CN115983097A - Fast inversion method of coal seam gas drainage characteristic parameters based on borehole drainage data - Google Patents

Abstract

The invention discloses a coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data, which comprises the steps of firstly establishing a gas seepage mathematical model in a coal seam, establishing a gas flow forward model by combining the characterization relation of gas extraction flow evolution and gas pressure distribution, determining coal seam physical property parameters and boundary conditions according to field conditions, and obtaining a forward gas flow function with coal seam initial permeability and extraction time as independent variables; fitting field extraction data as a field gas extraction flow function; taking the difference between the gas flow of the forward modeling and the gas flow fitted by the field data as a fitness function; searching the initial permeability and the borehole extraction time of the coal bed corresponding to the minimum fitness by adopting a particle swarm algorithm; and finally, substituting the obtained coal seam initial permeability and the drilling extraction time into a gas flow forward model, and calculating characteristic parameters such as coal seam residual gas pressure/content, extraction rate, extraction influence radius, permeability and the like.

Description

Rapid inversion method for coal seam gas extraction characteristic parameters based on drilling extraction data

Technical Field

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

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.

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.

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.

Different from the forward deduction used in general research, the process or mechanism of inferring the occurrence of an event based on the results or information is called "inversion", and 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 change characteristics of coal seam permeability, established a non-coupled mathematical model of coal seam gas flow under two-dimensional conditions, and used the super-relaxation iteration method to solve it, and finally realized the inversion of permeability through coal seam gas pressure. However, in the actual construction process, the coal seam pressure itself is used as a characteristic parameter of gas extraction to be measured, and the measurement often has the problem of complex operation and hysteresis. Other scholars have established a coupled dimensionless equation for the dual porosity of 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 higher accuracy. However, this study only uses trial matching, and does not involve specific nonlinear inversion methods, and the specific application effect is poor.

Therefore, how to provide a new method based on the coal seam multi-field coupled three-dimensional model, take the coal seam gas extraction characteristic parameters as the target, and build a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately obtain the coal seam extraction characteristic parameters, is one of the research directions of this industry.

Summary of the invention

In response to the problems existing in the above-mentioned prior art, the present invention provides a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data. The method is based on a three-dimensional model of coal seam multi-field coupling, takes coal seam gas extraction characteristic parameters as the target, and builds a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately derive the coal seam extraction characteristic parameters.

In order to achieve the above purpose, the technical solution adopted by the present invention is: a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data, the specific steps are:

Step 1: According to the gas seepage theory, a mathematical model of gas seepage in coal seams is first established. According to the mathematical model, the relationship between the initial permeability and the drilling extraction time and the coal seam gas pressure can be determined. Then, the relationship between the coal seam gas flow rate and the coal seam gas pressure is determined. The relationship is combined with the established mathematical model of gas seepage in coal seams to build a gas flow forward model. The coal seam physical parameters and boundary conditions involved in the gas flow forward model are determined according to the on-site geological conditions. Finally, according to the gas flow forward model, a forward gas flow function with the initial permeability of the coal seam and the extraction time as independent variables is obtained;

Step 2: Collect the on-site gas extraction flow rate through a gas flow sensor, and fit the obtained extraction data to form a continuous function, which is the fitting on-site gas extraction flow rate function;

Step 3: The difference function D(k ₀ ,t) between the forward modeling gas flow function obtained in step 1 and the fitted on-site gas extraction flow function obtained in step 2 is used as the fitness function, and the minimum value of the fitness function is taken as the target;

Step 4: Use the particle swarm algorithm to find the initial permeability of the coal seam and the drilling and extraction 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 drilling extraction time obtained in step 4 into the gas flow forward model established in step 1, and finally calculate and determine the gas extraction characteristic parameters of the coal seam based on the model.

