Coal seam gas pressure while-drilling flow inversion method based on conjugate gradient method

Abstract

The invention discloses a coal seam gas pressure while-drilling flow inversion method based on a conjugate gradient method. The method comprises the steps that firstly, a while-drilling gas flow mathematical model is constructed, and model parameters are determined; screening the field measured value of the gas flow while drilling; carrying out finite difference method forward modeling on the model, and calculating the drilling gas flow; constructing an objective function and calculating the gradient of the objective function by combining the calculated gas flow and the field measured value of the gas flow; and finally, on the basis of a regularization nonlinear conjugate gradient method, continuous iteration processing is carried out on the target function in combination with the search direction and the search step length, and an original coal seam gas pressure value is obtained through inversion output of the finally-iterated target function. The method is simple in implementation step, the inversion result is determined through test verification and has good accuracy and reliability, the pressure measuring time is shortened, the pressure measuring cost is reduced, the coal seam gas pressure measuring accuracy is improved, and the actual requirement of a coal mine for rapidly and accurately measuring coal seam gas parameters is met.

Description

Technical Field

[0001] The present invention relates to a method for measuring coal seam gas pressure, specifically a method for inverse calculation of coal seam gas pressure with drilling flow rate based on the conjugate gradient method, belonging to the technical field of coal mine gas parameter measurement. Background Technique

[0002] Coal seam gas pressure is the driving force for gas emission and outburst, and is the preferred index for predicting, evaluating the outburst risk of coal seams, and testing the effect of regional outburst elimination measures. At present, the methods for measuring coal seam gas pressure in China can be classified into two categories: direct method and indirect method. Although the direct method is accurate in measurement, it requires three steps: drilling, hole sealing, and pressure measurement, and has the disadvantages of long cycle, poor hole sealing quality, and complex operation process; the indirect method mainly inversely calculates the coal seam gas pressure through the coal seam gas content. Although the measurement is relatively fast, due to the fact that the measurement of coal seam gas content involves multiple links, this method has the disadvantages of low accuracy and poor applicability. At present, there are also some existing technologies. For example, the Chinese invention patent with the publication number CN109403865A and the name "Method and Device for Measuring Coal Seam Gas Parameters While Drilling" solves the problems of hard coal seam drilling blockage and inconvenient data transmission through an innovative drill bit structure, diversion groove design, and remote data transmission function; another example is the Chinese invention patent with the publication number CN113266347A and the name "A Near-Bit Comprehensive Measuring Device and Method for Coal Seam Gas Parameters While Drilling", whose solution realizes the on-the-fly measurement of near-bit gas content and gas emission volume, greatly improving the measurement efficiency of gas parameters; however, the measurement of gas emission volume in the above two solutions requires measurement after stopping drilling and sealing the hole, and the inverse calculation of coal seam gas pressure cannot be realized. The Chinese invention patent with the publication number CN113605880A and the name "A Device for Measuring Multi-Point and Precise Coal Seam Gas Pressure and Its Working Method" can measure the multi-point gas pressure in the coal seam at one time, solve the problem of gas leakage during the measurement of coal seam gas pressure, and improve the accuracy of the measurement result of coal seam gas pressure, but the gas pressure measurement still relies on sealed hole measurement.

[0003] Therefore, aiming at the deficiencies of the existing pressure measurement technologies, how to provide a new method that can realize the fast and accurate measurement of coal seam gas pressure without traditional sealed hole pressure measurement, and the whole process is simple to operate, is the research direction required by the present invention. Summary of the Invention

[0004] Aiming at the problems existing in the above-mentioned existing technologies, the present invention provides a method for inverse calculation of coal seam gas pressure with drilling flow rate based on the conjugate gradient method, which can realize the fast and accurate measurement of coal seam gas pressure without traditional sealed hole pressure measurement, and the whole process is simple to operate.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows: A method for inverse calculation of coal seam gas pressure with drilling flow based on the conjugate gradient method, and the specific steps are as follows:

[0006] ①Construct a mathematical model of gas flow in the borehole;

[0007] ②Determine the model parameters of the mathematical model of gas flow in the borehole in step ①;

[0008] ③Obtain the on-site gas flow data while drilling, and after screening, obtain the on-site measured value of the gas flow while drilling for inverse calculation;

[0009] ④Perform forward calculation on the model in step ① by the finite difference method to calculate the gas flow in the borehole; combine the calculated gas flow in the borehole and the on-site measured value of the gas flow while drilling after screening in step ③ to construct an objective function;

[0010] ⑤Construct a sensitivity matrix, and calculate the gradient of the objective function in combination with the objective function constructed in step ④;

[0011] ⑥Set the maximum number of iterations and the tolerance threshold σ. If the current gradient of the objective function is less than σ, then use the current objective function to output the original gas pressure value of the coal seam; otherwise, first determine the search direction and search step size of the current objective function; then, based on the regularized non-linear conjugate gradient method, combine the search direction and search step size to construct the objective function for the next iteration on the basis of the objective function, and repeat steps ⑤ and ⑥ until the gradient of the objective function in a certain iteration is less than the tolerance threshold σ or the iteration reaches the maximum number of iterations, stop the iteration and output the original gas pressure value of the coal seam.

