CN108228952B - Electrical anisotropy numerical simulation method for detecting goaf fracture zone by electrical method - Google Patents
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Abstract
An electrical anisotropy numerical simulation method for detecting a goaf fracture zone by an electrical method belongs to a mine electromagnetic detection numerical simulation method. The method comprises the following steps: 1. deducing an electrical method theory based on charged anisotropic characteristics of goaf cracks; 2. deducing according to an electrical law theory, and assembling a numerical simulation program; 3. establishing a geoelectricity model required by numerical simulation according to actual geological data of the goaf; 4. performing numerical simulation, rotating each power supply electrode by taking A as the center of a circle and AB as the radius, calculating a numerical value every 15 degrees, and calculating each power supply electrode AB; 5. changing the length of the AB, and repeating the step (4) until the length of the AB meets the design requirement; 6. and after the calculation result is output, drawing the calculation result in a polar coordinate system, and preliminarily judging the electrical anisotropy characteristics of the stratum according to the shape of apparent resistivity distribution and the length of AB. The advantages are that: the method can measure the apparent resistivity of different directions, and provides detailed geological data for mine water prevention and treatment.
Description
Technical Field
The invention relates to a mine electromagnetic detection numerical simulation method, in particular to an electrical anisotropy numerical simulation method for detecting a goaf fractured zone by an electrical method.
Background
The prevention and the suppression of major water inrush accidents in coal mines are always responsible for the implementation of safe production by various coal mine enterprises, coal mine safety monitoring departments, coal production management departments and various government management organizations, and the importance of hidden danger troubleshooting work is well made. In recent years, the goaf water permeability accidents of the serious water inrush accident type account for more than 70% of various coal mine water damage accidents. The key point of goaf water permeability is that a fracture zone forms a water guide channel, so that accumulated water in the goaf permeates into a mine to cause a mine water disaster accident.
Invar has published a method for calculating the electrical anisotropy characteristics of a layered medium by using a direct current method in 1999;
based on the Shenjinsong, calculation of the electrical anisotropy characteristics of the oil fracture reservoir is published in 2008;
the inventor calculates the electrical anisotropy characteristics of the water flowing fractured zone in 2016 on the basis of the prior art, and theoretically deduces the specific method steps as follows:
▽×E=0,▽·J=0 (1)
▽×H=J,▽·B=0 (2)
The magnetic field and current density can be expressed as:
wherein, TJAnd PHElectric and magnetic field spiral and polar scalar bits, respectively; t isHAnd PJMagnetic and electric field spiral and polar scalar bits, respectively;
in the same way, an expression of E can be obtained; from the fourier transform and boundary conditions; expression of horizontal electric field versus apparent resistivity:
wherein G is the coefficient of the electrode system; rhoaIs apparent resistivity; r is the distance from the coordinate origin O to the midpoint of the MN; erIs a midpoint electric field of MN; exIs the x-direction electric field at the midpoint of MN, EyIs the y-direction electric field at the midpoint of MN.
Disclosure of Invention
The invention aims to provide an electrical anisotropy numerical simulation method for detecting a goaf fractured zone by an electrical method, which provides further fractured zone information according to the development characteristics of the fracture of the water-flowing fractured zone, namely the trend or the tendency of the fracture, and provides more detailed geological information for a grouting technology in the prevention and treatment of goaf water permeability accidents.
