A transient electromagnetic formation conductivity multi-offset joint inversion method

Abstract

The application discloses a transient electromagnetic stratum conductivity multi-source distance joint inversion method, which comprises the following steps: obtaining a two-dimensional response matrix of different source distances and different depth positions by using a logging acquisition device; the response matrix, a geometric factor and stratum conductivity satisfy a convolution relationship in the longitudinal direction; discretizing the geometric factor and the stratum conductivity; expanding the two dimensions of the discretized geometric factor and the stratum conductivity into one-dimensional vectors, and constructing a form of geometric factor and stratum conductivity matrix multiplication V(x, L) = h * sigma(x, n) * g(n, L), wherein sigma(x, n) is a target value to be solved; solving the sigma(x, n) by using matrix decomposition; restoring the solved sigma(x, n) into a stratum conductivity matrix sigma(r, x, z) of spatial positions, superimposing the stratum conductivities sigma(r, z) of different longitudinal offset distances x, and calculating an estimation of the original stratum conductivity distribution. The conductivity distribution is estimated by discretization and matrix decomposition, so that the distribution conditions of water-bearing layers and remaining oil layers are judged, and the method has wide application range, high shallow layer resolution and fast calculation speed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of special instruments for measuring physical parameters of strata and evaluating lithology in petroleum engineering logging operation, in particular to a multi-source distance waveform data processing method for dual-coil transient electromagnetic logging, more particularly to a multi-source distance joint inversion method for transient electromagnetic strata conductivity, which is used to obtain the distribution of strata conductivity. BACKGROUND

[0002] In the process of oil development, strata conductivity is an important physical parameter, which can effectively identify strata data such as water-bearing layer, metal ore layer, and remaining oil distribution. For this reason, people have developed a transient electromagnetic excitation strata conductivity logging method and corresponding instruments and equipment. This method can detect rich strata conductivity information without directly contacting the strata, and has good environmental adaptability and detection accuracy. Due to the complexity of electromagnetic field propagation and induction in non-uniform medium, the original waveform of transient electromagnetic logging data contains a large amount of useless signals. Although the transient electromagnetic method can sensitively reflect the strata conductivity information, the detection results are often superimposed with strata information, which increases the difficulty of extracting effective data. The traditional strata conductivity inversion methods include deconvolution method, geometric factor focusing method, and least squares iteration method. The deconvolution method can only be used for one-dimensional conductivity inversion to obtain longitudinal conductivity curve, the geometric factor focusing method can only be used for multi-coil excitation mode, and the least squares iteration method has slow calculation speed. SUMMARY

[0003] To overcome the deficiencies in the prior art, based on the geometric factor theory and matrix decomposition method, the present application proposes an effective multi-source distance joint inversion method for transient electromagnetic strata conductivity, which is used for data processing and waveform interpretation of transient electromagnetic logging instrument. The fusion of multi-source distance data can effectively improve the detection resolution, and the matrix decomposition method can effectively improve the inversion speed. The present application is used to process the original waveform data collected by the transient electromagnetic logging instrument, estimate the conductivity distribution through discretization and matrix decomposition, and judge the distribution of water-bearing layer and remaining oil layer. The calculation results show that this method has good identification ability for low-resistance abnormal body and conductivity interface, and has many advantages such as wide application range, high shallow layer resolution, and fast calculation speed compared with the deconvolution method, geometric factor focusing method, and least squares iteration method.

[0004] The purpose of the present application is achieved by the following technical solutions.

[0005] The multi-source distance joint inversion method for transient electromagnetic strata conductivity of the present application is used for processing and inversion calculation of the waveform data collected by the receiving coil, including the following processes:

[0006] Step one, using coaxial transmission coil and receiving coil array as logging acquisition device, a transient excitation off current is input to the transmission coil, the electromagnetic field induced by the off current in the formation excites the induced electromotive force in the receiving coil array, the logging acquisition device is moved longitudinally at equal intervals and data is collected once every time, the data collected each time takes the waveform amplitude at a fixed time as the response amplitude of the corresponding position, and then a two-dimensional response matrix of different source distances and different depth positions is formed;

[0007] Step two, the propagation process of transient electromagnetic field in the formation satisfies the quasi-steady state condition, and the following formula is derived according to the Biot-Savart law:

[0008]

[0009] Wherein, x is the longitudinal offset distance, L is the source distance of the logging acquisition device, r is the radial coordinate, z is the longitudinal coordinate, h is a constant related to the coil, the response matrix V(x, L), the geometric factor g(r, L, x) and the formation conductivity σ(r, z) satisfy the convolution relationship in the longitudinal direction;

