Comparative Study on Gas Desorption Behaviors of Single-Size and Mixed-Size Coal Samples

Abstract

The gas desorption behavior of coal is a key basis for guiding gas parameter determination, optimizing gas extraction, and preventing gas-related disasters. Coal in mine working faces typically exhibits a mixed particle size distribution. However, research on the gas desorption behavior of mixed-size coal samples and comparative studies with single-sized samples remains insufficient. This study employed a self-developed experimental system for the multi-field coupled seepage desorption of gas-bearing coal to conduct comparative experiments on gas desorption behavior between single-sized and mixed-size coal samples. Systematic analysis revealed significant differences in their desorption and diffusion patterns: smaller particle sizes and higher proportions of small particles correlate with greater total gas desorption amounts and higher desorption rates. The desorption process exhibits distinct stages: the initial desorption amount is primarily influenced by the particle size, while the later stage is affected by the proportion of coal samples with different particle sizes. The desorption intensity for both single-sized and mixed-size samples decays exponentially over time, with the decay rate weakening as the proportion of small particles decreases. The gas diffusion coefficient decays over time during desorption, eventually approaching zero, and increases as the proportion of small particles rises. Conversely, the gas desorption attenuation coefficient increases with a higher proportion of fine particles. Based on the desorption laws of coal samples with single and mixed particle sizes, this study can be applied to coalbed gas content measurements, emission prediction, and extraction design, thereby providing a theoretical foundation and technical support for coal mine operations.

1. Introduction

As a vital basic energy source and chemical raw material in China, coal plays a crucial role in ensuring energy supply and supporting sustainable economic development [1,2]. In recent years, with the continuous increase in the mining depth, the coal seam gas content and pressure have risen significantly, making the prevention and control of dynamic disasters such as coal and gas outbursts increasingly challenging and posing serious threats to mine safety [3,4,5,6]. Gas desorption characteristics constitute a critical factor governing gas content determination, emission prediction, and extraction design optimization. For instance, when applying the direct method for gas content measurement, the magnitude of gas loss demonstrates a close correlation with desorption properties [7,8,9,10]. Therefore, in-depth research on gas desorption behavior is of great theoretical and practical significance for improving the accuracy of gas content measurement, optimizing gas extraction, and reducing the risk of gas-related accidents in coal mines.

Numerous factors influence the characteristics of gas desorption, among which the coal particle size is one of the most critical [11,12,13,14,15]. The occurrence, migration, and release characteristics of gas in coal are closely related to its particle size distribution. Different particle sizes result in variations in the specific surface area, pore structure, and permeability, leading to distinct desorption, diffusion, and seepage behaviors of gas [16,17]. These differences are key factors in the accurate determination of gas content and the effective prevention and control of gas hazards. Therefore, systematically studying the impact of particle size on the characteristics of gas desorption in coal provides an essential foundation for accurate early warning and the prevention of gas disasters.

Scholars have made significant progress in the field of gas desorption by independently developing experimental research platforms and using diverse research methods, greatly enriching and improving the fundamental theoretical system of gas desorption. Liang et al. [18] developed an experimental platform for coal gas desorption under pressure, conducting gas desorption experiments in both positive pressure and varying pressure environments, and established a gas desorption model for coal under pressure. Chen et al. [19] established a vibration–adsorption–desorption experimental system to study the impact of the vibration frequency on gas desorption. Mechanical vibrations generate shear forces in the adsorbed gas, promoting gas desorption. Within the experimental parameter range, larger amplitudes are more favorable for gas desorption. Li et al. [20] studied the gas desorption characteristics at different temperatures using a self-designed device and found that the gas desorption behavior follows a power function. Tu et al. [21] developed an infrared radiation experimental system to study the adsorption and desorption behavior of coal with different moisture contents. They proposed an improved Langmuir adsorption model that takes into account the infrared radiation power and moisture content and validated the model. Li et al. [22,23] developed a low-frequency vibration coal sample desorption characteristic testing system and a large-scale 3D coal and gas co-mining physical simulation system and applied them to study the gas desorption behavior of single-particle-size coal samples under different low-frequency vibrations, as well as the depressurization gas migration behavior in overlying rock fractures. These studies have made significant contributions to the prevention and control of coal mine gas disasters.

