Numerical simulation analysis of effect of borehole gas extraction under fluid‐structure interaction

Abstract

To study the effect of coal pressure on gas extraction under fluid‐solid coupling, the effect of gas extraction radius under different pore sizes and treatment methods was simulated by using COMSOL Multiphysics software, the time evolution law of gas pressure on coal surface was obtained, and the numerical simulation results were verified by the observation of flow rate and concentration in experimental mine combined with fluid‐solid interaction. The results show that the distance of extraction radius increases with the increase of borehole diameter, and the relation between extraction time and extraction radius is a power function, but the increase gets smaller and smaller until it becomes zero. For Φ98 mm borehole and Φ120 mm borehole, hydraulic treatment can increase the efficiency of gas extraction by 31.3% and 22.7%, respectively. For hydraulic treatment and conventional treatment, the ratio of gas drainage effect by enlarging hole size is 6.3% and 13.8% respectively. Compared with the areas without gas extraction under the four conditions, the descending speed of gas pressure from fast to slow is Φ120 mm hydraulic flushing treatment, Φ98 mm hydraulic flushing treatment, Φ120 mm conventional treatment, Φ98 mm conventional treatment. Compared with four different conditions, after 180 days of extraction the coal gas pressure decreased by 75.3% within reasonable hole spacing. At the same time, in multi‐hole pumping, the influence area of adjacent borehole is larger than that of single‐hole pumping, and the spacing of borehole should be less than twice the radius of pumping.

INTRODUCTION

China is a primary energy country, and coal is its main energy source. In the last ten years, the total consumption of coal is increasing year by year, and more than 50% of the total energy consumption, which plays an important role in steel, chemical and other industries. In the process of coal mining, there is always gas disaster, especially gas outburst threatens the life and health of mine workers, and gas is a kind of clean energy, the gas can be extracted and used as fuel. With the increase of coal seam mining depth, the stress conditions around the borehole become more complex, and the effect of gas drainage decreases.^1–8

Underground gas extraction can improve the safety of coal mining and reduce greenhouse gas emissions.^9–11 Along-seam gas extraction can usually be used to reduce the gas content of coal seam.¹² Du et al established the gas-solid coupling model based on the pore-fracture dual medium porous model.¹³ Many scholars have studied the influence of permeability, initial gas pressure, hole spacing, hole diameter and other factors on the radius of gas extraction or gas extraction effect.^14–24 There are also many scholars have studied the impact of hydraulic scouring, adding nitrogen and other different substances on coal gas extraction.^25-27 Some scholars have deduced the reasonable hole spacing by model calculation.^28,29 The above research all has the promotion function to the coal industry gas extraction and the control. However, there are some deficiencies in the study of the factors that affect the effect of gas extraction.

Based on the research of previous scholars and the deformation principle of solid mechanics of coal and rock, fluid-solid interaction differential equation of coal and gas have studied the influence of permeability characteristics of coal body under fluid-solid interaction on the effect of gas drainage. By comparing the influence degree of different pore sizes and different treatment methods on the radius of gas extraction, the influence proportion of different factors on the radius of gas extraction was determined.

SITE CONDITIONS AND RELATED TECHNOLOGY

Geographical conditions

The test coal mine is located in the eastern part of Qinshui County, Jincheng, Shanxi province, which is the southern end of the Taihang Mountains vein. The general surface trend is high in the east and low in the west. The bottom hole elevation at the highest point is +980.90 m, and that at the lowest point is + 588.40 m. The coal seam 3 #, 9 # and 15 # is mainly mined. The test site is located in 3117 and 3120 working faces of 3 # coal seam. The average coal thickness is 5.15 m, the permeability is 3.1 × 10⁻¹⁶ m², the porosity is 1.3%, and the density is 1650 kg/m ~ 3. Figure 1 shows the location of the mine and the layout of the workface. The schematic diagram of construction drilling is shown in Figure 2. 3117 working face has the same drill layout as 3120 working face, as shown in Figure 11.

