Fracture conductivity calculation method based on BP neural network

Abstract

The invention discloses a fracture conductivity calculation method based on a BP neural network. The fracture conductivity calculation method comprises the following steps: acquiring fracture conductivity influence factors and experiment test data of fracture conductivity; carrying out abnormal value detection on the experimental test data by adopting a box graph method, and removing abnormal data; a Pearson coefficient method is adopted to carry out correlation analysis on the fracture conductivity and the influence factors; preprocessing the data by adopting a minimum-maximum value normalization method; the yield increasing maintenance measures are coded in a one-heat coding mode; a data set is divided, 80% of the data set is randomly used as a training sample, and 20% of the data set is used as a test sample; establishing a BP neural network model; training data are input into the model for model training, the test data set is used for verifying the model after training is completed, and hyper-parameter tuning is carried out. According to the method, the fracture conductivity can be simply, quickly and accurately predicted, and support is provided for guiding production and improving oil and gas field intelligence.

Description

Technical Field

[0001] The present invention belongs to the field of oil and gas field development engineering, and particularly relates to a method for calculating fracture conductivity based on a BP neural network. Background Art

[0002] The amount of offshore low-permeability oil and gas resources in China is huge, which is the main force and important replacement area for increasing oil and gas reserves and production. Restricted by the offshore environment, the current number of construction wells is small and the operation cost is high. There is an urgent need to ensure the fracturing quality of a single well to increase the single-well production and achieve "high production with few wells".

[0003] For offshore low-permeability oil and gas reservoirs, fracturing stimulation is an important development technology. Offshore fracturing is different from onshore fracturing. It is restricted by factors such as the size of offshore platforms, load capacity, operation safety, and transportation conditions, making it difficult for offshore fracturing to support a large number of onshore fracturing equipment and devices, and the overall fracturing scale is relatively small. At the same time, compared with onshore oil and gas fields, the fracturing cost and logistics cost of a single well offshore are much higher than those of onshore fracturing. Therefore, higher requirements are put forward for the fracturing stimulation effect.

[0004] Fracture conductivity is one of the key parameters determining the effect of hydraulic fracturing. At present, many theoretical models have been proposed to predict the conductivity of propped fractures. Most of these models are empirical fittings based on experimental test data. However, fracture conductivity is closely related to factors such as reservoirs, proppants, and closure stress, which leads to great limitations of these empirical models and they are only applicable to specific target reservoirs. In addition, experimentally testing fracture conductivity is a time-consuming and costly process, especially for long-term conductivity testing, which also results in limited experimental data, and the accuracy of the empirical fitting models for conductivity established based on limited experimental data is also questionable. At present, a fast, inexpensive, and accurate method for predicting fracture conductivity is needed. Summary of the Invention

[0005] The present invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a method for calculating fracture conductivity based on a BP neural network.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for calculating fracture conductivity based on a BP neural network includes the following steps:

[0008] S1. Obtain the experimental test data of the factors affecting fracture conductivity and fracture conductivity;

[0009] S2. Use the box plot method to detect outliers in the experimental test data obtained in step S1. After completing the outlier identification, remove the abnormal experimental test data;

[0010] S3. Preprocess the experimental test data processed in step S2 using the min - max normalization method;

[0011] S4. Using the experimental test data preprocessed in step S3, analyze the correlation between fracture conductivity and influencing factors by the Pearson coefficient method;

[0012] S5. Encode the stimulation and maintenance measures in the one - hot encoding manner;

[0013] S6. Select the experimental test data of the influencing factors of fracture conductivity and fracture conductivity with Pearson coefficient greater than 0.5 and the stimulation and maintenance measures data to establish a data set, divide the data set, and randomly use 80% of the data set as training samples and 20% as test samples;

[0014] S7. Establish a BP neural network model;

[0015] S8. Input the training data into the model for training. After completion, use the test data set to verify the model, and set and optimize the hyperparameters.

[0016] In the above technical solution, the influencing factors of fracture conductivity include fracture direction, proppant size, sand concentration, closure stress, proppant - borne load, static Young's modulus, Poisson's ratio, and brittleness index.

[0017] In the above technical solution, the calculation formula of the Pearson coefficient is:

[0018]

[0019] In the formula: σ XY is the Pearson coefficient, dimensionless; N is the number of samples; X i is the i - th value of the experimental test data of fracture conductivity; Y i is the i - th value of the experimental test data of the influencing factors of fracture conductivity; σ XY ranges from - 1 ≤ σ XY ≤ 1, σ XY less than 0 indicates negative correlation, σ XY greater than 0 indicates positive correlation, and equal to 0 means no correlation exists.