Yang et al. [24] conducted gas desorption experiments on coal with three different particle sizes and found a negative correlation between the desorption rate and particle size. They also preliminarily established a mathematical model for the initial stage of gas desorption. Ye et al. [25] studied the gas desorption amount of coal with different particle sizes at various adsorption pressures and found that the desorption amount increased with the adsorption pressure and also increased as the coal sample particle size decreased. Zheng et al. [26] researched the gas desorption and diffusion behavior of coal with different particle sizes, discovering that the cumulative diffusion amount, diffusion rate, and effective diffusion coefficient, decreased with an increase in particle size. This indicates that gas desorbs and diffuses more easily from smaller coal particles. Li et al. [27] found that the gas diffusion process consists of three stages: rapid diffusion, slow diffusion, and smooth diffusion. The larger the particle size of the coal, the slower the gas diffusion rate, and the longer it takes to reach desorption equilibrium. Cheng et al. [28] studied the variation characteristics of gas desorption with different particle sizes of coal and, combining the particle size distribution of coal in mines and gas emission characteristics, developed a gas-emission-prediction model that considers the particle size distribution. This model was applied and verified in the field. Liu et al. [29] studied the gas diffusion kinetics of coal powder and lump coal, revealing a significant scale effect with a critical particle size: below this threshold, the diffusion rate decreases as the particle size increases, while above it, the rate remains largely unchanged. Mnzool M et al. [30] revealed the flow characteristics of gas within the borehole. Their method can be extended to simulate the impact of coal the particle size on gas desorption, providing theoretical support for optimizing gas extraction parameters.

Scholars have established experimental platforms to investigate the characteristics of gas desorption under various influencing factors, primarily focusing on coal samples with a single particle size. Coal in mine working faces typically exhibits a mixed particle size distribution. However, research on the gas desorption behavior of mixed-size coal samples and comparative studies with single-sized samples remain insufficient. The gas desorption characteristics of coal are an important basis for assessing and preventing coal and gas outbursts, predicting gas emission, and optimizing extraction strategies. For example, an increased desorption rate heightens the risk of coal outbursts, affects the prediction of gas emissions, and plays a key role in optimizing gas extraction strategies and parameters. Based on prior research and experience, this study independently developed a multi-field coupled seepage–desorption experimental system for gas-bearing coal. Using this system, gas desorption experiments were conducted under conditions involving single-size and mixed-size coal samples. Key gas desorption behaviors were analyzed to provide a theoretical basis for gas parameter determinations and gas extraction strategies.

2. Experimental System Design

The experimental system architecture diagram is shown in Figure 1, comprising functional design and system components. The system adopts a modular design and consists of seven key parts: a constant-pressure automatic gas injection and adsorption unit, a gas surface diffusion seepage–desorption unit, a gas extraction unit, a stress loading and unloading unit, an acoustic emission monitoring unit, a multi-parameter monitoring unit, and experimental system management software. These modules enable the dynamic acquisition and control of experimental parameters related to the coupling of stress, fracture, and seepage in coal seams and overlying strata. The system is designed to study gas adsorption/desorption in coal of varying particle sizes, seepage/desorption characteristics under different (including coupled) conditions, and the evolution of internal damage and fractures within the coal.

3. Construction of the Experimental System

3.1. Constant-Pressure Automatic Gas Injection and Adsorption Unit

The constant-pressure automatic gas injection and adsorption unit mainly consists of a gas cylinder, pressure-reducing valve, shut-off valve, buffer tank, and pipeline. It enables automatic regulation via pneumatic valves to maintain a constant charging pressure and ensure stable pressure adsorption. Gas from the cylinder flows through the buffer tank and pipeline into the gas surface diffusion device, creating a gas-bearing state in the coal sample that meets experimental conditions. The pressure-reducing valve is made of 304 stainless steel and is used to reduce and stabilize high-pressure gas to the required level. The buffer tank is made of 316 stainless steels, featuring a stable sealing structure to ensure the reliability of high-pressure gas containment.

