A method and device for 2.5D finite difference simulation of electromagnetic wave logging while drilling

Abstract

The application provides a method and device for 2.5D finite difference simulation of electromagnetic wave logging while drilling, and relates to the technical field of oil exploration and development. The method comprises the following steps: determining a source point and a field point; determining a calculation domain of simulation of electromagnetic wave logging while drilling response according to model parameters, a source point position and working parameters of an electromagnetic wave logging while drilling instrument; profiling the calculation domain to obtain a grid profiling result, and performing boundary processing on a grid discontinuous region to obtain a boundary region; performing wave number domain electromagnetic field calculation according to a sparse matrix, the grid profiling result and the boundary region, and performing inverse Fourier transform on a calculated electric field to obtain a space domain electric field until the field point corresponding to each source point is traversed. The device executes the above method. The method and device provided in the application can realize fast and fine simulation of electromagnetic wave logging while drilling in complex structure strata.

Description

Technical Field

[0001] This invention relates to the field of petroleum exploration and development technology, specifically to a 2.5D finite difference simulation method and apparatus for electromagnetic logging while drilling. Background Technology

[0002] Electromagnetic logging while drilling (EMWL) is sensitive to formation resistivity and formation interfaces, playing an increasingly important role in accurate horizontal well landing, real-time geological steering, and fine reservoir evaluation. Rapid and accurate simulation of the logging response is fundamental and crucial for the successful application of EWL. However, as the detection depth of EWL instruments increases, traditional 1D pseudo-analytical algorithms struggle to simulate complex formation structures and can no longer meet practical application requirements. In recent years, the industry has adopted algorithms such as 2.5D finite difference, 2.5D finite element method, and 2.5D finite volume method for simulating EWL responses, achieving some success. Among these, 2.5D finite difference has advantages such as ease of implementation and computational stability, making it the most widely used. Currently, 2.5D finite difference simulations for EWL are all based on continuous structured grids, which suffer from inflexible grid partitioning and poor matching with actual formation characteristics, leading to difficulties in grid partitioning and low computational efficiency. Summary of the Invention

[0003] To address the problems in the prior art, this invention provides a 2.5D finite difference simulation method and apparatus for electromagnetic logging while drilling, which can at least partially solve the problems existing in the prior art.

[0004] On one hand, this invention proposes a 2.5D finite-difference simulation method for electromagnetic logging while drilling, comprising:

[0005] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0006] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0007] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0008] The model parameters include formation resistivity, and the operating parameters include maximum detection distance and operating frequency. Correspondingly, determining the computational domain for the drilling electromagnetic wave logging response simulation based on the model parameters, source location, and operating parameters of the drilling electromagnetic wave logging instrument includes:

[0009] Draw a circle with the source point location as the center and the maximum detection distance as the radius, and determine the formation resistivity within the circle;

[0010] Based on the resistivity of the formation within the circle and the operating frequency, the skin depth of electromagnetic waves corresponding to different resistivities of the formation is calculated respectively.

[0011] A preset shape region is determined based on the skin depth of each electromagnetic wave and the location of the source point, and the preset shape region is defined as the computational domain.

[0012] The step of determining the preset shape region based on the skin depth of each electromagnetic wave and the location of the source point includes:

[0013] The average electromagnetic wave skin depth is obtained by averaging the skin depths of each electromagnetic wave.

[0014] A square is drawn with the source point location as the center and the average electromagnetic wave skin depth as a preset multiple as the side length, thus obtaining the preset shape region.

[0015] The step of partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions includes:

[0016] The computational domain is coarsely meshed to obtain coarse mesh regions;

[0017] The target coarse grid region corresponding to the location of the geological anomaly is subjected to mesh refinement processing to further divide the target coarse grid region into fine grid regions, and a 2.5D finite difference scheme of the magnetic dipole source excited electric field is obtained.

[0018] The boundary processing of discontinuous regions in the grid includes:

[0019] Based on the location of the electric field distribution nodes in the discontinuous region of the grid, the electric field relationship of the coarse grid and the electric field relationship of the fine grid are established by interpolation.