The purpose of the invention is realized as follows: the detection numerical simulation method comprises the following steps: on the basis of an electrical method detection theory, considering the charged anisotropic characteristics of the goaf water-conducting fracture, and researching the relationship between the fracture zone development condition and apparent resistance distribution by using a numerical simulation method; the method comprises the following specific steps:
(1) deducing an electrical method theory based on charged anisotropic characteristics of goaf cracks;
(2) deducing according to an electrical law theory, and assembling a numerical simulation program; the assembly numerical simulation program is divided into four modules: firstly, inputting model parameters; judging an electric anisotropy geoelectricity model; calculating the response of the electric anisotropic geoelectric model; fourthly, outputting a calculation result;
(3) establishing a geoelectricity model required by numerical simulation according to actual geological data of the goaf, and simplifying the actual goaf into three layers, wherein the middle layer is an electrically anisotropic fissure zone, and the upper layer and the lower layer of the fissure zone are both ideal uniform media;
(4) performing numerical simulation on the geoelectricity model established in the step (3); the numerical simulation is as follows: for each power supply electrode, rotating by taking A as a circle center and AB as a radius, calculating a numerical value every 15 degrees, and for each power supply electrode AB, calculating 24 apparent resistance values in total;
(5) changing the length of the AB, and repeating the step (4) to calculate until the length of the AB meets the requirement of the detection depth;
(6) performing numerical simulation by assembling a numerical simulation program, outputting a calculation result by a calculation result output module, and drawing in a polar coordinate system, wherein the apparent resistivity of a polar diagram is distributed in an elliptic diagram shape, the major axis direction points to the trend of crack distribution, and the property of the ellipse is related to the crack tendency; and estimating fracture distribution parameters of the underground stratum by using the elliptical characteristic parameters of the azimuth apparent resistivity.
The method has the beneficial effects that by adopting the scheme, the calculation formula for describing the goaf fissure zone by utilizing the apparent resistivity is obtained by considering the goaf fissure charged anisotropy based on the electromagnetic exploration theoryBy analyzing the distribution state of the apparent resistance values measured on the ground surface, the information of the goaf fracture zone can be obtained, and a theoretical basis is provided for the detection and prevention of the goaf water permeability accident by an electrical method.
The invention has the advantages that:
1. the method starts from a basic electromagnetic field theory, considers the charged anisotropic characteristics of the goaf crack, and obtains the relationship between the electromagnetic response and the apparent resistivity.
2. The method provided by the invention can estimate the trend and the tendency of the water flowing fractured zone cracks by utilizing the distribution morphological characteristics of the apparent resistivity of the earth surface, and provides detailed geological data for mine water prevention and treatment.
3. The apparent resistivity of different directions is measured, the development state of the goaf fractured zone can be judged according to the distribution state of the apparent resistivity, a theoretical basis is provided for detection of the goaf fractured zone, and the method is significant.
Drawings
FIG. 1 is a goaf geomodel diagram of the present invention.
Fig. 2(a) is a simplified diagram of the goaf electrical model of the present invention.
FIG. 2(b) is a schematic diagram of a goaf measurement mode according to the present invention.
FIG. 3(a) shows that the crack orientation of the present invention is consistent with the Y-axis, crack propensity: and alpha is a goaf electrical model diagram of 45 degrees.
FIG. 3(b) shows that the crack orientation of the present invention is consistent with the Y-axis, crack propensity: and alpha is 60 degrees of goaf electrical model diagram.
FIG. 3(c) shows the crack orientation of the present invention is consistent with the Y-axis, crack propensity: and alpha is a goaf electrical model diagram of 90 degrees.
Fig. 4(a) is a diagram showing a result of a numerical simulation of the geoelectric model of fig. 3 (a).
Fig. 4(b) is a diagram showing a result of a numerical simulation of the geoelectric model of fig. 3 (b).
Fig. 4(c) is a diagram showing a result of a numerical simulation of the geoelectricity model of fig. 3 (c).
FIG. 5(a) shows the fracture strike of the invention: β is 0 °, tendency: and alpha is a goaf electrical model diagram of 45 degrees.
FIG. 5(b) shows the fracture strike of the invention: β is 30 °, tendency: and alpha is a goaf electrical model diagram of 45 degrees.
FIG. 5(c) shows the fracture strike of the invention: β is 60 °, tendency: and alpha is a goaf electrical model diagram of 45 degrees.
Fig. 6(a) is a numerical simulation diagram of the geoelectrical model of fig. 5 (a).
Fig. 6(b) is a numerical simulation diagram of the geoelectrical model of fig. 5 (b).
Fig. 6(c) is a numerical simulation diagram of the geoelectrical model of fig. 5 (c).
