Fracture surface density parameter prediction method and device based on array induction logging

By acquiring resistivity curves at multiple depths through array induction logging and preprocessing them, combined with a neural network model, the problem of unstable prediction of fracture surface density parameters under high-angle or vertical fracture conditions in tight sandstone and mudstone reservoirs was solved, and accurate prediction of fracture surface density parameters was achieved.

CN122014218APending Publication Date: 2026-05-12CHINA UNIV OF GEOSCIENCES (WUHAN)
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
CHINA UNIV OF GEOSCIENCES (WUHAN)
Filing Date
2026-03-18
Publication Date
2026-05-12

AI Technical Summary

Technical Problem

Existing technologies struggle to reliably predict fracture surface density parameters in tight sandstone and mudstone reservoirs under conditions of high-angle or vertical fractures.

Method used

Initial resistivity curves at multiple depths are obtained using array induction logging. After preprocessing and noise reduction, fracture surface feature vectors are constructed and trained using a neural network model to achieve accurate prediction of fracture surface density parameters.

Benefits of technology

Under high-angle or vertical crack conditions, it can stably predict crack surface density parameters, improving the accuracy and reliability of the prediction.

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Abstract

The invention discloses a fracture surface density parameter prediction method and device based on array induction logging, and the method comprises the steps: obtaining at least three initial resistivity curves of a target well through an array induction mode; the at least three initial resistivity curves are preprocessed, at least three target resistivity curves are obtained, and data noise in the target resistivity curves is smaller than data noise in the initial resistivity curves; based on the at least three target resistivity curves, determining an initial crack surface feature vector of the target well, and performing normalization processing on the initial crack surface feature vector to obtain a target crack surface feature vector; and inputting the target fracture surface feature vector into the target prediction model for analysis to obtain a fracture surface density parameter of the target well, thereby solving the technical problem that the fracture surface density parameter is difficult to stably predict under the condition of a high-angle or vertical fracture.
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Description

Technical Field

[0001] This application relates to the field of oil and gas exploration and development technology, and in particular to a method and apparatus for predicting fracture surface density parameters based on array induction logging. Background Technology

[0002] Existing technologies have significant limitations in the identification and quantitative evaluation of fractures in tight sandstone and mudstone reservoirs. Current solutions mainly fall into three categories: First, direct evaluation methods based on imaging logging and core samples. These methods can visually reflect fracture geometry, but are costly, have limited implementation conditions, and are difficult to widely adopt. Second, experience-based or comprehensive index evaluation methods based on conventional logging. These methods typically construct fracture evaluation indicators based on anomalous responses or combinations of features from conventional logging curves such as resistivity and acoustic waves, indirectly characterizing the degree of fracture development. However, they exhibit weak responses in tight sandstone and mudstone reservoirs and under high-angle fracture conditions, are easily affected by lithology, intrusion effects, and other factors, and their quantitative relationships rely on empirical calibration. Third, data-driven fracture prediction methods. These methods directly utilize original logging curves or simple statistical features to establish prediction models, but the models lack stability and interpretability, and require high integrity of logging data. In summary, existing technologies face the technical challenge of stably predicting fracture areal density parameters under high-angle or vertical fracture conditions. Summary of the Invention

[0003] In view of this, embodiments of this application provide a method and apparatus for predicting fracture surface density parameters based on array induction logging, so as to at least solve the technical problem that fracture surface density parameters are difficult to predict stably under the conditions of high-angle or vertical fractures.

[0004] According to one aspect of this application, a method for predicting fracture surface density parameters based on array induction logging is provided. The method includes: acquiring at least three initial resistivity curves of a target well using array induction, wherein the resistivity in the initial resistivity curves characterizes the conductivity of fluids in the formation, and the three initial resistivity curves characterize resistivity changes at different probe depths; preprocessing the at least three initial resistivity curves to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves; determining an initial fracture surface feature vector of the target well based on the at least three target resistivity curves, and normalizing the initial fracture surface feature vector to obtain a target fracture surface feature vector; inputting the target fracture surface feature vector into a target prediction model for analysis to obtain the fracture surface density parameters of the target well, wherein the target prediction model is trained using historical data of the target fracture surface feature vector and historical data of the fracture surface density parameters, and the initial prediction model is constructed using a neural network.

[0005] Optionally, at least three initial resistivity curves are preprocessed to obtain at least three target resistivity curves, including: performing logarithmic transformation on the at least three initial resistivity curves to obtain at least three first resistivity curves; performing noise reduction on the at least three first resistivity curves to obtain at least three second resistivity curves; performing background separation on the at least three second resistivity curves to obtain at least three third resistivity curves; and determining at least three target resistivity curves based on the at least three first resistivity curves and the at least three second resistivity curves.

[0006] Optionally, at least three target resistivity curves include: a first target resistivity curve, a second target resistivity curve, and a third target resistivity curve, wherein the detection depth of the first target resistivity curve is less than the detection depth of the second target resistivity curve, and the detection depth of the second target resistivity curve is less than the detection depth of the third target resistivity curve. Based on at least three target resistivity curves, the initial fracture surface feature vector of the target well is determined, including: determining the radial difference parameter of the target well based on the third target resistivity curve and the first target resistivity curve; determining the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve; and determining the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve. The target resistivity curve and the third target resistivity curve are used to determine the first mean value corresponding to the first target resistivity curve, the second mean value corresponding to the second target resistivity curve, and the third mean value corresponding to the third target resistivity curve, respectively. Based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean value, the second mean value, and the third mean value, the radial consistency parameter of the target well is determined. Based on the third target resistivity curve, the boundary enhancement parameter of the target well is determined, and the third target resistivity curve is scale-smoothed to obtain the scale bandpass parameter. Based on the radial difference parameter, the radial curvature parameter, the radial consistency parameter, the boundary enhancement parameter, and the scale bandpass parameter, the initial fracture surface feature vector is constructed.

