Electromagnetic anomaly calculation method for charging conductor fracturing fracture

Abstract

This invention discloses a method for calculating electromagnetic anomalies in fracturing fractures of a charging conductor, comprising the following steps: S1, establishing a fracture model by monitoring the well location, burial depth, fracture size, power supply current, and frequency settings; S2, calculating the formation equivalent resistivity using multi-layer profile parameters; S3, dividing the charging conductor into Nd electric dipole sources and obtaining the vector potential and scalar potential Φ of each electric dipole source at the surface; S4, obtaining the E and H values ​​of the electric dipole sources at the surface according to the electric field and magnetic field calculation formulas, determining the reference point N, and obtaining the electric field E in the MN direction. MN and magnetic field H MN S5. Based on the principle of vector superposition, the electromagnetic fields of all the segmented electric dipole sources are superimposed to obtain the electromagnetic fields before and after fracturing, and the electric field anomaly E caused by the fracturing fracture is obtained by differential calculation. a and magnetic field anomaly H a The present invention aims to construct a model of a charging conductor crack to obtain electromagnetic anomalies generated by fracturing cracks, providing a theoretical basis for electromagnetic monitoring and crack identification.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydraulic fracturing electromagnetic monitoring, and particularly relates to a method for calculating electromagnetic anomaly of a charged conductor fracturing fracture. BACKGROUND

[0002] Hydraulic fracturing is a key technology for oil and gas production and energy conversion, and real-time monitoring is a key means to ensure that fracturing construction achieves an ideal effect. In order to understand fracture propagation, especially far-field reservoir reconstruction, an economic and effective monitoring technology is needed to analyze and evaluate fracturing construction quality and adjust construction parameters in real time. A large amount of water or fracturing fluid is injected during fracturing, and the fracturing fluid will flow along the microcracks and continuously expand. The fracturing fluid, conductive proppant and the reconstructed layer have obvious electrical differences, so the electromagnetic method has obvious advantages for fracture monitoring.

[0003] The current electromagnetic monitoring technology is either based on the traditional artificial source electromagnetic induction method, with small abnormal signals, or the charged fracture model is based on the direct current calculation method, with serious noise interference and limited monitoring depth.

[0004] Therefore, there is an urgent need to design a fracture monitoring method to overcome the above problems or at least partially solve the above problems to obtain effective electromagnetic anomalies. SUMMARY

[0005] The purpose of the present application is to solve the problem that the prior art cannot intuitively describe the growth of the fracturing fracture in the reservoir reconstruction process, and a method for calculating electromagnetic anomaly of a charged conductor fracturing fracture is provided.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] A method for calculating electromagnetic anomaly of a charged conductor fracturing fracture, comprising the following steps:

[0008] S1, monitoring the well position, depth, fracture size, power supply current and frequency setting to establish a fracture model;

[0009] S2, converting the formation equivalent resistivity by the multi-layer profile parameters;

[0010] S3, dividing the charged conductor source into Nd electric dipole sources to obtain the vector potential and scalar potential of each electric dipole source on the ground surface;

[0011] S4, electric dipole source electromagnetic field calculation: obtaining the electric field and magnetic field values of the electric dipole source on the ground surface according to the electric field and magnetic field calculation formula, determining the reference point, and obtaining the electric field and magnetic field in the direction;

[0012] ​S5, based on the principle of vector superposition, superimposing the electromagnetic field of all the split electric dipole sources, respectively obtaining the electromagnetic field before and after fracturing, and calculating the electric field anomaly E caused by the fracturing fracture through difference a and magnetic field anomaly H a .

[0013] Preferably, the formation equivalent resistivity in step 2 is calculated by formula (1)

[0014]

[0015] In resistivity logging, first form the integral resistance curve, that is,

[0016]

[0017] In the formula, ρ is the resistivity, Ω·m; H is the total thickness of all layer sets, m; ρ i and h i are the resistivity and thickness of the i-th layer, respectively.