[0020] The step of calculating the wavenumber domain electromagnetic field based on the sparse matrix, the mesh partitioning results, and the boundary region includes:

[0021] Based on the 2.5D finite difference scheme, the coarse-grid electric field relation, and the fine-grid electric field relation, a system of linear equations is established;

[0022] Using the sparse matrix as a parameter of the linear equation system, the linear equation system is solved to obtain the electric field of each grid node under different wavenumber conditions in the wavenumber domain.

[0023] On one hand, this invention proposes a 2.5D finite-difference simulation device for electromagnetic logging while drilling, comprising:

[0024] The determination unit is used to periodically perform source point determination based on each wellbore location and field point determination based on the structural parameters of the drilling electromagnetic logging instrument, using a complex formation model with input model parameters.

[0025] The processing unit is used to determine the computational domain for simulating the electromagnetic logging-while-drilling response based on the model parameters, the source point location, and the operating parameters of the electromagnetic logging-while-drilling instrument; to partition the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions; and to perform boundary processing on the discontinuous mesh regions to obtain the boundary regions.

[0026] The calculation unit is used to obtain the sparse matrix in the order of coarse grid region, fine grid region and boundary region, perform wavenumber domain electromagnetic field calculation based on the sparse matrix, the grid partitioning result and the boundary region, and perform inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until the field points corresponding to each source point are traversed.

[0027] In another aspect, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the following method:

[0028] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0029] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0030] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0031] This invention provides a computer-readable storage medium, comprising:

[0032] The computer-readable storage medium stores a computer program that, when executed by a processor, implements the following method:

[0033] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0034] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0035] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0036] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the following method:

[0037] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0038] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0039] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0040] The 2.5D finite difference simulation method and apparatus for electromagnetic logging while drilling provided in this invention utilizes a complex formation model with input model parameters and periodically executes the following steps: determining the source point based on each wellbore location and determining the field point based on the structural parameters of the electromagnetic logging while drilling instrument; determining the computational domain for electromagnetic logging response simulation based on the model parameters, source point locations, and the operating parameters of the electromagnetic logging while drilling instrument; partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions, and performing boundary processing on discontinuous mesh regions to obtain boundary regions; obtaining a sparse matrix in the order of coarse mesh regions, fine mesh regions, and boundary regions; performing wavenumber domain electromagnetic field calculation based on the sparse matrix, the mesh partitioning result, and the boundary regions; and performing an inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until all field points corresponding to each source point are traversed. By flexibly implementing mesh partitioning and better matching actual formation characteristics, rapid and precise electromagnetic logging while drilling simulation of complex formation structures can be achieved. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0042] Figure 1 This is a schematic flowchart of a 2.5D finite difference simulation method for electromagnetic logging while drilling provided in an embodiment of the present invention.

[0043] Figure 2 This is a flowchart illustrating the 2.5D finite difference simulation method for electromagnetic logging while drilling provided in another embodiment of the present invention.

[0044] Figure 3 This is a schematic diagram illustrating the coarse mesh subdivision provided in an embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram illustrating the discontinuous mesh partitioning provided in an embodiment of the present invention.

[0046] Figure 5(a) is a schematic diagram illustrating the unfolding of the grid around the electric field Ex provided in an embodiment of the present invention.

[0047] Figure 5(b) is a schematic diagram illustrating the unfolding of the electric field Ey grid provided in an embodiment of the present invention.

[0048] Figure 5(c) is a schematic diagram illustrating the unfolding of the electric field Ez grid provided in an embodiment of the present invention.

[0049] Figure 6 This is a schematic diagram illustrating the relationship between the electric field nodes of the discontinuous grid boundary provided in an embodiment of the present invention.

[0050] Figure 7 This is a schematic diagram illustrating the discontinuous grid partitioning of a uniform anisotropic stratigraphic model provided in an embodiment of the present invention.

[0051] Figure 8 This is a schematic diagram illustrating the comparison between calculation results of continuous and discontinuous grids provided in an embodiment of the present invention.

[0052] Figure 9 This is a schematic diagram of the structure of a 2.5D finite difference simulation device for electromagnetic logging while drilling provided in an embodiment of the present invention.