[0007] Optionally, the third target resistivity curve is scale-smoothed to obtain the scale bandpass parameter, including: performing short-scale smoothing on the third target resistivity curve to obtain a first smooth curve, and performing long-scale smoothing on the third target resistivity curve to obtain a second smooth curve; and determining the scale bandpass parameter based on the first smooth curve and the second smooth curve.

[0008] Optionally, the radial difference parameter of the target well is determined based on the third target resistivity curve and the first target resistivity curve using the following formula, including: DR L = R far_proc R near_proc in, DR L Used to represent radial difference parameters R far_proc Used to represent the resistivity curve of the third target. R near_proc Used to represent the first target resistivity curve.

[0009] Optionally, the radial curvature parameter of the target well is determined based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve using the following formula, including: C = R far_proc 2 R mid_proc + R near_proc in, C Used to represent radial curvature parameters. R mid_proc Used to represent the second target resistivity curve.

[0010] Optionally, the radial consistency parameters of the target well are determined based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean, the second mean, and the third mean, using the following formula:

[0011] in, RING The parameter used to represent radial consistency is N, where N is an integer and N≥3. Used to represent the i-th target resistivity curve Used to represent the mean value of the i-th target resistivity curve.

[0012] Optionally, the boundary enhancement parameters of the target well are determined based on the third target resistivity curve using the following formula, including:

[0013] in, EDGE M Used to represent boundary enhancement parameters Used to represent numerical derivatives / first-order differences.

[0014] According to another aspect of this application, a fracture surface density parameter prediction device based on array induction logging is provided. The device includes: a first acquisition unit, configured to acquire at least three initial resistivity curves of a target well using array induction, wherein the resistivity in the initial resistivity curves characterizes the conductivity of fluids in the formation, and the three initial resistivity curves characterize the resistivity changes at different probe depths; a second acquisition unit, configured to preprocess the at least three initial resistivity curves to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves; a determination unit, configured to determine the initial fracture surface feature vector of the target well based on the at least three target resistivity curves, and to normalize the initial fracture surface feature vector to obtain the target fracture surface feature vector; and a third acquisition unit, configured to input the target fracture surface feature vector into a target prediction model for analysis to obtain the fracture surface density parameter of the target well, wherein the target prediction model is obtained by training the initial prediction model using historical data of the target fracture surface feature vector and historical data of the fracture surface density parameter, and the initial prediction model is constructed using a neural network.

[0015] According to another aspect of this application, a storage medium is provided that stores a computer program thereon, which, when executed by a processor, implements the above-described method for predicting fracture surface density parameters based on array induction logging.

[0016] According to another aspect of this application, a computer device is provided, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the program, it implements the above-described method for predicting fracture surface density parameters based on array induction logging.

[0017] Using the above technical solution, this application provides a method for predicting fracture surface density parameters based on array induction logging. The method includes: first, acquiring at least three initial resistivity curves at different probe depths of the target well through array induction to characterize the conductivity of formation fluids; then, preprocessing these initial resistivity curves to reduce data noise and obtain target resistivity curves; next, constructing and normalizing initial fracture surface feature vectors based on these target resistivity curves to obtain target fracture surface feature vectors; finally, inputting the target fracture surface feature vectors into a target prediction model based on a neural network trained on historical data to analyze and derive the fracture surface density parameters of the target well. Since the array sensing method is used, the multi-depth resistivity curves obtained can accurately reflect the electrical changes caused by formation fractures. The effectiveness of the curves is improved by preprocessing and noise reduction. A targeted fracture surface feature vector is constructed and normalized to eliminate the influence of dimensions. At the same time, a neural network model trained with historical data is used to achieve accurate mapping between features and fracture surface density parameters. This solves the technical problem that fracture surface density parameters are difficult to predict stably under high-angle or vertical fracture conditions, and achieves the technical effect of stably predicting fracture surface density parameters under high-angle or vertical fracture conditions.

[0018] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0019] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A schematic flowchart of a fracture surface density parameter prediction method based on array inductive logging provided in an embodiment of this application is shown. Figure 2 This illustration shows a schematic diagram of the distribution structure of the fracture dip angle distribution characteristics provided in an embodiment of this application for imaging logging; Figure 3 This illustration shows a structural diagram of a method for detecting crack P32 using the KNN algorithm, as provided in an embodiment of this application. Figure 4 This illustration shows a structural schematic diagram of a fracture surface density parameter prediction device based on array induction logging provided in an embodiment of this application; Figure 5 A schematic diagram of the device structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0020] The present application will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0021] In this embodiment, Figure 1 This paper illustrates a flowchart of a fracture surface density parameter prediction method based on array inductive logging, as provided in an embodiment of this application. Figure 1 As shown, the method includes: Step S101: At least three initial resistivity curves of the target well are obtained using an array sensing method.

[0022] In the technical solution provided in step S101 of this application, an array sensing method can be used to acquire at least three initial resistivity curves of the well section to be predicted in the target well. The resistivity in the initial resistivity curves is used to characterize the conductivity of the fluid in the formation, and the three initial resistivity curves are used to characterize the resistivity changes at different detection depths.

[0023] Optionally, logging data for predicting fracture surface density parameters is acquired, and the logging data includes at least resistivity curves at different detection depths obtained from array induction logging. For example, resistivity curves at the near, middle, and far detection depths are acquired respectively, denoted as follows: R near , R mid , R far It can also be extended and remembered as R i (i=1,2,…,N,N≥3), where N represents a positive integer.