[0018] Preferably, in step S3, the vector potential is marked as The scalar potential is marked as Φ, and under the quasi-static condition, the vector potential and the scalar potential Φ are expressed in the form of Helmholtz equation, that is,

[0019]

[0020]

[0021] In the formula, k 2 = iωμσ, k is the frequency domain wave number, ω = 2πf is the angular frequency, f is the electromagnetic wave frequency, and μ and σ are the magnetic permeability and electrical conductivity of the medium, respectively.

[0022] Preferably, in step S3, the electric dipole source is located at the origin of the Cartesian coordinate system, and the direction is arbitrary, represented by vector , with a length of dl. The dipole source current is a harmonic current I = I0e -iωt , wherein I0 is the current intensity of the dipole source;

[0023] Preferably, when the frequency is zero, according to the Biot-Savart law, the magnetic induction intensity generated by the constant current at the vector is

[0024]

[0025] , wherein, is the electric dipole moment, I0 is the current intensity, and dl is the length of the electric dipole.

[0026] So, the stable magnetic field has a vector potential

[0027]

[0028] Preferably, the frequency is not zero, in the spherical coordinate system (r, φ, θ), equation (3) is expressed as

[0029]

[0030] Since the vector potential of the electric dipole source is spherically symmetric, the derivative terms related to φ and θ in equation (7) disappear, and it is simplified as

[0031]

[0032] where,

[0033]

[0034] Therefore, equation (8) becomes

[0035]

[0036] The general solution of equation (9) is

[0037]

[0038] where, is an unknown vector constant.

[0039] Preferably, when r→∞, e ikr tends to zero, and e -ikr tends to infinity. Therefore, is 0, then

[0040]

[0041] Using the limit condition of ω→0, and according to equation (6), determine that is,

[0042]

[0043] Therefore

[0044]

[0045] Substituting equation (13) into equation (11), we get

[0046]

[0047] Substituting equation (14) into the Lorentz gauge , we get the expression of scalar potential:​

[0048]

[0049] Preferably, in step S4, the expressions for calculating the electric field and the magnetic field are as follows:

[0050]

[0051]

[0052] Electromagnetic vector position Substituting the scalar potential Φ into equations (16) and (17), we obtain the expressions for the electric and magnetic fields excited by a time-varying current electric dipole source in a homogeneous isotropic infinite medium, respectively:

[0053]

[0054]

[0055] set up for and The included angle, express The angle between MN and express The angle between MN and Let MN be the angle between MN and MN. Then the expressions for the electric and magnetic fields in the MN direction are:

[0056]

[0057]

[0058] Preferably, in step S5, the charging wire of length L is equivalent to the superposition of Nd electric dipole sources. According to the principle of vector superposition, the electric field strength is expressed as:

[0059]

[0060] Similarly, the magnetic field strength of a charging wire of length L can be expressed as:

[0061]

[0062] Similarly, the scalar representation of a charging wire of length L is:

[0063]

[0064] In the formula, r i Let be the distance between the i-th electric dipole source and the observation point M, where i = 1, 2, 3... Nd, and Nd = L / dl.

[0065] The difference calculation, that is, the difference value of the observation signals before and after the crack formation, the electromagnetic field generated by the charging wellbore is also equivalent to the superposition of multiple electric dipole sources. Assuming that the electric fields before and after the crack formation are E w 、E w+f , the magnetic fields are H w 、H w+f , and the scalar potential is Φ w 、Φ w+f , then the electric field anomaly, the magnetic field anomaly and the potential anomaly are respectively:

[0066] E a =E w+f -E w (25)

[0067] H a =H w+f -H w (26)

[0068] Φ a =Φ w+f -Φ w (27)

[0069] The technical effects and advantages of the present application: the electromagnetic anomaly calculation method of the charged conductor fracturing crack provided by the present application has the following advantages compared with the traditional calculation method:

[0070] 1. The crack model constructed by the present application is based on a charged conductor, and the signal strength is much larger than the induced anomaly field of the traditional artificial source electromagnetic method;

