A Preliminary Experimental Study on the Effect of Confining Pressure or Gas Pressure on the Permeability of Coal Samples

Abstract

To provide technical support for gas extraction and gas accident prevention technology, the permeability law of gas in coal seams under different ground stress and gas pressure has been explored. The evolution law of coal sample permeability under different confining pressure and gas pressure was deeply studied by using the coal rock mechanics–permeability test system TAWD-2000. The conclusions are as follows. The permeability of coal samples can be divided into three stages in the whole stress–strain process, gradually decreasing stage, tending to be stable and slowly rising stage, and significantly rising stage. When the confining pressure and axial pressure of the coal sample are constant, the permeability of the coal sample decreases gradually with the increase in gas pressure. When the gas pressure and axial pressure of coal samples are constant, the permeability of the coal samples first decreases and then rises with the gradual increase of confining pressure. Under different confining pressures and gas pressures, the change degree and change rate of coal permeability and are different in the whole stress–strain process. The research results can provide necessary data support for subsequent numerical calculations and practical engineering application.

1. Introduction

As the main driver of economies, energy occupies a pivotal position in the process of national economic development [1,2]. With the continuous improvement of coal mining, the mining depth of coal mines is constantly developing, resulting in high in situ stress, high gas pressure and other characteristics, which in turn leads to the difficulty of gas extraction and coal seams prone to outburst and other issues [3,4,5,6,7]. An in-depth understanding of gas migration law in coal seams is of great significance in solving the problem of coal and gas outbursts. For this reason, many scholars at home and abroad have conducted in-depth research on the permeability characteristics of coal seams and achieved fruitful results. Li [8] carried out the mechanical and permeability tests of raw coal under loading and unloading stress conditions and obtained the permeability response law of raw coal under different loading and unloading rates. Li [9] established a modified double-L adsorption model and a coal permeability model considering the coupling effect of temperature and pore pressure through an isothermal adsorption test and permeability test of pore pressure reduction at different temperatures. Miao [10] studied the influence of carbon dioxide and methane adsorbed by outburst coal on the permeability characteristics by using a self-made triaxial permeability testing machine and obtained the variation law of coal permeability under different gas pressures. Liu [11] studied the relationship between permeability and pore pressure of raw coal under different effective confining pressures by injecting carbon dioxide and methane gas, respectively, and deduced the functional relationship between permeability and pore pressure of coal and rock. Slashchov [12] established the relationship between parameters of the geomechanical process (fracture porosity, angles of the fracture system incidence and strike) and parameters of the gas-dynamic process (intensity, flow rates, and direction of gas flowing). A mathematical model based on the finite element method is proposed, through which the reasonable parameters of the geomechanical and gas-dynamics process in a rock mass can be verified. By studying the adsorption capacity of coal with different water content to CH₄ and CO₂, Chen [13] found that with the increase in water content of coal, the adsorption capacity of coal to CH₄ and CO₂ gradually weakened, and the adsorption capacity of CO₂ was always greater than that of CH₄. The replacement rate of CH₄ and the injection ratio of CO₂ were negatively correlated with the water content of coal. The replacement amount of CH₄, replacement rate of CH₄, and CO₂ injection ratio are mainly related to CO₂ injection volume, coal water content, coal adsorption to gas, adsorption competition between gases, and “partial pressure” caused by high-pressure injection.

Previous studies focused on the relationship between permeability and stress [14,15,16,17,18], strain [19,20,21], gas pressure [22,23], and temperature [24,25,26,27,28], but the research on coal seam permeability characteristics under the coupling condition of in situ stress and gas pressure was rarely involved. In order to provide relevant theoretical support for coal seam gas extraction and coal seam outburst prevention, the permeability characteristics of coal in the full stress–strain process under different confining pressures and gas pressures are studied experimentally in this paper.

2. Test Materials and Test Scheme

2.1. Test Materials

The test rock samples were taken from No.8₂ coal seam of Zouzhuang Coal Mine in the southeast of the Huaibei Coalfield. Zouzhuang Coal Mine is bounded by the F22 fault and Shuangdui fault in the east, the first limestone outcrop line at the top of Taiyuan Formation of carboniferous in the south, Nanping fault in the west, and exploration line 27 in the north. The average thickness of coal seam 8₂ is 2.48 m, and the coal body is black powder-fragment, with weak glass luster and endogenous cracks that belongs to semi-bright briquette. Coal blocks are directly transported from the site to the Mechanics Experiment Center of China University of Mining and Technology, and are drilled and processed centrally. According to the test platform and test specifications, the processed rock samples are cylindrical samples with a height of 95–102 mm, a diameter of about 50 mm, parallelism of upper and lower end faces less than 0.05 mm, and flatness of end less than 0.02 mm of rock samples, as shown in Figure 1. All processed rock samples are sealed and preserved until the test is carried out.