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Test equipment and technology

To implement the hydraulic punching technology smoothly, the ZYL-15000D coal mine crawler type full hydraulic tunnel drill is adopted, which is a kind of low speed and high torque crawler type full hydraulic power head tunnel drill, suitable for medium and deep hole drilling. The drilling rig has the advantages of advanced technical performance, Strong Adaptability, safe and reliable, easy to move and so on. The utility model is mainly suitable for the construction of large-diameter medium-deep gas drainage holes and other engineering holes in coal mines. It can realize the construction of hole depth over 300m, and can be equipped with many kinds of drill pipe with Φ120 mm,Φ98 mm and other specifications.

Conventional treatment is drilling rig normal drilling, in the process of drilling using ordinary water drill slag, construction to a predetermined depth after the withdrawal of drill pipe. The hydraulic punching treatment is completed in the conventional drilling hole construction, and then the ordinary water is pressurized to the high-pressure water through the water pump station, and the drilling machine is connected with the high-pressure water to carry on the erosion and destruction to the original drilling hole wall, which causes the drilling hole wall to increase the crack, this makes the bore hole larger than the conventional borehole diameter.

MATHEMATICAL MODEL AND NUMERICAL SIMULATION

COMSOL Multiphysics is an analytical software that can couple multiple physical fields and simulate them from one to three dimensions. The numerical simulation involved a combination of fluid-solid coupled physical fields, solid mechanics physical fields, PDE differential equation, and the transport of dilute matter through porous media.

The theory and principle of gas drainage model simulation in coal seam

The gas in coal body can be divided into free gas and adsorbed gas. The free gas in coal body crack can be stripped from coal body surface and entered into coal body pore directly in the process of coal extraction, however, the adsorbed gas in coal matrix needs to enter into coal crevices through the diffusion process to transform into free gas and then peel off from the coal surface. The schematics are shown in Figure 3 and Figure 4.

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In the process of coal mine gas mining, the movement of gas in coal is affected by many factors, and the process is very complicated. In addition, the continuous change of coal stress around the borehole will also change the permeability of coal. To simplify this problem and highlight the research emphasis, the conventional gas extraction and hydraulically treated gas extraction in coal and rock were simulated by using COMSOL Multiphysics software. a. Coal and rock are considered to be isotropic elastic homogenates, and coal and rock are single-phase saturated gas fluids. b. The floor and roof of the coal are impermeable, the gas fluid flows only in the coal seam. c. The process of gas adsorption in coal and rock accords with Langmuir equation, and the process of adsorption and desorption is completed instantaneously. d. The free gas in the coal is ideal gas law, and the permeation of the gas follows Duthie's law, which is isothermal.

Under the action of unloading and gas flow, the deformation displacement of coal and rock will occur, and the deformation displacement follows Cauchy equation. According to the hypothesis (a), the coal and rock are isotropic. The deformation and displacement of coal and rock caused by unloading and gas flow can be regarded as compression deformation. Based on Terzaghi effective stress. 1$G\sum _{j=1}^3\frac{{\partial }^2{u}_i}{\partial x_j^2}+\frac{G}{1-2v}\sum _{j=1}^3\frac{{\partial }^2{u}_j}{\partial x_j\partial x_i}-\frac{(3\lambda -2G)}{3K_S}\frac{\partial p}{\partial x_i}+\alpha \frac{\partial p}{\partial x_i}+F_i=0$where $u$ is the displace, m; $\lambda$ is the Lamé constant; $F_i$ is the volume force on coal rock, N; $G=E/2(1-2v)$ is shear modulus; $E$ is elasticity modulus; $\alpha =1-K/K_S$ is Biot coefficient; $K_S$ is elastic modulus of skeleton; $v$ is poisson ratio.

In the process of gas flow in coal and rock, gas migration conforms to the law of conservation of mass, so the continuity equation of gas flow in coal and rock per unit volume can be obtained as: 2$\frac{\partial ({\rho }_g\varphi )}{\partial t}+\nabla ·({\rho }_g\varphi v)=0$

The gas density can be expressed as: 3${\rho }_g=\frac{M_g}{RT}p$

The gas flow rate can be expressed as: 4$v=-\frac{k}{{\mu }_g}(\nabla p+{\rho }_{g}g\nabla z)$where $M_g$ is Molecular mass of gas, kg/mol; $\varphi$ is porosity; $R$ is molar constant of gas, value is 8.314J/(mol·K); $T$ is temperature; $k$ is permeability; ${\mu }_g$ is permeability gas dynamic viscosity; $g$ is acceleration of gravity; $p$ is gas pressure, MPa.