Further, the step 1 is specifically as follows:

A): According to the gas seepage theory, a three-dimensional fluid-solid coupling mathematical model of gas seepage is established as shown in formula (1):

k表示煤层渗透率，

k₀表示煤层初始渗透率；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, respectively, 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 , S ₀ =(p ₀ /K _s )-ε _L p ₀ /(p ₀ +p _L ); p ₀ represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ ₀ represents the initial porosity of the coal seam; φ represents the porosity of the coal seam,

k represents the permeability of the coal seam,

k ₀ 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 the coal body in the coal seam at this time can be obtained, as shown in equation (2):

Wherein, _ρa is the gas density under standard conditions, kg/m ³ ; _ρc is the coal density, kg/m ³ ; _VL is the Langmuir volume constant, m ³ /kg; _PL represents the Langmuir pressure constant, MPa;

By dividing the gas content m| _t per unit volume of coal at extraction time t by the coal volume, the gas content M| _t of any volume of coal can be obtained, as shown in formula (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 extraction flow rate at any time t can be expressed as:

Where, Q| _t is the gas extraction flow rate at time t, m ³ /s;

From equations (1) to (4), we can see that the gas drainage flow rate Q is a function of the initial permeability _k0 and the drainage time t, that is,

Q＝Q(k ₀ ,t) (5)

Through steps A)-C), the relationship between the extracted gas flow rate and the initial permeability of the coal seam and the drilling extraction time, that is, the gas flow forward model, can be established. In the gas flow forward model, the borehole gas flow rate at that moment can be obtained by any given coal seam initial permeability _k0 and extraction time t.

Furthermore, the function of fitting the on-site gas extraction flow rate in step 2 is specifically:

Where, t represents the extraction time, d; _t0 represents the extraction time of the borehole when the gas flow is first recorded, d; _QR is the fitted on-site gas extraction flow, ^m3 /min; a and b represent function coefficients.

Furthermore, the difference function D(k ₀ ,t) in step 3 is specifically:

In the formula, subscript i = 1, 2, ..., n, represents the time point of the monitored data;

In the above formula, the smaller the value of D(k ₀ ,t) is, the closer the initial permeability k ₀ and extraction time t of the coal seam obtained by inversion are to the actual values. Therefore, the goal is to obtain the minimum value of this function.

Further, the specific process of step 4 is:

① Preset the parameters of the particle swarm algorithm: set the total number of individuals N contained in the population of the algorithm, the maximum number of iterations ger, the maximum speed V _max and minimum speed V _min of particle movement, the individual learning factor c ₁ , the social learning factor c ₂ , the inertia factor w, and the truncation error C;

② Determine the inversion interval boundary and randomly generate N particles in 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:

_Xi ＝( _k0it ) (7)

U≤X _i ≤T (8)

Where i = (1, 2, 3...N), U and T represent the lower and upper limits of the permeability of the particles, respectively;

Calculate the fitness of the current particle position according to the fitness function D(k ₀ ,t), compare the fitness of each particle, record the population's historical best position Gb_X and the population's historical best fitness Gb at this time, and initialize the particle group's historical best position Pb_X=X;

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

表示粒子移动速度，使用式(10)表示Where L is the current iteration number,

represents the particle moving speed, which can be expressed using formula (10):

The particle inertia factor w represents the tendency of the particle to move in its inherent direction of motion; the individual learning factor _c1 and the social learning factor _c2 respectively give the particle individual memory attributes and social attributes, representing the tendency of the particle to move toward its own historical best position and the population historical best position; _r1 and _r2 are two independent random parameters, which make the particle movement more random and increase the possibility of global optimization;

In order to prevent the particle from skipping the optimal position due to excessive strides during the optimization process, the particle velocity v _i is limited:

V _min <= _vi <= V _max (11)

Among them, V _min and V _max represent the lower and upper limits of particle velocity, respectively, that is, the range of permeability change during each iteration;

④ Compare the gas flow matching degree under the current coal seam initial permeability and extraction time and update Gb_X, Gb, Pb_X;

⑤ Determine whether the termination condition is met. If so, exit the iteration and output the initial permeability of the coal seam and the drilling extraction time corresponding to the minimum value of the fitness function. Otherwise, return to step ③ to continue the iterative calculation.

Furthermore, the gas extraction characteristic parameters of the coal seam in step five include coal seam gas pressure p, remaining coal seam gas content M, gas extraction rate η, coal seam permeability k and effective extraction radius r; wherein 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 extraction rate η is obtained by the ratio of the remaining coal seam gas amount M to the initial coal seam gas content _M0 , and the effective extraction radius r is set to the area where the residual coal seam gas pressure is lower than 0.74MPa.