[0010] Step three, the geometric factor and the formation conductivity are expressed in discrete form

[0011]

[0012] Wherein, N r , N z are the number of calculation points in the radial and longitudinal directions respectively; according to the property of convolution, the following formula is obtained by transformation:

[0013]

[0014] Step four, the r and z dimensions of the discrete geometric factor and the formation conductivity are expanded into one-dimensional vectors, and are constructed into the form of multiplication of the geometric factor and the formation conductivity matrix;

[0015] The response matrix V(x, L) in step three is equal to the inner product of the full-space formation conductivity and the geometric factor, so the discrete geometric factor g(r, L, z) and the formation conductivity σ(r, x, z) can be expanded into one-dimensional vectors in r and z dimensions, so as to construct the g(n, L) matrix representing the geometric factor and the σ(x, n) matrix representing the formation conductivity, wherein n is the subscript of the corresponding one-dimensional vector, that is, n∈[1, N], N=N r ×N z ; each column of the g(n, L) matrix is the one-dimensional expansion vector of the geometric factor corresponding to the current L, and each row of the σ(x, n) matrix is the right shift of the last row by N zThe vector is formed by the points, and the blank is filled by the boundary value, so that V(x, L) = h * sigma (x, n) * g (n, L), wherein sigma (x, n) is the target value to be solved;

[0016] Step five, the target value to be solved sigma (x, n) in step four is approximately solved by matrix decomposition, and the calculation formula is:

[0017]

[0018] Wherein, g -1 (n, L) represents the generalized inverse matrix of g (n, L) ; The solved formation conductivity matrix sigma (x, n) is still a two-dimensional matrix, so it is restored to the spatial position formation conductivity matrix sigma (r, x, z), and the formation conductivity sigma (r, z) of different longitudinal offset distances x is aligned and superimposed, and finally an estimate of the original formation conductivity distribution is calculated, that is, the sigma (x, n) matrix is restored to the sigma (r, z) matrix.

[0019] In step four, V (x, L), g (n, L) and sigma (x, n) are two-dimensional matrices, sigma (x, n) and g (n, L) are in the relationship of matrix multiplication, V (x, L) is the observation value, the parameters h and g (n, L) matrix are given by theoretical model and experience estimation, and the matrix g (n, L) represents the geometric factor, which is given by the Doll geometric factor in the infinite uniform medium under the condition of open hole, and is given by the deformed Doll geometric factor corrected by casing under the condition of cased hole.

[0020] The matrix decomposition method in step five includes Householder orthogonal decomposition, QR decomposition based on Givens transformation and SVD decomposition, and different decomposition methods have different calculation accuracy and calculation speed.

[0021] Compared with the prior art, the technical scheme of the present application has the following beneficial effects:

[0022] (1) The present application uses the data collected by the transient electromagnetic instrument for inversion calculation, and has good recognition ability for low resistance abnormal body and conductivity interface, and the application scene is wider than that of contact logging.

[0023] (2) Compared with the deconvolution method, the present application takes the radial and longitudinal two-dimensional conductivity distribution as the model parameter, and the inversion result can obtain more fine formation conductivity information.

[0024] (3) Compared with the geometric factor focusing method, the present application is not limited by the parameters and arrangement of the transmitting coil, and only needs to record the coil parameters and spacing.

[0025] (4) Compared with the least square iteration method, the present application uses the concurrent advantage, and the calculation speed is faster.

[0026] (5) The present application fully utilizes multi-source data for joint inversion calculation, effectively improving the shallow detection resolution. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a structural schematic diagram of a transient electromagnetic multi-source joint logging acquisition device adopted by the present application;

[0028] Figure 2 is a logic flow chart of the transient electromagnetic formation conductivity multi-source joint inversion method of the present application;

[0029] Figure 3 is an expansion schematic diagram of a geometric factor matrix of an embodiment of the present application;

[0030] Figure 4 is a calculation result schematic diagram of the transient electromagnetic formation conductivity multi-source joint inversion method of the present application. DETAILED DESCRIPTION

[0031] In order to further illustrate the inventive purpose, technical scheme and beneficial effects of the present application, the present application will be further described below with reference to the accompanying drawings.