3.2. Gas Surface Diffusion Seepage–Desorption Unit

The gas surface diffusion seepage–desorption device mainly shifts the gas diffusion mode from point diffusion to surface diffusion, allowing for a more realistic simulation of the gas adsorption, seepage, and desorption characteristics. It consists of a coal sample bin, a sealing rubber sleeve, and an air-permeable plate. The coal sample bin measures 200 mm × 200 mm × 200 mm, can withstand pressures up to 20 MPa, and is fabricated from forged stainless steel. Radiating grooves, arranged as concentric circles with a spacing of 15 mm and a depth of 0.5 mm are machined on the side panels of the coal sample bin where gas inlet and outlet ports are located, as shown in Figure 2. Additionally, a smaller coal sample bin (50 mm × 50 mm × 50 mm) was made for gas adsorption and desorption experiments involving coal samples of different particle sizes.

3.3. Gas Extraction Unit

The gas extraction unit mainly includes a vacuum pump, extraction pipelines, and flowmeter. The pump is housed within a cabinet and can be remotely controlled via the system management software, enabling gas extraction under various negative pressure conditions. The gas flowmeter is equipped with an RS-232 interface for communication with a computer, allowing real-time monitoring data of gas flow during extraction to be transmitted to the experimental system management software.

3.4. Stress Loading and Unloading Unit

The stress loading and unloading unit mainly consists of a loading pump, hydraulic cylinder, piston rod, and loading plate. The loading pump is a constant-pressure, constant-speed pump capable of applying stress at different levels, with start and stop functions controlled via computer programs. The piston rod is processed by roller burnishing to enhance its wear resistance. The diameter of the hydraulic cylinder is half the area of the coal sample bin, ensuring that the applied stress can reach up to 20 MPa. The loading plate matches the internal dimensions of the coal sample bin, enabling complete cross-sectional stress application on the coal within the bin.

3.5. Acoustic Emission Monitoring Unit

The acoustic emission monitoring unit consists of acoustic emission sensors and an amplifier. Sensors are placed on each of the four sidewalls of the coal sample bin, arranged in a cross pattern and close contact with the coal sample, shown in Figure 3. The acoustic emission amplifier records the signals generated during the loading and unloading to study internal damage and fracture development within the coal.

3.6. Multi-Parameter Monitoring Unit

The multi-parameter monitoring unit mainly consists of pressure gauges, a flowmeter, solenoid valves, a data-acquisition device, and a monitoring host. During the experiment, the data-acquisition device can record experimental data in real time and promptly store and upload information such as the gas flow, stress, and internal damage fractures to the monitoring host.

3.7. Management Software

The experimental system management software interface is shown in Figure 4. The experimental system interface consists of four areas: the menu area, the monitoring area, and the main interface and control area. The menu area allows users to retrieve relevant data and charts, such as the desorption flow rate, pressure, and stress. The monitoring area is used for the real-time monitoring of both instantaneous and cumulative flow rates of each flow meter, as well as data from pressure sensors. The main interface displays a schematic diagram of the experimental system and its components, showing key parameters such as the desorption flow rate, desorption intensity, and stress at the bottom. The control area provides functions for adjusting control valves and adsorption parameters. Integrating control over all system modules through a centralized software platform im-proves the system’s usability and convenience.

3.8. Assembly of the Experimental System

Through precision manufacturing, repeated debugging, and system integration of the above experimental components, along with verification via simulation testing, a multi-field coupled seepage–desorption experimental system for gas-bearing coal was successfully developed, as shown in Figure 5. The main experimental equipment and its technical parameters are listed in

Table 1. Main experimental equipment and its technical parameters.