Furthermore, the particle inertia factor w is a variable that changes with the number of iterations, as shown in formula (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 particles move in the variable space at a higher flying speed, which makes it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, which greatly improves the convergence of the algorithm.

Furthermore, the termination condition in step ⑤ is: the cycle reaches the maximum number of iterations, or the change of the fitness function D(k ₀ ,t) is less than the set truncation error C during three consecutive iterations.

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 gas extraction flow evolution characteristics and the gas pressure distribution characteristics to build a gas flow forward model. The coal seam physical parameters and boundary conditions involved in the gas flow forward model are determined according to the on-site geological conditions and obtained through the forward model; then the on-site gas extraction data are collected and fitted into a continuous function as the on-site gas extraction flow function; the above forward gas flow function and the on-site fitted gas extraction flow function are subtracted, and the difference function formed is used as the fitness function; the particle swarm algorithm is used to find the initial permeability and drilling extraction time of the coal seam corresponding to the minimum value of the fitness function; finally, the obtained initial permeability and drilling extraction time of the coal seam are substituted into the above gas flow forward model to calculate and determine the gas extraction characteristic parameters of the coal seam. Therefore, the present invention can be based on the coal seam multi-field coupling three-dimensional model, take the coal seam gas extraction characteristic parameters as the target, and build a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately obtain the coal seam extraction characteristic parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is an overall inversion flow chart of the present invention;

FIG2 is a flow chart of using a particle swarm algorithm to find the minimum value of a fitness function in the present invention;

FIG3 is a diagram of coal seam geometric parameters and boundary conditions in an embodiment of the present invention;

FIG4 is a graph showing the inversion results of the initial permeability of the coal seam and the extraction time in an embodiment of the present invention;

FIG5 is a diagram showing the distribution of coal seam gas pressure after 94 days of extraction in an embodiment of the present invention;

FIG6 is a diagram of the effective extraction radius when extraction is performed for 94 days in an embodiment of the present invention;

In the figure, the blank area represents the effective radius influence range;

FIG7 is a schematic diagram of the distribution of residual gas in the coal seam after 94 days of extraction in an embodiment of the present invention;

FIG8 is a coal seam permeability distribution diagram after 94 days of extraction in an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention will be further described below.

As shown in Figure 1, the specific steps of the present invention are:

Step 1: Establish a gas flow forward model:

A): According to the gas seepage theory, a three-dimensional fluid-solid coupling mathematical model of gas seepage is established as shown in formula (1):

k表示煤层渗透率，

k₀表示煤层初始渗透率；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, respectively, 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 , S ₀ =(p ₀ /K _s )-ε _L p ₀ /(p ₀ +p _L ); p ₀ represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ ₀ represents the initial porosity of the coal seam; φ represents the porosity of the coal seam,

k represents the permeability of the coal seam,

k ₀ 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 the coal body in the coal seam at this time can be obtained, as shown in equation (2):

Wherein, _ρa is the gas density under standard conditions, kg/m ³ ; _ρc is the coal density, kg/m ³ ; _VL is the Langmuir volume constant, m ³ /kg; _PL represents the Langmuir pressure constant, MPa;

By dividing the gas content m| _t per unit volume of coal at extraction time t by the coal volume, the gas content M| _t of any volume of coal can be obtained, as shown in formula (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 extraction flow rate at any time t can be expressed as:

Where, Q| _t is the gas extraction flow rate at time t, m ³ /s;

From equations (1) to (4), we can see that the gas drainage flow rate Q is a function of the initial permeability _k0 and the drainage time t, that is,

Q＝Q(k ₀ ,t) (5)

Through steps A)-C), the relationship between the extracted gas flow rate and the initial permeability of the coal seam and the drilling extraction time, that is, the gas flow forward model, can be established. In the gas flow forward model, the borehole gas flow rate at that moment can be obtained by any given coal seam initial permeability _k0 and extraction time t.

