased, and the increased rates are 4.03%, 10.07%, and 6.64%, respectively. It is revealed that the fractal characteristic is more obvious for the coal plugs during LCO₂ cryogenic freezing.

The above analysis shows that under the effect of the LCO₂ frost heaving force, there is multi-stress loading to the weaker surface area of the coal microstructure, which reflects that the original coal microstructure (pore, fracture, and matrix) has been changed and rebuilt. Thereby, the coal matrix surface roughness, irregularity, and fracture network connection structure are also more complex, which further indicates that the proportion of coal with an internal spatial structure is larger and the damage degree is increased compared with the original coal [53]. This is related to the general enhancement of permeability for the three coal plugs in the previous investigation of this paper, and a common relationship is consistent with the previous results [54].

3.5. Coal Deformation-Failure Mechanism by LCO₂ Cryogenic Freezing

Coal is a type of organic matter, which has a heterogeneous body formed by various mineral micro-element particles under the action of molecular force. In accordance with the molecular motion theory, the reservoir ambient temperature being closely related to the thermal motion of coal molecules, that is, the heterogeneity of coal and rock mass, makes the thermal expansion coefficient between coal molecules different, constraining the shape variable of the coal structural plane. With the ambient temperature in the coal reservoir changed, the uneven temperature distribution of the coal structural plane generates some amount of thermal stress; thus, the resulting temperature gradient affects the thermal movement of coal molecules, leading to a frequently uneven local thermal expansion and cold contraction with the coal matrix [28,55]. The temperature distribution equation of coal under LCO₂ cryogenic freezing can be expressed as follows [56]:

$$KT+q-\rho C\frac{\mathsf{\partial }T}{\mathsf{\partial }t}=0$$

(6)

where K represents the thermal conductivity, W/m·K; q represents the heat source intensity per unit volume, W/m³; C represents the specific heat capacity, J/kg·K; ρ represents the coal mass density, kg/m³; and T represents the temperature, °C.

As shown in Figure 9a, if LCO₂ is injected into the coalbed along the preset borehole according to a constant transmission pressure, when LCO₂ initially injected into the coalbed makes contact with the coal structural plane around the borehole for the convection heat transfer, a cryogenic-freezing damage effect on the coal within the scope of CO₂ seepage as a liquid-state is produced, forming a large temperature gradient in a short time. Simultaneously, with the increased volume of LCO₂ injected into the coalbed, the thermal stress generated by the accumulation of the cooling capacity is greater than the stress limit of the coal itself, which will induce coal deformation failure [32].

As shown in Figure 9b, if the coal unit is regarded as a 3D micro-element structural body, the thermal stress of LCO₂ acting along the fracture direction in the coal is considered parallel with the xy axis and perpendicular to the z-axis; thus, the cold shrinkage stress-strain of the coal matrix with its micro-element can be expressed as follows [57]:

$$\left\{\begin{array}{l}{\epsilon }_x=\frac{1}{E_H}[{\sigma }_x-v_v({\sigma }_y+{\sigma }_z)]+{\alpha }_H\Delta T\\ {\epsilon }_y=\frac{1}{E_H}[{\sigma }_y-v_v({\sigma }_x+{\sigma }_z)]+{\alpha }_H\Delta T\\ {\epsilon }_z=\frac{1}{E_v}[{\sigma }_z-v_H({\sigma }_x+{\sigma }_y)]+{\alpha }_v\Delta T\end{array}\right.$$

(7)

where ε_x, ε_y, and ε_z represent the shrinkage deformation of coal matrix, N/m; σ_x, σ_y, and σ_z represent the 3D shrinkage thermal stress of coal matrix-element, MPa; v_v and v_H represent the Poisson’s ratio of parallel and vertical coal cleat plane, constant; E_v and E_H represent the elastic modulus of parallel and vertical coal cleat plane, MPa; α_v and α_H represent the nonlinear thermal stress coefficient of parallel and vertical coal cleat plane, constant; ΔT represents the variation of coal temperature field, °C.