[0020] In the above technical solution, the calculation formula of the min - max normalization method is:

[0021]

[0022] In the formula: x is the sample data; x min 、x maxis the minimum and maximum value of the sample data; x′ is the result of min-max normalization.

[0023] In the above technical solution, 5-fold cross-validation is adopted in the process of dividing the data set.

[0024] In the above technical solution, the specific method for establishing the BP neural network model is as follows:

[0025] S71. Provide the training data to the neural network, and transmit it from the input layer, hidden layer to the output layer, which is a forward propagation process; assume that the input layer, hidden layer and output layer have m, q, and n nodes respectively, and the input signal xi in the forward propagation process is as follows:

[0026]

[0027] In the formula: F(x) is the activation function of the hidden layer; h j is the input value of the jth node in the hidden layer; w ij is the connection weight value between the ith node in the input layer and the jth node in the hidden layer; γ j is the threshold value of the jth node in the hidden layer; H j is the output value of the jth node in the hidden layer; Y k is the actual output value of the kth node in the output layer.

[0028] S72. After one forward propagation, if the calculated error exceeds the set value, enter the backpropagation process. Each neuron adjusts the weight and threshold of each layer according to the error information, and the neural network reduces the error to below the limit value through repeated learning.

[0029] In the above technical solution, the setting and tuning of the hyperparameters specifically include the following steps:

[0030] S81. Determine the number of input layer nodes according to the correlation analysis result determined in step S3;

[0031] S82. Set the model network output to the fracture conductivity, and set the number of output layer nodes to 1;

[0032] S83. Use an empirical formula to determine the number of hidden layer nodes;

[0033] S84. Use the Sigmoid function as the activation function, set the maximum number of iterations to 2000 times, and set the learning rate to 0.2.

[0034] In the above technical solution, the empirical formula for the number of hidden layer nodes is:

[0035]

[0036] Where: m and n are the number of nodes in the input layer and the output layer respectively, and a is a constant between [0, 10].

[0037] The beneficial effects of the present invention are:

[0038] The present invention provides a method for calculating the fracture conductivity based on the BP neural network. By determining the input features through the analysis results of the Pearson coefficient, the present invention can effectively avoid information omission or overfitting. Based on the BP neural network algorithm, through training and learning on the experimental data of the fracture conductivity, a modeling prediction with robustness and generalization ability is carried out. Compared with the traditional method, the present invention can predict the fracture conductivity more quickly and accurately, improve the intelligent level of the oilfield, and provide support for guiding on-site production. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the flowchart of the method of the present invention;

[0040] Figure 2 is the structure diagram of the three-layer BP neural network model established in Embodiment 1 of the present invention;

[0041] Figure 3 is the diagram of the Pearson coefficient correlation analysis result in Embodiment 1 of the present invention;

[0042] Figure 4 is the diagram of the fracture conductivity prediction result in Embodiment 1 of the present invention.

[0043] For those of ordinary skill in the art, without creative efforts, other related drawings can be obtained based on the above drawings. DETAILED DESCRIPTION OF THE INVENTION

[0044] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the drawings in the specification and through specific embodiments.

[0045] As Figure 1 shown, a method for calculating the fracture conductivity based on the BP neural network includes the following steps:

[0046] S1. Obtain the experimental test data of the factors affecting the fracture conductivity and the fracture conductivity;

[0047] The factors affecting the fracture conductivity include fracture direction, proppant size, sand concentration, closure stress, proppant load, static Young's modulus, Poisson's ratio, and brittleness index.

[0048] S2. Use the box plot method to detect outliers in the experimental test data obtained in step S1. After completing the outlier identification, remove the abnormal experimental test data to improve the data quality;

[0049] S3. Use the min-max normalization method to preprocess the data;

[0050] The min-max normalization method can map the value range of each parameter to [0, 1], retaining the relationship between the original data. Its calculation method is:

[0051]

[0052] In the formula, x is the sample data; x min 、x max are the minimum and maximum values of the sample data; x' is the result of data normalization.