[0053] Figure 10 This is a schematic diagram of the physical structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0055] Figure 1 This is a flowchart illustrating a 2.5D finite-difference simulation method for electromagnetic logging while drilling provided in an embodiment of the present invention, as shown below. Figure 1 As shown in the embodiment of the present invention, the 2.5D finite difference simulation method for electromagnetic logging while drilling provided includes:

[0056] Step S1: Utilize a complex formation model with input model parameters, and periodically execute the process of determining the source point based on each wellbore location, and determining the field point based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0057] Step S2: Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, determine the computational domain for the LWD electromagnetic wave (LWD) response simulation; divide the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions, and perform boundary processing on the discontinuous mesh regions to obtain the boundary regions.

[0058] Step S3: Obtain the sparse matrix in the order of coarse grid region, fine grid region and boundary region. Perform wavenumber domain electromagnetic field calculation based on the sparse matrix, the grid partitioning result and the boundary region, and perform inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0059] In step S1 above, the device utilizes a complex formation model with input model parameters and periodically performs operations to determine the source point based on each wellbore location and the field point based on the structural parameters of the electromagnetic logging-while-drilling (EMD) instrument. The device can be a computer device executing this method. The acquisition, storage, use, and processing of data in this application's technical solution all comply with relevant regulations.

[0060] Complex stratigraphic models can accurately reproduce the spatial distribution and morphological characteristics of geological bodies. By integrating geological data, two-dimensional geological modeling techniques can construct two-dimensional models of geological bodies, thereby simulating their spatial distribution and morphological characteristics.

[0061] Complex stratigraphic models and coordinate systems can be constructed based on actual strata, and stratigraphic boundary coordinates and stratigraphic resistivity can be used as model parameters and input into the complex stratigraphic model so that the complex stratigraphic model can simulate the spatial distribution and morphological characteristics of complex terrain.

[0062] like Figure 2 As shown, the source and field points can be determined by sequentially traversing each wellbore location. The structural parameters of the logging-while-drilling (LWD) instrument can include the location of its receiving antenna.

[0063] The source point and field point are related to the simulated instrument and wellbore trajectory. Each wellbore corresponds to one source point, which refers to the location of the transmitting source. During the simulation, the number of 2.5D simulations needs to be performed as many times as there are transmitting sources. The field point is the location of the instrument's receiving antenna. For the same transmitting source, the field at multiple receiving antennas can be calculated simultaneously. Without loss of generality, this example considers the case of a single transmitting source to verify the feasibility of the invention.

[0064] In step S2 above, the device determines the computational domain for simulating the electromagnetic logging-while-drilling response based on the model parameters, the source point location, and the operating parameters of the electromagnetic logging-while-drilling instrument; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the discontinuous mesh regions to obtain the boundary regions.

[0065] The model parameters include formation resistivity, and the operating parameters include maximum detection distance and operating frequency; correspondingly, determining the computational domain for the logging-while-drilling (LWD) response simulation based on the model parameters, source location, and operating parameters of the LWD instrument includes:

[0066] Draw a circle with the source point location as the center and the maximum detection distance as the radius, and determine the formation resistivity within the circle;

[0067] Based on the resistivity of the formation within the circle and the operating frequency, the skin depth of electromagnetic waves corresponding to different resistivities of the formation is calculated respectively.

[0068] A preset shape region is determined based on the skin depth of each electromagnetic wave and the location of the source point, and the preset shape region is defined as the computational domain.

[0069] The step of determining the preset shape region based on the skin depth of each electromagnetic wave and the location of the source point includes:

[0070] The average electromagnetic wave skin depth is obtained by averaging the skin depths of each electromagnetic wave.

[0071] A square is drawn with the source point location as the center and the average electromagnetic wave skin depth (at a preset multiple) as the side length, thus obtaining the preset shape region. The preset multiple can be set independently according to actual conditions, and can be selected as 6 times. Figure 3 As shown, the outermost outline of this region is a preset square shape area.

[0072] The process of partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions includes:

[0073] The computational domain is coarsely meshed to obtain a coarse-mesh region; the square centered on the source point is then coarsely meshed to obtain a coarse-mesh region as shown below. Figure 3 Each small square in the middle.

[0074] The target coarse grid region corresponding to the location of the geological anomaly is subjected to mesh refinement processing to further divide the target coarse grid region into fine grid regions, and a 2.5D finite difference scheme of the magnetic dipole source excited electric field is obtained.

[0075] A geological anomaly is a geological body or combination of geological bodies that differs significantly from its surrounding environment in terms of structure, tectonics, or genetic sequence.

