Optimization of drilling parameters for coal seam gas extraction considering fluid–solid coupling and field application

Affect gas extraction efficiency to find out the optimum well location parameters, based on the gray correlation analysis of borehole diameter, borehole spacing, and extraction pressure three boreholes parameters that influence efficiency of gas extraction from the design of orthogonal experiment, using COMSOL simulate the effective radius of extraction under different experiments, and the effective radius of extraction for optimizing index quantitative gas extraction efficiency. The results showed that: factors affecting the gas extraction efficiency of the correlation between high and low aperture drilling, borehole spacing, and extraction from extraction negative pressure, it is concluded that the influence parameters of optimal layout parameter values, respectively, borehole diameter 8 cm and 3 m borehole spacing, extraction pressure 50 kPa, combined with the numerical simulation analysis using the optimal layout of gas drilling extraction from about 30 days. The decrease in gas pressure is about 45%, which basically meets the extraction standard, and the decreasing trend of gas pressure is obviously slowed down when the extraction time is longer than 30 days. The engineering experiment is carried out in the 9306 transport lane of a mine in Guizhou Province, and the results are basically consistent with the simulation results, which verify the rationality of the gray correlation analysis method to optimize the drilling parameters, and provide a theoretical basis for the optimization of drilling parameters.

The decision on the efficiency of gas extraction is limited by the influence of several borehole parameters, and the efficiency of gas extraction varies under the influence of different borehole parameters.[9][10] Drilling for gas extraction is a process in which several physical fields are coupled with each other, and when underground mining operations are carried out, there is bound to be an effect on the surrounding coal body.The deformation of the coal body and the fractures in the coal body is the extrinsic cause of gas flow, and the effect of the adsorption capacity of the coal body under mechanical induction can be effectively described by establishing an adsorption-porous elasticity intrinsic model. 11The integrated gas dynamic viscosity, compression coefficient, and Klinkenberg effect can effectively show the seepage effect of gas in the coal seam. 12The intrinsic factor affecting the gas flow in the coal body is the change of permeability in the coal seam.The effective stress sensitivity coefficient is used to characterize the effect of the gas seepage process on the strain of the coal body, and the permeability sensitivity coefficient is higher than the surrounding pressure in the axial seepage process, and the sensitivity coefficient of gas pressure is higher than the permeability in the radial seepage process. 34][15][16] The variation of coal seam permeability is a geological factor that affects the efficiency of gas extraction, therefore, it is necessary to design boreholes with reasonable parameters to effectively coal seam gas concentration.On the basis of orthogonal experiments to analyze the construction efficiency and stability of the boreholes, the sensitivity effects of each influencing factor were derived. 17A multiple linear regression analysis of the borehole parameters was conducted by applying SPSS to the extraction radius as an indicator to derive the degree of influence of each parameter on the effective extraction radius, which can provide some basis for the design of gas parameters. 18,19any scholars at home and abroad have focused on the optimization of borehole parameters in terms of a single parameter of the borehole, but the efficiency of gas extraction from boreholes is the result of the joint influence of several borehole parameters, and different boreholes have different degrees of influence on the extraction efficiency, therefore, it is necessary to statistically analyze several borehole parameters to derive the most important parameters and the optimal arrangement values of each parameter of the borehole.This article quantifies the effect of gas extraction in terms of effective extraction radius, conducts orthogonal experiments on the three main parameters of borehole diameter, borehole spacing, and extraction negative pressure of gas extraction, and uses COMSOL numerical simulation to simulate the effective extraction radius under each experimental condition, and uses gray correlation analysis to derive the most important borehole parameters affecting the effect of gas extraction and the optimal arrangement of each parameter, which provides some theoretical basis for optimizing the design of borehole parameters.

