Method for predicting water saturation of reservoir by combining ordinary differential equation and neural network

Abstract

According to the method for predicting the reservoir water saturation by combining an ordinary differential equation and a neural network, logging data of a well are extracted from a petroleum reservoir geologic model, the logging data obtained after data preprocessing are firstly sent into a convolutional neural network for data feature amplification, then the logging data enter a long-short-term memory network to calculate the hidden layer state and the cell state, and the reservoir water saturation is predicted. Mainly, a fixed-step-length fourth-order Runge-Kutta method is used for numerical solution of a differential equation to obtain a new hidden layer state, so that the training prediction precision is improved, and finally, optimal model parameters are used for predicting the reservoir water saturation. According to the method, the dynamic change rule of effectively capturing the hidden state by introducing the ordinary differential equation is emphatically considered, the prediction precision and stability of the water saturation of the model are improved, and a more accurate basis is provided for the decision-making process of oil and gas field development.

Description

Technical Field

[0001] The invention relates to the technical field of petroleum oil and gas field development, and in particular to a method for predicting reservoir water saturation by combining ordinary differential equations with neural networks. Background Art

[0002] In the process of oil and gas field development, reservoir water saturation (SW) is one of the important parameters reflecting the distribution of reservoir fluids, and plays a key role in oil and gas production prediction, reservoir evaluation and production optimization. Traditional water saturation prediction methods mainly rely on well logging data and geological models, such as Archie's formula and other empirical formulas, but due to the complexity and heterogeneity of the reservoir, traditional methods are difficult to accurately describe the fluid distribution inside the reservoir, especially in the high water content period and complex geological conditions, and its prediction accuracy is limited.

[0003] With the rapid development of artificial intelligence technology, neural networks are widely used in data analysis and prediction tasks in petroleum engineering. Neural networks can automatically extract features and make high-precision predictions through the training of a large amount of historical logging data, overcoming the limitations of traditional empirical methods. For example, the patent application with patent publication number CN117954004A discloses a water saturation prediction method based on an adversarial neural network, the method comprising: S1: obtaining underground medium parameters by the AVO three-parameter inversion method; S2: using Aki-Richards to approximate underground medium parameters; obtaining elastic parameters; S3: constructing a Xu-White model based on elastic parameters to predict P-wave velocity, S-wave velocity and density; inputting water saturation, and using the adversarial neural network to iteratively optimize the objective function to obtain a water saturation SW calculation result that meets the accuracy. The use of this neural network method effectively improves the prediction accuracy of water saturation and improves prediction efficiency, and is suitable for small sample logging data. However, the neural network model essentially lacks the ability to explain the physical laws of the reservoir, which may cause instability or inaccuracy when predicting complex geological processes. Summary of the invention

[0004] In view of the problems and shortcomings of the prior art, the purpose of the present invention is to provide a method for predicting reservoir water saturation by combining ordinary differential equations with neural networks. The method comprises extracting logging data of a well from a petroleum reservoir geological model, performing data preprocessing on the data, amplifying the data in a convolutional neural network, and then placing the data in a long short-term memory unit containing an ordinary differential equation solution to calculate the output of the last time step, thereby training the overall network and preserving the optimal network model parameters to predict water saturation. The present invention calculates the hidden layer state by solving the ordinary differential equation, thereby improving the accuracy and stability of water saturation prediction, and can also provide a more accurate and reliable basis for oil and gas field development decisions, and has important theoretical value and practical application prospects.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] The method of predicting reservoir water saturation by combining ordinary differential equations with neural networks is implemented in the following steps:

[0007] Step 1: Extract the logging data of a well in the oil reservoir geological model and perform data preprocessing on it;

[0008] Step 2: The well logging data preprocessed in step 1 is fed into a three-layer one-dimensional convolutional neural network (CNN), which is amplified to extract the features of the input data and perform nonlinear activation;

[0009] Step 3: Reshape the data features after nonlinear activation in step 2 and send them to a 2-layer long short-term memory cell (LSTMCell) that contains an ordinary differential equation (ODE) solution to calculate the output of the last time step;

[0010] Step 4: Calculate the mean square error loss function for the output of the last time step obtained in step 3 to train the overall neural network and save the optimal network model parameters;

[0011] Step 5: Load the optimal network model parameters saved in step 4 to predict the water saturation of a section in the logging data to obtain the result.

[0012] The specific process of step 1 is:

[0013] Step 1.1: Convert the extracted LAS format well logging data into CSV format;

[0014] Step 1.2: Fill and replace missing values ​​and outliers by using the mean method;

[0015] Step 1.3: Use the CSV format file with 16 data as a time series, the remaining 10 logging parameters excluding water saturation as features, and the batch size set to 32 to construct the training data set.

