CN115983097A - Coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data - Google Patents
Coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data Download PDFInfo
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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
Technical Field
The invention relates to a method for quickly inverting coal seam gas extraction characteristic parameters, in particular to a method for quickly inverting coal seam gas extraction characteristic parameters based on drilling extraction data, and belongs to the technical field of coal mine gas extraction.
Background
As the foundation of gas resource utilization and the permanent measure of coal mine gas disasters, pre-extraction of coal seam gas is always an essential link in coal mining work. In the extraction process, basic parameters of gas extraction are basic scientific bases for planning design of a gas extraction system, evaluation of gas extraction effect and safety technical management of a gas extraction project. Therefore, how to quickly and accurately obtain the gas extraction parameters has important significance.
However, the problems of complex operation, time consumption and labor consumption commonly exist in the existing measurement of coal bed gas extraction characteristic parameters in the industry, and the coal bed permeability is taken as an example: at present, two methods of laboratory measurement and field test are mainly used for measuring the coal bed permeability of coal mines in the industry. In the process of measuring the permeability of the coal sample in a laboratory, the preparation difficulty of the complete coal sample is high, cracks are easy to appear in the drilling process of the coal sample, the anisotropic characteristics of the coal body and the like cause that the measurement result of the permeability of the coal layer has larger deviation than the field situation, so that the laboratory is difficult to simulate the real situation and only can carry out qualitative and regular research. When the permeability of the coal seam is measured on site, a drilling gas radial flow method is mainly adopted at home at present, the permeability measuring method has a good detection effect, but the radial flow method still has the defects of long measuring period, complex parameters to be measured and the like.
In the process of coal bed gas extraction operation, the dynamic change characteristics of gas extraction characteristic parameters are directly reflected through production data. The coal bed gas production data are the first hand data of a coal mine construction site, and have higher authenticity and accuracy. Therefore, the method has a good development prospect and needs further research on how to quickly and accurately reversely acquire the gas extraction characteristic parameters through production data and provide scientific support for safe and efficient exploitation of the coal bed gas.
Unlike the forward derivation used in general research, the process or mechanism of backstepping events according to results or information is called "inversion", and the core idea is that the observable parameters can infer the internal source parameters of the research object. Currently, scholars analyze the complex change characteristics of the coal bed permeability, establish a coal bed gas flow non-coupling mathematical model under a two-dimensional condition, solve the problem by using an ultra-relaxation iteration method, and finally realize the permeability inversion through the coal bed gas pressure. However, in the actual construction process, the coal bed pressure itself is used as a characteristic parameter of gas extraction to be measured, and the problems of complex operation and hysteresis exist in measurement. The learner also establishes a coupling dimensionless equation of the double pores of the coal seam, and provides a new inversion method of the coal matrix permeability and the fracture permeability on the basis, and the result shows that the inversion algorithm based on the fluid-solid coupling control equation has higher accuracy. However, the research only needs trial matching, does not relate to a specific nonlinear inversion method, and has a poor application effect.
Therefore, how to provide a new method is one of the research directions of the industry, and how to provide a new method, which is based on a coal seam multi-field coupling three-dimensional model, and build a coal seam gas extraction characteristic parameter inversion algorithm based on real production data by taking the coal seam gas extraction characteristic parameter as a target, so that the coal seam gas extraction characteristic parameter is obtained quickly and accurately.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data, which is based on a coal seam multi-field coupling three-dimensional model, takes the coal seam gas extraction characteristic parameter as a target, and builds a coal seam gas extraction characteristic parameter inversion algorithm based on real production data, thereby rapidly and accurately obtaining the coal seam gas extraction characteristic parameter.
In order to achieve the purpose, the invention adopts the technical scheme that: a coal seam gas extraction characteristic parameter rapid inversion method based on borehole extraction data comprises the following specific steps:
firstly, establishing a mathematical model of gas seepage in a coal seam according to a gas seepage theory, determining the relation between initial permeability and borehole extraction time and coal seam gas pressure according to the mathematical model, then determining a relational expression between coal seam gas flow and coal seam gas pressure, combining the relational expression with the established mathematical model of gas seepage in the coal seam so as to establish a gas flow forward modeling model, determining coal seam physical parameters and boundary conditions related in the gas flow forward modeling model according to field geological conditions, and finally obtaining a forward modeling gas flow function taking the coal seam initial permeability and the extraction time as independent variables according to the gas flow forward modeling model;
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.
Further, the first step specifically comprises:
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):
wherein G represents the shear modulus of coal, 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 formula (1) can obtain the initial permeability k of the coal bed 0 Gas pressure distribution at any time, and obtaining the unit in the coal seam at the momentThe volume coal gas content m is shown as the formula (2):
wherein ρ 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 gas content 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 follows:
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.
Further, the fitting of the field gas extraction flow function in the second step specifically includes:
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 on-site gas extraction flow, m 3 Min; a. b represents the coefficients of the function.