[0032] As shown in Figure 1 , the present application adopts a transient electromagnetic multi-source joint logging acquisition device for logging, which comprises a transmitting coil and a receiving coil array, the transmitting coil and the receiving coil array are coaxially arranged, the receiving coil array contains a plurality of receiving coils, and the optimal number of receiving coils should be determined comprehensively by the coil spacing, the number of turns of the coil, the excitation power, the number of system interface restrictions, etc. Figure 1 The first four are drawn as an illustration.

[0033] The transmitting coil and the receiving coil are both made by double-wire and winding with middle tap, which is used for collecting differential signals.

[0034] As shown in Figure 2 , the present application proposes a transient electromagnetic formation conductivity multi-source joint inversion method for processing and inversion calculation of the waveform data collected by the receiving coil. The specific implementation process is as follows:

[0035] Step one, a transient excitation off current is passed to the transmitting coil, the electromagnetic field induced in the formation by the off current excites an induced electromotive force in the receiving coil array, the logging acquisition device is moved longitudinally in the well at equal intervals and data is collected once every time it is moved, the data collected each time is taken as the response amplitude of the corresponding position at a fixed time, and then a two-dimensional response matrix of different source distances and different depth positions is formed.

[0036] Step two, the propagation of transient electromagnetic field in the formation satisfies quasi-steady condition, according to Biot-Savart law, the following formula is derived:

[0037]

[0038] Where x is the longitudinal offset distance, L is the source distance of the logging acquisition device, r is the radial coordinate, z is the longitudinal coordinate, h is the constant related to the coil, the response matrix V(x, L), the geometric factor g(r, L, x) and the formation conductivity σ(r, z) satisfy the convolution relationship in the longitudinal direction.

[0039] Step three, the geometric factor and the formation conductivity are expressed in discrete form

[0040]

[0041] Where N r , N z are the number of calculation points in the radial and longitudinal directions respectively. According to the convolution property, the transformation is carried out as follows:

[0042]

[0043] Step four, the r and z dimensions of the discrete geometric factor and the formation conductivity are both expanded into one-dimensional vectors, and are constructed into the form of the multiplication of the geometric factor and the formation conductivity matrix.

[0044] As Figure 3 shown, the response matrix V(x, L) in step three is equal to the inner product of the full-space formation conductivity and the geometric factor, so the discrete geometric factor g(r, L, z) and the formation conductivity σ(r, x, z) can both expand the r and z dimensions into one-dimensional vectors, under this condition, the g(n, L) matrix representing the geometric factor and the σ(x, n) matrix representing the formation conductivity can be constructed, where n is the subscript of the corresponding one-dimensional vector, i.e. n∈[1, N], N=N r ×N z . Due to the longitudinal relative offset of the formation and the logging acquisition device, each row of the σ(x, n) matrix is the right shift of the previous row by N zThe blank is filled by the boundary value. Each column of the g(n, L) matrix is a one-dimensional expansion vector of the geometric factor corresponding to the current L, so that V(x, L) = h·σ(x, n)·g(n, L). V(x, L), g(n, L) and σ(x, n) are all two-dimensional matrices, and there is a matrix multiplication relationship between σ(x, n) and g(n, L). V(x, L) is an observation value, the parameters h and the g(n, L) matrix are given by a theoretical model and empirical estimation, the g(n, L) matrix represents a geometric factor, which is given by the Doll geometric factor in an infinite homogeneous medium under the condition of a bare hole, and is given by a deformed Doll geometric factor corrected by a casing under the condition of a cased hole, and σ(x, n) is a target value to be solved.

[0045] Step five, the target value to be solved σ(x, n) in step four is approximately solved by matrix decomposition, and the calculation formula is:

[0046]

[0047] Where, g -1 (n, L) represents the generalized inverse matrix of g(n, L). The solved formation conductivity matrix σ(x, n) is still an expanded two-dimensional matrix, so it is necessary to restore it to the spatial position formation conductivity matrix σ(r, x, z), and the formation conductivity σ(r, z) at different longitudinal offset distances x is aligned and superimposed, and finally an estimate of the original formation conductivity distribution is calculated, that is, the σ(x, n) matrix is restored to the σ(r, z) matrix. The matrix decomposition method includes Householder orthogonal decomposition, QR decomposition based on Givens transformation and SVD decomposition, and different decomposition methods have different calculation accuracy and calculation speed.

[0048] Table 1

[0049]

[0050] The calculation accuracy and calculation speed of different matrix decomposition methods are compared in the present application, as shown in Table 1, it can be found that any kind of matrix decomposition method has the advantages of accuracy and speed compared with the least square iteration method, and the Householder orthogonal decomposition method has the best accuracy and speed in the present experimental scene.