[0024] Optionally, array induction refers to using array induction logging instruments to acquire formation resistivity data. This type of instrument can simultaneously emit electromagnetic waves of multiple different frequencies and receive induction signals from multiple different depths, thereby obtaining at least three resistivity curves (typically near, middle, and far depths) at different depths. These resistivity curves at different depths can reflect the resistivity variations within different radial ranges in the formation, providing fundamental data for subsequent fracture characteristic analysis and prediction.

[0025] It should be noted that this is only a preferred embodiment for obtaining at least three initial resistivity curves of the target well, and the process and method of obtaining at least three initial resistivity curves of the target well are not specifically limited.

[0026] Step S102: Preprocess at least three initial resistivity curves to obtain at least three target resistivity curves.

[0027] In the technical solution provided by step S102 of this application, after obtaining at least three initial resistivity curves, the at least three initial resistivity curves can be preprocessed to obtain at least three target resistivity curves.

[0028] Optionally, the data noise in the target resistivity curve is less than the data noise in the initial resistivity curve, and the target resistivity curve is the preprocessed resistivity curve, which can be obtained through... R i_proc (i=1,2,…,N,N≥3) are used for representation.

[0029] Optionally, preprocessing may include at least: logarithmic transformation, denoising and smoothing, and trend or background separation. It should be noted that this example only illustrates the preprocessing method for the initial resistivity curve and does not specify any particular method for preprocessing the initial resistivity curve.

[0030] Step S103: Based on at least three target resistivity curves, determine the initial fracture surface feature vector of the target well, and normalize the initial fracture surface feature vector to obtain the target fracture surface feature vector.

[0031] In the technical solution provided in step S103 of this application, the initial fracture surface feature vector of the target well can be determined based on the at least three target resistivity curves obtained above. Then, the initial fracture surface feature vector is normalized to achieve the purpose of obtaining the target fracture surface feature vector.

[0032] Optionally, the initial crack surface feature vector can be called the feature parameter vector, through... X The target crack surface feature vector can be represented as the normalized feature parameter vector.

[0033] For example, based on the three target resistivity curves obtained R near , R mid and R far Determine the characteristic parameter vector of the target well. X Furthermore, the feature parameter vector X Normalization is performed to obtain a normalized feature parameter vector.

[0034] It is understood that this is only a preferred embodiment for obtaining the feature vector of the target crack surface, and the process and method for obtaining the feature vector of the target crack surface are not specifically limited. As long as the process and method for obtaining the feature vector of the target crack surface are based on at least three target resistivity curves, they are all within the protection scope of this application and will not be listed here.

[0035] Step S104: Input the target fracture surface feature vector into the target prediction model for analysis to obtain the fracture surface density parameters of the target well.

[0036] In the technical solution provided in step S104 of this application, the obtained target fracture surface feature vector can be input into the target prediction model for analysis, so as to output the fracture surface density parameter of the target well.

[0037] Optionally, the target prediction model is obtained by training the initial prediction model with historical data of the target crack surface feature vector and historical data of the crack surface density parameter. The initial prediction model is constructed by a neural network.

[0038] Optionally, the target prediction model can be called the crack surface density prediction model, or simply the prediction model, and is represented by M(·). The initial prediction model can be called the supervised regression model. The crack surface density parameter can be obtained through... P 32 pred To express.

[0039] Optionally, a neural network is used to construct an initial prediction model. This initial prediction model is then trained and optimized as follows: First, a basic prediction model framework is built using a neural network; then, this initial neural network model is trained using historical data, namely, fracture surface feature vectors (input) and corresponding fracture surface density parameters (output label P32) that have been calibrated through imaging logging or core observation; finally, through the training process, the neural network model learns the complex mapping relationship between feature vectors and fracture surface density parameters, thus becoming a target prediction model capable of making predictions.

[0040] For example, well sections with imaging logging interpretation results and / or core observation results are selected, and the historical fracture surface density parameter (P32) at the corresponding well depth is obtained as a supervised learning label. At the same well depth, the corresponding historical feature parameter vector is calculated. X1 Supervised sample pairs are constructed, which can be represented by the following formula: X1 → P 32. The sample set is divided into a training set and a validation set. A supervised regression model is trained using the training set sample pairs (X1, P32) to obtain the prediction model M(·), whose output is: P 32 pred = M(X) ,in, P 32 pred The parameters used to represent the crack surface density predicted by the model can be used for model training, which can be achieved using supervised regression methods such as the K-Nearest Neighbors (KNN) algorithm.

[0041] Furthermore, after calculating the characteristic parameter vector X of the well section to be predicted according to the above steps, the characteristic parameter vector X is input into the prediction model M(·), and the fracture surface density parameter is output. P 32 pred And obtain a continuous curve of the crack surface density parameter.

[0042] In the technical solutions provided by steps S101 to S104 of this application, firstly, at least three initial resistivity curves at different detection depths of the target well are obtained by array sensing to characterize the conductivity of the formation fluid; then, these initial resistivity curves are preprocessed to reduce data noise and obtain the target resistivity curves; then, based on these target resistivity curves, the initial fracture surface feature vector is constructed and normalized to obtain the target fracture surface feature vector; finally, the target fracture surface feature vector is input into a target prediction model based on a neural network trained with historical data to analyze and obtain the fracture surface density parameters of the target well. Since the array sensing method is used, the multi-depth resistivity curves obtained can accurately reflect the electrical changes caused by formation fractures. The effectiveness of the curves is improved by preprocessing and noise reduction. A targeted fracture surface feature vector is constructed and normalized to eliminate the influence of dimensions. At the same time, a neural network model trained with historical data is used to achieve accurate mapping between features and fracture surface density parameters. This solves the technical problem that fracture surface density parameters are difficult to predict stably under high-angle or vertical fracture conditions, and achieves the technical effect of stably predicting fracture surface density parameters under high-angle or vertical fracture conditions.

