Fast inversion method for coal seam gas drainage characteristic parameters based on borehole drainage data

Abstract

The present invention discloses a rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data. First, a mathematical model of gas seepage in the coal seam is established, and combined with the characterization relationship between the evolution of gas drainage flow rate and the distribution of gas pressure, a forward gas flow model is built. By determining the physical properties parameters and boundary conditions of the coal seam according to the on-site situation, a forward gas flow function with the initial permeability of the coal seam and the drainage time as independent variables can be obtained; then the on-site drainage data is fitted as the on-site gas drainage flow function; the difference between the gas flow rate obtained from the above forward simulation and the gas flow rate fitted from the on-site data is used as the fitness function; the particle swarm algorithm is used to find the initial permeability of the coal seam and the borehole drainage time corresponding to the minimum value of the fitness; finally, the obtained initial permeability of the coal seam and the borehole drainage time are substituted into the forward gas flow model to calculate characteristic parameters such as the residual gas pressure / content, drainage rate, drainage influence radius, and permeability of the coal seam.

Description

Technical Field

[0001] The invention relates to a method for rapid inversion of coal seam gas extraction characteristic parameters, in particular to a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data, and belongs to the technical field of coal mine gas extraction. Background Art

[0002] As the basis for gas resource utilization and the fundamental measure for coal mine gas disasters, pre-extraction of coal seam gas has always been an indispensable part of coal mining. In the extraction process, the basic parameters of gas extraction are the basic scientific basis for the planning and design of gas extraction systems, the evaluation of gas extraction effects, and the safety and technical management of gas extraction projects. Therefore, how to quickly and accurately obtain gas extraction parameters is of great significance.

[0003] However, the determination of coal seam gas extraction characteristic parameters in the industry is generally complicated, time-consuming and labor-intensive. Take coal seam permeability as an example: There are currently two main methods for measuring coal seam permeability in coal mines in the industry: laboratory measurement and field testing. In the laboratory measurement of coal sample permeability, due to the difficulty in preparing complete coal samples, cracks in coal samples during drilling, and the anisotropic characteristics of coal bodies, the measurement results of coal seam permeability are significantly different from the on-site situation. Therefore, it is difficult for the laboratory to simulate the actual situation and can only conduct qualitative and regular research. When measuring coal seam permeability on-site, the borehole gas radial flow method is currently used in China. This permeability determination method has a good detection effect, but the radial flow method still has disadvantages such as a long measurement cycle and complex parameters to be measured.

[0004] During the coalbed methane extraction operation, the dynamic change characteristics of gas extraction characteristic parameters are directly reflected through production data. Coalbed methane production data is the first-hand data of coal mine construction site, with high authenticity and accuracy. Therefore, the problem of how to quickly and accurately reverse the gas extraction characteristic parameters through production data to provide scientific support for safe and efficient coalbed methane mining has a good development prospect and needs further research.

[0005] Different from the forward derivation used in general research institutes, inferring the process or mechanism of an event based on results or information is called "inversion". Its core idea is to infer the internal source parameters of the research object from observable parameters. At present, some scholars have analyzed the complex variation characteristics of coal seam permeability, established an uncoupled mathematical model of coal seam gas flow under two-dimensional conditions, and used the successive over-relaxation iteration method for solution, and finally realized the inversion of permeability through coal seam gas pressure. However, in the actual construction process, as a characteristic parameter to be measured for gas drainage in coal seams, the coal seam pressure measurement often has problems of complex operation and lag. Some scholars have also established a coupled dimensionless equation for double pores in coal seams, and on this basis, proposed a new inversion method for coal matrix permeability and fracture permeability. The results show that the inversion algorithm based on the fluid-solid coupling control equation has high accuracy. However, this research only involves trial calculation matching and does not involve specific non-linear inversion methods, and the specific application effect is poor.