[0012] Further, the mathematical model of gas flow in the borehole in step ① is as follows:

[0013]

[0014] In the formula, P represents the square of the original gas pressure of the coal seam, that is, P = p 0 2 , MPa 2 ; λ represents the coal seam gas permeability coefficient, m 2 / (MPa 2 ·s); a and b are the Langmuir constants of coal adsorbed gas, and the units are m 3 / t and MPa -1 ; φ represents the porosity of coal, %; r represents the gas flow radius, m; t represents the drilling time, s; r 1 represents the borehole radius, m; p 0 represents the original gas pressure of the coal seam, MPa; p 1 represents the atmospheric pressure in the borehole or the negative pressure generated by gas drainage, MPa.

[0015] Further, the specific content of step ② is as follows: Select the target coal seam in the underground coal mine, collect coal samples on-site and send them to the laboratory, and determine the model parameters of the mathematical model of borehole gas flow in step ① based on laboratory tests and on-site tests. The model parameters determined by laboratory tests include the Langmuir constants a and b of coal adsorbed gas and the porosity φ of coal, and the model parameters determined by on-site tests include the coal seam permeability coefficient λ, the borehole radius r 1 and the atmospheric pressure in the borehole or the negative pressure p generated by gas drainage 1 .

[0016] Further, the specific process of screening in step ③ is as follows: In the first stage, on-site gas flow data while drilling are obtained and data cleaning is carried out, that is, the missing flow values at the corresponding drilling time are marked as invalid data and do not participate in subsequent analysis; in the second stage, automatic screening is carried out, and the flow range is determined according to actual conditions, and the flow values less than and greater than the flow range are directly discarded; in the third stage, the monitoring data are fitted into a curve, and the values deviating from the gas flow curve are marked as curve deviation and do not participate in subsequent analysis; in the fourth stage, the remaining data are used as the on-site measured values of gas flow while drilling for inversion.

[0017] Further, when performing forward calculation on the model in step ④, the model (1) is expressed in the form of finite difference, and the specific formula is as follows:

[0018]

[0019] In the formula, Δr and Δt respectively represent the spatial and time grid step sizes, and M and N are two positive integers;

[0020]

[0021] B and C are triangular matrices, and the specific formula is as follows:

[0022]

[0023] In the formula,

[0024] The discrete formats of boundary conditions and initial conditions are as follows:

[0025]

[0026] Further, the specific calculation formula of the borehole gas flow in step ④ is as follows:

[0027]

[0028] In the formula, Q is the borehole gas flow, m 3 / s; l is the borehole length, m.

[0029] Furthermore, the specific formula of the objective function in step ④ is as follows:

[0030]

[0031] In the formula, v k > 0 is the regularization parameter, which is automatically adjusted through actual calculation; Y δ is the on-site measured value of the gas flow while drilling; is the original coal seam gas pressure value at the k-th iteration; is the flow rate obtained by forward calculation using the original coal seam gas pressure value at the k-th iteration, k = 0, 1, 2, 3,......; E is the initial estimated value of the original coal seam gas pressure.

[0032] Furthermore, step ⑤ is specifically: constructing the sensitivity matrix The specific formula is as follows:

[0033]

[0034] In the formula, ε is the numerical differential step size; e x is the unit vector, which is determined according to actual calculation;

[0035] Differentiate the objective function to obtain the objective function gradient The specific formula is as follows:

[0036]

[0037] In the formula, sp represents the sum of the main diagonals of the matrix;

[0038] And determine the conjugate coefficient β k , the specific formula is as follows:

[0039]

[0040] In the formula, is the transpose matrix of.

