Three-dimensional geostress prediction method based on parallel neural network with physical constraints

Abstract

The present invention discloses a three-dimensional geostress prediction method based on a parallel neural network with physical constraints, including collecting drilling data in a target area and expanding the drilling data; collecting well logging data of wells that have been drilled in the target area, and obtaining geostress attribute data of each well using well logging interpretation; constructing a parallel neural network model based on physical constraints; training the model and predicting the three-dimensional geostress of the entity. The present invention adopts a model based on physical constraints + parallel neural networks to predict geostress only by three-dimensional spatial coordinates. Its essence is to make up for the lack of measured geostress data. Starting from the three-dimensional spatial data derived from the terrain, the strong fitting function of the neural network is used, combined with the constraints of the geostress analytical model, and the geostress is predicted by physical constraints + data-driven. This method not only integrates the connection between terrain structure and geostress, but also effectively improves the accuracy and interpretability of the neural network model through the constraints of the mechanism model.

Description

Technical Field

[0001] The invention relates to a three-dimensional geostress prediction method of a parallel neural network based on physical constraints, and belongs to the technical field of oil and gas exploration and development. Background Art

[0002] Geostress is a natural stress existing in the rock mass, which is formed by the combined effects of gravity, tectonic force, fluid dynamics and crystallization force. It is usually characterized by three principal stresses: vertical geostress, maximum and minimum horizontal geostress. In the field of petroleum engineering, geostress is a key parameter affecting engineering problems such as well wall stability, fracturing design, casing damage, and sand production in oil reservoirs. As the depth of oil and gas exploration and development in my country increases, the geological environment it faces becomes more and more complex, and the study of geostress has also received increasing attention from all walks of life.

[0003] So far, the main methods for obtaining geostress in the field of petroleum engineering include indoor core testing technology, field measurement analysis, logging curve interpretation, seismic prediction method, numerical simulation technology, etc., and they are developing and improving towards comprehensive application and cross-verification. For one-dimensional geostress, a more accurate geostress profile can be obtained by using logging curve interpretation and single-point geostress measured data correction. This method is now relatively mature. However, one-dimensional geostress is constrained by range and can only characterize the geostress state of a single well. In engineering, predicting three-dimensional geostress is more meaningful. At present, the prediction of three-dimensional geostress mainly relies on seismic prediction method and numerical simulation technology, but both have certain defects. Among them, seismic prediction method is time-consuming, costly, and cumbersome. It requires precise quality control of key technical links such as pre-stack preprocessing, well-seismic calibration, seismic wavelet extraction, and pre-stack joint inversion; numerical simulation technology requires accurate geological models and effective initial conditions and boundary conditions. When facing strong structural formations, complex and changeable geological conditions are difficult to achieve with simple numerical methods. In recent years, with the widespread application of machine learning methods in the field of earth sciences, many scholars have used neural networks to study formation pore pressure, geostress, and formation drillability, and embedded mechanism models or domain knowledge into the models for different research objects to improve the prediction effect of the models.

[0004] At present, there is no report on the research of embedding mechanism model into neural network to predict three-dimensional geostress. Therefore, a three-dimensional geostress prediction method based on physical constraint + parallel neural network is invented to provide a new proxy model for three-dimensional geostress prediction. Summary of the invention

[0005] In order to overcome the problems in the prior art, the present invention provides a three-dimensional geostress prediction method based on a parallel neural network with physical constraints, which can quickly predict the three-dimensional geostress of a region according to the three-dimensional spatial coordinates.