Detailed Description
The detection numerical simulation method comprises the following steps: on the basis of an electrical method detection theory, considering the charged anisotropic characteristics of the goaf water-conducting fracture, and researching the relationship between the fracture zone development condition and apparent resistance distribution by using a numerical simulation method; the method comprises the following specific steps:
(1) deducing an electrical method theory based on charged anisotropic characteristics of goaf cracks;
(2) deducing according to an electrical law theory, and assembling a numerical simulation program; the assembly numerical simulation program is divided into four modules: firstly, inputting model parameters; judging an electric anisotropy geoelectricity model; calculating the response of the electric anisotropic geoelectric model; fourthly, outputting a calculation result;
(3) establishing a geoelectricity model required by numerical simulation according to actual geological data of the goaf, and simplifying the actual goaf into three layers, wherein the middle layer is an electrically anisotropic fissure zone, and the upper layer and the lower layer of the fissure zone are both ideal uniform media;
(4) performing numerical simulation on the geoelectricity model established in the step (3); the numerical simulation is as follows: for each power supply electrode, rotating by taking A as a circle center and AB as a radius, calculating a numerical value every 15 degrees, and for each power supply electrode AB, calculating 24 apparent resistance values in total;
(5) changing the length of the AB, and repeating the step (4) to calculate until the length of the AB meets the requirement of the detection depth;
(6) performing numerical simulation by assembling a numerical simulation program, outputting a calculation result by a calculation result output module, and drawing in a polar coordinate system, wherein the apparent resistivity of a polar diagram is distributed in an elliptic diagram shape, the major axis direction points to the trend of crack distribution, and the property of the ellipse is related to the crack tendency; and estimating fracture distribution parameters of the underground stratum by using the elliptical characteristic parameters of the azimuth apparent resistivity.
Example 1: the scalar bits of maxz's equations for electrical anisotropy are represented as spiral and polar scalar bits.
And (3) obtaining a wave number domain expression of the field component by means of two-dimensional Fourier transform of the current density and the magnetic field vector in the x and y directions by means of a fast algorithm.
Solving maxz's basic equations in the wavenumber domain yields a basic solution to the scalar electromagnetic field.
And obtaining a corresponding relational expression according to the continuity condition of the electromagnetic field at the stratum interface.
The current source is inserted at the earth's surface, taking into account the coupling conditions originating from the earth's surface.
And constructing a calculation recurrence relation based on the formation interface continuity condition and the source coupling condition of the earth surface to obtain the scalar potential current density and the scalar potential magnetic field.
Obtaining an electric field and a magnetic field of a spatial domain by utilizing two-dimensional Fourier inverse transformation; wherein the apparent resistivity of the anisotropic formation is expressed by using a horizontal electric field.
Wherein the content of the first and second substances,e is the electric field, x and y are respectively the abscissa and ordinate of the measuring point, G is the coefficient of the electrode system, G ═ π L2And L is AB/2, AB is the electrode distance, and I is the current.
Numerical simulation first studies the relationship between the crack tendency and the apparent resistivity distribution characteristics, and selects three goaf geoelectrical models, wherein the crack trend is always along the Y-axis direction, the trend angle is set as the included angle β with the Y-axis direction to be 0 °, and the crack inclination angles are different, wherein (a) the inclination angle is set to be 45 °, (b) the inclination angle is set to be 60 °, (c) the inclination angle is set to be 90 °, as shown in fig. 4, and the numerical simulation result is shown in fig. 5, and the morphological characteristics of the apparent resistivity distribution change with the change of the inclination angle. Comparing the earth electric model fig. 4 with the corresponding numerical simulation results fig. 5, it is possible to conclude (1): the shape of the polar diagram of the apparent resistivity distribution is related to the dip angle α.