[0041] Furthermore, the search direction d k in step ⑥ is related to the objective function gradient, and the specific formula is as follows:

[0042]

[0043] The search step size a k is determined by the sensitivity matrix and the search direction at the k-th iteration, and the specific formula is as follows:

[0044]

[0045] Construct the objective function for the next iteration based on the objective function in combination with the search direction and search step. The specific formula for the original coal seam gas pressure value in the objective function for the next iteration is as follows:

[0046]

[0047] Compared with the prior art, the present invention first constructs a mathematical model of gas flow while drilling and determines the model parameters; then screens out the on-site measured values of gas flow while drilling for inversion; then performs forward modeling of the model by the finite difference method to calculate the gas flow in the borehole; and combines the calculated gas flow in the borehole and the screened on-site measured values of gas flow while drilling to construct the objective function and calculate the gradient of the objective function; finally, based on the regularized nonlinear conjugate gradient method, constructs the objective function for the next iteration on the basis of the objective function in combination with the search direction and search step, and continuously iterates until the stopping condition is satisfied, and the original coal seam gas pressure value is inversely output by the objective function of the last iteration. The above method implementation steps of the present invention are simple, and through experimental verification, it is determined that the inversion result has good accuracy and reliability, solving the problems of long gas pressure measurement period, low accuracy, and few measurement points in the traditional method, not only shortening the pressure measurement time, reducing the pressure measurement cost, improving the accuracy of coal seam gas pressure measurement, and meeting the actual needs of coal mines for rapid and accurate determination of coal seam gas parameters. In addition, the method of the present invention is applicable to the determination of coal seam gas pressure under any working conditions and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the overall flow chart of the present invention;

[0049] Figure 2 is the calculated value and measured value of gas flow while drilling in Borehole No. 1 of a certain mine during experimental verification. DETAILED DESCRIPTION OF THE INVENTION

[0050] The present invention will be further described below.

[0051] As Figure 1 shown, the specific steps of the present invention are as follows:

[0052] ① Construct a mathematical model of gas flow in the borehole, and the specific formula is as follows:

[0053]

[0054] In the formula, P represents the square of the original coal seam gas pressure, that is, P = p 0 2 , MPa 2 ; λ represents the coal seam gas permeability coefficient, m 2 / (MPa 2 ·s); a and b are the Langmuir constants of coal adsorbed gas, and the units are m3 / t and MPa -1 ; φ represents the porosity of coal, %; r represents the gas flow radius, m; t represents the drilling time, s; r 1 represents the borehole radius, m; p 0 represents the original gas pressure of the coal seam, MPa; p 1 represents the atmospheric pressure in the borehole or the negative pressure generated by gas drainage, MPa.

[0055] ② Determine the model parameters of the borehole gas flow mathematical model in step ①, specifically: select the target coal seam in the coal mine, collect coal samples on-site and send them to the laboratory, and based on laboratory tests and on-site experiments, determine the model parameters of the borehole gas flow mathematical model in step ①. The model parameters determined by laboratory tests include the Langmuir constants a and b for coal to adsorb gas, and the porosity φ of coal. The model parameters determined by on-site experiments include the coal seam permeability coefficient λ, the borehole radius r 1 , the atmospheric pressure in the borehole or the negative pressure generated by gas drainage p 1 .

[0056] ③ Obtain the on-site gas flow data while drilling, and after screening, obtain the on-site measured values of the gas flow while drilling for inversion; the specific screening process is as follows: In the first stage, obtain the on-site gas flow data while drilling and perform data cleaning, that is, mark the missing flow values at the corresponding drilling time as invalid data and do not participate in subsequent analysis; in the second stage, perform automated screening, determine the flow range according to actual conditions, and directly discard the flow values that are less than and greater than the flow range; in the third stage, fit the monitoring data into a curve, and mark the values that deviate from the gas flow curve as curve deviation and do not participate in subsequent analysis; in the fourth stage, use the remaining data as the on-site measured values of the gas flow while drilling for inversion.

[0057] ④ Use Matlab to perform forward modeling of the model in step ① by the finite difference method to calculate the borehole gas flow, specifically:

[0058] Express the model (1) in the form of finite differences, and the specific formula is as follows:

[0059]

[0060] In the formula, Δr and Δt respectively represent the spatial and time grid step sizes, and M and N are two positive integers;

[0061]

[0062] B and C are triangular matrices, and the specific formulas are as follows:

[0063]

[0064] In the formula,

[0065] Discretization formats of boundary conditions and initial conditions, and the specific formulas are as follows:

[0066]

[0067] The specific calculation formula for the gas flow rate in the borehole is as follows:

[0068]

[0069] In the formula, Q is the gas flow rate in the borehole, m 3 / s; l is the length of the borehole, m.

