A calculation method for geometric factors of transient electromagnetic exploration in inclined shafts

Abstract

The present invention relates to a method for calculating the geometric factor of transient electromagnetic exploration in an inclined shaft, comprising the following steps: establishing a formation current loop model. For any point Q on the formation loop, the position of the transmitting coil in the inclined shaft relative to the formation loop remains unchanged, and only the coordinates of the receiving coil change after coordinate rotation; according to the Biot-Savart theorem, the magnetic induction intensity #imgabs0# generated by the current element at point Q at the position of the receiving coil gives the geometric factor g for reception in the z direction z , which reflects the contribution weight of the conductivity at point Q to the useful signal received in the z direction at the position P' of the receiving coil; integrating over the entire space dxdydz to obtain the total useful signal V R ; obtaining the geometric factor g in the y direction using the magnetic field in the y direction y ; obtaining the geometric factor g in the x direction using the magnetic field in the x direction x .

Description

Technical Field

[0001] The present invention belongs to the field of cross-well remaining oil monitoring and exploration in transient electromagnetic logging technology. More precisely, it is a method for calculating the geometric factor of the whole space when the well where the transmitting coil is located is inclined by using the transient electromagnetic exploration response and the useful signal re-excited by the eddy current. Background Art

[0002] In the field of oil exploration, useful signals and geometric factors are widely used for remaining oil monitoring. In the geometric factor theory proposed by Doll, the formation is disassembled into a series of formation current loop models located in the air, and the transient electric field excited by the transmitting coil in the formation is replaced by the electromagnetic field in the air. Given an excitation source to the transmitting coil, a magnetic field distributed in a dipole shape can be induced, and the induced electromotive force is in a closed state and distributed along the circumferential direction. As Figure 1 shown, the induced electromotive force in the loop will re-excite a current, i.e., eddy current, inside the loop, and its amplitude is proportional to the formation conductivity. The response re-excited by this eddy current at the receiving position is the secondary field response, i.e., the useful signal. The useless signal is the induced electromotive force generated by the magnetic field excited by the transmitting coil at the receiving position, which is not affected by the formation conductivity. The amplitude of this signal is relatively large and exists superimposed with the useful signal (Zhang Gengji. Electrical Logging [M]. Petroleum Industry Press, 1984: 128-137.). Based on this, the eddy current is obtained by using the electric field intensity response in the formation, and the derivative of it with respect to time is used to obtain the response of the formation eddy current re-excitation, and the polarity change of the eddy current excitation response is discovered. Li Hongrui extended the axisymmetric response in the well to the whole space and obtained the geometric factor of the whole space, converting the magnetic field characteristics in different azimuths and distances into geometric factors with different polarities and amplitudes, and discovered the polarity change of the geometric factor in space (Shen J G, Li H R, Shen Y J, Full Space Geometric Factors for Cross-well Transient Electromagnetic Exploration [J]. Geophysical Prospecting for Petroleum, 2020, 59(03): 462-471.).

[0003] When the transmitting coil is excited in an inclined well, the formation ring model also tilts, and the geometric relationship between the receiving position in the adjacent well and the formation ring changes. Its transient electromagnetic response is quite different from that in a vertical well excitation. When the well where the transmitting coil is located is inclined, relatively large changes occur in the transient electromagnetic responses received in all directions in the well and the re-excitation responses of formation eddy currents. Inclined wells are widely present in actual production such as offshore oilfields and mountainous areas. By exciting a transient electromagnetic field in an inclined well and receiving on the ground or in adjacent wells, the conductivity distribution of the formation around the well can be effectively detected. Studying the distribution of useful signals in the transient electromagnetic exploration of inclined wells has certain guiding significance for designing acquisition devices. Therefore, a full-space geometric factor for the transient electromagnetic exploration of inclined wells is proposed and its spatial distribution is analyzed. Summary of the Invention

[0004] The object of the present invention is to provide a method for calculating the geometric factor of transient electromagnetic exploration of inclined wells, and the technical solution is as follows:

[0005] A method for calculating the geometric factor of transient electromagnetic exploration of inclined wells includes the following steps:

[0006] (1) Establish a formation current loop model. Using the Cartesian coordinate system, z coincides with the axis of the transmitting well. The transmitting coil is regarded as a magnetic dipole with a dipole moment of M = n T S0I, with the direction along the z direction. S0 is the cross-sectional area of the transmitting and receiving coils. Let n T , n R be the number of turns of the transmitting coil and the receiving coil respectively. The horizontal distance between the axes of the transmitting coil and the receiving coil is c, the vertical distance is L, and I is the current excitation waveform;