[0053] S4. Use the experimental test data preprocessed in step S3 and adopt the Pearson coefficient method to analyze the correlation between the fracture conductivity and the influencing factors;

[0054] The Pearson coefficient is a dimensionless statistical index. The Pearson coefficient is represented by the symbol σ XY and its value range is -1 ≤ σ XY ≤ 1. When the Pearson coefficient is less than 0, it indicates a negative correlation; when the Pearson coefficient is greater than 0, it indicates a positive correlation; when the Pearson coefficient is equal to 0, it means there is no correlation;

[0055] The calculation formula of the Pearson coefficient σ XY is:

[0056]

[0057] In the formula: σ XY is the Pearson coefficient, dimensionless; N is the number of samples; X i is the i-th value of the experimental test data of the fracture conductivity; Y i is the i-th value of the experimental test data of the influencing factors of the fracture conductivity; The value range of σ XY is -1 ≤ σ XY ≤ 1. When σ XY is less than 0, it is a negative correlation; when σ XY is greater than 0, it is a positive correlation; when it is equal to 0, it means there is no correlation.

[0058] The Pearson coefficient can express the degree and direction of linear correlation between two variables. This method is not affected by the scale change of variables and can intuitively determine the correlation between data. The main controlling factors of fracture conductivity in different blocks may vary greatly. By analyzing the correlation between fracture conductivity and influencing factors, the influence degree of each influencing factor on fracture conductivity can be analyzed, and the influencing factors with high correlation can be selected to improve the feature quality, the operation speed and accuracy of the model.

[0059] S5. Encode the stimulation and maintenance measures in the one-hot encoding manner;

[0060] In step S5, the one-hot encoding manner can combine unstructured data and structured data, improving the learning ability and prediction effect of the BP neural network model. Specifically, for a fractured well, if its fracture direction is a horizontal fracture, it is marked as 1, and if the fracture direction is a vertical fracture, it is marked as 0.

[0061] S6. Select the influencing factors of fracture conductivity with a Pearson coefficient greater than 0.5, the experimental test data of fracture conductivity, and the stimulation and maintenance measure data to establish a data set. Divide the data set, and randomly use 80% of the data set as training samples and 20% as test samples;

[0062] In step S6, 5-fold cross-validation is adopted in the sample division process to avoid overfitting that may occur in the BP neural network process.

[0063] S7. Establish a BP neural network model;

[0064] The calculation process of the BP neural network model includes the following sub-steps:

[0065] S71. Provide the training data to the neural network and transmit it from the input layer, hidden layer to the output layer, which is a forward propagation process; Suppose the input layer, hidden layer and output layer have m, q, n nodes respectively, and the input signal is x i In the forward propagation process as follows:

[0066]

[0067]

[0068] In the formula, F(x) is the hidden layer activation function; h j is the input value of the j-th node in the hidden layer; w ij is the connection weight between the i-th node in the input layer and the j-th node in the hidden layer; γ j is the threshold of the j-th node in the hidden layer; H j is the output value of the j-th node in the hidden layer; Y kIt is the actual output value of the k-th node in the output layer.

[0069] S72. After one forward propagation, if the calculated error exceeds the set value, enter the backpropagation process. Each neuron continuously adjusts the weights and thresholds of each layer according to the error information. The neural network repeatedly learns to reduce the error below the limit value.

[0070] S8. Input the training data into the model for training. After completion, use the test data set to verify the model, and perform the setting and tuning of hyperparameters to improve the accuracy and generalization ability of the model.

[0071] The setting and tuning of the hyperparameters specifically include the following steps:

[0072] S81. Determine the number of nodes in the input layer according to the correlation analysis result;

[0073] S82. The output of the model network is the fracture conductivity, and the number of nodes in the output layer is taken as 1;

[0074] S83. Use an empirical formula to determine the number of nodes in the hidden layer:

[0075]

[0076] In the formula, m and n are the numbers of nodes in the input and output layers respectively, and a is a constant between [0, 10].

[0077] S84. Use the Sigmoid function as the activation function, the maximum number of iterations is taken as 2000 times, and the learning rate is taken as 0.2.

[0078] 107 groups of experimental data were collected from the previous experiments on shale formations. After data cleaning, 100 groups of valid data were retained for Pearson coefficient analysis. The analysis results are shown in Figure 3 . It can be obtained that the most important parameter affecting the fracture conductivity is the closure stress, which is negatively correlated with the fracture conductivity. And the proppant size, sand concentration, proppant load, static Young's modulus, brittleness index, and Poisson's ratio also have a positive impact on the fracture conductivity. Therefore, these seven influencing factors are selected and retained simultaneously as the input parameters of the model.

[0079] After determining the input parameters, standardize and encode the data, and randomly divide the data set. After completing the above steps, establish a three-layer BP neural network model as shown in Figure 2 . Take the fracture direction, proppant size, sand concentration, closure stress, proppant load, static Young's modulus, Poisson's ratio, and brittleness index as the input layer, and the fracture conductivity as the output layer to train the fracture conductivity prediction model. Finally, the R of the model on the training set and the test set 2They are 0.891 and 0.885 respectively. The average relative error is 0.074 in the training set and 0.089 in the test set. The optimal parameters of the model are finally determined as shown in Table 1.