And researching the relation between the fracture trend and the apparent resistivity distribution characteristics, and selecting three goaf geoelectrical models, as shown in fig. 6, wherein the fracture trends are all alpha-45 degrees, the fracture trend distribution is (a) trend: β is 0 °; (b) the trend is as follows: β -30 °; (c) the trend is as follows: β is 60 °, and the numerical simulation results are shown in fig. 6, where the orientation of the symmetry axis of the elliptical shape of the apparent resistivity distribution is related to the trend. Comparing the geoelectric model fig. 5 with the numerical simulation results fig. 6, the following conclusion (3) is reached: the symmetry axis orientation of the elliptical shape of the apparent resistivity distribution is related to the strike.
The technical solution of the present invention will be further specifically described with reference to the accompanying drawings and the detailed description.
FIG. 2(a) is a simplified diagram of a goaf geoelectrical model; FIG. 2(b) is a schematic view of a goaf measurement mode; taking A as the center of a circle and AB as the radius, calculating values every 15 degrees, and obtaining 24 values in a circle.
Fig. 3 shows three goaf geoelectrical models in which the fracture direction is constant (along the Y axis, the angle of the trajectory is 0 ° from the Y axis), and the fracture inclination angles are different, where (a) the inclination angle is 45 °, (b) the inclination angle is 60 °, (c) the inclination angle is 90 °.
Fig. 3 (a): tendency to crack: α is 45 °, the trend coincides with the Y-axis direction: β is 0 °; (b) the method comprises the following steps Tendency to crack: α is 60 °, the trend coincides with the Y-axis direction: β is 0 °; (c) the method comprises the following steps Tendency to crack: α is 90 °, the trend coincides with the Y-axis direction: β is 0 °.
FIG. 4 is a result of a geoelectrical model numerical simulation depicted in FIG. 3, wherein (a): tendency to crack: α is 45 °, trend: beta is 0 degrees, and the result of geoelectricity model numerical simulation; (b) the method comprises the following steps Tendency to crack: α is 60 °, trend: beta is 0 degrees, and the result of geoelectricity model numerical simulation; (c) the method comprises the following steps Tendency to crack: α is 90 °, trend: beta is 0 deg. and the result is simulated by geoelectric model numerical value.
FIG. 4 is a result of a geoelectrical model numerical simulation depicted in FIG. 3, wherein (a): tendency to crack: α is 45 °, trend: beta is 0 degrees, and the result of geoelectricity model numerical simulation; (b) the method comprises the following steps Tendency to crack: α is 60 °, trend: beta is 0 degrees, and the result of geoelectricity model numerical simulation; (c) the method comprises the following steps Tendency to crack: α is 90 °, trend: beta is 0 deg. and the result is simulated by geoelectric model numerical value.
FIG. 5 is a plot of a fracture dip goaf electrical model; when: (a) the trend is as follows: β is 0 °, tendency: α is 45 °; (b) the trend is as follows: β is 30 °, tendency: α is 45 °; (c) the trend is as follows: β is 60 °, tendency: α is 45 °.
Fig. 6 shows that the crack tendency was constant, and α was 45 °. Wherein (a) is oriented: β is 0 °; (b) the trend is as follows: β -30 °; (c) the trend is as follows: β is 60 °.
Three goaf geoelectrical models with different fracture dip angles are always run (along the Y-axis direction, the run angle is an included angle beta of 0 DEG with the Y-axis direction), wherein (a) the dip angle is 45 DEG, (b) the dip angle is 60 DEG, and (c) the dip angle is beta of 90 deg.
FIG. 6 is a numerical simulation result of the geoelectrical model depicted in FIG. 5. Wherein (a) is oriented: β is 0 °, tendency: alpha is 45 degrees, and the result of geoelectricity model numerical simulation; (b) the trend is as follows: β is 30 °, tendency: alpha is 45 degrees, and the result of geoelectricity model numerical simulation; (c) the trend is as follows: β is 60 °, tendency: alpha is 45 degrees, and the result is simulated by the geoelectricity model numerical value.