Equation (3) and Equation (4) are substituted into Equation (2) to obtain the equation of seepage field: 5$\frac{\partial \left(\frac{M_g}{RT}p\varphi \right)}{\partial t}+\nabla ·\left(-\frac{M_{g}p\varphi k}{RT{\mu }_g}\left(\nabla p+\frac{M_g}{RT}pg\nabla z\right)\right)=0$

The change of gas pressure also affects the size of porosity: 6$\frac{\varphi }{{\varphi }_0}=1+\frac{1}{M{\varphi }_0}(p-p_0)+\frac{{\epsilon }_L}{3{\varphi }_0}\left(\frac{K}{M}-1\right)\left(\frac{p}{p_L+p}-\frac{p_0}{p_L+p}\right)$where $M=E(1-v)/(1+v)(1+2v)$ is Lame constant; $K=E/3(1-2v)$ is bulk modulus; ${\varphi }_0$ is initial porosity of coal seam; $p_0$ is original gas pressure of coal seam.

It is calculated by the known related cubic law: 7$\frac{k}{k_0}={\left[1+\frac{1}{M{\varphi }_0}(p-p_0)+\frac{{\epsilon }_L}{3{\varphi }_0}\left(\frac{K}{M}-1\right)\left(\frac{p}{p_L+p}-\frac{p_0}{p_L+p}\right)\right]}^3$

In the gas stored in coal seam, 10%~20% of the gas exists in the fissure system in the free state, the free gas in the fissure system exists in the gas state, and the free gas content in the coal body is: 8$m_f={\varphi }_0\frac{M_g}{RT}{p}_0$where $m_f$ is free gas content in coal, m³/kg;

In the gas stored in coal seam, 80%–90% of the gas exists in the adsorption state in the pore system of coal matrix, and the adsorption state of the gas conforms to the Langmuir adsorption equilibrium state equation: 9$m_m=\frac{V_L{p}_0}{p_0+p_L}{\rho }_{\alpha }\frac{M_g}{V_M}$where is $m_m$ is adsorbed gas content in coal, m³/kg; $V_L$ is Langmuir limiting adsorption constant, m³/kg; $p_L$ is Langmuir pressure constant, MPa; ${\rho }_{\alpha }$ is apparent density of coal, kg/m³; ${\rho }_s$ is the density of gas under standard conditions, kg/m³; $V_M$ is the molar volume of methane in the standard state, m³/mol.

Combined with the above equation, the following formula can be used to obtain the gas content per unit volume of coal: 10$m=m_m+m_f=\frac{V_L{p}_0}{p_0+p_L}{\rho }_{\alpha }\frac{M_g}{V_M}+{\varphi }_0\frac{M_g}{RT}{p}_0$

By substituting the coupling terms (6) and (7) into Equation (5), the seepage field equation is obtained, and the joint Equations (1) and (10) is the fluid-structure coupling model.

Geometric model and parameter setting

It is considered that the coal seam satisfies the conditions of continuity and uniformity, and the gas flow is considered to be a constant temperature (25°C) process. The simplified model is established, and the size of coal seam is 100 m × 150 m × 5.15 m. The single-hole model places the drainage boreholes in the center of the coal body, while the multi-hole model places six boreholes in the coal seam in parallel, the middle four boreholes are gas drainage boreholes, and the outer two boreholes are contrast boreholes, the model mesh and drill hole layout are shown in Figure 5. Two observation sections and one three-dimensional observation section are set in the model, and their arrangement is shown in Figure 5.

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PDE differential equation for simulation using COMSOL numerical simulation software are set as shown in Table 1.

Table 1 Parameter settings.