[0043] The method described in this embodiment will be further described below.

[0044] As an optional embodiment, at least three initial resistivity curves are preprocessed to obtain at least three target resistivity curves, including: performing logarithmic transformation on each of the at least three initial resistivity curves to obtain at least three first resistivity curves; performing noise reduction processing on the at least three first resistivity curves to obtain at least three second resistivity curves; performing background separation processing on the at least three second resistivity curves to obtain at least three third resistivity curves; and determining at least three target resistivity curves based on the at least three first resistivity curves and the at least three second resistivity curves.

[0045] In this embodiment, at least three initial resistivity curves are logarithmically transformed to obtain at least three first resistivity curves. These first resistivity curves are then denoised to obtain at least three second resistivity curves. Further background separation processing is performed on these second resistivity curves to obtain at least three third resistivity curves. Finally, based on the at least three first and at least three second resistivity curves, at least three target resistivity curves are determined. The denoising process includes at least denoising and smoothing operations. The background separation processing can be referred to as trend separation processing. The target resistivity curves are the preprocessed curves, which can be called residual preprocessed curves.

[0046] Optionally, at least three initial resistivity curves can be logarithmically transformed using the following formula to obtain at least three first resistivity curves: R i_log = ln( R i ) in, R i_log Used to represent the first resistivity curve.

[0047] Optionally, by means of R i_log The second resistivity curve is obtained by denoising and smoothing. R i_sm For example, by using methods such as sliding window mean or median smoothing, the first resistivity curve can be smoothed. R i_log Perform noise reduction and smoothing processing.

[0048] Optionally, for the second resistivity curve R i_sm The third resistivity curve is obtained by extracting the background trend. R i_bg For example, by using methods such as long-window smoothing, low-pass filtering, or equivalent trend fitting, the second resistivity curve can be optimized. R i_sm Background separation processing is performed.

[0049] Optionally, at least three target resistivity curves are determined based on at least three first resistivity curves and at least three second resistivity curves using the following formula: R i_proc = R i_sm R i_bg It should be noted that the above processing is used to reduce noise and background trends, improve the comparability of curves at different detection depths, and provide input for subsequent feature parameter calculations.

[0050] As an optional embodiment, at least three target resistivity curves include: a first target resistivity curve, a second target resistivity curve, and a third target resistivity curve, wherein the detection depth of the first target resistivity curve is less than the detection depth of the second target resistivity curve, and the detection depth of the second target resistivity curve is less than the detection depth of the third target resistivity curve. Based on the at least three target resistivity curves, the initial fracture surface feature vector of the target well is determined, including: determining the radial difference parameter of the target well based on the third target resistivity curve and the first target resistivity curve; determining the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve; and determining the radial curvature parameter of the target well based on the first target resistivity curve. The first target resistivity curve and the third target resistivity curve are used to determine the first mean value corresponding to the first target resistivity curve, the second mean value corresponding to the second target resistivity curve, and the third mean value corresponding to the third target resistivity curve, respectively. Based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean value, the second mean value, and the third mean value, the radial consistency parameter of the target well is determined. Based on the third target resistivity curve, the boundary enhancement parameter of the target well is determined, and the third target resistivity curve is scaled to obtain the scale bandpass parameter. Based on the radial difference parameter, the radial curvature parameter, the radial consistency parameter, the boundary enhancement parameter, and the scale bandpass parameter, the initial fracture surface feature vector is constructed.

[0051] In this embodiment, at least three target resistivity curves are included: a first target resistivity curve, a second target resistivity curve, and a third target resistivity curve. Based on the third target resistivity curve and the first target resistivity curve, the radial difference parameter of the target well is determined. Based on the first, second, and third target resistivity curves, the radial curvature parameter of the target well is determined. Based on the first, second, and third target resistivity curves, a first mean value corresponding to the first target resistivity curve, a second mean value corresponding to the second target resistivity curve, and a third mean value corresponding to the third target resistivity curve are determined. Then, based on the first, second, and third target resistivity curves, the first mean value, the second mean value, and the third mean value, the radial consistency parameter of the target well is determined. Based on the third target resistivity curve, the boundary enhancement parameter of the target well is determined, and the third target resistivity curve is scale-smoothed to obtain a scale bandpass parameter. Based on the obtained radial difference parameter, radial curvature parameter, radial consistency parameter, boundary enhancement parameter, and scale bandpass parameter, an initial fracture surface feature vector can be constructed.

[0052] Optionally, the first target resistivity curve can be referred to as the near-probe depth preprocessed resistivity curve, through... R near_proc This is represented. The second target resistivity curve can be called the mid-depth preprocessed resistivity curve. It can be represented by... R mid_pro The resistivity curve of the third target can be called the preprocessed resistivity curve for far-field detection depth, which is represented by... R far_proc To express.

[0053] For example, different calculations are performed on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve to obtain the radial difference parameter. DR L Radial curvature parameter C Radial consistency parameters RINC Boundary reinforcement parameters EDGE M and scale bandpass parameters ( RT DOG_L The above parameters are calculated point by point according to the well depth using the following formula to form a characteristic parameter vector: .

[0054] As an optional embodiment, the third target resistivity curve is scale-smoothed to obtain the scale bandpass parameter, including: performing short-scale smoothing on the third target resistivity curve to obtain a first smooth curve, and performing long-scale smoothing on the third target resistivity curve to obtain a second smooth curve; and determining the scale bandpass parameter based on the first smooth curve and the second smooth curve.

[0055] In this embodiment, the third target resistivity curve is smoothed on a short scale to obtain a first smooth curve, and the third target resistivity curve is smoothed on a long scale to obtain a second smooth curve. Then, based on the first and second smooth curves obtained above, the scale bandpass parameter can be determined.