Claims (1)
1. An electrical anisotropy numerical simulation method for detecting a goaf fracture zone by an electrical method is characterized by comprising the following steps: the detection numerical simulation method comprises the following steps: on the basis of an electrical method detection theory, considering the charged anisotropic characteristics of the goaf water-conducting fracture, and researching the relationship between the fracture zone development condition and apparent resistance distribution by using a numerical simulation method;
the method comprises the following specific steps:
(1) deducing an electrical method theory based on charged anisotropic characteristics of goaf cracks;
(2) deducing according to an electrical law theory, and assembling a numerical simulation program; the assembly numerical simulation program is divided into four modules: firstly, inputting model parameters; judging an electric anisotropy geoelectricity model; calculating the response of the electric anisotropic geoelectric model; fourthly, outputting a calculation result;
(3) establishing a geoelectricity model required by numerical simulation according to actual geological data of the goaf, and simplifying the actual goaf into three layers, wherein the middle layer is an electrically anisotropic fissure zone, and the upper layer and the lower layer of the fissure zone are both ideal uniform media;
(4) performing numerical simulation on the geoelectricity model established in the step (3); the numerical simulation is as follows: for each power supply electrode, rotating by taking A as a circle center and AB as a radius, calculating a numerical value every 15 degrees, and for each power supply electrode AB, calculating 24 apparent resistance values in total;
(5) changing the length of the AB, and repeating the step (4) to calculate until the length of the AB meets the requirement of the detection depth;
(6) performing numerical simulation by assembling a numerical simulation program, outputting a calculation result by a calculation result output module, and drawing in a polar coordinate system, wherein the apparent resistivity of a polar diagram is distributed in an elliptic diagram shape, the major axis direction points to the trend of crack distribution, and the property of the ellipse is related to the crack tendency; estimating fracture distribution parameters of the underground stratum by utilizing the elliptical characteristic parameters of the azimuth apparent resistivity;
step 1 (in), the electric method theory derivation of the charged anisotropic characteristics is to express scalar bits of Max equation of the electric anisotropy into spiral scalar bits and polar scalar bits;
measuring the current density and the magnetic field vector by two-dimensional Fourier transform in the x and y directions by means of a fast algorithm to obtain a wave number domain expression of the field component;
solving a Max basic equation in a wave number domain to obtain a basic solution of an electromagnetic field scalar;
obtaining a corresponding relational expression according to the continuity condition of the electromagnetic field at the stratum interface;
the current source is inserted at the earth surface, and the coupling condition from the earth surface is considered;
constructing a calculation recurrence relation based on the stratum interface continuity condition and the earth surface source coupling condition to obtain scalar potential current density and a scalar potential magnetic field;
obtaining an electric field and a magnetic field of a spatial domain by utilizing two-dimensional Fourier inverse transformation; wherein, the apparent resistivity of the anisotropic stratum is expressed by utilizing a horizontal electric field;
wherein the content of the first and second substances,e is the electric field, x and y are respectively the abscissa and ordinate of the measuring point, G is the coefficient of the electrode system, G ═ π L2L is AB/2, AB is electrode distance, I is current;
in the step (6), in the numerical simulation, three goaf geoelectrical models are selected according to the relationship between the crack tendency and the apparent resistivity distribution characteristics, wherein the crack trend is always along the Y-axis direction, the trend angle is set as an included angle β of 0 ° with the Y-axis direction, and the three goaf geoelectrical models with different crack dip angles are selected, wherein (a) the dip angle is α of 45 °, (b) the dip angle is α of 60 °, (c) the dip angle is β of 90 °, and the numerical simulation result changes according to the form characteristics of the resistivity distribution along with the change of the dip angle, so that the conclusion is obtained: a polar diagram of the apparent resistivity distribution, the shape of which is related to the dip angle α;
the trend of the crack distribution, the relation between the crack trend and the apparent resistivity distribution, three goaf earth-electricity models are selected, the crack trend is always alpha-45 degrees, the crack trend distribution is (a) trend: β is 0 °; (b) the trend is as follows: β -30 °; (c) the trend is as follows: β is 60 °, depending on the orientation of the symmetry axis of the elliptical shape of the resistivity distribution.
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