[0006] Therefore, how to provide a new method, which is based on the three-dimensional model of multi-field coupling in coal seams, takes the characteristic parameters of coal seam gas drainage as the target, and constructs an inversion algorithm for the characteristic parameters of coal seam drainage based on real production data, so as to quickly and accurately obtain the characteristic parameters of coal seam drainage, is one of the research directions in this industry. Summary of the Invention

[0007] In view of the problems existing in the above-mentioned prior art, the present invention provides a rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data, which is based on the three-dimensional model of multi-field coupling in coal seams, takes the characteristic parameters of coal seam gas drainage as the target, and constructs an inversion algorithm for the characteristic parameters of coal seam drainage based on real production data, so as to quickly and accurately obtain the characteristic parameters of coal seam drainage.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is: a rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data, and the specific steps are as follows:

[0009] Step 1: According to the gas seepage theory, first establish a mathematical model of gas seepage in the coal seam. According to this mathematical model, the initial permeability and the relationship between the borehole drainage time and the coal seam gas pressure can be determined. Then, determine the relationship formula between the coal seam gas flow rate and the coal seam gas pressure, and combine this relationship formula with the established mathematical model of gas seepage in the coal seam, so as to establish a forward gas flow model. The coal seam physical property parameters and boundary conditions involved in this forward gas flow model are determined according to the on-site geological conditions. Finally, according to this forward gas flow model, obtain a forward gas flow function with the initial permeability of the coal seam and the drainage time as independent variables;

[0010] Step 2: Collect the on-site gas drainage flow rate through a gas flow sensor, and fit the obtained drainage data to form a continuous function, which is the fitted on-site gas drainage flow function;

[0011] Step 3: Take the difference function D(k0,t) between the forward gas flow rate function obtained in Step 1 and the fitted on-site gas drainage flow rate function obtained in Step 2 as the fitness function, and aim at the minimum value of the fitness function.

[0012] Step 4: Use the particle swarm optimization algorithm to find the corresponding initial coal seam permeability and borehole drainage time when the minimum value of the fitness function in Step 3 is achieved.

[0013] Step 5: Substitute the initial coal seam permeability and borehole drainage time obtained in Step 4 into the gas flow rate forward model established in Step 1, and finally calculate and determine the gas drainage characteristic parameters of the coal seam according to this model.

[0014] Further, the specific content of Step 1 is as follows:

[0015] A): According to the gas seepage theory, establish a three-dimensional fluid-solid coupling mathematical model of gas seepage as shown in Equation (1):

[0016]

[0017] In the formula, G represents the shear modulus of coal, in MPa, G = E / 2(1 + v); K and E are the bulk modulus and Young's modulus of coal, in MPa, K = E / 3(1 - 2v); v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α = 1 - K / K S ; ε s is the adsorption-induced volume strain of coal; ε L is the Langmuir volume strain constant; S = ε v +(P / K s ) - ε s , S0 = (p0 / K s ) - ε L p0 / (p0 + p L ); p0 represents the initial coal seam pressure; p represents the coal seam gas pressure; φ0 represents the initial porosity of the coal seam; φ represents the porosity of the coal seam, k represents the coal seam permeability, k0 represents the initial coal seam permeability;

[0018] B): Solving Equation (1) can obtain the gas pressure distribution at any time under the initial coal seam permeability k0, and based on this, obtain the gas content m per unit volume of coal in the coal seam at this time, as shown in Equation (2):

[0019]

[0020] Among them, ρ a is the gas density under standard conditions, in kg / m 3; ρ c is the coal density, kg / m 3 ; V L is the Langmuir volume constant, m 3 / kg; P L represents the Langmuir pressure constant, MPa;

[0021] Integrating the gas volume m in unit volume of coal at time t of gas extraction with respect to the coal volume can obtain the gas content M in any volume of coal body, t as shown in Equation (3): t as follows:

[0022] M t = ∫∫∫ V m t dx dy dz (3)

[0023] In the formula: M t is the gas content in the coal seam at time t, kg.

[0024] C): The gas extraction flow rate at any time t can be expressed as:

[0025]

[0026] In the formula, Q t is the gas extraction flow rate at time t, m 3 / s;

[0027] From Equations (1) to (4), it can be obtained that the gas extraction flow rate Q is a function of the initial permeability k0 and the extraction time t, that is

[0028] Q = Q(k0, t) (5)

[0029] Through steps A)-C), the relationship between the gas extraction flow rate, the initial permeability of the coal seam, and the borehole extraction time can be established, that is, the forward gas flow model. In the forward gas flow model, the borehole gas flow rate at that time can be obtained by arbitrarily specifying the initial permeability k0 of the coal seam and the extraction time t.

[0030] Furthermore, the specific form of fitting the on-site gas extraction flow rate function in step two is:

[0031]

[0032] In the formula, t represents the extraction time, d; t0 represents the extraction time of the borehole when the gas flow rate is first recorded, d; Q R is the fitted on-site gas extraction flow rate, m 3 / min; a and b represent the function coefficients.