[0076] Geological anomalies often exhibit differences in geophysical fields, geochemical fields, and remote sensing imagery. These differences make geological anomalies significant in mineral prediction, geological exploration, and other fields. Specifically, geological anomalies may be the cause of geophysical anomalies, such as bodies of different densities causing gravity anomalies, magnetic bodies causing magnetic anomalies, and geological bodies with electrical differences causing electrical anomalies; these are collectively referred to as anomalies.

[0077] The main functions of grid encryption are:

[0078] Improving simulation accuracy: In numerical simulations, local mesh refinement can capture the physical processes in key areas more precisely, thereby improving simulation accuracy. For example, in complex areas such as near fractures in oil reservoirs, around wellbores, or at oil-water interfaces, local mesh refinement can better describe the flow characteristics of these areas.

[0079] Optimizing computational resources: Using a fine mesh globally can lead to excessive computation, while local mesh refinement allows for smaller mesh sizes in critical areas and coarser meshes in other areas, thus optimizing computational resource usage while maintaining simulation accuracy. For example, dividing the original mesh into thirds... Figure 4 As shown, each target coarse grid region can be divided into 9 tiny squares.

[0080] The 2.5D finite difference scheme for obtaining the excited electric field of the magnetic dipole source includes:

[0081] The Maxwell's equations in the spatial domain are transformed into a wave function relating to the electric field. The electric field is then separated into the incident and scattered fields. The wave function is then transformed to the wavenumber domain using a Fourier transform, yielding the wavenumber domain electric field wave function. The wavenumber domain electric field wave function can be expressed as follows:

[0082]

[0083] Where E represents the electric field, the wavy line represents the wavenumber domain, and the superscripts s and i represent the scattered field and the incident field, respectively; ω is the angular frequency, μ0 is the permeability, σ is the conductivity, and σ0 is the conductivity at the source point.

[0084] For both coarse and fine mesh regions, the wavenumber domain electric field wavefunction is subjected to finite difference processing, and the 2.5D finite difference scheme is obtained by combining the mesh partitioning. Taking the x-coordinate as an example, the Ex(i,j) difference scheme is expressed as follows:

[0085]

[0086] Wherein, the subscript of the electric field E indicates the component and the grid node, k y Indicates the wave number. Around E y E z The expanded difference scheme can be obtained in the same way, and will not be described again. As shown in Figure 5(a), corresponding to E x The expanded difference scheme; as shown in Figure 5(b), corresponding to E y The expanded difference scheme; as shown in Figure 5(c), corresponding to E z Expanded difference scheme.

[0087] The boundary processing of discontinuous regions in the grid includes:

[0088] Based on the location of the electric field distribution nodes in the discontinuous regions of the grid, interpolation is used to establish the electric field relationships for both the coarse and fine grids. The discontinuous grid boundaries between the coarse and fine grids are processed, and based on the location of the electric field distribution nodes at these boundaries, interpolation is used to establish the electric field relationships for both the coarse and fine grids.

[0089] Based on the above mesh partitioning results, the coordinates of the refined partitioning region and its boundaries are determined; Figure 6 As shown, for any discontinuous region of the grid, there are four boundaries (upper, lower, left, and right) between the sparse and dense grids. The upper and lower boundaries are considered using the x-component of the electric field, and the left and right boundaries are considered using the z-component of the electric field. First, the lower boundary is processed; the electric fields in the sparse grid are numbered as follows: ExC i 、ExC (i+1) 、ExC (i+2) 、ExC (i+3) 、ExC (i+4) ; and ExC i The electric fields on the dense grid sharing the electric field boundary are numbered as follows: E xF1 E xF2 and E xF3 The electric field relationship is established at the boundary of the fine mesh as follows:

[0090]

[0091] E xF2 -E xC(i+1) =0

[0092]

[0093] The electric field relationship is established at the boundary of the coarse grid as follows:

[0094] E xC(i+1) -E xF2 =0

[0095] In step S3 above, the device obtains a sparse matrix in the order of coarse grid region, fine grid region and boundary region, performs wavenumber domain electromagnetic field calculation based on the sparse matrix, the grid partitioning result and the boundary region, and performs inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until the field points corresponding to each source point are traversed.