Step 2: Collect the on-site gas extraction flow rate through the gas flow sensor, and fit the obtained extraction data to form a continuous function, which is the fitting on-site gas extraction flow rate function, wherein the fitting on-site gas extraction flow rate function is specifically:

Where, t represents the extraction time, d; _t0 represents the extraction time of the borehole when the gas flow is first recorded, d; _QR is the fitted on-site gas extraction flow, ^m3 /min; a and b represent function coefficients.

Step 3: The difference function D(k ₀ , t) between the forward modeling gas flow function obtained in step 1 and the fitted on-site gas extraction flow function obtained in step 2 is used as the fitness function, wherein the difference function D(k ₀ , t) is specifically:

In the formula, subscript i = 1, 2, ..., n, represents the time point of the monitored data;

In the above formula, the smaller the value of D(k ₀ ,t) is, the closer the inverted initial permeability k ₀ of the coal seam and the extraction time t are to the actual values. Therefore, the goal is to obtain the minimum value of this function.

Step 4: Use the particle swarm algorithm to find the initial permeability of the coal seam and the drilling and extraction time corresponding to the minimum value of the fitness function in step 3. The specific process is as follows:

① Preset the parameters of the particle swarm algorithm: set the total number of individuals N contained in the population of the algorithm, the maximum number of iterations ger, the maximum speed V _max and minimum speed V _min of particle movement, the individual learning factor c1, the social learning factor c2, the inertia factor w, and the truncation error C;

② Determine the inversion interval boundary and randomly generate N particles in 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:

_Xi ＝( _k0it ) (7)

U≤X _i ≤T (8)

Where i = (1, 2, 3...N), U and T represent the lower and upper limits of the permeability of the particles, respectively;

Calculate the fitness of the current particle position according to the fitness function D(k ₀ ,t), compare the fitness of each particle, record the population's historical best position Gb_X and the population's historical best fitness Gb at this time, and initialize the particle group's historical best position Pb_X=X;

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

表示粒子移动速度，使用式(10)表示Where L is the current iteration number,

represents the particle moving speed, which can be expressed using formula (10):

The particle inertia factor w represents the tendency of the particle to move in its inherent direction of motion; the individual learning factor _c1 and the social learning factor _c2 respectively give the particle individual memory attributes and social attributes, representing the tendency of the particle to move toward its own historical best position and the population historical best position; _r1 and _r2 are two independent random parameters, which make the particle movement more random and increase the possibility of global optimization;

The above particle swarm algorithm does not set a mutation process and is prone to fall into a local optimal solution and ultimately cannot 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 formula (11):

w＝w_1-(w_1-w_2)*L/ger (11)

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 particles move in the variable space at a higher flying speed, which makes it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, which greatly improves the convergence of the algorithm.

In order to prevent the particle from skipping the optimal position due to excessive strides during the optimization process, the particle velocity v _i is limited:

V _min <= _vi <= V _max (12)

Among them, V _min and V _max represent the lower and upper limits of particle velocity, respectively, that is, the range of permeability change during each iteration;

④ Compare the gas flow matching degree under the current coal seam initial permeability and extraction time and update Gb_X, Gb, Pb_X;

⑤ Determine whether the termination condition is met, which is: the cycle reaches the maximum number of iterations, or the change of the fitness function D(k ₀ ,t) is less than the set truncation error C during three consecutive iterations; if it is met, the iteration is jumped out, and the initial permeability of the coal seam and the drilling and extraction time corresponding to the minimum value of the fitness function are output, otherwise return to step ③ to continue the iterative calculation.

Step 5. Substitute the initial permeability of the coal seam and the drilling extraction time obtained in step 4 into the gas flow forward model established in step 1, and finally calculate and determine the gas extraction characteristic parameters of the coal seam based on the model, wherein the gas extraction characteristic parameters of the coal seam include coal seam gas pressure p, remaining coal seam gas content M, gas extraction rate η, coal seam permeability k and effective extraction radius r; wherein 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 extraction rate η is obtained by the ratio of the remaining coal seam gas content M to the initial coal seam gas content _M0 , and the effective extraction radius r is set to the area where the residual coal seam gas pressure is lower than 0.74MPa.