[0033] Furthermore, the specific form of the difference function D(k0, t) in step three is:

[0034]

[0035] In the formula, the subscript i = 1, 2... n represents the monitoring data time points;

[0036] In the above formula, the smaller the value of D(k0, t), the closer the initial permeability k0 of the coal seam and the drainage time t obtained by inversion are to the actual values. Therefore, the goal is to obtain the minimum value of this function.

[0037] Furthermore, the specific process of the fourth step is as follows:

[0038] ① Preset the parameters of the particle swarm algorithm: Set the total number of individuals N included in the population in the algorithm, the maximum number of iterations ger, the maximum speed V of particle movement max and the minimum speed V min , the individual learning factor c1, the social learning factor c2, the inertia factor w, and the truncation error C;

[0039] ② Determine the boundaries of the inversion interval, and randomly generate N particles within the inversion interval. The initial position Xi of the i-th particle and the particle change interval are shown in formulas (7) and (8) respectively:

[0040] X i =(k 0i t) (7)

[0041] U ≤ X i ≤ T (8)

[0042] where i = (1, 2, 3... N), and U and T represent the lower and upper limits of the particle permeability respectively;

[0043] Calculate the fitness of the current particle position according to the fitness function D(k0, t). After comparing the fitness of each particle, record the population historical best position Gb_X and the population historical best fitness Gb at this time, and initialize the particle swarm historical best position Pb_X = X;

[0044] ③ Start iteration and update the particle swarm position. The position update formula of the i-th particle is shown in formula (9):

[0045]

[0046] where L is the current number of iterations, represents the particle movement speed, and is expressed by formula (10)

[0047]

[0048] Among them, the particle inertia factor w represents the tendency of the particle to move in its own inherent motion direction; the individual learning factor c1 and the social learning factor c2 endow the particle with individual memory attributes and social attributes respectively, representing the tendency of the particle to move closer to its own historical best position and the historical best position of the population; r1 and r2 are two independent random parameters, making the movement of the particle more random and increasing the possibility of global optimization;

[0049] To prevent the particle from striding too large and skipping the optimal position during the optimization process, the velocity v of the particle i is restricted as follows:

[0050] V min <= v i <= V max (11)

[0051] Among them, V min , V max represent the lower and upper limits of the particle velocity respectively, that is, the change range of the permeability during each iteration process;

[0052] ④ Compare the matching degree of the gas flow rate under the initial permeability of the current coal seam and the drainage time, and update Gb_X, Gb, Pb_X;

[0053] ⑤ Judge whether the termination condition is satisfied. If it is satisfied, jump out of the iteration and output the initial permeability of the coal seam and the borehole drainage time corresponding to the minimum value of the fitness function. Otherwise, return to step ③ to continue the iterative calculation.

[0054] Furthermore, the gas drainage characteristic parameters of the coal seam in step ⑤ include the coal seam gas pressure p, the remaining coal seam gas content M, the gas drainage rate η, the coal seam permeability k, and the effective drainage radius r; among them, the coal seam gas pressure p, the remaining coal seam gas content M, and the coal seam permeability k are obtained by solving the gas flow forward model, the gas drainage rate η is obtained by the ratio of the remaining gas volume M in the coal seam to the initial gas content M0 of the coal seam, and the effective drainage radius r is set as the area where the residual coal seam gas pressure is lower than 0.74 MPa.

[0055] Furthermore, the particle inertia factor w is a variable that changes with the number of iterations, as shown in Equation (12):

[0056] w = w_1 - (w_1 - w_2) * L / ger (12)

[0057] Among them, w_1 and w_2 represent the upper and lower limits of the inertia coefficient respectively, L is the current number of iterations, and ger is the maximum number of iterations; in the early stage of iteration, the inertia factor w is larger, and the particle moves in the variable space at a larger flight speed, making it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, greatly improving the convergence of the algorithm.

[0058] Further, the termination condition in step ⑤ is: the loop reaches the maximum number of iterations, or the change in the fitness function D(k0,t) is less than the set truncation error C during three consecutive iterations.