2.2. Test Equipment and Principle

The coal and rock mechanics–permeability test system of China University of Mining and Technology (TAWD-2000) was used for the test, as shown in Figure 2. The system is composed of a pressure host system, a pressure and temperature control system, a microcomputer operating system, etc. It can be used to measure rock permeability under different pressure conditions. The maximum working pressure of confining pressure and injection pressure is 70 MPa, the maximum working pressure of axial pressure is 800 MPa, and the pressure fluctuation is less than 0.5% within 48 h. The experiment was carried out under a constant temperature of 25 °C, and CH₄ was used as the permeability medium.

The principle of the coal permeability measurement test is shown in Figure 3. According to the device principle of this test system, the steady-state method is adopted to test the permeability, specifically, the gas pressure with a certain pressure difference is applied at both ends of the coal sample, and the pressure difference is kept constant, so that a certain pressure gradient is maintained in the coal sample to promote the gas to flow through the cracks of the coal body, and the gas flow through the coal sample is measured. When the flow rate in the coal sample is stable and forms a steady flow, the gas flow through the coal sample in a period of time can be recorded, and the permeability of the coal sample can be calculated by using the control Equation (1) [5].

$$K=\frac{2p_{0}Q{L}_{\mathrm{m}}{\mu }_{C{H}_4}}{A{(p_1-p_2)}^2}$$

(1)

where, $K$ is permeability, 10–15 m²; $p_0$ is atmospheric pressure, 0.1 MPa; $Q$ is the gas flow rate flowing through the coal sample, cm³/s; $L_m$ is the length of standard coal sample, mm; ${\mu }_{C{H}_4}$ is the gas dynamic viscosity coefficient, MPa·s; $A$ is the cross-sectional area of coal sample, mm²; $p_1$ is inlet pressure, MPa; $p_2$ is outlet pressure, MPa.

2.3. Test Scheme

The physical and mechanical parameters of the test coal sample are shown in

Table 1. Table of physical and mechanical parameters of test coal samples.

Elastic Modulus E (GPa)	Poisson’s Ratio μ	Tensile Strength t (MPa)	Cohesion c (MPa)	Angle of Internal Friction φ (°)	Compressive Strength σ (MPa)
1.60	0.15	1.09	1.14	36.61	14.73

. According to the connection requirements of the test system, the coal sample, and each pipeline are connected in place, the coal sample and the gas pipeline of the test system are vacuumized, and the air tightness test of the device is carried out to ensure the air tightness of the system. According to the hydrostatic pressure level, the axial pressure (${\sigma }_1$) and confining pressure (${\sigma }_2={\sigma }_3$) are loaded to a certain pressure level. After the stress stabilizes, gas with different or the same pressure is introduced. When the deformation and gas flow rate of coal samples have no change, axial pressure is continuously applied until failure, according to the stress path shown in Figure 4 and the control mode required in

Table 2. Loading test scheme.

Scheme Number	Test Scheme	Test Number	Gas Pressure (MPa)	Lateral Pressure (MPa)	Rate of Loading (N/s)
1	Constant confining pressure Different gas pressure	XP-1	0.5	4	0.01
		XP-2	1.0	4
		XP-3	1.5	4
		XP-4	2.0	4
2	Constant gas pressure Different confining pressures	XW-1	1.5	4
		XW-2	1.5	5
		XW-3	1.5	6
		XW-4	1.5	7

, until the test ends or any deformation reaches the maximum range of strain gauge, and the data collected by the data monitoring and control system is stored and analyzed.

3. Test Results and Analysis

3.1. Variation Law of Permeability of Coal Samples under Different Gas Pressures

According to the stress path of scheme 1, the relationship between stress difference, permeability, and strain of axially loaded coal samples under constant confining pressure (${\sigma }_2={\sigma }_3=4 \mathrm{MPa}$) and different gas pressures (p = 0. 5 MPa, 1.0 MPa, 1.5 MPa, and 2.0 MPa in turn) is shown in Figure 5.