| FLUID-SOLID COUPLING MODEL CONSIDERING MATRIX GAS SEEPAGE
In the process of simulating borehole gas extraction, the gas flow model established should meet the following assumptions: (1) Coal is isotropic, (2) the deformation of coal is small, (3) coal is in the stage of linear elastic deformation, and (4) the temperature of the gas in the flow process is constant, and the seepage law conforms to Darcy's law.
In the process of drilling gas extraction, the total amount of gas in the coal seam remains unchanged, but the gas is constantly extracted by drilling, so the gas concentration in the process of extraction is constantly changing: where ρ g is the gas density, kg/m 3 ; M g is the gas molecular weight, kg/mol; T is the temperature, K; p is the gas pressure, Pa; R is the mole constant of gas, and its value is 8.314 J/(mol K).
In the three-dimensional coordinates, the flow of gas on the unit system follows the mass conservation equation.At a specific time, as shown in Figure 1, the number of molecules left in the system is the number of molecules entering the system minus the number of molecules leaving the system: The above formula can be simplified as Extending the above formula to the threedimensional space in the Cartesian coordinate system: In the assumed model, the loss of mass source is not considered.Therefore, the continuity equation of gas in a coal seam is where t is the time, v e is the flow rate of gas flowing in the coal seam, and φ is the porosity.The gas flow rate v e can be expressed as where u g is the gas dynamic viscosity, g is the acceleration of gravity, and z = (0, 0, 1)  .Xu et al. established a dynamic evolution model of coal porosity based on effective adsorption stress and matrix shrinkage 20 : There is a cubed relationship between permeability and porosity: where φ and φ 0 are the porosity and initial porosity; k and k 0 are the permeability and initial permeability, m 2 ; E is the elastic modulus of coal, MPa; v is Poisson's ratio of coal; α is the limit adsorption capacity, cm 3 /g; ρ c is the density of coal body, kg/m 3 ; V m is the molar volume of gas, which is 22.4 L/mol; b is the gas adsorption constant, MPa −1 ; K is the bulk modulus, The seepage field equation is obtained by substituting formulas (1) and ( 6) into formula (5): In the above hypothesis, coal is completely elastic.Therefore, in the process of gas flow, the expression of coal strain (Liu et al.) 21 can be expressed as where ε ij is the strain tensor; σ ij is the stress tensor, where i and j are the components of i direction and j direction, respectively; α = 1 − K Ks is the Biot coefficient; ε L and p L are Langmuir volume strain constant and pressure constant of gas.
The equilibrium differential equation of coal skeleton deformation containing gas is The geometric equation of the continuous deformation of coal-containing gas is F I G U R E 1 Gas flow diagram on the unit system.
where F i is the physical strength; u i,j and u j,i are the displacement components, m.Combined the equilibrium differential equation ( 11) and the geometric equation ( 12) of continuous deformation of coal body skeleton deformation into Equation (10)  to obtain the equation of stress field affected by coal body deformation in the process of gas extraction 22 : where u i,jj is the tensor form of displacement, the first subscript is the component of displacement in the i direction, the second and third subscripts are the partial derivative form of the displacement component with respect to j and the partial derivative form of u i,j with respect to j. p L is the Langmuir pressure constant, Pa; ε L is the Langmuir volume strain constant.
The coupling term formulas ( 7) and ( 8) are brought into the formula ( 9) to obtain the seepage field equation considering the seepage of the matrix, and the combined formula ( 13) is the fluid-solid coupling model.

| SIMULATION DESIGN
The dynamic change process of borehole gas extraction was simulated by COMSOL multiphysics.It is assumed that coal is the homogeneous isotropic linear elastic body in the process of borehole gas extraction.Therefore, twodimensional simulation can be used bore instead of threedimensional simulation to reduce a lot of calculations.Figure 2 shows the two-dimensional simulation model.The model is a 30 m × 30 m square two-dimensional model.Two boreholes were constructed in the center of the model.Two physical field modules of solid mechanics and Darcy's law were added to the established model to simulate the fluid-solid coupling state during the extraction process.A fixed load of 18 MPa is set at the top of the model, a fixed constraint is set at the bottom of the model, a roller support is set on the left and right sides of the model, and a body load is set on the whole model.The fluid-solid coupling model equation established above is imported into the simulated model, and the initial gas pressure of the coal seam is set to 1.2 MPa.Specific parameter values are shown in Table 1.
It is mentioned in the Method of Predicting Coal and Gas Herniation Hazard Area that the area with residual gas pressure less than 0.74 MPa or residual gas content less than 8 m 3 /t in the coal body can be predicted as no herniation hazard area.On the basis of the geological conditions of the mine under study, this paper takes the residual gas pressure contour of 0.74 MPa as the effective extraction radius and the area within the contour as the effective extraction range, which is effective for studying the It is effective to study the effective extraction range of gas in the cascade borehole of the mine. 23