Equipment	Brand or Model	Key Specifications
Coal sample bin	Self-developed	200 mm × 200 mm × 200 mm and 50 mm × 50 mm × 50 mm Pressure resistance: 20 Mpa
Vacuum pump	SC920G	Maximum vacuum: 2.0 mbar Power: 135 W
Flowmeter	Mini CORI-FLOW M14	Pressure resistance: 3 MPa Accuracy: 0.2% FS
Solenoid valves	SY3120	Maximum working pressure: 0.1 ~ 0.8 MPa Response time: ≤10 ms
pressure gauges	HONGQI	Range: 5 MPa Accuracy: 0.1%
Loading pump	RLBHD-2	Working pressure: 50 MPa Flow rate: 0–30 mL/min Accuracy: 0.01 mL/min
Acoustic emission monitoring unit	Micro-II Express Digital AE System	A/D Resolution: 18-bit Sampling Rate: 2 MSPS

. The system features a highly integrated design with coordinated operation among its units, enabling the realistic simulation of key processes such as gas adsorption, desorption, seepage, fracture, and stress variation within the coal. It also supports a synchronized observation and analysis of these multi-physical field coupling processes. The system provides a solid experimental foundation and theoretical support for accurately obtaining fundamental gas parameters, exploring gas migration mechanisms, and achieving precise and efficient gas extraction.

4. Experimental Plan

4.1. Coal Sample Preparation

Gas desorption experiments were conducted on coal samples with mixed particle sizes in different proportions using the experimental system. The coal was sourced from the Wangjialing Coal Mine in Xiangning County, Shanxi Province, China, and the basic physical properties of the coal are listed in

Table 2. Basic physical property parameters of coal samples.

Coal Type	Density (g/cm3)	Moisture (%)	Ash Content (%)	Volatile Matte (%)	Porosity (%)	Vitrinite (%)	Inertinite (%)
Lean coal	1.39	0.55	8.48	17.08	4.20	78.13	21.87

. The raw coal was placed in sealed bags, filled with helium gas, and transported to the laboratory. The flowchart of the coal sample preparation process is shown in Figure 6. A crusher was used to crush the coal, which was then sieved into three particle size ranges: 1–0.5 mm, 0.5–0.25 mm, and <0.25 mm. According to GB/T 23250-2009 [31], “The direct method of determining coalbed gas content in the mine,” the first crushing step requires the proportion of coal with a particle size of <0.25 mm to exceed 80%, and the second crushing step requires the proportion to exceed 95%. The coal samples of different particle sizes were mixed in six different proportions, as shown in

Table 3. Proportion of coal samples with different particle sizes.

Coal Sample No.	Mass (g)	1–0.5 mm	0.5–0.25 mm	<0.25 mm	Particle Size
S1	70	100%	0%	0%	Particle Size Proportion
S2	70	0%	100%	0%
S3	70	0%	0%	100%
M1	70	2%	3%	95%
M2	70	5%	15%	80%
M3	70	15%	5%	80%

. To minimize the impact of the moisture and ash content on the experimental results, the coal samples were dried for 12 h at 30 °C before being used in the experiments.

4.2. Experimental Process

The coal samples were placed in a small coal sample bin for adsorption and desorption experiments. The gas adsorption equilibrium pressure was set to 1.5 MPa to study the desorption behavior and desorption parameters of coal samples. The flowchart of the experimental procedure is shown in Figure 7. ① Connect the coal sample bin to the pipelines and valves, and use helium gas to check the system’s airtightness. ② Perform vacuum degassing on the coal sample bin and pipeline. When the vacuum gauge reading is below 20 Pa, vacuum degassing is complete. ③ Open the adsorption valve and allow the coal sample to adsorb gas at 1.5 MPa for 24 h. The adsorption process is considered complete if the pressure in the coal sample bin remains constant within 8 h. ④ Open the computer data-acquisition software, set the data collection interval to 5 s, and open the desorption valve to initiate the desorption process. ⑤ Replace the coal sample in the bin and repeat steps ①–④ to conduct adsorption and desorption experiments for other coal samples.