[0006] The technical solution provided by the present invention to solve the above technical problems is: a three-dimensional geostress prediction method based on a parallel neural network with physical constraints, comprising the following steps:

[0007] Step S1, collecting drilling data of the target area, and expanding the drilling data using Kriging interpolation method;

[0008] Step S2, using the expanded drilling data as control points to generate NURBS surfaces and entities, and obtaining the three-dimensional space coordinates of the entities;

[0009] Step S3, collecting logging data of wells drilled in the current area, and performing logging interpretation for each well;

[0010] Step S4, dividing the drilled wells into training wells and test wells;

[0011] Step S5, obtaining the three-dimensional spatial coordinates of the borehole trajectory of the training well and the ground stress attribute data along the borehole trajectory path according to the well logging interpretation;

[0012] Step S6, normalizing the three-dimensional space coordinates from the entity and the wellbore trajectory respectively;

[0013] Step S7, constructing a parallel neural network model based on theoretical constraints, and determining the input characteristics and output characteristics of the model;

[0014] Step S8, using the data from the training well to train the parallel neural network model based on theoretical constraints, to obtain a trained parallel neural network model based on theoretical constraints;

[0015] Step S9: testing the prediction accuracy of the trained parallel neural network model based on theoretical constraints according to the test well data, and predicting the three-dimensional geostress of the entity.

[0016] A further technical solution is that the drilling data includes X, Y, and Z coordinate values ​​of each geological layer interface.

[0017] A further technical solution is that the specific steps of expanding the drilling data using the Kriging interpolation method are as follows:

[0018] Step S11, calculating the semivariance value of the known data point by using the empirical semivariance function, and then constructing a scatter plot of distance and semivariance value;

[0019] Step S12, fitting the scatter plot using a spherical fitting function;

[0020] Step S13: Determine the weight corresponding to the unknown point by using the semivariance function, and then weight the unknown point to obtain the value corresponding to the unknown point.

[0021] A further technical solution is that the empirical semivariance function is as follows:

[0022]

[0023] Where: γ(h) represents the semi-variance value when the distance is h; N(h) represents the number of data pairs separated by a distance of h; P(i)-P(i,h) represents the difference between the i-th pair of data pairs separated by a distance of h.

[0024] A further technical solution is that the calculation formula in step S13 is as follows:

[0025]

[0026] Where: P(x, y) represents the predicted value corresponding to the interpolation point; P(i) represents the i-th interpolation point; λ i (x i ,y i ) represents the weight corresponding to the interpolation point; n represents the number of interpolation points.

[0027] A further technical solution is that the specific process of step S2 is: using the expanded drilling data of each geological layer interface as control points to generate a NURBS surface; and then generating a BURBS entity along the longitudinal direction of the generated NURBS surface.

[0028] A further technical solution is that the geostress attribute data includes formation pore pressure, vertical geostress, maximum and minimum horizontal geostress.

[0029] A further technical solution is that in step S5, the geostress attribute data obtained by the interpretation of each well is filtered using the Savitzky-Golay filtering algorithm, and the geostress attributes are thinned out at a ratio of 1:10 while ensuring that the overall trend and shape of the curve remain unchanged.

[0030] A further technical solution is that the input features of the model in step S7 include X, Y, and Z coordinate values; and the output features include formation pore pressure, vertical geostress, and maximum and minimum horizontal geostress.

[0031] A further technical solution is that the calculation process of the model in step S7 is:

[0032] 1) The three-dimensional spatial coordinates of the normalized entity and the wellbore trajectory are input into the single network model A, the single network model B, and the single network model C respectively. The outputs of the three single network models A, B, and C are Poisson's ratio, Biot coefficient, and geostress attributes respectively. When the model is output, the Sigmoid activation function is used to limit the Poisson's ratio and Biot coefficient to between 0 and 1. Then, the output values ​​of the above single network models are substituted into Huang's geostress model to constitute the physical constraint term loss;

[0033] 2) At the same time, the three-dimensional spatial coordinates of the normalized wellbore trajectory are input into the single network model C, and the corresponding output is the in-situ stress attribute, which is compared with the actual in-situ stress attribute data to form the data constraint term loss;

[0034] 3) Add the physical constraint loss and the data constraint loss together, and assign weights so that the weighted sum is 1, thus forming a loss function containing both physical constraint and data constraint.