[0056] Optionally, the first smooth curve can be obtained by R far_s This can be represented. The second smooth curve can be represented by... R far_l The scale bandpass parameter can be represented as the two-scale smoothing difference.

[0057] Optionally, the third target resistivity curve can be smoothed using short-scale processing to obtain the first smoothed curve. For example, the third target resistivity curve... R far_procA short-scale smoothing process of 2 meters (m) is performed to obtain the first smooth curve. R far_s .

[0058] Optionally, the third target resistivity curve can be smoothed over a long scale to obtain a second smoothed curve. For example, the third target resistivity curve... R far_proc A 5-meter long-scale smoothing process was performed to obtain the second smooth curve. R far_l .

[0059] Optionally, the scale bandpass parameter can be determined by the difference between the first smooth curve and the second smooth curve, for example, for... R far_proc Short-scale smoothing and long-scale smoothing are performed to obtain the following results respectively. R far_s , R far_l (The two have different scales), and the scale bandpass parameter is calculated using the following formula. RT DOG_L : .

[0060] As an optional embodiment, the radial difference parameter of the target well is determined based on the third target resistivity curve and the first target resistivity curve using the following formula, including: DR L = R far_proc R near_proc in, DR L Used to represent radial difference parameters R far_proc Used to represent the resistivity curve of the third target. R near_proc Used to represent the first target resistivity curve.

[0061] In this embodiment, through the third target resistivity curve R far_proc With the first target resistivity curve R near_proc The difference between them is used to determine the radial difference parameter. DR L That is, the above process can be represented by the following formula: DR L = R far_proc Rnear_proc .

[0062] For example, the radial difference parameter is calculated from the difference between the preprocessed resistivity curve at far detection depth and the preprocessed resistivity curve at near detection depth, and the smoothing window length is set to 3m.

[0063] As an optional embodiment, the radial curvature parameter of the target well is determined based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve using the following formula, including: C = R far_proc 2 R mid_proc + R near_proc in, C Used to represent radial curvature parameters. R mid_proc Used to represent the second target resistivity curve.

[0064] In this embodiment, the second target resistivity curve is multiplied by the target value to obtain the target product; the difference between the third target resistivity curve and the target product is determined as the target difference; the sum of the target difference and the first target resistivity curve is determined as the radial curvature parameter, and the above process can be calculated using the following formula: C = R far_proc 2 R mid_proc + R near_proc .

[0065] For example, the radial curvature parameter C can be calculated by second-order difference from the preprocessed resistivity curves of near, middle, and far detection depths.

[0066] As an optional embodiment, the radial consistency parameter of the target well is determined based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean, the second mean, and the third mean using the following formula, including:

[0067] in, RING The parameter used to represent radial consistency is N, where N is an integer and N≥3. Used to represent the i-th target resistivity curve Used to represent the mean value of the i-th target resistivity curve.

[0068] In this embodiment, the first target resistivity curve can also be obtained through... This can be represented. The second target resistivity curve can also be obtained through... This can be represented. The third target resistivity curve can also be obtained through... The first mean can be represented as follows. The second mean can be represented as follows. The third mean can be represented as follows. To express.

[0069] For example, the radial consistency parameter RINC is calculated from the degree of dispersion of the preprocessed resistivity curves at the same well depth.

[0070] As an optional embodiment, the boundary enhancement parameters of the target well are determined based on the third target resistivity curve using the following formula, including:

[0071] in, EDGE M Used to represent boundary enhancement parameters Used to represent numerical derivatives / first-order differences.

[0072] In this embodiment, the boundary reinforcement parameters are determined by performing first-order difference processing on the third target resistivity curve. EDGE M The purpose, that is, the above process, can be calculated using the following formula: .

[0073] For example, the first-order difference calculation along the well depth direction is obtained based on the preprocessed resistivity curve of the far-seeking depth, and the smoothing window length is set to 3 m.

[0074] By applying the technical solution of this embodiment, at least three initial resistivity curves at different detection depths of the target well are first acquired through array sensing to characterize the conductivity of the formation fluid. Next, these initial resistivity curves are preprocessed to reduce data noise, resulting in target resistivity curves. Then, based on these target resistivity curves, initial fracture surface feature vectors are constructed and normalized to obtain target fracture surface feature vectors. Finally, the target fracture surface feature vectors are input into a target prediction model based on a neural network trained on historical data, thereby analyzing and deriving the fracture surface density parameters of the target well. Considering that the multi-depth resistivity curves obtained through array sensing can accurately reflect the electrical changes induced by formation fractures, the effectiveness of the curves is improved through preprocessing and noise reduction. Targeted fracture surface feature vectors are constructed and normalized to eliminate dimensional influences. Simultaneously, a neural network model trained on historical data is used to achieve accurate mapping between features and fracture surface density parameters. This solves the technical problem of unstable prediction of fracture surface density parameters under high-angle or vertical fracture conditions, achieving the technical effect of stable prediction of fracture surface density parameters under high-angle or vertical fracture conditions.

[0075] Furthermore, as a refinement and extension of the specific implementation of the above embodiments, in order to fully illustrate the specific implementation process of this embodiment, this embodiment selects the Chang 8 tight sandstone and mudstone reservoir in an oil field as the application object. Figure 2 This application provides a schematic diagram illustrating the distribution structure of fracture dip angle characteristics in imaging logging, as shown in the embodiment of this application. Figure 2 As shown, the reservoir in this area is dense, with high-angle structural fractures as the main feature. It has array induction logging and imaging logging data, making it suitable for calibration and prediction verification of the fracture surface density parameter P32.