Parameter	Expression	Value	Unit
Density of coal and rock	ρcoal	1650	kg·m−3
Initial porosity of coal rock	Φ	1.300	%
Initial permeability of coal rock	k	3.100 × 10−16	m2
Ash	Aad	8.100	%
Moisture	Mad	0.930	%
Initial gas pressure of coal and rock	P0	0.310	MPa
Pumping negative pressure	Pout	17.000	kPa
Langmuir constant	a	0.037	m3·kg−1
Langmuir constant	b	1.334	MPa−1
Initial gas density	ρg	0.703	kg·m−3
Poisson's ratio of coal to rock	ν	0.250	-
Young's modulus of coal and rock	Е	2880.000	MPa

Numerical simulation

Study on the effect of single hole pumping

The middle borehole of No. 3 coal seam is simulated by using COMSOL Multiphysics software, and the output is respectively in Φ98mm conventional treatment and Φ98 mm hydraulic punching treatment, the time-varying borehole gas pressure cloud images of Φ120 mm conventional treatment and Φ120 mm hydraulic punching treatment are shown in Figure 6.

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Compared with the gas pressure cloud chart above, the gas pressure of borehole decreases gradually with the increase of extraction time. Under the use of conventional treatment or hydraulic punching treatment, the gas pressure of borehole can also decrease by enlarging the diameter of borehole, under the condition of the same drilling hole diameter, the hydraulic punching treatment can make the drilling gas pressure drop more obviously than the conventional treatment.

Based on the fact that the gas is less than 0.74 MPa, it can be seen that the extraction radius is 5.45 m, 7.12 m, 6.15 m, 7.44 m on the 180th day, and 5.53 m, 7.21 m, 6.22 m, 7.55 m on the 360th day respectively. Therefore, to compare the ratio of the influence of changing the aperture and the treatment method on the extraction radius, the differential value of the relation curve between the extraction radius and the time is calculated through the calculus, which can reflect the difference of the extraction quantity, the larger the extraction radius is, the larger the influence area is, and therefore the larger the extraction amount will be.

Under the same treatment method or the same bore diameter, the trend line of its extraction radius changing with time is shown in Figure 7.

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Taking the data of 0d, 30d, 60d, 90d, Φ120d, 180d and 360d together, it can be seen from Figure 6 that the extraction radius increases with the increase of extraction time, but the speed of the increase of extraction radius decreases, after 180 days, the growth almost stopped.

The comparison of extraction effect is shown in Figure 7. The fitting equations of four cases are obtained by taking extraction time as independent variable t, Unit d, dependent variable R as extraction radius, and unit m:

The fitting equations of Φ98 mm conventional treatment is R = 5.2657–5.1243exp(−0.0259t)

The fitting equations of Φ98 mm hydraulic flushing treatment is R = 6.9858–6.8392exp(−0.0266t)

The fitting equations of Φ120 mm conventional treatment is R = 6.0239–5.8599exp(−0.0255t)

The fitting equations of Φ120 mm hydraulic flushing treatment is R = 7.3342–7.2368exp(−0.0292t)

The area from 0 to 360 days was 1719.9 for Φ98 mm conventional treatment, 2258.1 for Φ98 mm hydraulic treatment, 1956.5 for Φ120 mm conventional treatment, and 2400.2 for Φ120 mm hydraulic treatment. In contrast to Figure 7 and Figure 8, the effect of hydraulic treatment on gas extraction is increased by 31.3% and 22.7%, respectively, the effect of small diameter borehole through hydraulic punching treatment is more obvious than that of conventional treatment. The ratio of gas extraction effect by enlarging the hole size is 6.3% and 13.8% respectively, so the effect of gas extraction is more obvious when the smaller hole is treated by hydraulic punching. Compared with enlarging the hole diameter and using hydraulic punching treatment, the effect of hydraulic punching treatment on gas drainage is more significant.