[0035] The mathematical expression of the model loss function is as follows:

[0036] L TCANN (θ)=λL Phy (θ)+(1-λ)L Data (θ)

[0037] in:

[0038]

[0039]

[0040] Where: λ represents the weight parameter; L Phy (θ) represents the physical constraint loss; L Data (θ) represents the data constraint loss; N P Represents the number of spatial coordinate points of the three-dimensional geological model; N P Represents the number of spatial coordinate points of the drilled wellbore trajectory; represents the predicted vertical in-situ stress; represents the predicted maximum horizontal ground stress, MPa; represents the predicted minimum horizontal ground stress, MPa; Represents the predicted formation pore pressure, MPa; σ v represents the actual vertical stress; σ H Indicates the actual maximum horizontal ground stress, MPa; σ h Indicates the actual minimum horizontal ground stress, MPa; p p Indicates the actual formation pore pressure, MPa;

[0041] 4) The back-propagation algorithm is used to calculate the derivatives of the loss function with respect to the weights and bias terms in the neural network, and then it is iteratively updated according to the gradient descent algorithm so that the loss function value continuously approaches the global minimum and gradually determines the optimal weights and bias terms in the neural network.

[0042] The present invention has the following beneficial effects: the present invention adopts physical constraints + parallel neural network to predict three-dimensional geostress. By embedding Huang's geostress model into the neural network model, the formation pore pressure, vertical geostress, maximum and minimum horizontal geostress are balanced with each other. In addition to satisfying the constraints in the data-driven mode, it also satisfies the constraints in the mechanism-driven mode, which enhances the interpretability of the model to a certain extent. The three-dimensional geostress of the region can be obtained only by relying on spatial geographic coordinates. It has the characteristics of high degree of automation and high speed, and plays a very important role in geostress evaluation, wellbore stability analysis and hydraulic fracturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the present invention;

[0044] Figure 2 It is a solid model diagram;

[0045] Figure 3 This is the ground stress curve of the test well;

[0046] Figure 4 This is the three-dimensional geostress prediction result diagram for the entire target area. DETAILED DESCRIPTION

[0047] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] The three-dimensional geostress prediction method of the parallel neural network based on physical constraints of the present invention comprises the following steps:

[0049] Step S1, collecting drilling data of the target area, and expanding the drilling data using Kriging interpolation method;

[0050] Step S11, collecting X, Y, and Z coordinate values ​​of each geological layer interface in the target area;

[0051] Step S12, calculating the semivariance value of the known data point by using the empirical semivariance function, and then constructing a scatter plot of the distance and the semivariance value, the empirical semivariance function is as follows:

[0052]

[0053] Where: γ(h) represents the semivariance value when the distance is h; N(h) represents the number of data pairs separated by a distance of h; P(i)-P(i,h) represents the difference between the i-th pair of data pairs separated by a distance of h;

[0054] Step S13, using existing fitting functions, such as exponential, circular, spherical and other functions to fit the scatter plot, the present invention preferably uses a spherical fitting function, the spherical fitting function is as follows:

[0055]

[0056] Where: c o represents nugget; a represents range; c represents partial sill value; c o +c indicates base;

[0057] Step S14, predicting the value of the unknown point, first determining the weight corresponding to the unknown point by using the semivariance function, and then weighting the unknown point to obtain the value corresponding to the unknown point;

[0058]

[0059] Where: P(x, y) represents the predicted value corresponding to the interpolation point; P(i) represents the i-th interpolation point; λ i (x i ,y i ) represents the weight corresponding to the interpolation point; n represents the number of interpolation points;

[0060] Step S2, using the expanded drilling data of each geological layer interface as control points to generate a NURBS surface; then generating a BURBS entity along the longitudinal direction of the generated NURBS surface, the entity model is as follows Figure 2 As shown, the three-dimensional space coordinates of the entity are obtained;

[0061] Step S3, collecting logging data of wells drilled in the current area, and performing logging interpretation for each well;

[0062] Step S4: Divide the drilled wells into training wells and test wells; for the training wells in this example, Figure 2 As shown in X1, X2, X3, X4, and X5, the test well is shown in X6;