[0007] The transmitting well rotates around the x-axis. Let the coordinates of the rotated inclined well coordinate system be X, Y, Z, and the coordinates of the original geodetic coordinate system be x1, y1, z1:

[0008]

[0009] That is, x1 = x, y1 = ycosθ + zsinθ, z1 = zcosθ - ysinθ;

[0010] For any point Q on the formation ring, the relative position of the transmitting coil in the inclined well with respect to the formation ring remains unchanged. After the coordinate rotation, only the coordinates of the receiving coil change. Represent the point Q with the inclined well coordinates (x, y, z), then:

[0011]

[0012]

[0013] where ρ R , ρ TThey respectively represent the distances from any point Q on the formation ring to the receiving coil and the transmitting coil;

[0014] (2) Calculate the magnetic flux passing through the formation ring using the magnetic field excited by a magnetic dipole. According to Faraday's law of electromagnetic induction, the induced electromotive force in the formation ring is obtained, and then multiplied by the conductivity σ of the formation to get the formation eddy current

[0015]

[0016] where S0 is the cross-sectional area of the transmitting and receiving coils, and the formation eddy current is in the shape of a circular ring, with the same magnitude throughout the formation ring and the direction along the tangent direction of the formation ring, varying with position. At point Q, the unit vector of its direction

[0017]

[0018] The unit vector from point Q to the position of the receiving coil is:

[0019]

[0020] (3) According to the Biot - Savart theorem, the magnetic induction intensity generated by the current element at point Q at the position of the receiving coil is:

[0021]

[0022] The magnetic induction intensity generated by the current element at point Q at the position of the receiving coil is a vector, including magnetic field components in 3 directions. Among them, the induced electromotive force V RR generated by the magnetic field component in the z - direction at the receiving coil is:

[0023] V RR = kg z σ

[0024] where k is an instrument constant independent of the formation conductivity, and g z is the geometric factor in the z - direction reception;

[0025]

[0026]

[0027] g z reflects the contribution weight of the conductivity at point Q to the useful signal received in the z - direction at the position P' of the receiving coil; Integrating over the entire space dxdydz gives the total useful signal V R :

[0028]

[0029] Among them

[0030] (4) Obtain the geometric factor g in the y direction using the magnetic field in the y direction y :

[0031]

[0032] (5) Obtain the geometric factor g in the x direction using the magnetic field in the x direction x :

[0033] BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of the relative positions of the emission well and the reception well of the present invention;

[0035] Figure 2 is a three-dimensional diagram of the full space of a vertical well and the single-point geometric factor of the present invention;

[0036] Figure 3 is a contour map of the modulus value of the geometric factor in the z direction at different inclination angles of the present invention;

[0037] Figure 4 is a three-dimensional distribution of the geometric factor in the z direction when the inclination angle of the emission well is different in the present invention.

[0038] Figure 5 is an excitation signal diagram for the drive emission circuit to generate forward conduction, forward turn-off, reverse conduction, and reverse turn-off.

[0039] Figure 6 is a schematic diagram of the transient electromagnetic exploration geometric factor experiment of an inclined well.

[0040] Figure 7 is a formation conductivity curve graph of the transient electromagnetic response under the condition of different inclination angles of the emission well. DETAILED DESCRIPTION OF THE INVENTION

[0041] The present invention will now be described in conjunction with the accompanying drawings and specific embodiments.

[0042] The present invention provides a method for calculating the geometric factor of transient electromagnetic exploration in an inclined shaft. Based on the geometric factor in the full space, according to the Euler coordinate transformation matrix, taking the inclined coordinate system as the reference, the transient electromagnetic responses excited again in three directions at various positions in space by the inclined formation loop, that is, the useful signals of the transient electromagnetic, are calculated. The geometric position relationships among them are grouped together to give the geometric factor when the emission well is inclined. The distribution of this geometric factor in three-dimensional space and the influence of different inclination angles on the geometric factor are calculated. The characteristics of the useful signals of cross-hole transient electromagnetic are analyzed by the geometric factor: when the emission well rotates and inclines along the x-axis, the amplitude of the geometric factor at the receiving position shifts towards the direction of the transmitting coil and the polarity changes; the symmetry of the geometric factor also changes. These changes are based on the Biot-Savart theorem and are the reflections of the formation eddy current and the magnetic field excited again by it changing with spatial position in the polarity, amplitude, and symmetry of the useful signals.

[0043] As shown in the appendix Figure 1 is the geometric factor formation current loop model proposed by Doll. On this basis, the geometric factor is extended to the full space to obtain the geometric factor in the full space, and its formation current loop model is shown in the appendix Figure 2 .