[0096] When installing a sparse matrix, it's common practice to proceed in the order of coarse grid regions, fine grid regions, and boundary regions. This is typically done to more effectively manage and organize data, especially when dealing with large sparse matrices. The following are the general steps and considerations for this installation method:

[0097] 1. Coarse grid area:

[0098] Defining the coarse mesh: First, determine the approximate partitions or coarse mesh regions of the entire matrix. These regions are typically defined based on the nature of the physical problem or the needs of the numerical method.

[0099] Allocate storage space: Allocate appropriate storage space for the coarse grid region. Since most elements of a sparse matrix are zero, special data structures (such as compressed row storage, compressed column storage, etc.) can be used to save space.

[0100] Initialization: Initialize the non-zero elements within the coarse mesh region, which may represent key connections or interactions in the physical model.

[0101] 2. Fine grid area:

[0102] Refine the mesh: Further subdivide the coarse mesh area into finer mesh regions. These finer mesh regions provide a finer resolution to capture details in physical phenomena.

[0103] Fill details: Fill the fine mesh areas with non-zero elements of the matrix. These elements may represent finer physical connections or local properties.

[0104] Optimize storage: Continue to utilize sparse matrix data structures to optimize storage and access efficiency.

[0105] 3. Boundary area:

[0106] Identify boundaries: Determine the boundary regions within the matrix. These regions are typically interfaces between different physical or computational domains, or the external boundaries of the physical model.

[0107] Handling boundary conditions: Apply appropriate boundary conditions within the boundary region. These conditions may include fixed values, periodic conditions, symmetric conditions, etc.

[0108] Update matrix: Update the element values ​​corresponding to the boundary conditions to the sparse matrix.

[0109] Other points to note include:

[0110] Data access patterns: When designing the storage and access patterns of sparse matrices, the locality and continuity of data access should be considered to reduce cache misses and memory access overhead.

[0111] Parallel processing: For large sparse matrices, parallel processing can be considered to accelerate the matrix construction and solution process. This may require the use of parallel programming models (such as MPI, OpenMP, etc.) and parallel sparse matrix libraries (such as PETSc, Trilinos, etc.).

[0112] Numerical stability: When constructing and solving sparse matrices, attention must be paid to numerical stability issues, such as rounding errors and iterative convergence. This may require the use of appropriate numerical methods and preprocessing techniques (such as preconditioners, iterative solvers, etc.).

[0113] By arranging sparse matrices in the order of coarse grid regions, fine grid regions, and boundary regions, data can be organized and managed more effectively, improving computational efficiency and accuracy. This method is particularly useful when dealing with complex physical problems and large-scale numerical calculations.

[0114] The calculation of the wavenumber domain electromagnetic field based on the sparse matrix, the mesh partitioning results, and the boundary region includes:

[0115] Based on the 2.5D finite difference scheme, the coarse-grid electric field relation, and the fine-grid electric field relation, a system of linear equations is established;

[0116] Using the sparse matrix as a parameter of the linear equation system, the linear equation system is solved to obtain the electric field of each grid node under different wavenumber conditions in the wavenumber domain.

[0117] like Figure 7 As shown, a homogeneous anisotropic stratigraphic model is established, with a horizontal resistivity of 5 Ω·m and a vertical resistivity of 20 Ω·m, which includes coarse and fine grids.

[0118] like Figure 8 As shown, E is located at -10m in the longitudinal direction. yx The real part results are shown, where the solid line represents the exact analytical solution, the dots represent the finite difference results of the discontinuous grid of the present invention, and the dashed line represents the results of the traditional continuous grid. It can be seen that the electric field obtained by local refinement using the method of the present invention matches the analytical solution, verifying the feasibility of the method.

[0119] The 2.5D finite-difference simulation method for electromagnetic logging while drilling provided in this invention divides the 2.5D finite-difference grid into two categories: coarse and fine grids. A system of linear equations is established based on the electric field relationship at the grid boundaries, thereby achieving 2.5D finite-difference simulation with discontinuous grids. The advantages of this invention are that, through the treatment of discontinuous grid boundaries, localized differentiated grid partitioning of the formation model is achieved. On the one hand, using fine grid partitioning at geological anomalies can better characterize the geological body morphology and ensure computational accuracy; on the other hand, using coarse grid partitioning in other areas reduces the number of grids and effectively improves computational efficiency.