Further, the step three median difference function D (k) 0 And t) is specifically:
in the formula, subscript i =1,2 ...n, indicating the time point of the monitored data;
in the above formula D (k) 0 The smaller the value of t) is, the coal bed initial permeability k obtained by inversion is shown 0 The closer the extraction time t is to the actual value, the minimum value obtained by the function is taken as a target.
Further, the specific 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 in the algorithm, the maximum iteration number ger and the maximum speed V of particle motion 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 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 process, the velocity v of the particles is therefore adjusted 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 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.
Further, the gas extraction characteristic parameters of the coal seam in the fifth step comprise coal seam gas pressure p, residual coal seam gas content M, gas extraction rate eta, coal seam permeability k and 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 of a gas flow forward model, and the gas extraction rate eta is obtained by solving 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.
Further, the particle inertia factor w is a variable that varies with the number of iterations, as shown in equation (12):
w＝w_1-(w_1-w_2)*L/ger (12)
wherein w _1 and w _2 respectively represent the upper limit and the lower limit of the inertia coefficient, L is the current iteration number, and ger is the maximum iteration number; 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.
Further, the termination conditions in the step (5) are: 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.
Compared with the prior art, the method comprises the steps of firstly establishing a gas seepage mathematical model in the coal seam, and establishing a gas flow forward model by combining a parameter characterization relation of gas extraction flow evolution characteristics and gas pressure distribution characteristics, wherein coal seam physical property parameters and boundary conditions related in the gas flow forward model are determined according to field geological conditions and are obtained through the forward model; then acquiring field gas extraction data and fitting the data into a continuous function as a field gas extraction flow function; the forward gas flow function and the field-fitted gas extraction flow function are subjected to difference, and a formed difference function is used as a fitness function; searching the coal bed initial permeability and the drilling extraction time corresponding to the minimum value of the fitness function by adopting a particle swarm optimization; and finally, substituting the obtained coal seam initial permeability and the drilling extraction time into the gas flow forward modeling model, and calculating and determining gas extraction characteristic parameters of the coal seam. Therefore, the method can be used for constructing the coal seam gas extraction characteristic parameter inversion algorithm based on the real production data by taking the coal seam multi-field coupling three-dimensional model as a basis and taking the coal seam gas extraction characteristic parameters as targets, so that the coal seam gas extraction characteristic parameters can be quickly and accurately obtained.
Drawings
FIG. 1 is a flowchart of the inversion of the ensemble of the present invention;
FIG. 2 is a flow chart of the present invention for finding the minimum value of the fitness function using a particle swarm algorithm;
FIG. 3 is a graph of coal seam geometry and boundary conditions in an embodiment of the present invention;
FIG. 4 is a diagram of inversion results of coal seam initial permeability and extraction time in an embodiment of the invention;
FIG. 5 is a coal seam gas pressure distribution diagram at 94 days of extraction in the embodiment of the invention;
FIG. 6 is a graph of effective extraction radius at 94 days of extraction in the embodiment of the invention;
in the figure, the blank area represents the effective radius influence range;
FIG. 7 is a schematic diagram of distribution of residual gas of a coal seam at 94 days after extraction in the embodiment of the invention;
FIG. 8 is a permeability distribution diagram of a coal seam at 94 days of extraction in the embodiment of the invention.
Detailed Description
The present invention will be further explained below.
As shown in fig. 1, the method comprises the following specific steps:
step one, establishing a gas flow forward model:
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):
wherein G represents the shear modulus of coal, 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 representsThe 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 the 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 formula (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 gas content 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 follows:
in the formula, Q # t Is the gas extraction flow at 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.
Step two, 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, and the fitting field gas extraction flow function specifically comprises the following steps:
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 on-site gas extraction flow, m 3 Min; a. b represents the coefficients of the 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, wherein the difference function D (k) 0 And t) is specifically:
in the formula, subscript i =1,2 ...n, indicating the time point of the monitored data;
in the above formula D (k) 0 The smaller the value of t), the inverted coal bed initial permeability k is shown 0 The closer the extraction time t is to the actual value, the minimum value obtained by the function is taken 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, wherein the concrete process 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 a minimum velocity V min An individual learning factor C1, a social learning factor C2, an inertia factor w and a 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 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 1 ，r 2 The two independent random parameters make the motion of the particles more random, and increase the possibility of global optimization;
the particle swarm algorithm does not set a variation process, is easy to fall into a local optimal solution, and finally cannot converge to a global optimal position, so that the particle inertia factor w in the velocity formula is changed from a fixed value to a variable which changes along with the iteration number, namely the particle inertia factor w is a variable which changes along with the iteration number, as shown in formula (11):
w＝w_1-(w_1-w_2)*L/ger (11)
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.