[0044] The first step: Based on the geometric factor in the full space, the expressions of the geometric factors in the x, y, and z directions are derived, and its formation current loop model is shown in the appendix Figure 3 .

[0045] In this paper, the Cartesian coordinate system is used, and z coincides with the axis of the emission well, as shown in the appendix Figure 3 . The transmitting coil is regarded as a magnetic dipole, and the dipole moment is M = n0S0I, with the direction along the z direction. Where S0 is the cross-sectional area of the transmitting and receiving coils, n T , n R are the number of turns of the transmitting coil and the receiving coil respectively. The horizontal distance between the axes of the transmitting coil and the receiving coil is c, the vertical distance is L, and I is the current excitation waveform.

[0046] The Euler rotation matrix is used to derive the calculation method of the useful signal and the geometric factor. The rectangular coordinate system (x, y, z) rotates by angles θ, α, β around the x, y, z axes in turn to obtain a new coordinate system (X, Y, Z). The rotation matrix of the coordinate system is:

[0047]

[0048] In the present invention, the emission well rotates around the x-axis. Let the coordinates of the inclined well after rotation be x, y, z, and the coordinates of the original geodetic coordinate system be x1, y1, z1:

[0049]

[0050] That is, x1 = x, y1 = ycosθ + zsinθ, z1 = zcosθ - ysinθ.

[0051] Let the coordinates of any point Q on the formation ring be (x, y, z). The position of the transmitting coil in the deviated well relative to the formation ring remains unchanged. After the coordinate rotation, only the coordinates of the receiving coil change. Expressing it in the deviated well coordinates (x, y, z), we get:

[0052]

[0053]

[0054] where ρ R , ρ T respectively represent the distances from any point Q on the formation ring to the receiving coil and the transmitting coil.

[0055] Calculate the magnetic flux passing through the formation ring using the magnetic field excited by a magnetic dipole. According to the law of electromagnetic induction, obtain the induced electromotive force in the formation ring, and multiply it by the conductivity σ of the formation to get the formation eddy current I1:

[0056]

[0057] where S0 is the cross-sectional area of the transmitting and receiving coils. This eddy current is in the shape of a ring, with the same magnitude of the modulus throughout the formation ring and the direction along the tangent direction of the formation ring, changing with position. At point Q, the unit vector of its direction

[0058]

[0059] The unit vector from point Q to the position of the receiving coil is:

[0060]

[0061] According to the Biot - Savart theorem, the magnetic induction intensity generated by the current element at point Q at the position of the receiving coil

[0062]

[0063] This is a vector, containing the magnetic field components in 3 directions. Among them, the induced electromotive force V RR generated by the magnetic field component in the z direction at the receiving coil

[0064] V RR = kg z σ (9)

[0065] where k is an instrument constant independent of the formation conductivity, that is, a constant related to instruments such as the transmitting coil and the receiving coil, gz It is the geometric factor during reception in the z - direction.

[0066]

[0067]

[0068] g z It reflects the contribution weight of the conductivity at point Q to the useful signal received in the z - direction at point P'. The change of (x, y, z) describes the contribution of the conductivity at each position of an infinitely large homogeneous formation (after the transmitting coil and the receiving coil are fixed) to the useful signal. The larger the geometric factor, the greater the contribution of the conductivity at this point to the useful signal. Integrating over the entire space dxdydz gives the total useful signal V R :

[0069]

[0070] Similarly, the geometric factor gy in the y - direction is obtained using the magnetic field in the y - direction y :

[0071]

[0072] The geometric factor gx in the x - direction is obtained using the magnetic field in the x - direction x :

[0073]

[0074] Step 2: Connect the signal acquisition system.

[0075] The ADC acquisition circuit starts to work after receiving the start command from the host computer as shown in the appendix Figure 4 . The regulated DC power supply supplies power to the transmitting circuit. The 8 - channel ADC acquisition circuit provides a 5V DC regulated power supply to the transmitting circuit and also provides control signals to the circuit for controlling the transmitting waveform. These two control signals can control the drive circuit to generate two drive signals, which in turn drive the transmitting circuit to generate excitation signals of forward conduction, forward turn - off, reverse conduction, and reverse turn - off (appendix Figure 5 ). At the moment of the high - low level conversion in the excitation signal, the magnetic flux in the transmitting coil changes violently, thus generating a transient electromagnetic field. Meanwhile, the received response waveform signals of the 8 receiving coils in the receiving array are processed by the signal conditioning circuit and then transmitted to the 8 - channel AD acquisition circuit. Then, the main control circuit based on ARM conducts data interaction with the ADS1278 acquisition circuit through the SPI protocol, and finally transmits the data to the computer using the USB3.0 protocol. The host computer stores the data by number and draws the response waveform diagram.