[0071] 2. The electromagnetic field generated by the fracturing crack based on the charged conductor obtained by the present application has frequency characteristics, solving the problem of serious direct current noise interference;

[0072] 3. The present application obtains the anomaly of the multi-field component of the electric field, the magnetic field and the scalar potential, which can more effectively monitor and identify the fracturing crack;

[0073] 4. The present application carries out complex crack electromagnetic field calculation to obtain its electromagnetic anomaly, which provides a theoretical basis for realizing electromagnetic monitoring crack identification. BRIEF DESCRIPTION OF DRAWINGS

[0074] The features and advantages of the present application can be more clearly understood by referring to the accompanying drawings, which are schematic and should not be understood as limiting the present application. In the drawings:

[0075] Figure 1 A flowchart of the electromagnetic anomaly calculation method of the charged conductor fracturing crack provided by an embodiment of the present application is shown;

[0076] Figure 2 A schematic diagram of the electric dipole source coordinates provided by an embodiment of the present application is shown.

[0077] Figure 3 A horizontal well single fracture model schematic diagram provided by an embodiment of the present application;

[0078] Figure 4 A surface potential and anomaly distribution map provided by an embodiment of the present application. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0080] The present application provides an electromagnetic anomaly calculation method of a charged conductor fracturing fracture: Figures 1-4

[0081] As shown in a flowchart of an electromagnetic anomaly calculation method of a charged conductor fracturing fracture, the electromagnetic anomaly calculation method comprises the following steps: Figure 1

[0082] S1, monitoring well position, burial depth, fracture size, power supply current and frequency setting to establish a fracture model;

[0083] S2, converting the formation equivalent resistivity by multi-layer profile parameters;

[0084] The formation equivalent resistivity is calculated by formula (1)

[0085]

[0086] In resistivity logging, an integral resistance curve is first formed, that is,

[0087]

[0088] In the formula, ρ is the resistivity, Ω·m; H is the total thickness of all layer sets, m; ρ i and h i are the resistivity and thickness of the i-th layer, respectively.

[0089] S3, the charged wire source is divided into Nd electric dipole sources, and the vector potential and the scalar potential Φ of each electric dipole source at the surface are obtained;

[0090] Under quasi-static conditions, the vector potential and the scalar potential Φ are expressed in the form of the Helmholtz equation, that is, ​​

[0091]

[0092]

[0093] In the formula, k 2 =iωμσ, k is the wavenumber in the frequency domain, ω = 2πf is the angular frequency, f is the electromagnetic wave frequency, and μ and σ are the magnetic permeability and electrical conductivity of the medium, respectively.

[0094] Assuming the electric dipole source is located at the origin of the Cartesian coordinate system, such as Figure 2 The diagram shown illustrates the coordinates of an electric dipole source. Its direction is arbitrary and can be represented by a vector. This indicates that the length is dl. The dipole source current is a harmonic current I = I0e -iωt Where I0 is the current intensity of the dipole source.

[0095] When the frequency of the dipole source current is zero, according to the Biot-Savart law, the position vector... The magnetic flux density produced by the constant current at point is

[0096]

[0097] in, It is an electric dipole moment. I0 is the current intensity, and dl is the length of the electric dipole.

[0098] So, stable magnetic field vector position for

[0099]

[0100] When the frequency of the dipole source current is not zero, in the spherical coordinate system (r,φ,θ), equation (3) is expressed as:

[0101]

[0102] Due to the electric dipole source vector potential It is spherically symmetric, and the derivative terms related to φ and θ in equation (7) disappear, simplifying to

[0103]

[0104] in,

[0105]

[0106] Therefore, equation (8) becomes

[0107]

[0108] The general solution of equation (9) is

[0109]

[0110] where, is an unknown vector constant.

[0111] When r→∞, e ikr tends to zero, while e -ikr tends to infinity. Therefore, is 0, then we have

[0112]

[0113] Using the limit condition of ω→0, we determine i.e.