[0120] The 2.5D finite-difference simulation method for electromagnetic logging while drilling provided in this invention utilizes a complex formation model with input model parameters and periodically executes the following steps: determining the source point based on each wellbore location and determining the field point based on the structural parameters of the electromagnetic logging while drilling instrument; determining the computational domain for the electromagnetic logging while drilling response simulation based on the model parameters, source point locations, and the operating parameters of the electromagnetic logging while drilling instrument; partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions, and performing boundary processing on discontinuous mesh regions to obtain boundary regions; obtaining a sparse matrix in the order of coarse mesh regions, fine mesh regions, and boundary regions; calculating the wavenumber domain electromagnetic field based on the sparse matrix, the mesh partitioning result, and the boundary regions; and performing an inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until all field points corresponding to each source point are traversed. By flexibly implementing mesh partitioning and better matching actual formation characteristics, rapid and precise simulation of electromagnetic logging while drilling in complex formations can be achieved.

[0121] Further, the model parameters include formation resistivity, and the operating parameters include maximum detection distance and operating frequency; correspondingly, determining the computational domain for the simulation of the logging-while-drilling (LWD) response based on the model parameters, source location, and operating parameters of the LWD instrument includes:

[0122] A circle is drawn with the source point location as the center and the maximum detection distance as the radius to determine the formation resistivity within the circle; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0123] Based on the resistivity of the formation within the circle and the operating frequency, the skin depth of electromagnetic waves corresponding to different formation resistivities is calculated respectively; the above embodiments can be referred to for explanation, and will not be repeated here.

[0124] A preset shape region is determined based on the skin depth of each electromagnetic wave and the location of the source point, and this preset shape region is defined as the computational domain. This can be referred to the above embodiments for further explanation, and will not be repeated here.

[0125] Further, determining the preset shape region based on the skin depth of each electromagnetic wave and the location of the source point includes:

[0126] The average electromagnetic wave skin depth is obtained by averaging the skin depths of each electromagnetic wave; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0127] A square is drawn with the source point location as the center and the average electromagnetic wave skin depth as a preset multiple as the side length, thus obtaining the preset shape region. This can be referred to the above embodiment for further explanation and will not be repeated here.

[0128] Further, the step of partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions includes:

[0129] The computational domain is coarsely meshed to obtain a coarse mesh region; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0130] The target coarse-grid region corresponding to the location of the geological anomaly is subjected to mesh refinement processing to further divide the target coarse-grid region into fine-grid regions, and a 2.5D finite-difference scheme for the electric field excited by the magnetic dipole source is obtained. This can be referred to the above embodiment for explanation, and will not be repeated here.

[0131] Furthermore, the boundary processing of discontinuous regions in the grid includes:

[0132] Based on the location of the electric field distribution nodes in the discontinuous regions of the grid, interpolation is used to establish the electric field relationships for the coarse and fine grids. Refer to the above embodiments for further details.

[0133] Further, the wavenumber domain electromagnetic field calculation based on the sparse matrix, the mesh partitioning result, and the boundary region includes:

[0134] A system of linear equations is established based on the 2.5D finite difference scheme, the coarse-grid electric field relation, and the fine-grid electric field relation; the above embodiments can be referred to for explanation, and will not be repeated here.

[0135] The sparse matrix is ​​used as a parameter of the linear equation system, which is then solved to obtain the electric field of each grid node under different wavenumber conditions in the wavenumber domain. This can be referred to the above embodiment for further explanation, and will not be repeated here.

[0136] Figure 9 This is a schematic diagram of the structure of a 2.5D finite difference simulation device for electromagnetic logging while drilling provided in an embodiment of the present invention, as shown below. Figure 9 As shown, the 2.5D finite difference simulation device for electromagnetic logging while drilling provided in this embodiment of the invention includes a determination unit 901, a processing unit 902, and a calculation unit 903, wherein:

[0137] The determination unit 901 is used to periodically determine the source point based on each wellbore location and the field point based on the structural parameters of the logging-while-drilling (LWD) instrument using a complex formation model with input model parameters. The processing unit 902 is used to determine the computational domain for the LWD response simulation based on the model parameters, source point locations, and the operating parameters of the LWD instrument. The computational domain is then partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on discontinuous mesh regions to obtain boundary regions. The calculation unit 903 is used to obtain a sparse matrix in the order of coarse mesh region, fine mesh region, and boundary region. Wavenumber domain electromagnetic field calculation is performed based on the sparse matrix, the mesh partitioning result, and the boundary region. The calculated electric field is then subjected to an inverse Fourier transform to obtain the spatial domain electric field, until the field points corresponding to each source point are traversed.