4.3. Experimental Data Processing

The gas desorption amount is converted to standard conditions using Equation (1):

$$Q_t={\displaystyle \frac{273.2}{1.01325\times {10}^5\times \left(273.2+T_s\right)}}\left(P_0-9.81H_s-P_b\right)\times Q_S$$

(1)

where Q_t is the desorption amount of the unit mass of the coal sample at standard conditions, T_s is the water column temperature during desorption, P₀ is atmospheric pressure, H_s is the height of the water column in the graduated cylinder, P_b is the saturated water vapor pressure at T_s condition, and Q_s is the desorption amount of unit mass of coal sample measured under experimental conditions.

The ultimate gas desorption amount of the unit mass of coal sample Q_∞ is calculated using Equation (2) [32]:

$$Q_{\infty }=\left[{\displaystyle \frac{abP}{1+bP}}\exp \left[n\left(T_1-T\right)\right]-{\displaystyle \frac{ab{P}_0}{1+b{P}_0}}\exp \left[n\left(T_1-T_0\right)\right]\right]\times {\displaystyle \frac{1}{1+0.31M_{ad}}}{\displaystyle \frac{100-A_{ad}-M_{ad}}{100}}$$

(2)

where a is the ultimate gas adsorption capacity of the coal, b is the adsorption constant, P is the gas adsorption equilibrium pressure, n is a coefficient, T₁ is the temperature when a and b values are determined, T₀ is the temperature when the coal sample adsorbs gas, M_ad is the moisture content in the coal, and A_ad is the ash content in the coal.

5. Experimental Results Analysis

5.1. Gas Desorption Behavior of Coal Samples

5.1.1. Gas Desorption Amount and Desorption Rate

The gas desorption amount and desorption rate of coal samples with single-size and mixed-size over time are shown in Figure 8. In the initial desorption stage (within 500 s), the gas desorption amount accounts for 50% to 70% of the total desorption. After that, the desorption rate gradually slows down, and the desorption amount tends to stabilize. The desorption amount in the early desorption stage differs for coal samples with different particle sizes, indicating that the main factor affecting the desorption amount in the early stage is the particle size of the coal sample. This is because smaller coal particles have shorter and simpler gas diffusion paths, and their pore structures are also simpler, making it easier for gas adsorbed in the coal matrix to desorb and diffuse into the external environment during the initial desorption stage.

At 2000 s, the gas desorption amount of coal sample S1 was 8.36 cm³/g, while the coal sample S2 was 10.76 cm³/g, representing an increase of 28.7% compared to S1. The gas desorption of coal sample S3 was 12.58 cm³/g, showing a 16.91% increase compared to S2. The gas desorption of coal sample M1 was 11.68 cm³/g, while the coal sample M2 was 9.99 cm³/g, which is a 14.46% decrease compared to M1. The desorption of coal sample M3 was 9.52 cm³/g, showing a 4.7% decrease compared to M2. The gas desorption amount of coal samples with different particle sizes, from highest to lowest, is as follows: S3 > M1 > S2 > M2 > M3 > S1. Coal samples with a higher proportion of smaller particles exhibited significantly higher gas desorption than those with a lower proportion, indicating that the particle size proportion plays a significant role in gas desorption during the later stages.

The desorption rate refers to the ratio of the gas desorption amount to the adsorption volume and is a key indicator for evaluating the desorption efficiency of coal. The experimental results show that the desorption process can be divided into two stages: the initial stage (within 500 s), where the desorption rate rises rapidly, followed by a stable stage where the rate of increase slows down and eventually reaches equilibrium. Sample S3 exhibited the best desorption performance, with a final desorption rate of 73.25%, while sample S1 showed relatively poor desorption performance, with a final desorption rate of only 48.7%. The tests revealed a significant correlation between the desorption rate and the particle size composition, showing a decreasing trend as follows: S3 > M1 > S2 > M2 > M3 > S1. As the proportion of smaller particles increased, the desorption rate of the coal sample showed a noticeable upward trend. This phenomenon is likely closely related to the specific surface area of the coal samples.