[0059] Compared with the prior art, the present invention first establishes a mathematical model of gas seepage in the coal seam, and combines the parameter characterization relationship between the evolution characteristics of gas extraction flow rate and the distribution characteristics of gas pressure to build a forward model of gas flow rate. The coal seam physical property parameters and boundary conditions involved in the forward model of gas flow rate are determined according to the on-site geological conditions and obtained through the forward model. Then, the on-site gas extraction data is collected and fitted into a continuous function as the on-site gas extraction flow rate function. The difference between the above forward gas flow rate function and the on-site fitted gas extraction flow rate function is formed, and the difference function is used as the fitness function. The particle swarm optimization algorithm is used to find the initial coal seam permeability and borehole extraction time corresponding to the minimum value of the fitness function. Finally, the obtained initial coal seam permeability and borehole extraction time are substituted into the above forward model of gas flow rate to calculate and determine the gas extraction characteristic parameters of the coal seam. Therefore, the present invention can be based on the multi-field coupling three-dimensional model of the coal seam, take the gas extraction characteristic parameters of the coal seam as the target, build an inversion algorithm for the gas extraction characteristic parameters of the coal seam based on real production data, and thus quickly and accurately obtain the gas extraction characteristic parameters of the coal seam. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the overall inversion flowchart of the present invention;

[0061] Figure 2 is the flowchart of using the particle swarm optimization algorithm to find the minimum value of the fitness function in the present invention;

[0062] Figure 3 is the diagram of the coal seam geometric parameters and boundary conditions in the embodiment of the present invention;

[0063] Figure 4 is the diagram of the inversion results of the initial coal seam permeability and extraction time in the embodiment of the present invention;

[0064] Figure 5 is the diagram of the gas pressure distribution in the coal seam when extracting gas for 94 days in the embodiment of the present invention;

[0065] Figure 6 is the diagram of the effective extraction radius when extracting gas for 94 days in the embodiment of the present invention;

[0066] In the figure, the blank area represents the influence range of the effective radius;

[0067] Figure 7 is the schematic diagram of the remaining gas distribution in the coal seam when extracting gas for 94 days in the embodiment of the present invention;

[0068] Figure 8 is the diagram of the coal seam permeability distribution when extracting gas for 94 days in the embodiment of the present invention. Detailed implementation mode

[0069] The present invention will be further described below.

[0070] As Figure 1 shown, the specific steps of the present invention are as follows:

[0071] Step 1: Establish a forward model of gas flow rate:

[0072] A): According to the gas seepage theory, establish a three-dimensional fluid-solid coupling mathematical model of gas seepage as shown in Equation (1):

[0073]

[0074] In the formula, G represents the shear modulus of coal, MPa, G = E / 2(1 + v); K and E are the bulk modulus and Young's modulus of coal, MPa, K = E / 3(1 - 2v); v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α = 1 - K / K S ; ε s is the adsorption-induced volumetric strain of coal; ε L is the Langmuir volumetric strain constant; S = ε v +(P / K s ) - ε s , S0 = (p0 / K s ) - ε L p0 / (p0 + p L ); p0 represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ0 represents the initial porosity of the coal seam; φ represents the porosity of the coal seam, k represents the permeability of the coal seam, k0 represents the initial permeability of the coal seam;

[0075] B): Solving Equation (1) can obtain the gas pressure distribution at any time under the initial permeability k0 of the coal seam, and based on this, obtain the gas content m per unit volume of coal in the coal seam at this time, as shown in Equation (2):

[0076]

[0077] Among them, ρ a is the gas density under standard conditions, kg / m 3 ; ρ c is the coal density, kg / m 3 ; V L is the Langmuir volume constant, m 3 / kg; P L represents the Langmuir pressure constant, MPa;

[0078] The gas volume m per unit volume of coal at the extraction time t|t Integrating with respect to the volume of coal can obtain the gas content M of any volume of coal body| t as shown in Equation (3):

[0079] M| t = ∫∫∫ V m| t dx dy dz (3)

[0080] In the formula: M| t is the gas content in the coal seam at time t, in kg.

[0081] C): The gas drainage flow rate at any time t can be expressed as:

[0082]

[0083] In the formula, Q| t is the gas drainage flow rate at time t, in m 3 / s;

[0084] From Equations (1) to (4), it can be obtained that the gas drainage flow rate Q is a function of the initial permeability k0 and the drainage time t, that is

[0085] Q = Q(k0, t) (5)

[0086] Through steps A)-C), the relationship between the gas drainage flow rate, the initial permeability of the coal seam, and the borehole drainage time can be established, that is, the forward gas flow model. In the forward gas flow model, the borehole gas flow rate at that moment can be obtained by arbitrarily specifying the initial permeability k0 of the coal seam and the drainage time t.