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Study on pumping effect of multiple boreholes

According to the simulation results of single hole pumping, after 180 days, the effect is not obviously improved, the pumping time is set to 180 days. The spacing of Φ98 mm borehole and Φ120 mm borehole with hydraulic punching treatment is set at twice the radius of pumping, that is, 14.24 m and 14.88 m, and that of Φ98 mm borehole and Φ120 mm borehole with conventional treatment is set at 10.90 m and 12.30 m, respectively, according to this spacing, 6 boreholes are arranged in parallel, the middle 4 boreholes are used for gas extraction, and the two boreholes on both sides are used for comparison without gas extraction. Two situations of hydraulic punching treatment are as follows: from left to right, the positions of six boreholes in Φ98mm borehole are x = −35.60, x = −21.36, x = −7.12, x = 7.12, x = 21.36, x = 35.60, respectively, from left to right, the positions of the six boreholes in the Φ120 mm borehole are x = −37.20, x = −22.32, x = −7.44, x = 7.44, x = 22.32, x = 37.20 respectively. Two cases of conventional treatment: from left to right, the positions of six boreholes in Φ98mm borehole are x = −27.25, x = −16.35, x = −5.45, x = 5.45, x = 16.35, x = 27.25, respectively, from left to right, the positions of the six boreholes in the Φ120 mm borehole are x = −30.75, x = −18.45, x = −6.15, x = 6.15, x = 18.45, x = 30.75 respectively.

According to the results of single-hole drainage drill hole layout, through the three-dimensional cross-section of the gas pressure around the drill hole changes in the law curve, as shown in Figure 9. According to “Coal Mine Safety Regulation”, when the gas pressure of coal body is below 0.74 MPa, the coal seam can be mined, so a 0.74 MPa isoline is set to observe the pressure reaching the standard range around the borehole.

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In the case of hole spacing 7.24 m for Φ98 mm boreholes and 7.44 m for Φ120 mm boreholes, before 180 days, there are a lot of blank zones between pumping boreholes, that is, there is a large area of gas pressure between the drill hole and 0.74 MPa area, in 180d, the gas pressure between the adjacent drill hole most of the areas up to standard. It can be found that, with the passage of time, the gas pressure around the borehole shows a decreasing trend, and the low pressure area becomes larger and larger.

As can be seen from Figure 10, the area where the gas pressure of the drainage borehole is less than 0.74 MPa before 180 d is less than the spacing between holes, and the area below 0.74 MPa after 180 d is greater than or equal to the spacing between holes, the gas pressure can be pumped below the standard between the extraction boreholes.

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Compared with the four areas without drilling, the rate of gas pressure drop from fast to slow is Φ120 mm hydraulic flushing treatment, Φ98 mm hydraulic flushing treatment, Φ120 mm conventional treatment, Φ98 mm conventional treatment. Compared with four different conditions, after 180 days of extraction, the coal gas pressure decreased by 75.3% in reasonable hole spacing, which greatly reduced the coal gas pressure and improved the safety.

In the case of multi-hole extraction, the radius of gas extraction obtained by numerical simulation of single borehole is relatively large, that is, when multi-hole extraction occurs, the area actually affected by gas extraction is larger than expected due to the mutual influence of adjacent boreholes, the pumping radius is larger, therefore, in the arrangement of multiple pumping holes, the interval between them should be less than two times the pumping radius distance.

FIELD TEST VERIFICATION

If the spacing of boreholes is too large, it is easy to form a blank area in the coal seam, and if the spacing of boreholes is too small, it will increase the amount of drilling, cause unnecessary waste. Therefore, the layout of the gas drainage borehole should be based on the radius of the borehole, so as to achieve the optimal design, the minimum amount of work and the best drainage effect.

The testing points are all located in 3117 and 3120 working faces. Two groups of boreholes are arranged in each working face. On the 180th day of the four conditions, the extraction radius was 5.45 m, 7.12 m, 6.15 m and 7.44 m. the first set of test sites was selected for the 5 # and 8 # drilling sites of the No.3117 track main lane, with a diameter of Φ120 mm, the hole spacing is 12.30 m and 14.88 m respectively. The second group of test sites selected are 1 # and 3 # drilling site of 3120 belt main road. The diameter of the hole is Φ98 mm. The hole spacing is 10.90 m and 14.24 m respectively, the distance is the distance between the end of directional drilling and the length of sealing hole is 12 m. The borehole trajectory is shown in Figure 11.