| DESIGN ORTHOGONAL EXPERIMENT SCHEME
A comprehensive analysis is made on three main factors affecting the efficiency of gas extraction by drilling: borehole diameter, borehole spacing and extraction negative pressure in boreholes, and design orthogonal experiment.The larger the borehole diameter, the higher the gas extraction efficiency, but the large-diameter   17,[25][26][27][28] Design of borehole diameter, spacing, and extraction negative pressure in the borehole three factors each five levels.There are five groups of designed boreholes ranging from 8 cm to 12 dm, with a difference of 0.1 m in each group.The spacing between the designed boreholes is 2-4 m in five groups, and the spacing between the designed boreholes in each group is 0.5 m apart.The extraction negative pressure of extraction in the designed borehole is 20-80 kPa in five groups, and the extraction negative pressure of extraction in each group is 15 kPa different.Each design factor level is shown in Table 2.And a total of 25 orthogonal experiments were designed.The effective extraction range of gas is an important index to judge the efficiency of borehole extraction.Therefore, the effective extraction range of gas extraction for 90 days was used to quantify the gas extraction effect, which was used as the optimization index to evaluate the gas extraction effect, and 25 orthogonal experiments were constructed as shown in Table 3.

| GRAY CORRELATION ANALYSIS
Gray correlation analysis can describe the correlation degree of the system with the change of the factors affecting the system behavior.If there is a strong consistent change trend between the system and the influencing factors, it is considered that the correlation between the system and the influencing factors is high.On the contrary, it is considered that the correlation between the system and the influencing factors is low.In this article, the effective extraction range of gas is the optimization index, the correlation between the three factors of borehole diameter, spacing and extraction negative pressure, and the effective extraction range is studied.By analyzing the correlation degree between the three factors and the optimization index, the optimal optimization value of the optimization index and the factors with the highest correlation degree with the optimization index were determined.

| Normalization processing
To determine the correlation between the optimization index and the influencing factors, the analytical model needs to be de-quantified.The effective extraction range as an optimization index and the borehole aperture, spacing, and extraction negative pressure as an influencing factor are all dimensional data.Therefore, the average value of the data of each index and influencing factors of the analysis model is solved.The data under each index and influencing factors were divided by the obtained average value to obtain the dimensionless data under each index.After obtaining the dimensionless data under each index, it is necessary to make a connection between the optimization index and the influencing factors.By solving the absolute value of the difference between the optimization index and the influencing factors, the relationship between the optimization index and the influencing factors is generated.The experimental data after normalized treatment are shown in Table 4. | 661