[0051] The detection ability of different matrix decomposition methods to low resistance bodies is compared in the present application, as shown in Table 2, the results show that the method has higher resolution for shallow conductivity detection, and the Householder decomposition method has obvious advantages in detecting low resistance bodies compared with the QR (Givens transformation) and SVD methods. Figure 4

[0052] ​Although the functions and working processes of the present application are described above in combination with the drawings, the present application is not limited to the specific functions and working processes described above, and the specific embodiments described above are merely illustrative but not restrictive, and those of ordinary skill in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, which all belong to the protection of the present application.

Claims

1. A transient electromagnetic formation conductivity multi-offset joint inversion method for processing and inversion calculation of waveform data collected by a receiving coil, characterized in that, The method comprises the following steps: Step one, using a coaxial transmitter coil and a receiving coil array as a logging acquisition device, a transient excitation off current is input to the transmitter coil, the electromagnetic field induced in the stratum by the off current excites an induced electromotive force in the receiving coil array, the logging acquisition device is moved longitudinally in the well at equal intervals and data is collected once per movement, the waveform amplitude at a fixed time is taken as the response amplitude of the corresponding position each time data is collected, and a two-dimensional response matrix of different source distances and different depth positions is formed; Step two, the propagation process of the transient electromagnetic field in the stratum satisfies the quasi-steady state condition, and the following formula is derived according to the Biot-Savart law: Wherein, x is the longitudinal offset distance, L is the source distance of the logging acquisition device, r is the radial coordinate, z is the longitudinal coordinate, h is a constant related to the coil, the response matrix V(x, L), the geometric factor g(r, L, x) and the stratum conductivity σ(r, z) satisfy the convolution relationship in the longitudinal direction; Step three, the geometric factor and the stratum conductivity are expressed in a discrete form where N r , N z are the number of points in the radial and longitudinal directions, respectively; by the properties of the convolution, we have the transformation Step four, the r and z dimensions of the discretized geometric factor and stratum conductivity are both expanded into one-dimensional vectors, and are constructed into the form of multiplication of the geometric factor and the stratum conductivity matrix; The response matrix V(x, L) in step three is equal to the inner product of the full-space formation conductivity and the geometry factor, so the discretized geometry factor g(r, L, z) and the formation conductivity σ(r, x, z) can both be expanded to one-dimensional vectors in the r and z dimensions, thereby constructing a g(n, L) matrix representing the geometry factor and a σ(x, n) matrix representing the formation conductivity, where n is the subscript of the corresponding one-dimensional vector, i.e. n ∈ [1, N], N = N r × N z ; each column of the g(n, L) matrix is a one-dimensional expansion vector of the geometry factor corresponding to the current L, and each row of the σ(x, n) matrix is a vector formed by shifting the row above to the right by N z points, with the blank filled by the boundary value, so that V(x, L) = h·σ(x, n)·g(n, L), where σ(x, n) is the target value to be solved. Step five, the target to be solved σ(x, n) in step four is approximately solved by using matrix decomposition, and the calculation formula is: where g -1 (n, L) represents the generalized inverse matrix of g(n, L); the solved formation conductivity matrix σ(x, n) is still a developed two-dimensional matrix, so it is restored to the spatial position formation conductivity matrix σ(r, x, z), and the formation conductivity σ(r, z) at different longitudinal offset distances x is aligned and stacked, and finally an estimate of the original formation conductivity distribution is calculated, that is, the σ(x, n) matrix is restored to the σ(r, z) matrix.

2. The transient electromagnetic formation conductivity multioffset joint inversion method of claim 1, wherein, In step four, V(x, L), g(n, L) and σ(x, n) are all two-dimensional matrices, there is a matrix multiplication relationship between σ(x, n) and g(n, L), V(x, L) is an observation value, the parameters h and g(n, L) matrix are given by a theoretical model and empirical estimation, the matrix g(n, L) represents a geometric factor, which is given by the Doll geometric factor in an infinite uniform medium under the condition of an open hole well, and is given by a deformed Doll geometric factor corrected by a casing under the condition of a cased hole.

3. The method of claim 1, wherein, The matrix decomposition method in step five includes Householder orthogonal decomposition, QR decomposition based on Givens transformation and SVD decomposition, and different decomposition methods have different calculation accuracy and calculation speed.

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