[0076] In this embodiment, firstly, the data conditions and sample sources are determined, namely, the well logging data uses multi-depth resistivity curves obtained from array induction logging as the main input. Figure 3 This illustration shows a structural diagram of a method for inspecting crack P32 using the KNN algorithm, as provided in an embodiment of this application. Figure 3As shown, resistivity curves at near (AT10), mid (AT30), and far (AT90) depths were selected for feature construction, with all resistivity curves measured in ohms-meters (OHMM). Simultaneously, conventional logging curves such as spontaneous potential (SP), natural gamma ray (GR), and borehole diameter were introduced to constrain lithology and wellbore conditions. The unit of measurement for spontaneous potential curves is millivolts (MV), and the standard unit of measurement for natural gamma ray curves is gamma units (GAPI). Furthermore, density logging curves and acoustic logging curves were introduced for comparison with the curves in this application, with the unit of density logging curves being grams per cubic centimeter (G / CM). 3 The unit of sonic logging curves is microseconds per meter (US / M); lithology includes siltstone, fine sandstone, and mudstone; the labeled well depth (METRES) ranges from 1400 to 1425 meters, with a scale of 1:200, serving as the depth alignment benchmark for all logging data and interpretation results; fracture occurrence (DEGREES) are fracture development sections marked with black dots, visually indicating the distribution of high-angle or vertical fractures within the well, providing a direct geological marker of fracture development. P32 (m) is interpreted using imaging logging. 2 / m 3 Based on the results and core observations, the fracture surface density parameter P32 was used as a supervised learning label, and 2633 sets of supervised samples were compiled in well sections with corresponding data. Each set of samples consists of a feature parameter vector at the same well depth and the corresponding P32.

[0077] Optionally, AT10 is a resistivity profile identifier for array induction logging with a vertical resolution of 2 feet and a radial detection depth of 10 inches, representing array induction resistivity logging data near the detection depth. AT30 is a resistivity profile identifier for array induction logging with a vertical resolution of 2 feet and a radial detection depth of 30 inches. AT90 is a resistivity profile identifier for array induction logging with a vertical resolution of 2 feet and a radial detection depth of 90 inches.

[0078] Then, the characteristic parameters are calculated and set. Following the aforementioned step S102, logarithmic transformation, noise reduction, smoothing, and trend separation are performed on the resistivity curves at different detection depths of the array sensing to construct preprocessed resistivity curves, and the crack characterization characteristic parameters are further calculated.

[0079] Furthermore, the model is trained and validated. The obtained and normalized historical feature parameter vector is used as the model input, and the fracture surface density parameter P32 obtained from imaging logging interpretation and / or core observation is used as the model output. A supervised regression method is employed to train the fracture surface density prediction model, with KNN regression used as one implementation method, and Mahalanobis distance is introduced as a measure of sample similarity.

[0080] In addition, to verify the engineering validity of the model's prediction results, well sections that were not involved in the training but had imaging logging data were selected as blind wells for verification, such as... Figure 3 As shown, the P32 prediction results obtained based on the method of this application are compared with the fracture zone interpreted by imaging logging. When the degree of overlap between the fracture development section reflected by the prediction results and the fracture section interpreted by imaging logging in the well depth direction meets the predetermined consistency criterion, the identification result is determined to be consistent. Statistical results show that the fracture zone identification consistency rate reaches 82.1%.

[0081] Finally, the results are output and applied. The trained prediction model is applied to the target well section. The array induction multi-detection depth resistivity curves are preprocessed and feature parameters are calculated using the same steps, and then input into the prediction model. The output is the predicted fracture surface density at the corresponding well depth. P 32 pred This forms a continuous prediction curve for the crack surface density parameter.

[0082] In this embodiment, at least three initial resistivity curves at different probe depths of the target well are first acquired using an array sensing method to characterize the conductivity of the formation fluid. Next, these initial resistivity curves are preprocessed to reduce data noise, resulting in target resistivity curves. Then, based on these target resistivity curves, initial fracture surface feature vectors are constructed and normalized to obtain target fracture surface feature vectors. Finally, the target fracture surface feature vectors are input into a target prediction model based on a neural network trained on historical data, thereby analyzing and deriving the fracture surface density parameters of the target well. Considering that the multi-probe-depth resistivity curves obtained using an array sensing method can accurately reflect the electrical changes induced by formation fractures, the effectiveness of the curves is improved through preprocessing and noise reduction. A targeted fracture surface feature vector is constructed and normalized to eliminate dimensional influences. Simultaneously, a neural network model trained on historical data is used to achieve accurate mapping between features and fracture surface density parameters. This solves the technical problem of unstable prediction of fracture surface density parameters under high-angle or vertical fracture conditions, achieving the technical effect of stable prediction of fracture surface density parameters under high-angle or vertical fracture conditions.

[0083] Furthermore, as Figure 1 In the specific implementation of the method, in the embodiments of this application, Figure 4This illustration shows a structural schematic diagram of a fracture surface density parameter prediction device based on array induction logging provided in an embodiment of this application. Figure 4 As shown, the fracture surface density parameter prediction device 400 based on array induction logging includes: a first acquisition unit 401, a second acquisition unit 402, a determination unit 403 and a third acquisition unit 404.

[0084] The first acquisition unit 401 is used to acquire at least three initial resistivity curves of the target well using an array sensing method. The resistivity in the initial resistivity curve is used to characterize the conductivity of the fluid in the formation, and the three initial resistivity curves are used to characterize the resistivity changes at different detection depths.

[0085] The second acquisition unit 402 is used to preprocess at least three initial resistivity curves to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves.

[0086] The determination unit 403 is used to determine the initial fracture surface feature vector of the target well based on at least three target resistivity curves, and to normalize the initial fracture surface feature vector to obtain the target fracture surface feature vector.