[0063] Step S5, obtaining the three-dimensional spatial coordinates of the borehole trajectory of the training well and the geostress attribute data (formation pore pressure, vertical geostress, maximum and minimum horizontal geostress) along the borehole trajectory according to the well logging interpretation, filtering the geostress attribute data using the Savitzky-Golay filtering algorithm, and thinning the data at a ratio of 1:10 while ensuring that the overall trend and shape of the curve remain unchanged;

[0064] The wellbore trajectory is calculated from the wellhead coordinates, well inclination angle, and azimuth angle, and is expressed by X, Y, and Z coordinate values;

[0065] Step S6, normalizing the three-dimensional space coordinates from the entity and the wellbore trajectory respectively;

[0066] The normalized mathematical expression is as follows:

[0067]

[0068] Where: x i Represents the original three-dimensional space coordinates; minx i Indicates the minimum value in three-dimensional space coordinates; maxx i Indicates the maximum value in three-dimensional space coordinates; x i 'Indicates the maximum value in three-dimensional space coordinates;

[0069] Step S7, constructing a parallel neural network model based on theoretical constraints, and determining the input characteristics and output characteristics of the model, wherein the input characteristics include X, Y, and Z coordinate values, and the output characteristics include formation pore pressure, vertical geostress, and maximum and minimum horizontal geostress;

[0070] The calculation process of the model is as follows: 1) The normalized three-dimensional spatial coordinates (including those from the physical geological model and the borehole trajectory) are input into the three single network models A, B, and C respectively. The outputs of the three single network models A, B, and C are Poisson's ratio, Biot coefficient, and geostress attributes, respectively. It should be noted that when the model is output, the Sigmoid activation function is used to limit the Poisson's ratio and Biot coefficient to between 0 and 1. Then, the output values ​​of the above single network models are substituted into the Huang geostress model to constitute the physical constraint term loss; 2) At the same time, the normalized three-dimensional spatial coordinates (only The data from the borehole trajectory are input into the single network model C, and the corresponding output is the geostress attribute. The mean square error is calculated between it and the actual geostress attribute value to form the data constraint term loss; 3) the physical constraint term loss and the data constraint term loss are added together, and the weights are matched so that the weighted sum is 1, which constitutes the loss function containing the physical constraint term and the data constraint term; 4) the back propagation algorithm is used to calculate the derivative of the loss function with respect to the weights and bias terms in the neural network, and then it is iteratively updated according to the gradient descent algorithm, so that the loss function value continuously approaches the global minimum, and gradually determines the optimal weights and bias terms in the neural network.

[0071] The mathematical expression of the model loss function is as follows:

[0072] L TCANN (θ)=λL Phy (θ)+(1-λ)L Data(θ)

[0073] in:

[0074]

[0075]

[0076] Where: λ represents the weight parameter; L Phy (θ) represents the physical constraint loss; L Data (θ) represents the data constraint loss; N P Represents the number of spatial coordinate points of the three-dimensional geological model; N P Represents the number of spatial coordinate points of the drilled wellbore trajectory; represents the predicted vertical in-situ stress; represents the predicted maximum horizontal ground stress, MPa; represents the predicted minimum horizontal ground stress, MPa; Represents the predicted formation pore pressure, MPa; σ v represents the actual vertical stress; σ H Indicates the actual maximum horizontal ground stress, MPa; σ h Indicates the actual minimum horizontal ground stress, MPa; p p Indicates the actual formation pore pressure, MPa.

[0077] In the above models, single network models A, B, and C have exactly the same model structure, and each single network model consists of 5 fully connected layers. Among them, except for the output of the last layer of single network models A and B, which uses the Sigmoid activation function, the output of the remaining layers uses the ReLU activation function; while the output of the last layer of single network model C does not use any activation function, that is, it is directly mapped to the geostress attribute value, and the output of the remaining layers uses the ReLU activation function.

[0078] The single network model is also called an artificial neural network model (ANN), which is a biologically inspired computational model that simulates the operating principle of the neural network in the human brain. Artificial neurons with hierarchical and connection relationships are composed into a network structure, and the signal transmission between neurons is simulated by mathematical expression, thereby establishing a nonlinear equation with input and output relationships that can be visualized through the network. Generally, a reasonably configured ANN network structure can be used to process nonlinear systems with complex internal expressions.