To avoid the particles stepping too far past the optimal position during the optimization process, the velocity v of the particles is therefore adjusted i And (4) limiting:
V min <＝v i <＝V max (12)
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 extraction time, and updating Gb _ X, gb and Pb _ X;
(5) judging whether a termination condition is met, and terminatingThe end conditions 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 T) is less than the set truncation error C; and (4) if so, jumping out iteration, outputting the coal seam initial permeability and the drilling extraction time corresponding to the minimum value of the fitness function, and otherwise, returning to the step (3) to continue iterative computation.
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 gas extraction characteristic parameters of the coal seam according to the model, wherein the gas extraction characteristic parameters of the coal seam comprise the 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 of a gas flow forward model, and the gas extraction rate eta is obtained by solving 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.
The test proves that:
in order to verify the specific process of obtaining the gas extraction characteristic parameters of the coal seam by inversion, the method adopts an actual coal mine to perform simulation verification: the method is characterized by selecting the No. 1 drill hole in the 125 th group of ten mine (penta 8.9-20230 machine lane) of the flat coal as a study object, and performing inversion by using the method with the initial permeability of the coal bed and the drill hole extraction time when the drill hole flow is recorded for the first time as an inversion target. The gas flow forward model consists of a series of partial differential equations and can be solved by means of a COMSOL with MATLAB platform. The geometrical 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 bed physical property parameter table
The initial conditions for simulating gas extraction are as follows:
at the time t =0, the initial pressure of gas in the coal rock mass is 2MPa, and the boundary displacement is 0, that is:
in the formula, p- t＝0 And u < u > t＝0 Respectively representing the gas pressure (MPa) and the displacement value (m) in the model at the initial moment.
The boundary conditions of the gas extraction simulation are as follows:
(1) seepage boundary conditions: setting no-flow boundary conditions on the boundary of the outer surface of the model and the wall surface of the hole sealing section of the drill hole, and setting a constant pressure boundary in the extraction section according to extraction negative pressure, namely
Wherein n.v # Outer boundary And n.v- Drilling hole sealing section Respectively representing the gas flow per unit area (kg/(s.m) through the outer boundary of the model and the hole sealing section of the drill hole 2 ))；p| Drilling extraction section And the boundary pressure of the extraction section of the drill hole is expressed in MPa.
(2) Coal body deformation boundary conditions: according to the coal seam buried depth condition, 8MPa of uniform load is exerted on the upper surface to simulate the dead weight of the upper coal rock mass, the bottom surface and the drilling hole sealing section are provided with fixed constraint boundaries, the side boundary is provided with a normal constraint boundary, and the extraction section is provided with a free deformation boundary, namely:
in the formula, -sigma ij n j | Upper surface of Representing the load (MPa) borne by the upper surface of the model; u < u > C Bottom surface And u < u > Drilling hole sealing section Respectively representing the deformation displacement (m) of the bottom surface of the model and the hole sealing section of the drill hole; u.n- Side boundary Representing the model side normal displacement (m).
Fitting the field gas extraction flow data according to the form shown in the formula (5), wherein the result is as follows:
the particle swarm algorithm parameter initialization data is set by actual geological parameters, and the coal bed initial permeability k 0 The range is (1X 10) -20 ，1×10 -16 ) The initial permeability range is 10% in the speed limiting interval, i.e., - 5X 10 -18 ，5×10 -18 ) (ii) a Setting the number N of particles as 50, the maximum iteration number ger as 100, the truncation error as 0.001 and the individual learning factor c 1 Get 2, social learning factor c 2 And taking 2.
The final inversion results are shown in fig. 4 to 8; wherein, fig. 4 is a diagram of the inversion result of the coal seam initial permeability and the borehole extraction time, and it can be seen from the diagram that the initial permeability obtained by inversion is 3.79 multiplied by 10 -17 m 2 And the drilling extraction time is 94 days. And further calculating the evolution condition of coal seam extraction parameters on the basis of the coal seam initial permeability and the drill hole extraction time obtained by inversion. According to the gas flow forward model, the gas pressure distribution of the coal seam at the 94 th day is extracted and shown in fig. 5, the effective pressure radius of the gas in the coal seam and the residual gas content distribution of the coal seam are respectively shown in fig. 6 and 7, the residual gas amount of the coal seam at the moment is 3321.8kg, the gas extraction rate is 61.6%, and the permeability distribution map of the coal seam at the 94 th day is extracted and shown in fig. 8. And then comparing the coal seam extraction characteristic parameter data obtained by inversion with actual data of the coal mine to obtain the coal seam extraction characteristic parameter data.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention, and such modifications and adaptations are intended to be within the scope of the 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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| CN116663276A (en) * | 2023-05-23 | 2023-08-29 | 中国矿业大学 | Synchronous inversion method for coal bed gas pressure and permeability |
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| CN116663276A (en) * | 2023-05-23 | 2023-08-29 | 中国矿业大学 | Synchronous inversion method for coal bed gas pressure and permeability |
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