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To compare the difference of extraction effect, the total extraction concentration and the total extraction purity were taken as the indexes of comparison, and the extraction borehole was observed and recorded for two consecutive months. The result is shown in Figure 12.

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Comparing the extraction concentration and extraction rate of the two, the value of Φ120mm is higher than that of Φ98 mm in general, especially in the first 30 days, the effect is the most obvious, in some cases, the data of Φ98 mm gas extraction concentration with hydraulic treatment is slightly higher than Φ120 mm with hydraulic treatment, which may be due to other mining activities or the permeability of coal body itself.

The maximum, minimum and average extraction concentration of Φ120 mm borehole after hydraulic treatment are 97.3%, 80.2% and 88.3%, respectively, and the maximum, minimum and average extraction concentration of Φ98 mm borehole is 94.1%, 79.1% and 84.3%, respectively. The maximum, minimum and average extraction concentrations of Φ120 mm borehole with conventional treatment were 89.7%, 73.9% and 79.6%, respectively, while those of Φ98 mm borehole with conventional treatment were 93.1%, 72.2% and 77.5%, respectively.

The data of Φ120 mm hydraulic flushing treatment, Φ98 mm hydraulic flushing treatment, Φ120 mm conventional treatment and Φ98 mm conventional treatment are recorded as A, B, C and D respectively. The difference of the average extraction purity and the average extraction concentration are shown in Table 2, the lower half represents the difference on average extraction concentration.

Table 2 Compares the difference.

	A	B	C	D
A	/	0.840	1.990	2.770
B	0.040	/	1.150	1.930
C	0.087	0.047	/	0.780
D	0.108	0.068	0.021	/

According to the above results, the average extraction rate and concentration of the hydraulic punching hole are higher than those of the conventional hole, and the extraction rate and concentration of the larger hole are higher than those of the smaller hole.

CONCLUSION

• (1)

  With the increase of extraction time, the radius of gas extraction increases gradually, but the increasing speed decreases gradually, and finally becomes 0. The variation of extraction radius and extraction time accords with the power function.

• (2)

  For Φ98 mm borehole and Φ120 mm borehole, the ratio of hydraulic treatment to gas drainage is 31.3% and 22.7%, respectively. For hydraulic treatment and conventional treatment, the ratio of gas drainage effect by enlarging hole size is 6.3% and 13.8% respectively.

• (3)

  Compared with the four areas without gas extraction, the descending rate of gas pressure was Φ120 mm hydraulic flushing treatment, Φ98 mm hydraulic flushing treatment, Φ120 mm conventional treatment and Φ98 mm conventional treatment. Compared with four different conditions, after 180 days of extraction, the coal gas pressure decreased by 75.3% within reasonable hole spacing.

• (4)

  According to the field results, the average extraction rate and concentration of the hydraulic perforated boreholes are higher than those of the conventional ones, and the extraction rate and concentration of the larger bore holes are higher than those of the smaller bore holes.

AUTHOR CONTRIBUTION

All authors contributed to the study conception and design. Conceived the ideas, software and were performed by Lin Wang. Conceptualization, investigation, methodology, software, visualization and writing – original draft was performed by Ziyao Yang. Funding acquisition, project administration and supervision were performed by Xiangjun Chen. Validation and formal analysis were performed by Shuailong Feng. Resources and writing–review & editing were performed by Lin Wang and Xiangjun Chen. The first draft of the manuscript was written by Ziyao Yang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

ACKNOWLEDGMENTS

This research was supported by the National Natural Science Foundation of China (Nos. 52074105, 52374195), the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (24IRTSTHN013), the Key Scientific Research Projects of Colleges and Universities in Henan Province (No. 22B620002), the Key Science and Technology Project of Henan Province (No. 222102320017), the Fundamental Research Funds for the Universities of Henan Province (NSFRF230103, NSFRF230401, NSFRF230420), the Fundamental Research Funds for the Universities of Henan Province (NSFRF230103, NSFRF230401, and NSFRF230420)， the Safety Discipline “double first- class” Creation Project of Henan Polytechnic University (AQ20230305，AQ20230702).

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

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