[0087] The third acquisition unit 404 is used to input the target fracture surface feature vector into the target prediction model for analysis to obtain the fracture surface density parameter of the target well. The target prediction model is obtained by training the initial prediction model with historical data of the target fracture surface feature vector and historical data of the fracture surface density parameter. The initial prediction model is constructed by a neural network.

[0088] Optionally, the device is further configured to: preprocess at least three initial resistivity curves to obtain at least three target resistivity curves, including: performing logarithmic transformation on the at least three initial resistivity curves respectively to obtain at least three first resistivity curves; performing noise reduction processing on the at least three first resistivity curves to obtain at least three second resistivity curves; performing background separation processing on the at least three second resistivity curves to obtain at least three third resistivity curves; and determining at least three target resistivity curves based on the at least three first resistivity curves and the at least three second resistivity curves.

[0089] Optionally, the device is further configured to: determine the initial fracture surface feature vector of the target well based on at least three target resistivity curves, including: a first target resistivity curve, a second target resistivity curve, and a third target resistivity curve, wherein the detection depth of the first target resistivity curve is less than the detection depth of the second target resistivity curve, and the detection depth of the second target resistivity curve is less than the detection depth of the third target resistivity curve; and determine the initial fracture surface feature vector of the target well based on the at least three target resistivity curves, including: determining the radial difference parameter of the target well based on the third target resistivity curve and the first target resistivity curve; determining the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve; and determining the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve; and determining the radial difference parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve; and determining the radial difference parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve. The second and third target resistivity curves are used to determine the first mean value corresponding to the first target resistivity curve, the second mean value corresponding to the second target resistivity curve, and the third mean value corresponding to the third target resistivity curve, respectively. Based on the first, second, and third target resistivity curves, the first mean value, the second mean value, and the third mean value, the radial consistency parameter of the target well is determined. Based on the third target resistivity curve, the boundary enhancement parameter of the target well is determined, and the third target resistivity curve is scale-smoothed to obtain the scale bandpass parameter. Based on the radial difference parameter, radial curvature parameter, radial consistency parameter, boundary enhancement parameter, and scale bandpass parameter, an initial fracture surface feature vector is constructed.

[0090] Optionally, the device is further configured to: perform scale smoothing on the third target resistivity curve to obtain scale bandpass parameters, including: performing short-scale smoothing on the third target resistivity curve to obtain a first smoothed curve, and performing long-scale smoothing on the third target resistivity curve to obtain a second smoothed curve; and determining the scale bandpass parameters based on the first smoothed curve and the second smoothed curve.

[0091] Optionally, the device is also used to: determine the radial difference parameter of the target well based on the third target resistivity curve and the first target resistivity curve using the following formula, including: DR L = R far_proc R near_proc in, DR L Used to represent radial difference parameters R far_proc Used to represent the resistivity curve of the third target. R near_proc Used to represent the first target resistivity curve.

[0092] Optionally, the device is further configured to: determine the radial curvature parameter of the target well based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve using the following formula, including: C = R far_proc 2 R mid_proc + R near_proc in, C Used to represent radial curvature parameters. R mid_proc Used to represent the second target resistivity curve.

[0093] Optionally, the device is further configured to: determine the radial consistency parameters of the target well based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean, the second mean, and the third mean using the following formula, including:

[0094] in, RING The parameter used to represent radial consistency is N, where N is an integer and N≥3. Used to represent the i-th target resistivity curve Used to represent the mean value of the i-th target resistivity curve.

[0095] Optionally, the boundary enhancement parameters of the target well are determined based on the third target resistivity curve using the following formula, including:

[0096] in, EDGE M Used to represent boundary enhancement parameters Used to represent numerical derivatives / first-order differences.

[0097] In this embodiment, a first acquisition unit uses an array sensing method to acquire at least three initial resistivity curves of the target well. The resistivity in the initial resistivity curves characterizes the conductivity of fluids in the formation, and the three initial resistivity curves characterize the resistivity changes at different probe depths. A second acquisition unit preprocesses the at least three initial resistivity curves to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves. A determination unit determines the initial fracture surface feature vector of the target well based on the at least three target resistivity curves, and further refines the initial resistivity curves. The initial fracture surface feature vector is normalized to obtain the target fracture surface feature vector. The target fracture surface feature vector is then input into the target prediction model for analysis through the third acquisition unit to obtain the fracture surface density parameter of the target well. The target prediction model is obtained by training the initial prediction model with historical data of the target fracture surface feature vector and historical data of the fracture surface density parameter. The initial prediction model is constructed through a neural network, which can solve the technical problem that it is difficult to stably predict the fracture surface density parameter under high-angle or vertical fracture conditions, and achieve the technical effect of stably predicting the fracture surface density parameter under high-angle or vertical fracture conditions.

[0098] It should be noted that other corresponding descriptions of the functional units involved in the fracture surface density parameter prediction device based on array induction logging provided in this application embodiment can be found in the following references. Figure 1 The corresponding descriptions in [the document] will not be repeated here.

[0099] This application also provides a computer device, which may specifically be a personal computer, a server, a network device, etc. Figure 5 This application provides a schematic diagram of the device structure of a computer device according to an embodiment of the present application. Figure 5 As shown, the computer device includes a bus, a processor, memory, and a communication interface, and may also include an input / output interface and a display device. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores location information. The network interface allows communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the steps in the various method embodiments.

[0100] Those skilled in the art will understand that Figure 5The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0101] In one embodiment, a computer-readable storage medium is provided, which may be non-volatile or volatile, having stored thereon a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0102] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0103] It should be noted that the user personal information involved in the embodiments of this application is all authorized (with the knowledge and consent) by the relevant parties or fully authorized by all parties, and the executing entity can obtain it through various legal and compliant means. The collection, storage, use, processing, transmission, provision, and disclosure of the information, data, and signals involved all comply with the relevant laws and regulations of the relevant countries and regions, and do not violate public order and good morals. It should be noted that if any software tools or components other than those of this company appear in the embodiments of this application, they are merely illustrative examples and do not represent actual use.