[0070] Then, combining the calculated gas flow rate in the borehole and the on-site measured value of the gas flow rate while drilling screened in step ③, construct the objective function for the k-th iteration, and the specific formula is as follows:

[0071]

[0072] In the formula, v k >0 is the regularization parameter, which is automatically adjusted through actual calculation; Y δ is the on-site measured value of the gas flow rate while drilling; is the original gas pressure value of the coal seam for the k-th iteration; is the flow rate obtained by forward calculation using the original gas pressure value of the coal seam for the k-th iteration, k = 0, 1, 2, 3,......; E is the initial estimated value of the original gas pressure of the coal seam.

[0073] ⑤ Construct the sensitivity matrix for the k-th iteration, and the specific formula is as follows:

[0074]

[0075] In the formula, ε is the numerical differential step size; e x is the unit vector, which is determined according to actual calculation;

[0076] Differentiate the objective function to calculate the gradient of the objective function for the k-th iteration The specific formula is as follows:

[0077]

[0078] In the formula, sp represents the sum of the main diagonal of the matrix;

[0079] And determine the conjugate coefficient β k , and the specific formula is as follows:

[0080]

[0081] In the formula, is The transposed matrix of

[0082] ⑥ Set the maximum number of iterations and the tolerance threshold σ. If the gradient of the objective function in the k-th iteration is less than σ, stop the iteration and use the current output of the objective function to obtain the original coal seam gas pressure value; otherwise, first determine the search direction and search step size of the current objective function. The search direction d k is related to the gradient of the objective function in the k-th iteration and the specific formula is as follows:

[0083]

[0084] The search step size a k is determined by the sensitivity matrix and the search direction in the k-th iteration, and the specific formula is as follows:

[0085]

[0086] Based on the search direction and search step size, construct the objective function of the (k + 1)-th iteration on the basis of the objective function of the k-th iteration. The specific formula of the original coal seam gas pressure value in the objective function of the (k + 1)-th iteration is as follows:

[0087]

[0088] Then repeat steps ⑤ and ⑥ until the gradient of the objective function in a certain iteration is less than the tolerance threshold σ or the iteration reaches the maximum number of iterations, stop the iteration and output the original coal seam gas pressure value.

[0089] Experimental verification:

[0090] Use the method of the embodiment of the present invention to perform real-time flow inversion on the No. 1 borehole of a certain coal seam in a certain mine. The specific steps are as follows:

[0091] ① Before measuring the gas flow in the borehole, collect the geological basic data of this coal seam in advance, and collect enough coal samples to the laboratory. Measure the basic parameters of the coal samples and the model parameters of the borehole gas flow mathematical model according to the relevant test standards, as shown in Table 1.

[0092] Table 1 Model parameter values of the No. 1 borehole in a certain mine

[0093] parameter value parameter value <![CDATA[r 1 — Drilling radius]]> 0.042 b — adsorption constant 0.93 λ — coal seam gas permeability coefficient <![CDATA[1.029×10 -5 > φ — porosity 4.37 l — borehole length 100 a — adsorption constant 22.27

[0094] ② Before drilling, install a flow monitor at the hole mouth, record the coal-seeing time and drilling time, and the flow monitor automatically records the total gas flow at the hole mouth.

[0095] ③ After performing inversion calculation and processing on the model parameters and the on-site measured values of the borehole flow using the method of the embodiment of the present invention, the original coal seam gas pressure of the No. 1 borehole can be calculated.

[0096] ④ The original gas pressure of the coal seam obtained by inversion of Borehole No. 1 is 0.88 MPa. Then, the original gas pressure measured by the more accurate cross-cut boreholes (i.e., the direct method) on-site in the mine is 1.0 MPa, and the relative error is 12%. This indicates that the inversion method of gas pressure with flow rate while drilling based on the conjugate gradient method has good correctness and reliability.

[0097] ⑤ Using the original gas pressure of the coal seam obtained by inversion, the gas flow rate while drilling is further calculated, and the calculated value is compared with the on-site measured value. The results are as Figure 2 shown. According to the comparison results, the error between the calculated value and the measured value is small and they basically match, indicating that the method of the present invention can effectively reflect the variation law of the gas flow rate in the borehole.