[0138] Specifically, the determination unit 901 in the device is used to periodically determine the source point based on each wellbore location and the field point based on the structural parameters of the logging-while-drilling (LWD) instrument using a complex formation model with input model parameters; the processing unit 902 is used to determine the computational domain for the LWD response simulation based on the model parameters, source point locations, and the operating parameters of the LWD instrument; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on discontinuous mesh regions to obtain boundary regions; the calculation unit 903 is used to obtain a sparse matrix in the order of coarse mesh region, fine mesh region, and boundary region, perform wavenumber domain electromagnetic field calculation based on the sparse matrix, the mesh partitioning result, and the boundary region, and perform an inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until the field points corresponding to each source point are traversed.

[0139] The 2.5D finite difference simulation device for electromagnetic logging while drilling provided in this invention utilizes a complex formation model with input model parameters and periodically executes the following steps: determining the source point based on each wellbore location and determining the field point based on the structural parameters of the electromagnetic logging while drilling instrument; determining the computational domain for electromagnetic logging response simulation based on the model parameters, source point locations, and the operating parameters of the electromagnetic logging while drilling instrument; partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions, and performing boundary processing on discontinuous mesh regions to obtain boundary regions; obtaining a sparse matrix in the order of coarse mesh regions, fine mesh regions, and boundary regions; performing wavenumber domain electromagnetic field calculation based on the sparse matrix, the mesh partitioning result, and the boundary regions; and performing an inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until all field points corresponding to each source point are traversed. By flexibly implementing mesh partitioning and better matching actual formation characteristics, rapid and precise simulation of electromagnetic logging while drilling in complex formations can be achieved.

[0140] The embodiments of the present invention provide a 2.5D finite difference simulation device for logging while drilling electromagnetic waves. Specifically, it can be used to execute the processing flow of the above-described method embodiments. Its functions will not be repeated here, but can be referred to the detailed description of the above-described method embodiments.

[0141] Figure 10 This is a schematic diagram of the physical structure of a computer device provided in an embodiment of the present invention, such as... Figure 10 As shown, the computer device includes: a memory 1001, a processor 1002, and a computer program stored in the memory 1001 and executable on the processor 1002. When the processor 1002 executes the computer program, it implements the following method:

[0142] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0143] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0144] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0145] This embodiment discloses a computer program product, which includes a computer program that, when executed by a processor, implements the following method:

[0146] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0147] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0148] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0149] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the following method:

[0150] Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument.

[0151] Based on the model parameters, source point location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for LWD electromagnetic wave (LWD) response simulation is determined; the computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the mesh discontinuous regions to obtain the boundary regions;

[0152] The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

[0153] Compared with existing technologies, the 2.5D finite difference simulation method for electromagnetic logging while drilling provided in this invention utilizes a complex formation model with input model parameters and periodically executes the following steps: determining the source point based on each wellbore location and the field point based on the structural parameters of the electromagnetic logging while drilling instrument; determining the computational domain for the electromagnetic logging while drilling response simulation based on the model parameters, source point locations, and the operating parameters of the electromagnetic logging while drilling instrument; partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions, and performing boundary processing on discontinuous mesh regions to obtain boundary regions; obtaining a sparse matrix in the order of coarse mesh regions, fine mesh regions, and boundary regions; performing wavenumber domain electromagnetic field calculation based on the sparse matrix, the mesh partitioning result, and the boundary regions; and performing an inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until all field points corresponding to each source point are traversed. By flexibly implementing mesh partitioning and better matching actual formation characteristics, this method achieves rapid and precise simulation of electromagnetic logging while drilling in complex formations.