[0087] Step 2: Collect the on-site gas drainage flow rate through a gas flow sensor, and fit the obtained drainage data to form a continuous function. This continuous function is the fitted on-site gas drainage flow rate function, where the fitted on-site gas drainage flow rate function is specifically:

[0088]

[0089] In the formula, t represents the drainage time, in d; t0 represents the drainage time of the borehole when the gas flow rate is first recorded, in d; Q R is the fitted on-site gas drainage flow rate, in m 3 / min; a and b represent function coefficients.

[0090] Step 3: Take the difference function D(k0, t) between the forward gas flow function obtained in Step 1 and the fitted on-site gas drainage flow rate function obtained in Step 2 as the fitness function, where the difference function D(k0, t) is specifically:

[0091]

[0092] In the formula, the subscript i = 1, 2... n represents the monitoring data time points;

[0093] In the above formula, the smaller the value of D(k0, t), the closer the inversed initial coal seam permeability k0 and drainage time t are to the actual values. Therefore, the goal is to obtain the minimum value of this function.

[0094] Step 4: Use the particle swarm optimization algorithm to find the corresponding initial coal seam permeability and borehole drainage time when the fitness function in Step 3 reaches the minimum value. The specific process is as follows:

[0095] ① Preset the parameters of the particle swarm optimization algorithm: Set the total number of individuals N in the population in the algorithm, the maximum number of iterations ger, the maximum velocity V of particle movement max and the minimum velocity V min , the individual learning factor c1, the social learning factor c2, the inertia factor w, and the truncation error C;

[0096] ② Determine the boundaries of the inversion interval, and randomly generate N particles within the inversion interval. The initial position Xi of the i-th particle and the particle change interval are shown in Equations (7) and (8) respectively:

[0097] X i =(k 0i t) (7)

[0098] U ≤ X i ≤ T (8)

[0099] where i = (1, 2, 3... N), and U and T represent the lower and upper limits of the particle permeability respectively;

[0100] Calculate the fitness of the current particle position according to the fitness function D(k0, t). After comparing the fitness of each particle, record the population historical best position Gb_X and the current population historical best fitness Gb, and initialize the particle swarm historical best position Pb_X = X;

[0101] ③ Start iteration and update the particle swarm position. The position update formula of the i-th particle is shown in Equation (9):

[0102]

[0103] where L is the current number of iterations, represents the particle movement speed, which is expressed by Equation (10)

[0104]

[0105] Among them, the particle inertia factor w represents the tendency of the particle to move in its own inherent motion direction; the individual learning factor c1 and the social learning factor c2 endow the particle with individual memory attributes and social attributes respectively, representing the tendency of the particle to approach its own historical best position and the historical best position of the population; r1 and r2 are two independent random parameters, making the movement of the particle more random and increasing the possibility of global optimization;

[0106] The above particle swarm algorithm does not have a mutation process and is prone to falling into a local optimal solution and finally unable to converge to the global optimal position. Therefore, the particle inertia factor w in the velocity formula is changed from a fixed value to a variable that changes with the number of iterations, that is, the particle inertia factor w is a variable that changes with the number of iterations, as shown in Equation (11):

[0107] w = w_1 - (w_1 - w_2) * L / ger (11)

[0108] Among them, w_1 and w_2 represent the upper and lower limits of the inertia coefficient respectively, L is the current number of iterations, and ger is the maximum number of iterations; in the early stage of iteration, the inertia factor w is larger, and the particle moves in the variable space at a larger flight speed, making it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, greatly improving the convergence of the algorithm.

[0109] To avoid the particle's stride being too large and skipping the optimal position during the optimization process, the velocity v of the particle i is restricted:

[0110] V min <= v i <= V max (12)

[0111] Among them, V min , V max represent the lower and upper limits of the particle velocity respectively, that is, the change range of the permeability during each iteration process;

[0112] ④ Compare the gas flow matching degree at the initial permeability and drainage time of the current coal seam and update Gb_X, Gb, Pb_X;

[0113] ⑤ Judge whether the termination condition is satisfied. The termination condition is: the loop reaches the maximum number of iterations, or the change of the fitness function D(k0, t) is less than the set truncation error C during three consecutive iterations; if satisfied, jump out of the iteration and output the initial permeability of the coal seam and the borehole drainage time corresponding to the minimum value of the fitness function, otherwise return to step ③ to continue the iterative calculation.