5.1.2. Gas Desorption Intensity

The gas desorption intensity of coal samples is shown in Figure 9. The desorption intensity trends of coal samples with single-size and mixed-size samples are similar, but there are specific differences. In the first 5 min, the desorption intensity and the desorption rate are rapid. However, the desorption intensity quickly decreases over time. The maximum desorption intensity for sample S3 was 20.61 cm³/g/min, while for sample S1, it was 10.15 cm³/g/min. The desorption intensity of different-particle-size mixed coal samples follows an exponential decay function y = y₀ + αe^−βt, and this model was used to fit the curves, resulting in the relationship between the gas desorption intensity and time for different-particle-size mixed coal samples, as shown in

Table 4. Fitting equation of gas desorption intensity of coal samples.

Coal Sample No.	Fitting Equation	Correlation Coefficient R2
S1	y = 10.0122·e−t/2.03728 + 0.14396	0.99966
S2	y = 19.06512·e−t/1.55318 + 0.13465	0.9999
S3	y = 20.52601·e−t/1.53546 + 0.0881	0.99994
M1	y = 20.40653·e−t/1.80549 + 0.16424	0.99987
M2	y = 18.26168·e−t/1.86648 + 0.16611	0.99985
M3	y = 15.87114·e−t/1.76723 + 0.15689	0.99982

. In the fitting equation, α represents the initial amplitude of the desorption intensity, indicating how quickly the coal sample can release gas at the beginning. A higher α value means a higher risk of gas emission, which is crucial for evaluating coal and gas outburst risks. Therefore, for single particle size samples S1, S2, and S3, α increases as the particle size decreases. For mixed-particle-size samples M1, M2, and M3, the higher the proportion of small-particle-size coal, the larger α becomes. The desorption intensity decreases as the proportion of smaller-particle-size coal samples decreases. This is because smaller coal particles have a larger exposed surface area, allowing for more complete gas release within the coal. Therefore, the desorption intensity increases with the proportion of smaller particle size coal samples.

5.2. Gas Diffusion Coefficient of Coal Samples

The diffusion coefficient is one of the key parameters describing the gas desorption and diffusion behavior. It plays a vital role in understanding the gas migration mechanism and accurately preventing and controlling gas disasters. The variation in the gas diffusion coefficient over time for coal samples is shown in Figure 10. The diffusion coefficient decreases over time and gradually approaches zero. The phenomenon of the diffusion coefficient decaying over time is fundamentally linked to the properties of the coal, especially the heterogeneity of the pore structure and the influence of factors such as moisture. During the initial stage of diffusion, gas molecules adsorbed on the surface of coal, large pores, and fractures desorb first and escape quickly through low-resistance pathways, leading to a higher apparent diffusion coefficient. As the diffusion process continues, the concentration gradient decreases, and the diffusion path extends into finer, more tortuous micropores, which significantly increases the resistance, causing the diffusion coefficient to decay and eventually approach zero.

The gas diffusion coefficient of coal samples with single-size and mixed-size samples, from highest to lowest, is as follows: S3 > M3 > M2 > S2 > M1 > S1. This indicates that the diffusion coefficient of coal samples increases as the proportion of smaller-particle-size coal rises. The diffusion coefficient is mainly influenced by the effective diffusion area. Smaller-particle-size coal has a larger specific surface area compared to larger-particle-size coal, and the increase in the effective diffusion area leads to a reduction in the diffusion coefficient. The gas diffusion coefficients of coal samples with different particle sizes are shown in

Table 5. Gas diffusion coefficients of coal samples.