| Determine the correlation degree
After normalization, the analysis model needs to further solve the correlation coefficient to obtain the gray correlation degree between the optimization index and the influencing factors, the calculation formula of the gray correlation coefficient is shown in Equation (8).
where ξ(k) is the gray correlation coefficient of the number k influencing factor; Δmin and Δmax are the minimum and maximum values in the analysis model after normalization.ρ is the discrimination coefficient, the value range is 0-1, the value of this article is 0.5.The gray correlation coefficient of each influencing factor in each experiment was calculated through Equation (8).The gray correlation degree of each influencing factor is obtained by means of the mean processing of each influencing factor.Table 5 shows the gray correlation coefficient and gray correlation degree of influencing factors of gas extraction in each group of experiments.
The data in Table 5 show that effective extraction range instead of gas drilling with gas to optimize the extraction efficiency index, borehole diameter, spacing, and extraction pressure three influence factors and optimization index of correlation were 0.803, 0.787, and 0.572, drilling maximum aperture of gray correlation degree, borehole spacing, extraction of gray correlation degree extraction negative pressure to a minimum, and the gray correlation degree of borehole aperture and spacing is basically the same.Therefore, it can be considered that borehole diameter has the greatest impact on gas extraction efficiency, followed by borehole spacing, and the influence degree of borehole spacing on gas extraction efficiency is close to that of borehole aperture, and the extraction negative pressure in the borehole has the least influence on gas extraction efficiency.On the basis of Table 5, the average gray correlation degree of the three influencing parameters at each level is constructed, and the variation trend chart of the gray correlation degree of each level parameter is drawn.The change trend is shown in Figure 3, and the gray correlation degree of each level parameter is shown in Table 6.
According to the data in the table and the change trend in the figure, with the increase of borehole aperture, the gray correlation degree shows a decreasing trend.The peak gray correlation degree is 0.848 at the borehole aperture A1 level, and the minimum gray correlation degree is 0.76 at the A5 level.As for the variation trend of borehole spacing, with the increase of borehole spacing, the gray correlation degree showed a change trend of increasing first and then decreasing.The gray correlation degree at both ends of the curve was the smallest, and the gray correlation degree was 0.701 and | 663 0.706 of borehole spacing B1 and B5 levels, respectively.The variation curve of the gray correlation degree of borehole spacing peaked at the B3 level.The peak gray correlation degree was 0.921 of the B3 level.The variation trend of the gray correlation degree of the extraction negative pressure is similar to that of the borehole spacing, which increases first and then decreases.However, the variation trend of the extraction negative pressure is larger, and the minimum gray correlation degree lies at both ends of the curve, which are 0.411 and 0.41 of the extraction negative pressure C1 and C5 levels, respectively.The peak gray correlation degree of extraction negative pressure extraction is 0.88 of the C3 level, which is about 2.14 times the minimum gray correlation degree.On the basis of the above analysis, it can be concluded from the gray correlation theory that the most influential factor on gas extraction efficiency is borehole aperture, and the gray correlation degree is 0.803, while the extraction negative pressure of gas extraction is the least influential factor.On this basis, the gray correlation degree of five levels in each influencing factor is analyzed, and the maximum gray correlation degree of three influencing factors, namely, borehole aperture, borehole spacing, and extraction negative pressure, is A1, B3, and C3 levels, respectively.It can be concluded that the optimal drilling parameters with gas extraction efficiency as the optimization index are that the borehole diameter is 8 cm, the borehole spacing is 3 m, and the extraction negative pressure is 50 kPa.

| Numerical simulation analysis
Will the optimum drilling parameters are obtained by gray correlation analysis method, the import into the  It can be seen from Figures 4B and 5A that the gas pressure at the measuring point decreases rapidly when the extraction time is short, while the pressure reduction trend is relatively gentle in the later stage of gas extraction.The gas pressure at the measuring point is affected by the superposition of the two boreholes in a short time, and the gas pressure drops rapidly.The gas pressure has reached the extraction standard in about 15 days, indicating that the gas extraction efficiency is high.When the extraction time is 30 days, the gas pressure has decreased by about 45%, and the gas pressure at this time is 0.661 MPa.However, when the extraction time is longer than 30 days, the downward trend of gas pressure obviously slows down.The reason is that the measuring point area is greatly affected by the superposition of two boreholes in