[0114] Step 5: Substitute the initial coal seam permeability and borehole drainage time obtained in Step 4 into the gas flow forward model established in Step 1, and finally calculate and determine the gas drainage characteristic parameters of the coal seam according to this model. The gas drainage characteristic parameters of the coal seam include coal seam gas pressure p, remaining coal seam gas content M, gas drainage rate η, coal seam permeability k, and effective drainage radius r. Among them, the coal seam gas pressure p, remaining coal seam gas content M, and coal seam permeability k are obtained by solving the gas flow forward model, the gas drainage rate η is obtained from the ratio of the remaining gas volume M in the coal seam to the initial gas content M0 of the coal seam, and the effective drainage radius r is set as the area where the residual coal seam gas pressure is lower than 0.74 MPa.

[0115] Experimental verification shows that:

[0116] To verify the specific process of obtaining the gas drainage characteristic parameters of the coal seam by inversion using the present invention, an actual coal mine was used for simulation verification: The No. 1 borehole in Group 125 of the 8.9 - 20230 fully - mechanized gateway entry of the 10th Coal Mine of Pingdingshan Coal Group was selected as the research object, and the present invention was used for inversion with the initial coal seam permeability and the borehole drainage time when the borehole flow rate was first recorded as the inversion target. Since the gas flow forward model in the present invention consists of a series of partial differential equations, it can be solved with the help of the COMSOL with MATLAB platform. Determine the coal seam geometric parameters and boundary conditions as Figure 3 shown, and the physical property parameters are shown in Table 1:

[0117] Table 1 Coal seam physical property parameter table

[0118]

[0119] The initial conditions for gas drainage simulation are:

[0120] At t = 0, the initial gas pressure in the coal and rock mass is 2 MPa, and the boundary displacement is 0, that is:

[0121]

[0122] In the formula, p| t＝0 and u| t＝0 respectively represent the gas pressure (MPa) and displacement value (m) in the model at the initial moment.

[0123] The boundary conditions for gas drainage simulation are:

[0124] ① Seepage boundary conditions: Set no - flow boundary conditions on the outer surface boundary of the model and the wall surface of the borehole sealing section, and set a constant - pressure boundary according to the drainage negative pressure for the drainage section, that is

[0125]

[0126] In the formula, n·v| 外边界 and n·v|钻孔封孔段 respectively represent the gas flow rate per unit area (kg / (s·m 2 )) passing through the outer boundary of the model and the grouted section of the borehole; p| 钻孔抽采段 represents the boundary pressure of the borehole drainage section, in MPa.

[0127] ② Coal body deformation boundary conditions: According to the coal seam burial depth, a uniform load of 8 MPa is applied on the upper surface to simulate the self-weight of the overlying coal and rock mass. Fixed constraint boundaries are set on the bottom surface and the grouted section of the borehole, a normal constraint boundary is set on the side boundary, and a free deformation boundary is set on the drainage section, that is:

[0128]

[0129] In the formula, -σ ij n j | 上表面 represents the load (MPa) on the upper surface of the model; u| 底面 and u| 钻孔封孔段 respectively represent the deformation displacements (m) of the bottom surface of the model and the grouted section of the borehole; u·n| 侧边界 represents the normal displacement (m) of the side surface of the model.

[0130] The on-site gas drainage flow rate data is fitted in the form shown in Equation (5), and the result is:

[0131]

[0132] The initial data of the particle swarm algorithm parameters are set by the actual geological parameters. The range of the initial coal seam permeability k0 is (1×10 -20 , 1×10 -16 ), and the velocity limit interval is taken as 10% of the initial permeability range, that is, (-5×10 -18 , 5×10 -18 ); the number of particles N is set to 50, the maximum number of iterations ger is set to 100, the truncation error is 0.001, the individual learning factor c1 is taken as 2, and the social learning factor c2 is taken as 2.

[0133] The final inversion result is as shown in Figures 4 to 8 ; among them Figure 4 is the inversion result diagram of the initial coal seam permeability and the borehole drainage time. It can be seen from the figure that the inverted initial permeability is 3.79×10 -17 m 2 , and the borehole drainage time is 94 days. Further, based on the inverted initial coal seam permeability and borehole drainage time, the evolution of the coal seam drainage parameters is deduced. According to the gas flow forward model, the gas pressure distribution in the coal seam at the 94th day of drainage is as shown in Figure 5 , and at this time, the effective gas pressure radius in the coal seam and the distribution of the remaining gas content in the coal seam are respectively as shown in Figure 6 andFigure 7 As shown, integrating the total coal volume gives the remaining gas volume in the coal seam at this time as 3321.8 kg, and the gas extraction rate is 61.6%. Figure 8 It is the permeability distribution map in the coal seam on the 94th day of extraction. Then, by comparing the coal seam extraction characteristic parameter data obtained by the above inversion with the actual data of this coal mine, it is concluded that the inversion method of the present invention can quickly and accurately obtain the coal seam extraction characteristic parameters.