Tests prove:

In order to verify the specific process of obtaining the gas extraction characteristic parameters of the coal seam by inversion using the present invention, a simulation verification was carried out using an actual coal mine: the 1# borehole of the 125th group of Pingmei Tenth Mine (E 8.9-20230 machine lane) was selected as the research object, and the initial permeability of the coal seam and the drilling extraction time when the drilling flow was first recorded were used as the inversion targets to perform inversion using the present invention. Since the gas flow forward model in the present invention is composed of a series of partial differential equations, it can be solved with the help of the COMSOL with MATLAB platform. The geometric parameters and boundary conditions of the coal seam are determined as shown in Figure 3, and the physical parameters are shown in Table 1:

Table 1 Coal seam physical properties parameters

The initial conditions for gas extraction simulation are:

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

Where p| _t=0 and u| _t=0 represent the gas pressure (MPa) and displacement value (m) in the model at the initial moment, respectively.

The boundary conditions for gas extraction simulation are:

① Seepage boundary conditions: The model outer surface boundary and the borehole sealing section wall are set with no flow boundary conditions, and the extraction section is set with a fixed pressure boundary according to the extraction negative pressure, that is,

Where n·v| _{outer boundary} and n·v| _{borehole sealing section} represent the gas flow rate per unit area through the model outer boundary and borehole sealing section, respectively (kg/(s·m ² )); p| _{borehole extraction section} represents the boundary pressure of the borehole extraction section, MPa.

② Coal deformation boundary conditions: According to the buried depth of the coal seam, a uniform load of 8MPa is applied on the upper surface to simulate the deadweight of the upper coal and rock mass. Fixed constraint boundaries are set on the bottom surface and the borehole sealing section, normal constraint boundaries are set on the side boundaries, and free deformation boundaries are set on the extraction section, that is:

Where -σ _ij n _j | _{upper surface} represents the load on the upper surface of the model (MPa); u| _{bottom surface} and u| _{drilling and sealing section} represent the deformation displacement of the bottom surface of the model and the drilling and sealing section respectively (m); u·n| _{side boundary} represents the normal displacement of the side surface of the model (m).

The on-site gas extraction flow data is fitted according to the form shown in formula (5), and the result is:

The parameter initialization data of the particle swarm algorithm is set by the actual geological parameters. The initial permeability _k0 of the coal seam is in the range of (1× ^10-20 , 1× ^10-16 ), and the velocity limit interval is 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 100 times, the truncation error is 0.001, the individual learning factor _c1 is 2, and the social learning factor _c2 is 2.

The final inversion results are shown in Figures 4 to 8; Figure 4 is the inversion result diagram of the initial permeability of the coal seam and the drilling extraction time. It can be seen from the figure that the initial permeability obtained by inversion is 3.79× ^{10-17 m2} , and the drilling extraction time is 94 days. The evolution of coal seam extraction parameters is further estimated based on the initial permeability and drilling extraction time of the coal seam obtained by inversion. According to the gas flow forward model, the gas pressure distribution of the coal seam on the 94th day of extraction is shown in Figure 5. 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 shown in Figures 6 and 7 respectively. By integrating the total coal volume, the remaining gas amount in the coal seam at this time is 3321.8kg, and the gas extraction rate is 61.6%. Figure 8 is a permeability distribution diagram in the coal seam on the 94th day of extraction. Then the coal seam extraction characteristic parameter data obtained by the above inversion is compared with the actual data of the coal mine. The inversion method of the present invention can quickly and accurately obtain the coal seam extraction characteristic parameters.

The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims (8)