| Engineering practice
The 9# coal seam is mined in a mine in Guizhou Province.The 9# coal seam is near the horizontal coal seam, the buried depth is −302 m, the average thickness of the coal seam is 2.5 m, the thickness is stable, the maximum gas content is 9.2 m 3 /t, the maximum gas pressure in the 9# coal seam is 1.2 MPa, the gas content in the coal seam is 8.13 m 3 /t, and the mine has the danger of coal and gas outburst.The SF6 tracer method was used to detect the effective extraction radius of the cascade borehole, which is a nontoxic, highly diffusible, stable, and naturally occurring gas with very low content, so the SF6 was used to detect the effective extraction radius of the cascade borehole with high accuracy.To detect the effective extraction radius of cascade boreholes at different extraction times, four different sets of cascade boreholes and SF6-injected gas injection boreholes were designed, the distances of the four sets of gas injection boreholes from cascade boreholes were 1, 1.5, 2, and 2.5 m, respectively.After connecting the gas extraction system and the SF6 gas detector, gas extraction can be carried out, and at the same time, the SF6 gas detector is checked daily to see if SF6 gas is detected, the experimental design scheme diagram is shown in Figure 6.Through 90 days of gas extraction and SF6 gas detection, SF6 gas was detected in the four cascade boreholes on 15, 29, 44, and 65 days of gas extraction, respectively.The effective extraction radius of the cascade borehole for extracting gas from the seam is 1, 1.5, 2, and 2.5 m for 19, 36, 55, Figure 7 shows the relationship between the effective radius of gas extraction and extraction time.
Combined with the borehole layout parameters obtained from the above analysis, boreholes are arranged in the 9306 transport lane of the experimental mine.The diagram of the borehole layout is shown in Figure 8.
Three volume fraction change processes are selected to detect gas extraction, and the gas extraction concentration change of the optimized drilling parameter layout scheme is shown in Figure 9.In the early stage of gas extraction, the volume fraction of the three boreholes is 89%, 93%, and 85%, respectively, and the volume fraction is relatively large in the early stage of gas extraction.As can be seen from the gas extraction concentration diagram, the gas volume fraction of the three boreholes decreased to a certain extent after 30 days of extraction, and the gas volume fraction decreased rapidly, which were 39%, 28%, and 33, respectively.After 30 days of extraction, the gas volume fraction decreased significantly.After 90 days of extraction, the gas volume fraction of the three boreholes decreased to less than 20%, and the gas volume fraction was 19%, 17%, and 18%, respectively, which had little change compared with the gas reduction fraction 30 days before extraction.The overall gas concentration variation trend was similar to the simulation results.
To verify the rationality of the layout of the drilling parameters obtained by the gray correlation analysis method, gas inspection boreholes were arranged in the 9306 transportation lane at the same time as the drainage boreholes were arranged.After 90 days of gas extraction, the gas pressure of the coal seam was detected by gas inspection drilling, and it was detected that the maximum gas pressure of the coal seam was 0.52 MPa, which was about 8% different from the simulation result.The optimized drilling parameters arranged by boreholes had  a good gas extraction effect in this mine, which verified the rationality of the optimization of drilling parameters by the gray correlation analysis method.It provides a theoretical basis for drilling parameter optimization design.

| CONCLUSION
(1) Set up 25 groups of the orthogonal experiment of aperture drilling, borehole spacing, and extraction pressure three main factors affecting gas extraction efficiency of correlation are analyzed, and it is concluded that the size of the correlation of aperture drilling, borehole spacing, and extraction from extraction negative pressure, the best optimization parameters for drilling aperture for 8 cm, borehole spacing for 3 m and extraction pressure 50 kPa.
(2) Combined with numerical simulation using the optimized drilling parameters extraction gas basic standard about 30 days, 30 days before the gas extraction efficiency is high, the gas pressure drop of about 45%, the effective extraction gas range is 9.319 m 2 , 30 days after the gas pressure and the effective extraction range change trend obviously slow, eventually will tend to a stable value curve.
(3) The optimized drilling parameters obtained from the gray correlation analysis were experimentally verified in a mine in Guizhou Province.Through the analysis of the change of gas volume fraction of three test boreholes, it is shown that the optimized borehole distribution scheme has high gas extraction efficiency.After 90 days of gas extraction, the gas pressure in the coal seam was detected, and the maximum gas pressure detected was only 8% different from the simulation result, which verified the rationality of the gray correlation analysis method to optimize the drilling parameters.