[0134] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data, characterized in that, The specific steps are as follows: Step 1: According to the gas seepage theory, first establish a mathematical model of gas seepage in the coal seam. Based on this mathematical model, the initial permeability of the coal seam and the relationship between the borehole drainage time and the gas pressure in the coal seam can be determined. Then, combined with the parameter characterization relationship between the evolution characteristics of the gas drainage flow rate and the gas pressure distribution characteristics, a forward gas flow model is established. The physical properties parameters of the coal seam and the boundary conditions involved in this forward gas flow model are determined according to the on-site geological conditions. Finally, according to this forward gas flow model, the forward gas flow function of the coal seam is obtained; Step 2: Collect the on-site gas drainage flow rate through a gas flow sensor, and fit the obtained drainage data to form a continuous function, which is the fitted on-site gas drainage flow function; Step 3: Take the difference function D(k0,t) between the forward gas flow function obtained in Step 1 and the fitted on-site gas drainage flow function obtained in Step 2 as the fitness function, and aim at the minimum value of the fitness function; Step 4: Use the particle swarm algorithm to find the initial permeability of the coal seam and the borehole drainage time corresponding to the minimum value of the fitness function in Step 3; Step 5: Substitute the initial permeability of the coal seam and the borehole drainage time obtained in Step 4 into the forward gas flow model established in Step 1, and finally calculate and determine the gas drainage characteristic parameters of the coal seam according to this model.

2. The rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data according to claim 1, wherein The specific content of Step 1 is as follows: A): According to the gas seepage theory, establish a three-dimensional fluid-solid coupling mathematical model of gas seepage as shown in Equation (1): In the formula, G represents the shear modulus of coal, in MPa, G = E / 2(1 + v); K and E are the bulk modulus and Young's modulus of coal respectively, in MPa, K = E / 3(1 - 2v); v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α = 1 - K / K S ; ε s is the adsorption-induced volumetric strain of coal; ε L is the Langmuir volumetric strain constant; S = ε v +(P / K s ) - ε s , S0 = (p0 / K s ) - ε L p0 / (p0 + p L ); p0 represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ0 represents the initial porosity of the coal seam; φ represents the porosity of the coal seam, k represents the permeability of the coal seam, k0 represents the initial permeability of the coal seam; B): Solving Equation (1) can obtain the gas pressure distribution at any time under the initial permeability k0 of the coal seam, and based on this, the gas content m per unit volume of coal in the coal seam at this time can be obtained, as shown in Equation (2): where ρ a is the gas density under standard conditions, kg / m 3 ; ρ c is the coal density, kg / m 3 ; V L is the Langmuir volume constant, m 3 / kg; P L represents the Langmuir pressure constant, MPa; The gas quantity m in unit volume of coal at the extraction time t| t Integrating with respect to the coal volume can obtain the gas content M of any volume of coal body| t , as shown in Equation (3): M| t = ∫∫∫ V m| t dx dy dz (3) Where: M| t is the gas content in the coal seam at time t, kg; C): The gas drainage flow rate at any time t can be expressed as: Wherein, Q| t is the gas drainage flow rate at time t, m 3 / s; From Equation (1) to Equation (4), it can be obtained that the gas drainage flow rate Q is a function of the initial permeability k0 and the drainage time t, that is Q = Q(k0,t) (5) Through Steps A)-C), the relationship between the drained gas flow rate and the initial permeability of the coal seam and the borehole drainage time can be established, that is, the forward gas flow model. In the forward gas flow model, the borehole gas flow rate at this time can be obtained by arbitrarily specifying the initial permeability k0 of the coal seam and the drainage time t.

3. The rapid inversion method for coal seam gas drainage characteristic parameters based on borehole drainage data according to claim 1, characterized in that The specific content of the fitted on-site gas drainage flow function in Step 2 is as follows: In the formula, t represents the drainage time, d; $t_0$ represents the extraction time of the borehole when the gas flow rate is first recorded, d; $Q$ R is for fitting the on-site gas extraction flow rate, m 3 / min; a and b represent function coefficients.