[0076] Step 3: Conduct the geometric factor experiment of transient electromagnetic exploration in the inclined well. The experimental schematic diagram is as shown in the appendix Figure 6As shown. According to the Doll current loop model, the transient electromagnetic well response excited in the well can be divided into two parts: one part is the direct coupling response, which is the useless signal; the other part is the response re-excited by the formation eddy current, which is the useful signal. The phase difference between the two is 90°, and they are superimposed together to form the total response. The approximate expansion of the analytical solution shows that these two parts of the response respectively correspond to the first-order approximation of the real part and the imaginary part of the response. The Doll current loop model gives the Doll geometric factor, which describes the weight of the formation conductivity on the response re-excited by the eddy current. This weight is related to the geometric position. The derivation process of Doll also gives the first-order approximation of the useful signal in the transient electromagnetic response, its physical meaning, and the solution method (Zhang Gengji. Electrical Logging [M]. Petroleum Industry Press, 1984: 128-137). The response re-excited by the formation eddy current is its useful signal, which is distributed in the response waveform. Based on this theory, according to the formation conductivity information measured by the deviated well experiment, the changes of the geometric factor at the peak and the arrival time of the peak can be fed back when the emission well is tilted.

[0077] Using matlab programming to plot the data into a waveform diagram, the formation conductivity curves of the transient electromagnetic response under different tilting angles of the emission well are obtained. Figure 7 As can be seen from the figure, as the θ angle increases from 0 degrees to 45 degrees, the peak amplitudes of the received response waveforms at the on and off times gradually increase. When the θ angle is equal to 60 degrees, the peak amplitude decreases compared with that at the θ angle of 45 degrees, and the peak amplitude of the received response waveform at the on time is greater than that at the off time. This verifies that the tilting of the emission well will cause changes in the characteristics of the transient electromagnetic received response, thereby affecting the distribution characteristics of the geometric factor.

Claims

1. A calculation method for the geometric factor of transient electromagnetic exploration in inclined wells, comprising the following steps: (1) Establish a formation current loop model: Using the Cartesian coordinate system, z coincides with the axis of the emission well. The emission coil is regarded as a magnetic dipole, and the dipole moment is M = n T S0I, with the direction along the z direction. S0 is the cross-sectional area of the emission and receiving coils. Let n T , n R be the number of turns of the emission coil and the receiving coil respectively. The horizontal distance between the axes of the emission coil and the receiving coil is c, the vertical distance is L, and I is the current excitation waveform; The emission well rotates around the x axis. Let the coordinates of the rotated inclined well coordinate system be X, Y, Z, and the coordinates of the original geodetic coordinate system be x1, y1, z1: That is, x1 = x, y1 = ycosθ + zsinθ, z1 = zcosθ - ysinθ; For any point Q on the formation loop, the position of the emission coil in the inclined well relative to the formation loop remains unchanged. After coordinate rotation, only the coordinates of the receiving coil change. Represent the point Q with the inclined well coordinates (x, y, z), then: where ρ R , ρ T represent the distances from any point Q on the formation loop to the receiving coil and the emission coil respectively; (2) Calculate the magnetic flux passing through the formation loop using the magnetic field excited by the magnetic dipole. According to the electromagnetic induction law, obtain the induced electromotive force in the formation loop, and multiply it by the conductivity σ of the formation to get the formation eddy current where S0 is the cross-sectional area of the emission and receiving coils. The formation eddy current is in the shape of a circular ring, with the same magnitude of the modulus throughout the formation loop and the direction along the tangent direction of the formation loop, changing with position. At point Q, the unit vector of its direction The unit vector from point Q to the position of the receiving coil is: (3) According to the Biot - Savart theorem, the magnetic induction intensity generated by the current element at point Q at the position of the receiving coil is: The magnetic induction intensity is a vector, including magnetic field components in three directions, where the induced electromotive force V generated by the magnetic field component in the z direction in the receiving coil RR is: V RR = kg z σ where k is an instrument constant independent of formation conductivity, and g z is the geometric factor for reception in the z direction; g z It reflects the contribution weight of the conductivity at point Q to the useful signal received in the z - direction at point P' of the receiving coil; integrating over the entire space dxdydz gives the total useful signal V R : Among them (4) Obtain the geometric factor g in the y direction using the magnetic field in the y direction y : (5) Obtain the geometric factor g in the x direction using a magnetic field in the x direction x :

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