F
I G U R E 2 Extraction borehole grid model diagram.T A B L E 1 Model parameter values.Parameter Value Elastic modulus of coal E 3.2 GPa Poisson's ratio of coal v 0.3 Coal density ρ c 1340 kg/m 3

T A B L E 2
Specific values of experimental factors.
simulation model, and other parameters in the model of fluid-solid coupling equation is changeless, a measurement point was placed between two boreholes, the numerical simulation group can monitor the changes of stress, strain, gas pressure, and other related parameters of this measurement point.A transient solution study was applied to the model to analyze the variation of gas pressure in the coal seam for 180 days of model gas extraction, using gas pressure less than 0.74 MPa as the effective extraction range.The changes of gas pressure and permeability in coal seams during 15, 30, 60, and 90 days are shown in Figure 4.The changes in gas pressure and effective gas extraction range at measuring points during 180 days of extraction are shown in Figure 4.

F
I G U R E 5 Change curve of gas pressure and effective extraction range at measuring points.(A) Pressure change curve of measuring point and (B) variation curve of effective extraction range.and 81 days, respectively, r = At b .The above data were analyzed by ORIGIN nonlinear regression fitting to obtain the effective extraction radius of gas extraction from this cascade borehole versus extraction time as r = 0.15t 0.63 .Therefore, the effective extraction radius of a 90-day cascade borehole for gas extraction is 2.69 m.

F I G U R E 6
Diagram of effective extraction radius detection scheme.F I G U R E 7 Relationship curve between effective radius of gas extraction and extraction time.

F I G U R E 8
Schematic diagram of borehole arrangement.F I G U R E 9 Gas extraction concentration after drilling parameter optimization.
24 easily affected by stress.24Thestability of largediameter boreholes in coal is poor, especially in plastic zone.Affected by mining, cracks are easy to occur around the borehole, which reduces the sealing of borehole gas extraction, and lead to low efficiency of gas extraction.There is a linear relationship between borehole spacing and gas extraction efficiency, the smaller the borehole spacing, the higher the extraction efficiency, so that the gas extraction can reach the extraction standard in a short time.However, the decrease in borehole spacing means that the number of boreholes increases, which increases the construction cost of boreholes.The larger the borehole spacing is, the smaller the gas extraction area between boreholes is affected by the extraction of nearby boreholes.And it is easy to lead to the occurrence of substandard extraction areas between boreholes.The extraction negative pressure of borehole gas extraction is also closely related to extraction efficiency.The greater the extraction negative pressure, the smaller the pressure difference between gas pressure and extraction negative pressure, the lower the efficiency of gas extraction.On the contrary, the higher the extraction efficiency.Therefore, under the premise of ensuring gas extraction efficiency and construction cost.It is very important to find the optimal arrangement parameters of borehole diameter, borehole spacing, and extraction negative pressure in the borehole. borehole Gray correlation coefficient and gray correlation degree of influencing factors in each group of experiments.
T A B L E 5 Gas pressure and permeability variation.(A)Gaspressurevariationand (B) permeability variation.665theearlystage of extraction, and the gas pressure at the measuring point has decreased obviously.The pressure difference formed with the extraction negative pressure of extraction is greatly reduced, resulting in a certain degree of decline in the drilling extraction efficiency.Therefore, the gas pressure at the measuring point in the late stage of extraction has a slow downward trend, resulting in little change in the overall gas pressure in the late stage of extraction.When the extraction time is 90 days, the gas pressure at the measuring point is 0.563 MPa, and the gas pressure drop is about 53%.The gas pressure at the measuring point is about 0.1 MPa different from that at 30 and 90 days.The permeability range of the area around the 90d borehole is in an increasing trend, and with the increase of the extraction time, the permeability increase range is getting larger and larger.It shows that the area affected by drilling is getting larger and larger.It can be seen from Figure5Bthat the pressure difference between the extraction negative pressure of extraction and the initial gas pressure of the coal seam is large 30 days before the extraction time, and the gas extraction efficiency is high.Therefore, the effective extraction range rises rapidly, and the curve growth trend is close to the linear growth.When the extraction time is 30 days, the effective extraction range reaches 9.391 m 2 .When the extraction time is longer than 30 days, the gas in the area far away from the drilling is less affected by the drilling, and the growth trend of the effective extraction range gradually slows down.The longer the extraction time is, the smaller the growth trend of the effective extraction range will be, and eventually, it will tend to a stable value. |