As shown in Figure 9c, the injection of LCO₂ into the coalbed, driven by its transmission pressure, penetrates the internal structure of coal along the connected fracture channel. Meanwhile, the local thermal stress is generated by contact with the cold source of the heterogeneous structural plane of coal in the process of CO₂ seepage as a liquid state, which leads to a tensile damage effect on the coal’s original microstructure and thus causes coal matrix shrinkage, forcing the secondary development of the coal pore and fracture microstructure. Additionally, when the thermal stress generated by LCO₂ cryogenic freezing reaches and exceeds the tensile, compressive, and even shear stress that the coal skeleton structure with coal plugs can withstand, the elongation, bifurcation, and crack width increase in new fracture germination, and the original fractures are produced inside the coal. Eventually, this leads to the deformation-failure of coal, accompanied by the microstructure, mechanical properties, and fluid-structure within its interaction effect as LCO₂ injected into the coalbed also changes [58].

4. Conclusions

In this paper, three coal plugs with different metamorphic degrees are tested by using X-ray CT scanning technology. Avizo system software 2019 is adopted to quantitatively analyze the damage characteristics and permeability variations in coal before and after treatment. Then, the mechanical properties and deformation-failure characteristics of coal are described by a combined method of single-cycle compression and acoustic emission, then the damage degree and mechanism of coal under the LCO₂ cryogenic-freezing effect are characterized. The main conclusions are as follows:

(1) With the help of image processing and the 3D visualization functions of the Avizo software, the methods of median filtering, threshold segmentation, two-dimensional fracture parameter extraction, and 3D reconstruction are performed on CT scanning coal slices, and the coal microstructure parameters are quantitatively characterized. The CT scanning coal slice parameters of l₀, w₀, S₀, and μ₀ have average growth rates of 37.01%, 23.38%, 84.01%, and 82.53%, respectively; the average increased ratios of V_t, V₀, and μ₀ for treated coal plugs are 17.11%, 56.57%, and 55.59%, respectively. This shows that the spatial distribution and regeneration characteristics of coal micro-fracture networks are obvious under the damaging effect of LCO₂ cryogenic freezing.

(2) The percolation theoretical model of gas-solid coupling for the coal plugs is established, and the percolation curve density, single value function coverage area, and permeability of coal plugs are quantitatively calculated. For the treated coal plugs, the coverage area of the single value function becomes larger, the percolation curve is relatively dense, and the permeability is enhanced significantly, with average growth rates of 65.83%, 40.52%, and 79.97%, respectively.

(3) The results of uniaxial compression and acoustic emission combined with the testing of coal plugs show that the external load stress required by treated coal plugs in their compaction and elastic deformation stages is reduced, and the peak stress-strain in the instability failure is decreased on average by 14.69% and 3.17%, respectively; while the acoustic emission energy is increased by 59.31% on average, which indicates that the limit stress intensity value of the coal plugs is reduced under the LCO₂ cryogenic-freezing damage effect; thus, the micro-space of coal fracture structure is increased.

(4) The fractal characteristics of the coal-fracture network are quantitatively calculated by using the fractal box dimension method, comparatively analyzing that the average increased ratios of D_i for the treated coal plugs are 6.16%, 18.22%, and 16.34%, respectively, which reveal that the fracture network and coal matrix structure are complex and the damage degree of the coal plugs is more serious after LCO₂ cryogenic freezing. Moreover, when the local thermal stress generated by cold contact between the LCO₂ and structural plane is bigger than the stress limit strength of coal itself, the deformation-failure will occur and the mechanical properties of coal will be changed, enhancing the space proportion of the coal microstructure and the permeability of the coal matrix block, thereby reducing the difficulty of multi-gaseous seepage in the coal, which is favorable for the desorption and extraction of CH₄ in the coalbed.