[0079] Given an input x, it can be mapped to an output Np(x) through an ANN, where ANN can be defined as a functional structure composed of a series of fully connected layers and activation functions. Usually, the first fully connected layer is called the input layer, the last fully connected layer is called the output layer, and the middle fully connected layer is called the hidden layer. The neurons in each layer are connected to each neuron in the next layer. The number of neurons and the number of fully connected layers depends on the specific application scenario;

[0080] Therefore, ANN can be expressed as:

[0081]

[0082] Where: is the output layer; is the input layer; is the hidden layer; x represents the input data;

[0083] The role of the activation function is to add nonlinear factors and solve the problem of insufficient expression of linear models. In ANN, the activation function will act on the neurons of the set network layer, and the value of the neuron is calculated by linearly combining the output of the neurons in the previous layer of the network. The corresponding weight matrix and bias vector are represented by w and b respectively; then the lth layer of the network can be expressed as:

[0084]

[0085] Where: j represents the jth neuron; n i-1 represents the number of neurons in the i-1th network layer; i represents the i-th network layer;

[0086] Step S8, using the data from the training well to train the parallel neural network model based on theoretical constraints, to obtain a trained parallel neural network model based on theoretical constraints;

[0087] In step S8, the number of iterations is set, the Adam optimizer is selected, and the learning efficiency is set, and the data is fed into the neural network model in set batches for training;

[0088] Step S9, testing the prediction accuracy of the trained parallel neural network model based on theoretical constraints according to the test well data;

[0089] Specifically, the trained model is saved, the data of the test well is brought into the model for prediction, and the error between the true value and the predicted value is calculated;

[0090] The formula for measuring error is as follows:

[0091] Mean Square Error:

[0092] Root Mean Square Error:

[0093] Mean absolute error:

[0094] Mean absolute percentage error:

[0095] Where: n is the total number of evaluation samples; y i is the actual sample value of the ith sample; is the predicted value of the i-th sample; MSE is the mean square error; RMSE is the root mean square error; MAE is the mean absolute error; MAPE is the mean absolute percentage error;

[0096] Step S10: predicting the three-dimensional geostress of the entity according to the parallel neural network model based on theoretical constraints.

[0097] The test well in-situ stress curve is as follows: Figure 3 As shown in the figure, the curves are the first to fourth tracks, which are vertical geostress, minimum horizontal geostress, maximum horizontal geostress, and pore pressure, respectively. The solid line is obtained by logging interpretation, and the dotted line is predicted by the above parallel neural network model. The errors of the two are shown in Table 1. In addition, the three-dimensional geostress of the entire target area is predicted, and the prediction results are shown in Figure 4 shown.

[0098] Table 1

[0099]

[0100] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A three-dimensional geostress prediction method based on a parallel neural network with physical constraints, characterized in that: The following steps are involved: Step S1, collecting drilling data of the target area, and expanding the drilling data using Kriging interpolation method; Step S2, using the expanded drilling data as control points to generate NURBS surfaces and entities, and obtaining the three-dimensional space coordinates of the entities; Step S3, collecting logging data of wells drilled in the current area, and performing logging interpretation for each well; Step S4, dividing the drilled wells into training wells and test wells; Step S5, obtaining the three-dimensional spatial coordinates of the borehole trajectory of the training well and the ground stress attribute data along the borehole trajectory path according to the well logging interpretation; Step S6, normalizing the three-dimensional space coordinates from the entity and the wellbore trajectory respectively; Step S7, constructing a parallel neural network model based on theoretical constraints, and determining the input characteristics and output characteristics of the model; Step S8, using the data from the training well to train the parallel neural network model based on theoretical constraints, to obtain a trained parallel neural network model based on theoretical constraints; Step S9: testing the prediction accuracy of the trained parallel neural network model based on theoretical constraints according to the test well data, and predicting the three-dimensional geostress of the entity.

2. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 1 is characterized in that: The drilling data includes X, Y, and Z coordinate values ​​of each geological layer interface.

3. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 1 is characterized in that: The specific steps of using Kriging interpolation method to expand the drilling data are as follows: Step S11, calculating the semivariance value of the known data point by using the empirical semivariance function, and then constructing a scatter plot of distance and semivariance value; Step S12, fitting the scatter plot using a spherical fitting function; Step S13: Determine the weight corresponding to the unknown point by using the semivariance function, and then weight the unknown point to obtain the value corresponding to the unknown point.

4. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 3 is characterized in that: The empirical semivariogram function is as follows: Where: γ(h) represents the semi-variance value when the distance is h; N(h) represents the number of data pairs separated by a distance of h; P(i)-P(i,h) represents the difference between the i-th pair of data pairs separated by a distance of h.

5. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 3 is characterized in that: The calculation formula in step S13 is as follows: Where: P(x, y) represents the predicted value corresponding to the interpolation point; P(i) represents the i-th interpolation point; λ i (x i ,y i ) represents the weight corresponding to the interpolation point; n represents the number of interpolation points.

6. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 1 is characterized in that: The specific process of step S2 is: using the expanded drilling data of each geological layer interface as control points to generate a NURBS surface; and then generating a BURBS entity along the longitudinal direction of the generated NURBS surface.

7. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 1 is characterized in that: The geostress attribute data include formation pore pressure, vertical geostress, and maximum and minimum horizontal geostress.

8. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 7 is characterized in that: In step S5, the in-situ stress attribute data obtained from the interpretation of each well are filtered using the Savitzky-Golay filtering algorithm, and the in-situ stress attributes are thinned out at a ratio of 1:10 while ensuring that the overall trend and shape of the curve remain unchanged.

9. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 1 is characterized in that: The input features of the model in step S7 include X, Y, and Z coordinate values; the output features include formation pore pressure, vertical geostress, and maximum and minimum horizontal geostress.

10. The three-dimensional geostress prediction method based on parallel neural network with physical constraints according to claim 9, characterized in that: The calculation process of the model in step S7 is: 1) The three-dimensional spatial coordinates of the normalized entity and the wellbore trajectory are input into the single network model A, the single network model B, and the single network model C respectively. The outputs of the three single network models A, B, and C are Poisson's ratio, Biot coefficient, and geostress attributes respectively. When the model is output, the Sigmoid activation function is used to limit the Poisson's ratio and Biot coefficient to between 0 and 1. Then, the output values ​​of the above single network models are substituted into Huang's geostress model to constitute the physical constraint term loss; 2) At the same time, the three-dimensional spatial coordinates of the normalized wellbore trajectory are input into the single network model C, and the corresponding output is the in-situ stress attribute, which is compared with the actual in-situ stress attribute data to form the data constraint term loss; 3) Add the physical constraint loss and the data constraint loss together, and assign weights so that the weighted sum is 1, thus forming a loss function containing both physical constraint and data constraint. The mathematical expression of the model loss function is as follows: L TCANN (θ)=λL Phy (θ)+(1-λ)L Data (i) in: Where: λ represents the weight parameter; L Phy (θ) represents the physical constraint loss; L Data (θ) represents the data constraint loss; N P Represents the number of spatial coordinate points of the three-dimensional geological model; N P Represents the number of spatial coordinate points of the drilled wellbore trajectory; represents the predicted vertical in-situ stress; represents the predicted maximum horizontal ground stress, MPa; represents the predicted minimum horizontal ground stress, MPa; Represents the predicted formation pore pressure, MPa; σ v represents the actual vertical ground stress; σ H Indicates the actual maximum horizontal ground stress, MPa; σ h Indicates the actual minimum horizontal ground stress, MPa; p p Indicates the actual formation pore pressure, MPa; 4) The back-propagation algorithm is used to calculate the derivatives of the loss function with respect to the weights and bias terms in the neural network, and then it is iteratively updated according to the gradient descent algorithm so that the loss function value continuously approaches the global minimum and gradually determines the optimal weights and bias terms in the neural network.

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