[0154] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0156] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0157] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0158] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0159] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A 2.5D finite-difference simulation method for electromagnetic logging while drilling, characterized in that, include: Using a complex formation model with input model parameters, the system periodically performs source point determination based on each wellbore location and field point determination based on the structural parameters of the logging-while-drilling (LWD) instrument. Based on the model parameters, source location, and operating parameters of the logging-while-drilling (LWD) electromagnetic wave (LWD) instrument, the computational domain for the LWD electromagnetic wave (LWD) response simulation is determined. The computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the discontinuous mesh regions to obtain boundary regions. The sparse matrix is ​​obtained in the order of coarse grid region, fine grid region and boundary region. Wavenumber domain electromagnetic field is calculated based on the sparse matrix, the grid partitioning result and the boundary region. The calculated electric field is then subjected to inverse Fourier transform to obtain the spatial domain electric field until the field points corresponding to each source point are traversed.

2. The 2.5D finite-difference simulation method for electromagnetic logging while drilling according to claim 1, characterized in that, The model parameters include formation resistivity, and the operating parameters include maximum detection distance and operating frequency; correspondingly, determining the computational domain for the logging-while-drilling (LWD) response simulation based on the model parameters, source location, and operating parameters of the LWD instrument includes: Draw a circle with the source point location as the center and the maximum detection distance as the radius, and determine the formation resistivity within the circle; Based on the resistivity of the formation within the circle and the operating frequency, the skin depth of electromagnetic waves corresponding to different resistivities of the formation is calculated respectively. A preset shape region is determined based on the skin depth of each electromagnetic wave and the location of the source point, and the preset shape region is defined as the computational domain.

3. The 2.5D finite-difference simulation method for electromagnetic logging while drilling according to claim 2, characterized in that, The step of determining the preset shape region based on the skin depth of each electromagnetic wave and the location of the source point includes: The average electromagnetic wave skin depth is obtained by averaging the skin depths of each electromagnetic wave. A square is drawn with the source point location as the center and the average electromagnetic wave skin depth as a preset multiple as the side length, thus obtaining the preset shape region.

4. The 2.5D finite-difference simulation method for electromagnetic logging while drilling according to claim 1, characterized in that, The process of partitioning the computational domain to obtain a mesh partitioning result containing coarse and fine mesh regions includes: The computational domain is coarsely meshed to obtain coarse mesh regions; The target coarse grid region corresponding to the location of the geological anomaly is subjected to mesh refinement processing to further divide the target coarse grid region into fine grid regions, and a 2.5D finite difference scheme of the magnetic dipole source excited electric field is obtained.

5. The 2.5D finite-difference simulation method for electromagnetic logging while drilling according to claim 4, characterized in that, The boundary processing of discontinuous regions in the grid includes: Based on the location of the electric field distribution nodes in the discontinuous region of the grid, the electric field relationship of the coarse grid and the electric field relationship of the fine grid are established by interpolation.

6. The 2.5D finite-difference simulation method for electromagnetic logging while drilling according to claim 5, characterized in that, The calculation of the wavenumber domain electromagnetic field based on the sparse matrix, the mesh partitioning results, and the boundary region includes: Based on the 2.5D finite difference scheme, the coarse-grid electric field relation, and the fine-grid electric field relation, a system of linear equations is established; Using the sparse matrix as a parameter of the linear equation system, the linear equation system is solved to obtain the electric field of each grid node under different wavenumber conditions in the wavenumber domain.

7. A 2.5D finite-difference simulation device for electromagnetic logging while drilling, characterized in that, include: The determination unit is used to periodically perform source point determination based on each wellbore location and field point determination based on the structural parameters of the drilling electromagnetic logging instrument, using a complex formation model with input model parameters. The processing unit is used to determine the computational domain of the drilling electromagnetic wave logging response simulation based on the model parameters, the source point location, and the operating parameters of the drilling electromagnetic wave logging instrument. The computational domain is partitioned to obtain a mesh partitioning result containing coarse and fine mesh regions, and boundary processing is performed on the discontinuous mesh regions to obtain boundary regions. The calculation unit is used to obtain the sparse matrix in the order of coarse grid region, fine grid region and boundary region, perform wavenumber domain electromagnetic field calculation based on the sparse matrix, the grid partitioning result and the boundary region, and perform inverse Fourier transform on the calculated electric field to obtain the spatial domain electric field, until the field points corresponding to each source point are traversed.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

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