1. A coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data is characterized by comprising the following specific steps:

firstly, according to a gas seepage theory, establishing a gas seepage mathematical model in a coal seam, determining the relation between the initial permeability of the coal seam and the extraction time of a drill hole and the gas pressure of the coal seam according to the mathematical model, then combining the parameter characterization relation of the gas extraction flow evolution characteristic and the gas pressure distribution characteristic to establish a gas flow forward modeling, determining the coal seam physical property parameters and boundary conditions related in the gas flow forward modeling according to the field geological condition, and finally obtaining a forward gas flow function of the coal seam according to the gas flow forward modeling;

acquiring field gas extraction flow through a gas flow sensor, and fitting the acquired extraction data to form a continuous function, wherein the continuous function is a fitting field gas extraction flow function;

step three, the forward gas flow function obtained in the step one and the fitted field gas extraction flow function obtained in the step two are combined to form a difference function D (k) between the forward gas flow function and the fitted field gas extraction flow function ₀ T) as a fitness function, and taking the minimum value of the fitness function as a target;

step four, searching the coal bed initial permeability and the drilling extraction time corresponding to the minimum fitness function in the step three by adopting a particle swarm optimization;

and step five, substituting the data into the gas flow forward modeling model established in the step one through the coal seam initial permeability and the drilling extraction time obtained in the step four, and finally calculating and determining the gas extraction characteristic parameters of the coal seam according to the modeling.

2. The method for quickly inverting the coal seam gas extraction characteristic parameters based on the borehole extraction data according to claim 1, wherein the first step specifically comprises the following steps:

a) The method comprises the following steps According to the gas seepage theory, establishing a gas seepage three-dimensional fluid-solid coupling mathematical model as shown in the formula (1):

in the formula, G stands forTABLE coal shear modulus, MPa, G = E/2 (1 + v); k and E are the bulk and young's modulus of coal, MPa, K = E/3 (1-2 v), respectively; v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α =1-K/K _S ；ε _s Inducing volumetric strain for adsorption of coal; epsilon _L Is the langmuir volume strain constant; s = ε _v +(P/K _s )-ε _s ,S ₀ ＝(p ₀ /K _s )-ε _L p ₀ /(p ₀ +p _L )；p ₀ Representing the initial pressure of the coal bed; p represents the coal bed gas pressure; phi is a ₀ Representing the initial porosity of the coal bed; phi represents the porosity of the coal bed,

k represents the permeability of the coal seam, and>

k ₀ representing the initial permeability of the coal bed;

b) The method comprises the following steps Solving the equation (1) can obtain the initial permeability k of the coal bed ₀ And (3) gas pressure distribution at any time, and obtaining the gas content m of the coal body in unit volume in the coal seam at the time according to the formula (2):

where ρ is _a Is gas density in kg/m under standard condition ³ ；ρ _c Is the coal density in kg/m ³ ；V _L Is Langmuir volume constant, m ³ /kg；P _L Represents Langmuir pressure constant, MPa;

the gas quantity m in the unit volume coal body at the extraction time t is subjected to air induction _t The gas content M of the coal body with any volume can be obtained by integrating the coal body _t As shown in formula (3):

M| _t ＝∫∫∫ _V m| _t dx dy dz (3)

in the formula: m- _t The content of gas in the coal seam at the time t is kg;

c) The method comprises the following steps The flow of gas extraction at any time t can be expressed as:

in the formula, Q # _t Is the gas extraction flow at the time t, m ³ /s；

Obtained by the formulas (1) to (4), and the gas extraction flow Q is the initial permeability k ₀ And extraction time t, i.e.

Q＝Q(k ₀ ,t) (5)

Through the steps A) to C), the relation between the extracted gas flow and the coal seam initial permeability and the borehole extraction time can be established, namely a gas flow forward model, and the initial permeability k of any given coal seam is passed through in the gas flow forward model ₀ And the extraction time t can obtain the borehole gas flow at the moment.

3. The method for quickly inverting coal seam gas extraction characteristic parameters based on borehole extraction data according to claim 1, wherein the fitting field gas extraction flow function in the second step is specifically as follows:

in the formula, t represents extraction time, d; t is t ₀ D, representing the extracted time of the drill hole when the gas flow is recorded for the first time; q _R To fit the field gas extraction flow, m ³ Min; a. b represents the coefficients of the function.

4. The method for quickly inverting coal seam gas extraction characteristic parameters based on borehole extraction data according to claim 1, wherein the step three median difference function D (k) ₀ And t) is specifically:

in the formula, subscript i =1,2 ...nindicates the time point of monitored data;

in the above formula, D (k) ₀ The smaller the value of t) is, the initial permeability k of the coal bed obtained by inversion is shown ₀ The closer the extraction time t is to the actual value, the minimum value of the function is taken as a target.