[0080] Table 1 Optimal Parameters of the Model

[0081] BP neural network model parameters Optimal value Input layer nodes 8 Hidden layer nodes 11 Output layer nodes 1 Learning rate 0.2 Activation function Sigmoid

[0082] Predictive analysis was performed on an additional 10 sets of experimental data, and the average relative error between the predicted values and the actual values is shown in Figure 4 , Figure 4 where 1# to 10# represent the numbers of 10 groups of experiments respectively.

[0083] It can be seen from Figure 4 that the average relative error is 8.53%, and the prediction error is within the range allowed by the project, indicating that this method is practical and can provide theoretical and technical support for the site.

[0084] The applicant declares that the above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention fall within the protection scope and the disclosure scope of the present invention.

Claims

1. A method for calculating fracture conductivity based on BP neural network, characterized in that: The following steps are involved: S1. Obtaining the factors affecting fracture conductivity and experimental test data of fracture conductivity; S2, using the box plot method to perform outlier detection on the experimental test data obtained in step S1, and after completing the outlier identification, remove the abnormal experimental test data; S3, preprocessing the experimental test data processed in step S2 using a minimum-maximum normalization method; S4, using the experimental test data preprocessed in step S3, using the Pearson coefficient method to analyze the correlation between the fracture conductivity and the influencing factors; S5. Encode the production increase maintenance measures using one-hot encoding; S6. Taking the factors affecting fracture conductivity with a Pearson coefficient greater than 0.5, the experimental test data of fracture conductivity, and the data of production increase and maintenance measures to establish a data set, dividing the data set, and randomly using 80% of the data set as training samples and 20% as test samples; S7, establish BP neural network model; S8. Input the training data into the model for model training. After completion, use the test data set to verify the model and set and tune the hyperparameters.

2. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: The factors affecting fracture conductivity include fracture direction, proppant size, sand concentration, closure stress, proppant load, static Young's modulus, Poisson's ratio and brittleness index.

3. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: The calculation formula of the Pearson coefficient is: Where: XY is the Pearson coefficient, dimensionless; N is the sample size; X i is the i-th value of the experimental test data of fracture conductivity; Y i is the i-th value of the experimental test data of the factors affecting fracture conductivity; σ XY The value range is -1≤σ XY ≤1,σ XY Less than 0 means negative correlation, σ XY A value greater than 0 indicates a positive correlation, and a value equal to 0 indicates no correlation.

4. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: The calculation formula of the minimum-maximum normalization method is: Where: x is the sample data; x min 、x max are the minimum and maximum values ​​of the sample data; x′ is the minimum-maximum normalization result.

5. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: A 5-fold cross validation was used in the data set partitioning process.

6. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: The specific method of establishing the BP neural network model is: S71. Provide the training data to the neural network and transfer it from the input layer, hidden layer to the output layer, which is a forward propagation process. Assume that the input layer, hidden layer and output layer have m, q and n nodes respectively, and the input signal x i The forward propagation process is as follows: Where: F(x) is the hidden layer activation function; h j is the input value of the jth node in the hidden layer; w ij is the connection weight between the i-th node in the input layer and the j-th node in the hidden layer; γ j is the threshold of the jth node in the hidden layer; H j is the output value of the jth node in the hidden layer; Y k is the actual output value of the kth node in the output layer. S72. After one forward propagation, if the calculation error exceeds the set value, the back propagation process begins. Each neuron continuously adjusts the weights and thresholds of each layer based on the error information. The neural network reduces the error to below the limit through repeated learning.

7. The method for calculating fracture conductivity based on BP neural network according to claim 1, characterized in that: The setting and tuning of the hyperparameters specifically include the following steps: S81, determining the number of input layer nodes based on the correlation analysis result determined in step S3; S82, the model network output is set to fracture conductivity, and the number of output layer nodes is set to 1; S83, using an empirical formula to determine the number of hidden layer nodes; S84, the Sigmoid function is used as the activation function, the maximum number of iterations is set to 2000, and the learning rate is set to 0.

2.

8. The method for calculating fracture conductivity based on BP neural network according to claim 7, characterized in that: The empirical formula for the number of hidden layer nodes is: Where: m and n are the number of input layer nodes and output layer nodes respectively, and a is a constant between [0,10].

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