Time (s)	Gas Diffusion Coefficients (m2/s)
	S1	S2	S3	M1	M2	M3
15	6.87 × 10−11	5.01 × 10−11	1.20 × 10−11	3.14 × 10−11	5.84 × 10−11	6.50 × 10−11
60	3.24 × 10−11	2.32 × 10−11	5.41 × 10−12	1.44 × 10−11	2.73 × 10−11	3.07 × 10−11
120	2.22 × 10−11	1.58 × 10−11	3.63 × 10−12	9.65 × 10−12	1.86 × 10−11	2.10 × 10−11
180	1.78 × 10−11	1.27 × 10−11	2.88 × 10−12	7.66 × 10−12	1.49 × 10−11	1.69 × 10−11
240	1.53 × 10−11	1.08 × 10−11	2.44 × 10−12	6.51 × 10−12	1.27 × 10−11	1.44 × 10−11
300	1.35 × 10−11	9.54 × 10−12	2.14 × 10−12	5.74 × 10−12	1.13 × 10−11	1.28 × 10−11
420	1.13 × 10−11	7.92 × 10−12	1.77 × 10−12	4.74 × 10−12	9.36 × 10−12	1.07 × 10−11
540	9.82 × 10−12	6.89 × 10−12	1.53 × 10−12	4.11 × 10−12	8.15 × 10−12	9.29 × 10−12
660	8.81 × 10−12	6.17 × 10−12	1.36 × 10−12	3.67 × 10−12	7.30 × 10−12	8.33 × 10−12
780	8.05 × 10−12	5.63 × 10−12	1.24 × 10−12	3.33 × 10−12	6.66 × 10−12	7.61 × 10−12
900	7.45 × 10−12	5.19 × 10−12	1.14 × 10−12	3.07 × 10−12	6.16 × 10−12	7.04 × 10−12
1200	6.37 × 10−12	4.43 × 10−12	9.66 × 10−13	2.61 × 10−12	5.26 × 10−12	6.02 × 10−12
1500	5.64 × 10−12	3.91 × 10−12	8.50 × 10−13	2.30 × 10−12	4.66 × 10−12	5.34 × 10−12
2000	4.83 × 10−12	3.34 × 10−12	7.20 × 10−13	1.95 × 10−12	3.97 × 10−12	4.56 × 10−12

. Throughout the experiment, the diffusion coefficient of D3 coal decreased by two orders of magnitude, while other coal samples decreased by one order of magnitude.

5.3. Gas Desorption Attenuation Coefficient of Coal Samples

The gas desorption attenuation coefficients of coal samples are shown in Figure 11. The attenuation coefficients, from highest to lowest, are as follows: S3 > M1 > M2 > S2 > M3 > S1. This indicates that as the proportion of smaller-particle-size coal increases, the desorption attenuation coefficient increases, which significantly affects gas loss and reduces the accuracy of gas content measurements. The primary reason is that gas desorption reduces the pore pressure within the coal. In smaller-particle-size coal, this leads to the shrinkage of internal micropores and small pores, causing them to transition from open to closed. Furthermore, the smaller the particle size, the shorter the gas diffusion path within the pores. Therefore, increasing the proportion of larger-particle-size coal samples during underground gas content measurements can reduce gas loss and improve the accuracy of gas content determination.

6. Discussion

The key highlight of this study is the independent development of a multi-field coupled seepage desorption system for gas-containing coal. This system enables multi-field coupled experiments on coal stress fields, fracture fields, and seepage fields, allowing for synchronous capture of internal damage, fracture evolution, and gas desorption behavior, thereby enhancing the simulation capacity of underground real environments. This experimental system enabled the first systematic investigation of gas desorption in mixed-particle-size coal samples, addressing the research gap mainly focusing on single-particle-size coal. The experiments revealed that particle size has a significant impact during the early desorption stage, while the particle size distribution affects the later stages. This finding overcomes the limitations of single-particle-size coal desorption models and reveals the influence of particle size distribution on gas desorption. Although increasing the proportion of smaller-particle-size coal enhances the desorption amount, it also leads to a significant reduction in the diffusion coefficient and an increase in the desorption attenuation coefficient. This indicates that smaller particles accelerate gas release by increasing the initial desorption intensity, but the diffusion efficiency decreases due to the complex pore structure. This conclusion provides key parameters for optimizing the gas loss model, emission prediction, and extraction design.