5. The method for quickly inverting the coal seam gas extraction characteristic parameters based on the borehole extraction data according to claim 1, wherein the concrete process of the fourth step is as follows:

(1) presetting parameters of a particle swarm algorithm: setting the total number N of individuals contained in the population, the maximum iteration number ger and the maximum speed V of particle motion in the algorithm _max And minimum velocity V _min Individual learning factor c ₁ Social learning factor c ₂ Inertia factor w, truncation error C;

(2) determining an inversion interval boundary, and randomly generating N particles in the inversion interval, wherein the initial position Xi and the particle variation interval of the ith particle are respectively shown as formula (7) and formula (8):

X _i ＝(k _0i t) (7)

U≤X _i ≤T (8)

wherein i = (1, 2,3.. N), U, T represent the lower and upper permeability limits of the particles, respectively;

according to a fitness function D (k) ₀ T) calculating the position fitness of the current particle, comparing the position fitness of each particle, recording a historical optimal position Gb _ X of the population and the historical optimal fitness Gb of the population at the moment, and initializing a historical optimal position Pb _ X = X of the particle swarm;

(3) starting iteration, updating the position of the particle swarm, wherein the position updating formula of the ith particle is shown as formula (9):

wherein, L is the current iteration number,

the moving speed of the particles is expressed by the following formula (10)

The particle inertia factor w represents the tendency of the particles to move towards the inherent movement direction of the particles; individual learning factor c ₁ And social learning factor c ₂ Respectively endowing the particles with individual memory attributes and social attributes, representing the trend that the particles approach to the self historical optimal position and the population historical optimal position; r is a radical of hydrogen ₁ ，r ₂ The two independent random parameters make the motion of the particles more random, and increase the possibility of global optimization;

to avoid the particles stepping too far past the optimal position during the optimization, the velocity v of the particles is therefore measured _i And (4) limiting:

V _min <＝v _i <＝V _max (11)

wherein, V _min ，V _max Respectively representing the lower limit and the upper limit of the particle speed, namely the variation range of the permeability in each iteration process;

(4) comparing the initial permeability of the current coal seam and the gas flow matching degree in the drilling extraction time, and updating Gb _ X, gb and Pb _ X;

(5) and (4) judging whether a termination condition is met, if so, jumping out iteration, outputting the initial permeability of the coal bed and the extraction time of the drilled hole corresponding to the minimum value of the fitness function, and otherwise, returning to the step (3) to continue iterative computation.

6. The method for quickly inverting coal seam gas extraction characteristic parameters based on borehole extraction data according to claim 1, wherein the coal seam gas extraction characteristic parameters in the fifth step comprise coal seam gas pressure p,The residual coal seam gas content M, the gas extraction rate eta, the coal seam permeability k and the effective extraction radius r; the coal seam gas pressure p, the residual coal seam gas content M and the coal seam permeability k are obtained through solving by a gas flow forward modeling model, and the gas extraction rate eta is obtained by the residual coal seam gas content M and the initial coal seam gas content M ₀ And obtaining a ratio, and setting the effective extraction radius r to be a region with the residual coal seam gas pressure lower than 0.74 MPa.

7. The method for quickly inverting coal seam gas extraction characteristic parameters based on borehole extraction data according to claim 4, wherein the particle inertia factor w is a variable that changes with the number of iterations, as shown in formula (12):

w＝w_1-(w_1-w_2)*L/ger (12)

wherein w _1 and w _2 represent the upper limit and the lower limit of the inertia coefficient respectively, L is the current iteration frequency, and ger is the maximum iteration frequency; the inertia factor w in the earlier stage of iteration is large, and the particles move in a variable space at a large flying speed, so that the global optimum value is easier to find; and the inertia factor w at the later stage of iteration is small, so that the convergence of the algorithm is greatly improved.

8. The method for quickly inverting coal seam gas extraction characteristic parameters based on borehole extraction data according to claim 4, wherein the termination conditions in the step (5) are as follows: the loop reaches the maximum number of iterations, or the fitness function D (k) in the process of three successive iterations ₀ And t) is less than the set truncation error C.

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