4. The rapid inversion method for coal seam gas drainage characteristic parameters based on borehole drainage data according to claim 1, characterized in that The specific content of the difference function D(k0,t) in Step 3 is as follows: In the formula, the subscript i = 1, 2... n represents the monitored data time points; In the above formula, the smaller the value of D(k0,t), the closer the inversely obtained initial permeability k0 of the coal seam and the drainage time t are to the actual values. Therefore, the minimum value of this function is taken as the goal.

5. The rapid inversion method for coal seam gas extraction characteristic parameters based on borehole drainage data according to claim 1, wherein The specific process of Step 4 is as follows: ① Parameters of the preset particle swarm optimization algorithm: Set the total number of individuals N in the population in the algorithm, the maximum number of iterations ger, the maximum velocity V of particle movement max and the minimum velocity V min , the individual learning factor c1, the social learning factor c2, the inertia factor w, the truncation error C; ② Determine the boundaries of the inversion interval, and randomly generate N particles within the inversion interval. The initial position Xi of the i-th particle and the particle change interval are shown in Equation (7) and Equation (8) respectively: X i = (k 0i t) (7) U ≤ X i ≤ T (8) Among them, i = (1, 2, 3... N), U, and T respectively represent the lower and upper limits of the permeability of the particles; Calculate the fitness of the current particle position according to the fitness function D(k0,t), record the best position Gb_X in the population history and the best fitness Gb in the population at this time after comparing the fitness of each particle, and initialize the best position Pb_X in the particle swarm history = X; ③ Start iteration, update the particle swarm position, and the position update formula of the i-th particle is shown in Equation (9): where L is the current iteration number, represents the particle movement speed, which is expressed by Equation (10) Among them, the particle inertia factor w represents the tendency of the particle to move in its own inherent motion direction; the individual learning factor c1 and the social learning factor c2 endow the particle with individual memory attributes and social attributes respectively, representing the tendency of the particle to move closer to its own historical best position and the best position in the population history; r1 and r2 are two independent random parameters, making the movement of the particle more random and increasing the possibility of global optimization; To avoid the particle's step size being too large during the optimization process and skipping the optimal position, the velocity v of the particle is restricted: i ​ V min <= v i <= V max (11) Among them, V min , V max respectively represent the lower and upper limits of the particle velocity, that is, the change range of the permeability in each iteration process; ④ Compare the matching degree of gas flow under the current initial coal seam permeability and borehole drainage time and update Gb_X, Gb, Pb_X; ⑤ Judge whether the termination condition is satisfied. If it is satisfied, jump out of the iteration and output the initial coal seam permeability and borehole drainage time corresponding to the minimum value of the fitness function. Otherwise, return to step ③ to continue the iterative calculation.

6. The rapid inversion method for coal seam gas drainage characteristic parameters based on borehole drainage data according to claim 1, wherein The gas drainage characteristic parameters of the coal seam in step ⑤ include coal seam gas pressure p, remaining coal seam gas content M, gas drainage rate η, coal seam permeability k, and effective drainage radius r; among them, the coal seam gas pressure p, remaining coal seam gas content M, and coal seam permeability k are obtained by solving the forward gas flow model, the gas drainage rate η is obtained by the ratio of the remaining gas volume M in the coal seam to the initial gas content M0 in the coal seam, and the effective drainage radius r is set as the area where the residual coal seam gas pressure is lower than 0.74 MPa.

7. The rapid inversion method for characteristic parameters of coal seam gas drainage based on borehole drainage data according to claim 4, wherein The particle inertia factor w is a variable that changes with the number of iterations, as shown in Equation (12): w = w_1 - (w_1 - w_2) * L / ger (12) Among them, w_1 and w_2 represent the upper and lower limits of the inertia coefficient respectively, L is the current number of iterations, and ger is the maximum number of iterations; in the early stage of iteration, the inertia factor w is larger, and the particle moves in the variable space at a larger flight speed, making it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, greatly improving the convergence of the algorithm.

8. The rapid inversion method for coal seam gas drainage characteristic parameters based on borehole drainage data according to claim 4, characterized in that The termination condition in step ⑤ is: the loop reaches the maximum number of iterations, or the change in the fitness function D(k0,t) is less than the set truncation error C in three consecutive iterations.

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