[0098] The above are only the preferred embodiments of the present invention. It should be pointed out 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 coal seam gas pressure while drilling flow inversion method based on conjugate gradient method, characterized in that: The specific steps are as follows: ①Construct a mathematical model of borehole gas flow; ② Determine the model parameters of the borehole gas flow mathematical model in step ①; ③ Obtain on-site gas flow data while drilling, and obtain the on-site measured value of gas flow while drilling for inversion after screening; ④ Perform finite difference forward modeling on the model in step ① to calculate the borehole gas flow rate; The objective function is constructed by combining the calculated borehole gas flow and the field measured value of the gas flow while drilling after screening in step ③; ⑤Construct a sensitivity matrix and calculate the objective function gradient in combination with the objective function constructed in step ④; ⑥ Set the maximum number of iterations and the tolerance threshold σ. If the current objective function gradient is less than σ, the current objective function output is used to obtain the original gas pressure value of the coal seam; if not, first determine the search direction and search step of the current objective function, and then based on the regularized nonlinear conjugate gradient method, combine the search direction and search step to construct the objective function of the next iteration on the basis of the objective function, and repeat steps ⑤ and ⑥ until the objective function gradient of a certain iteration is less than the tolerance threshold σ or the iteration reaches the maximum number of iterations, stop the iteration and output the original gas pressure value of the coal seam.

2. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 1 is characterized in that: The mathematical model of borehole gas flow in step ① is specifically formulated as follows: In the formula, P represents the square of the original gas pressure of the coal seam, that is, P = p0 2 ; λ represents the permeability coefficient of the coal seam; a and b are the Langmuir constants of coal gas adsorption; φ represents the porosity of the coal; r represents the gas flow radius; t represents the drilling time; r1 represents the borehole radius; p0 represents the original gas pressure of the coal seam; p1 represents the atmospheric pressure in the borehole or the negative pressure caused by extraction.

3. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 1 is characterized in that: The step ② is specifically as follows: selecting a target coal seam in a coal mine, collecting coal samples on site and sending them to a laboratory, and determining the model parameters of the mathematical model of borehole gas flow in step ① based on laboratory tests and field tests, wherein the model parameters determined by laboratory tests include the Langmuir constants a and b of coal gas adsorption and the porosity φ of the coal, and the model parameters determined by field tests include the coal seam permeability coefficient λ, the borehole radius r1, and the atmospheric pressure in the borehole or the negative pressure p1 generated by extraction.

4. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 1 is characterized in that: The specific process of screening in step ③ is as follows: in the first stage, the on-site gas flow data while drilling is obtained and data cleaning is performed, that is, the missing flow values ​​at the corresponding drilling time are marked as invalid data and do not participate in subsequent analysis; The second stage conducts automated screening to determine the flow range based on actual conditions, and directly discards flow values ​​that are smaller or larger than the flow range; In the third stage, the monitoring data are fitted into a curve, and the values ​​that deviate from the gas flow curve are marked as curve deviations and do not participate in subsequent analysis; in the fourth stage, the remaining data are used as the field measured values ​​of the gas flow while drilling for inversion.

5. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 2 is characterized in that: When the model is forward calculated in step ④, the model (1) is expressed in finite difference form, and the specific formula is as follows: Where Δr and Δt represent the spatial and temporal grid steps, respectively, and M and N are two positive integers; B and C are triangular matrices, and the specific formulas are as follows: In the formula, The boundary conditions and initial conditions are discrete formats, and the specific formulas are as follows:

6. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 1 is characterized in that: The specific calculation formula for the borehole gas flow in step ④ is as follows: Where Q is the borehole gas flow rate; l is the borehole length.

7. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 1 is characterized in that: The specific formula of the objective function in step ④ is as follows: In the formula, v k >0 is the regularization parameter, which is automatically adjusted through actual calculations; Y δ It is the field measured value of gas flow while drilling; is the original gas pressure value of the coal seam at the kth iteration; is the flow rate obtained by forward calculation using the original gas pressure value of the coal seam of the kth iteration, k = 0, 1, 2, 3, ...; E is the initial estimated value of the original gas pressure of the coal seam.

8. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 7 is characterized in that: The step ⑤ is specifically as follows: constructing a sensitivity matrix The specific formula is as follows: Where ε is the numerical differentiation step size; e x is a unit vector, determined according to actual calculation; Differentiate the objective function to obtain the objective function gradient The specific formula is as follows: In the formula, sp represents the sum of the main diagonal of the matrix; And determine the conjugation coefficient β k , the specific formula is as follows: In the formula, for The transposed matrix of .

9. The coal seam gas pressure while drilling flow inversion method based on the conjugate gradient method according to claim 8 is characterized in that: In step ⑥, the search direction d k Related to the objective function gradient, the specific formula is as follows: Search step length a k It is determined by the sensitivity matrix and search direction of the kth iteration. The specific formula is as follows: The objective function of the next iteration is constructed based on the objective function in combination with the search direction and the search step length. The specific formula of the original gas pressure value of the coal seam in the objective function of the next iteration is as follows:

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