However, this study still has certain limitations. This experiment used discrete proportions of mixed coal particles with different particle sizes, without considering the impact of continuous particle size distribution on pore connectivity. Desorption experiments were conducted at 1.5 MPa. While this pressure condition is comparable to the reservoir pressure of some shallow and medium-depth coal seams, it may be significantly lower than the actual in situ adsorption pressure of deep coal seams. Therefore, extra caution is needed when extrapolating the conclusions of this study to deep high-pressure coal seams. Furthermore, the evolution of gas desorption and its coupling with the coal’s microstructure and diffusion coefficient have not been thoroughly explored. Future research could investigate the gas desorption behavior of coal samples with continuous and non-continuous particle size distributions under varying temperatures and adsorption pressures and explore the quantitative relationship between the gas desorption intensity and diffusion coefficient. Techniques such as CT scanning could be employed to reveal the microscopic mechanisms of gas adsorption and desorption. Additionally, integrating multiple factors such as the particle size distribution and temperature, studies could investigate the relationship between the gas desorption intensity and diffusion coefficient, leading to the development of a comprehensive gas desorption kinetic model. This would enhance the accuracy of gas content measurements and provide more reliable theoretical and technical support for gas extraction and coal and gas outburst prevention in coal mines.

7. Conclusions

In this study, the independently developed multi-field coupled seepage desorption experimental system for gas-containing coal was employed to conduct gas desorption experiments on coal samples with single-size and mixed-size samples. Through depth analysis of the experimental data, the gas desorption behavior was systematically explored, and the variations in diffusion coefficients and desorption attenuation coefficients were compared. The main conclusions were summarized as follows:

(1)

A modular approach was used to design and develop a multi-field coupled seepage desorption experimental system for gas-containing coal. The system consists of seven main components and is capable of conducting gas desorption, seepage, and internal damage studies. It also supports coupled experiments of the coal stress field, fracture field, and seepage field. Using this experimental system, gas desorption experiments on coal samples with single-size and mixed-size samples were conducted.

(2)

Within the particle size range of this study, smaller particle sizes and higher proportions of small particles correlate with greater total gas desorption amounts and higher desorption rates. The particle size primarily influences the desorption amount in the early stage, while the proportion of particle sizes dominates in the later stage. The desorption intensity for both single-sized and mixed-size samples decays exponentially over time, with the decay rate weakening as the proportion of small particles decreases.

(3)

The gas diffusion coefficient of coal samples decreases over time and eventually approaches zero. As the proportion of small-particle-size coal increases, the diffusion coefficient decreases, and the gas desorption attenuation coefficient increases. These findings provide an important theoretical foundation for coal seam gas disaster prevention and control. For example, higher gas desorption rates and intensities correlate with increased risks of coal and gas outbursts, providing a reference for outburst hazard assessments. Desorption patterns can also guide the optimization of gas extraction parameters, such as adjusting the borehole density according to the desorption intensity.

(4)

This study systematically investigated the gas desorption and diffusion patterns of coal with single and mixed particle sizes by constructing an experimental system. We compared and analyzed the desorption behavior differences under different particle size combinations. The findings provide an important theoretical basis for accurate gas content measurements, risk assessments of coal and gas outbursts, and the optimization of extraction parameters. However, this study has not fully considered the impact of key parameters such as the pore structure, moisture, and temperature on the desorption process, nor has it explored the connection between macroscopic desorption patterns and microscopic mechanisms. Future research will comprehensively consider the coupling of multiple factors and conduct further experiments and a mechanism analysis at the micro-scale to more deeply reveal the gas desorption mechanisms.