It can be seen from Figure 5 that the permeability of coal samples mainly presents the change law shown in Figure 6 in the stress–strain process, which can be divided into four stages:

(1)

Initial compaction stage (OA): The whole coal sample is rapidly compressed, which is an early nonlinear deformation. The original cracks are gradually compacted and closed, and the permeability channel decreases. Macroscopically, the gas flow rate decreases, resulting in a sharp decline in permeability.

(2)

Elastic deformation stage (AB): With the continuous loading of axial compression, the structure of the original tiny pores and elastic cracks in the coal sample changes due to the stress, the pores in the coal sample are further squeezed, the pore diameter is reduced or even closed, the gas flow channel is further compressed, the stress–strain curve and the stress-permeability curve are approximately straight, and the permeability of coal near point B reaches the minimum. This stage and the initial compaction stage are the main stages of qualitative change of coal sample permeability, and the coal sample permeability has the highest sensitivity to stress.

(3)

In the stage of plastic deformation (BC): When axial compression is continued, the development of micro-cracks in coal samples is no longer a continuation of previous closure, but a qualitative change occurs, the original cracks expand, and new cracks occur, and the permeability gradually increases, but the increasing rate is not large. At this stage, irrecoverable plastic deformation begins to occur, which leads to the development of new micro-cracks in coal samples and promotes the expansion of cracks, improves the inner surface area of coal samples and gas circulation channels, and promotes the reduction of coal strength. At this time, the stress value has reached peak strength.

(4)

Instability and failure stage (CD): After entering the peak intensity, the internal structure of the coal sample is constantly destroyed, and the bearing capacity can no longer be increased. By continuing to apply axial compression in the way of displacement control, the coal sample basically keeps the whole shape and has residual strength. At this time, cracks develop rapidly, cross and combine with each other to form macroscopic fracture surfaces. At the same time, the permeability of the coal sample gradually increases, but it always fails to reach the initial permeability.

It can be seen from the above that the variation trend of permeability–strain of coal samples under axial compression loading under a constant confining pressure of 4 MPa and different gas pressures is basically the same, showing an asymmetric “V” shaped distribution law of first decreasing and then increasing. Compared with the stress–strain relationship curve, it is advanced and antisymmetric, that is, in the stress–strain process, with the increase of axial stress and strain, the permeability of coal samples decreases first and then increases. The concrete performance is as follows, the permeability of the coal sample decreases rapidly at the initial stage of axial compression loading, decreases slowly with the continuous loading, and begins to increase slowly when entering the plastic yield stage. The coal sample reaches the minimum permeability before reaching the peak strength, and the permeability can only partially rise before the coal body is destroyed but can not reach the initial permeability.

3.2. Variation Law of Permeability of Coal Samples under Different Confining Pressures

According to the stress path of scheme 2, the relationship between stress difference, permeability, and strain of axially loaded coal samples under constant gas pressure (p = 1.5 MPa) and different confining pressures (${\sigma }_2={\sigma }_3$ = 4 MPa, 5 MPa, 6 MPa, and 7 MPa in turn) is shown in Figure 7.

As shown in Figure 7, constant air pressure 1.5 MPa, the changing trend of permeability–strain of coal samples under axial compression under different confining pressures is basically the same, and it is basically consistent with the overall change law of permeability characteristics of loaded coal samples under constant confining pressure and different gas pressures. That is to say, with the increase of stress, the axial strain of coal samples increases, the permeability decreases, and the permeability decreases to the lowest value before the peak strength. Then with the increase of stress and axial strain, the coal samples enter the plastic stage, and the permeability gradually increases.

4. Discussion

4.1. Discussion on the Law between Permeability and Gas Pressure

From the above research, it can be seen that the change of coal permeability under less gas pressure in the stress–strain process generally shows the law of first decreasing and then increasing. Therefore, this paper will take the minimum time of permeability as the characteristic point, study the influence law of confining pressure and gas pressure on coal permeability, and name it as the minimum permeability $K_{\min }$. According to the statistics of permeability changes of coal samples in the loading stage under a constant confining pressure of 4 MPa and different gas pressures, the permeability–strain relationship curves of coal samples under different gas pressures are obtained, as shown in Figure 8. When the gas pressure increases from 0.5 MPa to 2.0 MPa, the minimum permeability $K_{\min }$ of coal samples is 0.51 × 10⁻¹⁵ m², 0.38 × 10⁻¹⁵ m², 0.41 × 10⁻¹⁵ m², and 0.46 × 10⁻¹⁵ m², respectively.