[0114]

[0115] Therefore

[0116]

[0117] Substituting equation (13) into equation (11), we obtain

[0118]

[0119] Substituting equation (14) into the Lorentz gauge , we obtain the expression of the scalar potential:

[0120]

[0121] S4, electromagnetic field calculation of electric dipole source: according to the electric field and magnetic field calculation formula, the E and H values of the electric dipole source on the ground surface are obtained, the reference point N is determined, and the MN direction electric field E MN and magnetic field H MN are obtained.

[0122] The electric field and magnetic field calculation expressions are respectively:

[0123]

[0124]

[0125] The electromagnetic vector potential and the scalar potential Φ are brought into equation (16) and equation (17), and the expressions of the electric field and the magnetic field excited by the time-varying electric dipole source in the uniform and isotropic infinite medium are respectively:

[0126]

[0127]

[0128] Let For with angle, represent angle with MN, represent angle with MN, For angle with MN, the electric field and magnetic field expressions in the MN direction are written as:

[0129]

[0130]

[0131] S5, based on the principle of vector superposition, the electromagnetic field of all the split electric dipole sources is superimposed, the electromagnetic fields before and after fracturing are obtained respectively, and the electric field anomaly E a and the magnetic field anomaly H a caused by the fracturing fracture are obtained by difference calculation.

[0132] The equivalent of the charged wire with length L is the superposition of Nd electric dipole sources. According to the principle of vector superposition, the electric field intensity is represented as:

[0133]

[0134] Similarly, the magnetic field intensity of the charged wire with length L is represented as:

[0135]

[0136] Similarly, the scalar potential of the charged wire with length L is represented as:

[0137]

[0138] In the formula, r i is the distance between the ith electric dipole source and the observation point M, i=1,2,3...Nd, Nd=L / dl.

[0139] The difference calculation is the difference value of the observation signals before and after the fracture formation. The electromagnetic field generated by the charged wellbore is also equivalent to the superposition of multiple electric dipole sources. Let the electric fields before and after the fracture formation be E w , E w+f , the magnetic fields be H w , H w+f , and the scalar potentials be Φ w , Φ w+f , then the electric field anomaly, the magnetic field anomaly, and the potential anomaly are respectively:

[0140] E a =E w+f -E w (25)

[0141] H a =H w+f -H w (26)

[0142] Φ a =Φ w+f -Φ w (27)

[0143] It is known from formulae (22)-(24) that the formulae for calculating the electromagnetic field generated by the charged conductor fracture derived by the present application are related to the frequency f, and therefore have frequency response characteristics, and according to the fracturing site environment, a square wave signal of a specific frequency is transmitted to improve the signal-to-noise ratio of the electromagnetic signal;

[0144] If there are multiple charged conductor fractures, the electromagnetic field thereof is still obtained by superposition, and therefore the present application performs simulation research on complex fractures;

[0145] It is known from formulae (25)-(27) that the electromagnetic anomaly of the fracturing fracture based on the charged conductor underground according to the present application is obtained by differentiating the observation signals before and after the fracture is generated, and the fracture characteristics are reflected through the electromagnetic anomaly.

[0146] Consider Figure 3 The horizontal well single fracture model diagram shown in the figure, the equivalent conductivity of the formation is 1 / 1000 S / m, the wellhead coordinates are A(-500, 0, 0), the vertical depth is 4 km, the horizontal well section length is 1 km, the single fracture length is set to 200 m, which is perpendicular to the horizontal well, and the two end point coordinates are (0, -100, 4000) and (0, 100, 4000) respectively. The transmission current is set to 10 A, the measurement range is 2 km x 2 km, the measurement network density is 10 m x 10 m, and the frequency is 1 Hz. Since the frequency is very small, the scalar potential Φ is equivalent to the electric potential U, and the surface observation potential and the fracturing fracture anomaly distribution are shown in Figure 4 The potential value reaches 10 8 μV, and the potential anomaly exceeds 2000 μV; the potential anomaly plan view is symmetrical about the Y axis, and is consistent with the fracture position and orientation.