[0104] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, graphics processors, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0105] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for predicting fracture surface density parameters based on array induction logging, characterized in that, The method includes: At least three initial resistivity curves of the target well are acquired using an array sensing method. The resistivity in the initial resistivity curve is used to characterize the conductivity of fluids in the formation, and the three initial resistivity curves are used to characterize the resistivity changes at different detection depths. At least three initial resistivity curves are preprocessed to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves; Based on at least three target resistivity curves, the initial fracture surface feature vector of the target well is determined, and the initial fracture surface feature vector is normalized to obtain the target fracture surface feature vector. The target fracture surface feature vector is input into the target prediction model for analysis to obtain the fracture surface density parameter of the target well. The target prediction model is obtained by training an initial prediction model with historical data of the target fracture surface feature vector and historical data of the fracture surface density parameter. The initial prediction model is constructed by a neural network.

2. The method according to claim 1, characterized in that, Preprocessing at least three initial resistivity curves yields at least three target resistivity curves, including: At least three initial resistivity curves are subjected to logarithmic transformation to obtain at least three first resistivity curves; At least three of the first resistivity curves are denoised to obtain at least three second resistivity curves; At least three of the second resistivity curves are subjected to background separation processing to obtain at least three third resistivity curves; Based on at least three of the first resistivity curves and at least three of the second resistivity curves, at least three target resistivity curves are determined.

3. The method according to claim 1, characterized in that, The at least three target resistivity curves include: a first target resistivity curve, a second target resistivity curve, and a third target resistivity curve, wherein the detection depth of the first target resistivity curve is less than the detection depth of the second target resistivity curve, and the detection depth of the second target resistivity curve is less than the detection depth of the third target resistivity curve. Based on the at least three target resistivity curves, the initial fracture surface feature vector of the target well is determined, including: Based on the third target resistivity curve and the first target resistivity curve, the radial difference parameter of the target well is determined; Based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve, the radial curvature parameter of the target well is determined; Based on the first target resistivity curve, the second target resistivity curve and the third target resistivity curve, a first mean value corresponding to the first target resistivity curve, a second mean value corresponding to the second target resistivity curve and a third mean value corresponding to the third target resistivity curve are determined respectively. Based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean, the second mean, and the third mean, the radial consistency parameter of the target well is determined; Based on the third target resistivity curve, the boundary enhancement parameters of the target well are determined, and the third target resistivity curve is scale-smoothed to obtain the scale bandpass parameters. The initial crack surface feature vector is constructed based on the radial difference parameter, the radial curvature parameter, the radial consistency parameter, the boundary enhancement parameter, and the scale bandpass parameter.

4. The method according to claim 3, characterized in that, The resistivity curve of the third target is scale-smoothed to obtain the scale bandpass parameters, including: The third target resistivity curve is smoothed on a short scale to obtain a first smooth curve, and the third target resistivity curve is smoothed on a long scale to obtain a second smooth curve. The scale bandpass parameter is determined based on the first smooth curve and the second smooth curve.

5. The method according to claim 3, characterized in that, The radial difference parameter of the target well is determined based on the third target resistivity curve and the first target resistivity curve using the following formula, including: DR L = R far_proc R near_proc in, DR L Used to represent the radial difference parameter. R far_proc Used to represent the third target resistivity curve. R near_proc Used to represent the resistivity curve of the first target.

6. The method according to claim 3, characterized in that, The radial curvature parameter of the target well is determined based on the first target resistivity curve, the second target resistivity curve, and the third target resistivity curve using the following formula, including: C = R far_proc 2 R mid_proc + R near_proc in, C Used to represent radial curvature parameters. R mid_proc Used to represent the second target resistivity curve.

7. The method according to claim 3, characterized in that, The radial consistency parameter of the target well is determined using the following formula, based on the first target resistivity curve, the second target resistivity curve, the third target resistivity curve, the first mean, the second mean, and the third mean, including: Wherein, RING represents the radial consistency parameter, N represents an integer, and N≥3, Used to represent the i-th target resistivity curve Used to represent the mean value of the i-th target resistivity curve.

8. The method according to claim 3, characterized in that, The boundary enhancement parameters of the target well are determined based on the third target resistivity curve using the following formula, including: in, EDGE M Used to represent the boundary enhancement parameters Used to represent numerical derivatives / first-order differences.

9. A fracture surface density parameter prediction device based on array induction logging, characterized in that, The device includes: The first acquisition unit is used to acquire at least three initial resistivity curves of the target well using an array sensing method. The resistivity in the initial resistivity curve is used to characterize the conductivity of the fluid in the formation, and the three initial resistivity curves are used to characterize the resistivity changes at different detection depths. The second acquisition unit is used to preprocess at least three initial resistivity curves to obtain at least three target resistivity curves, wherein the data noise in the target resistivity curves is less than the data noise in the initial resistivity curves. The determining unit is used to determine the initial fracture surface feature vector of the target well based on at least three target resistivity curves, and to normalize the initial fracture surface feature vector to obtain the target fracture surface feature vector. The third acquisition unit is used to input the target fracture surface feature vector into the target prediction model for analysis to obtain the fracture surface density parameter of the target well. The target prediction model is obtained by training an initial prediction model with historical data of the target fracture surface feature vector and historical data of the fracture surface density parameter. The initial prediction model is constructed by a neural network.

10. A computer device, comprising a storage medium, a processor, and a computer program stored on the storage medium 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 8.