By fitting the test data, the variation law of permeability of coal samples with gas pressure at characteristic points, as shown in Figure 9, is obtained. For the change of minimum permeability of the coal sample, there is a critical gas pressure value. When it is less than the critical value, the minimum permeability decreases continuously and reaches the minimum value, and when it is greater than the critical value, the minimum permeability increases continuously. When the gas pressure is less than the critical value, the crack width caused by the adsorbed gas of the coal sample and the adsorbed expansion of the coal matrix decreases, but the axial loading increases the crack width. But the decrease caused by adsorption is larger than the increase caused by loading, the total fracture width decreases, and the coal permeability decreases. With the increase of gas pressure, the increase of adsorption expansion deformation gradually slows down, which leads to a decrease in fracture width and the decrease in coal permeability. When the gas pressure increases to the critical value, the coal body is no longer adsorbed, the amount of fracture reduction caused by adsorption expansion stops decreasing, and the total fracture amount begins to increase. With the increase of gas pressure, the fracture width of coal begins to increase, and the minimum permeability begins to rise. According to Figure 9, the critical gas pressure value of the coal sample in No. 82 coal seam of Zouzhuang Coal Mine in Huaibei Coalfield is about 1.3 MPa, and the expression of minimum permeability $K_{\min }$ and gas pressure p is fitted as follows:

$$K_{\min }=1.7451p^2-4.6263p+6.9093,{ \mathrm{R}}^2=0.8816\hspace{1em}(0.5 \mathrm{MPa}\le p\le 2.0 \mathrm{MPa})$$

(2)

4.2. Discussion on the Law between Permeability and Confining Pressure

Through the statistics of permeability change of coal sample under constant gas pressure of 1.5 MPa and different confining pressure, the permeability–strain relationship curve of coal sample under different axial pressure is shown in Figure 10. When confining pressure increases from 4.0 MPa to 7.0 MPa, the minimum permeability $K_{\min }$ of coal sample is 0.41 × 10⁻¹⁵ m², 0.23 × 10⁻¹⁵ m², 0.22 × 10⁻¹⁵ m², and 0.21 × 10⁻¹⁵ m², respectively.

By fitting the test data, the variation law of permeability of coal samples with confining pressure at characteristic points, as shown in Figure 11, is obtained. Under the same gas pressure, the higher the confining pressure, the greater the elastic modulus of coal samples. That is, the greater the stiffness of coal samples, the stronger the deformation resistance and the higher the bearing capacity. Therefore, confining pressure can hinder axial deformation and circumferential compaction. When the confining pressure increases from 4 MPa to 7 MPa, the high confining pressure inhibits the development and expansion of cracks in coal samples, and the permeability channels in coal samples will show a gradual compaction trend. Therefore, with the increase of confining pressure, the development degree of pores and fractures decreases, which increases the difficulty of effective flow channel expansion, the porosity decreases, and the minimum permeability of coal samples shows a downward trend as a whole. According to the test data, the expression of minimum permeability $K_{\min }$ and confining pressure ${\sigma }_3$ is as follows:

$$K_{\min }=0.49261{\sigma }_3{}^2-6.12402{\sigma }_3+20.93423, R^2=0.94094 \left(4 \mathrm{MPa}\le {\sigma }_2={\sigma }_3\le 7 \mathrm{MPa}\right)$$

(3)

5. Conclusions and Recommendations

• During the stress–strain process of coal samples, the variation law of permeability can be divided into three stages: gradually decreasing, tending to be stable and slowly rising, and significantly rising, which correspond to the elastic deformation stage, plastic deformation stage, and instability failure stage in the stress–strain process respectively.
• When the axial pressure and confining pressure of the coal sample are constant, with the gradual increase of gas pressure, there is a critical gas pressure value for the change of minimum permeability of coal samples. When it is less than the critical value, the minimum permeability decreases continuously and reaches the minimum value. And when it is greater than the critical value, the minimum permeability increases continuously. On the whole, the relationship between the minimum permeability of coal samples and gas pressure can be expressed.
• When the axial pressure and gas pressure of the coal sample are constant, the permeability channel inside the coal sample is gradually compressed with the increase of confining pressure, which leads to the gradual decline of permeability. The evolution law between them can be expressed.
• Under different confining pressure and gas pressure, the change degree and change rate of coal permeability in the whole stress–strain process are different. So the schemes of coal seam gas extraction and coal seam outburst prevention need to be designed according to the conditions of coal seam confining pressure and gas pressure.