[0147] Finally, it should be noted that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent replacements to some technical features, and any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for calculating electromagnetic anomalies in fracturing cracks of charged conductors, characterized in that, Includes the following steps: S1. Establish a fracture model by monitoring the location and depth of the well, the size of the fracture, and setting the power supply current and frequency. S2. The formation equivalent resistivity is calculated by converting multi-layer profile parameters. S3. Divide the charging wire source into Nd electric dipole sources and obtain the vector potential of each electric dipole source on the ground surface. and scalar position Φ; S4. Electromagnetic field calculation of electric dipole source: Obtain the E and H values ​​of the electric dipole source at the Earth's surface using the electric and magnetic field calculation formulas, determine the reference point N, and obtain the electric field E in the MN direction. MN and magnetic field H MN In step S4, the electric and magnetic fields of the electric dipole source on the Earth's surface are represented as follows: Substituting equations (3) and (4) into equations (5) and (6), we obtain the expressions for the electric and magnetic fields excited by an electric dipole source in a homogeneous isotropic infinite medium when supplied with a time-varying current, respectively: set up for and The included angle, express The angle between MN and express The angle between MN and Let MN be the angle between MN and MN. Then the expressions for the electric and magnetic fields in the MN direction are: S5. Based on the principle of vector superposition, the electromagnetic fields of all the segmented electric dipole sources are superimposed to obtain the electromagnetic fields before and after fracturing, and the electric field anomaly E caused by the fracturing fracture is obtained by differential calculation. a and magnetic field anomaly H a .

2. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1, characterized in that: The formation equivalent resistivity mentioned in step S2 is calculated by the following formula (1). In resistivity logging, the integrated resistance curve is first formed, i.e. In the formula, ρ is the resistivity, Ω·m; H is the total thickness of all layers, m; ρ i and h i Hereinafter, we have the resistivity and thickness of the i-th layer, respectively.

3. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1, characterized in that: In step S3, the vector potential of the electric dipole source The scalar value Φ is calculated from equations (3) and (4). Where, k 2 =iωμσ, k is the wave number in the frequency domain, ω = 2πf is the angular frequency, f is the electromagnetic wave frequency, and μ and σ are the magnetic permeability and electrical conductivity of the medium, respectively; It is an electric dipole moment. I0 is the current intensity, and dl is the length of the electric dipole, with arbitrary direction, expressed as a vector. express.

4. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1, characterized in that: In step S5, the charging wire of length L is equivalent to the superposition of Nd electric dipole sources. According to the principle of vector superposition, the electric field strength is expressed as: Similarly, the magnetic field and scalar potential of the charging wire of length L are obtained from equations (12) and (13). In the formula, r i Let Nd be the distance between the i-th electric dipole source and the observation point M, where i = 1, 2, 3...Nd, and Nd = L / dl. The differential calculation refers to the difference between the observed signals before and after the fracture formation. The electromagnetic field generated by the charging well is also equivalent to the superposition of multiple electric dipole sources. Let the electric fields before and after the fracture formation be E... w E w+f The magnetic fields are H w H w+f Scalar bit is Φ w Φ w+f Then, the electric field anomaly, magnetic field anomaly, and potential anomaly are respectively: AND a =And w+f -AND w (14) H a =H w+f- H w (15) F a =Φ w+f -F w (16)。 5. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1 or 3, characterized in that, The electromagnetic field generated by the charging conductor has frequency characteristics, which solves the problem of severe DC noise interference in practice.

6. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1, characterized in that, The charging conductor represents a fracturing fracture model, and the signal strength it generates is much greater than the induction anomaly of the traditional artificial source electromagnetic method.

7. The method for calculating electromagnetic anomalies in a charging conductor fracturing crack according to claim 1 or 4, characterized in that: If there are multiple charging conductor cracks, their electromagnetic fields are still obtained by superposition using equations (11) to (13), and then electromagnetic anomalies are obtained using equations (14) to (16), that is, simulation calculations of complex cracks are performed.

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