[0016] The specific process of step 2 is:

[0017] Step 2.1: Adjust the number of input features of the first convolution layer to 10 to fit the 32×16×10 dataset obtained at the end of step 1;

[0018] Step 2.2: Send the dataset into a 3-layer convolutional network and perform ReLu nonlinear activation on it.

[0019] The specific process of step 3 is:

[0020] Step 3.1: Reshape the data feature shape after nonlinear activation in step 2 into a shape adapted to LSTMCell;

[0021] Step 3.2: Traverse the 16 time series, and use the long short-term memory network (LSTM) to calculate the reshaped data in each time series to obtain the hidden layer state h and cell state c of the current time series;

[0022] Step 3.3: Input the hidden layer state h obtained in step 3.2 into the fourth-order Runge-Kutta method with a fixed step size to numerically solve the differential equation. The calculated result is used as the new hidden layer state new_h after smoothing. The calculation formula is as follows:

[0023]

[0024] in:

[0025] k 1 =f(t n ,y n )

[0026]

[0027] k 4 =f(t n +Δt,y n +Δtk 3 )

[0028] In the formula, y n is the function value of the current state; y n+1 represents the function value of the next time step state; Δt is the time step; k 1 , k 2 , k 3 , k 4 Represents the differential value at different time points and states, used to update the state of y;

[0029] Step 3.4: The new hidden layer state new_h obtained in step 3.3 is input into the network for calculation. After all 16 time series are calculated, the output of the last time step is obtained.

[0030] The specific process of step 4 is:

[0031] Step 4.1: Calculate the mean square error loss function for the output of the last time step obtained in step 3. The formula is:

[0032]

[0034] In the formula, n is the number of samples, y is i is the true value of the i-th sample, is the predicted value of the i-th sample;

[0035] Step 4.2: Train the entire network model, stop when the loss rate converges and record and save the current model parameters.

[0036] The specific process of step 5 is:

[0037] Step 5.1: Load the network model parameters saved at the end of step 4 and cancel the loss function calculation;

[0038] Step 5.2: Take out any segment of the logging data and feed it into the network model loaded with the optimal parameters in step 5.1 to obtain the predicted value.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] (1) Since step 2 adopts the CNN method, this method effectively extracts the local features of the whole logging data by introducing a one-dimensional convolution operation, and uses weight sharing and dimensionality reduction technology to reduce the number of parameters and improve training efficiency.

[0041] (2) Since step 3 adopts the LSTMCell method, this method can effectively alleviate the gradient vanishing problem that is prone to occur in traditional recurrent neural networks when processing long sequence data by introducing a gating mechanism, even when there is less logging data, which helps to better understand the formation and improve the drilling and completion strategy.

[0042] (3) Since step 3 introduces the solution method of ordinary differential equations, the fourth-order Runge-Kutta method with a fixed step size is used to numerically solve the differential equations. By accurately calculating the intermediate steps and weighted average, this method can achieve the effect of data smoothing after the secondary solution calculation of the hidden layer values ​​generated by LSTMCell, thereby improving the model's expression ability and stability for well logging data.

[0043] Due to the combined effect of steps 2 and 3, the combination of one-dimensional convolution operation and LSTMCell can not only efficiently extract the local features of logging data, but also maintain the stability of the model and the ability to capture global features when processing data. In addition, by introducing the numerical solution method of ordinary differential equations, the hidden layer values ​​of LSTMCell are further smoothed, which improves the model's expression accuracy of logging data. This multi-step collaborative method significantly improves the model's ability to understand formation characteristics and provides effective support for optimizing drilling and completion strategies.

[0044] In summary, the method of combining the ordinary differential equation (ODE) solution method with the long short-term memory cell (LSTMCell) can dynamically smooth the hidden layer change state of LSTMCell after solving the initial and current hidden layer states through ODE, thereby improving the accuracy and stability of water saturation prediction. This method can not only improve the prediction accuracy, but also provide a more accurate and reliable basis for oil and gas field development decisions, and has important theoretical value and practical application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the overall flow chart of the present invention.

[0046] Figure 2 This is a graph showing the number of training rounds for the model of the present invention and the corresponding coefficient of determination.

[0047] Figure 3 It is a scatter plot of the water saturation values ​​predicted by the present invention and their true values.

[0048] Figure 4 This is a curve comparison diagram of the water saturation value predicted by the present invention and its actual value. DETAILED DESCRIPTION

[0049] The present invention is described in detail below through the accompanying drawings and specific implementation methods.

[0050] See also Figure 1 , a method for predicting reservoir water saturation by combining ordinary differential equations with neural networks, including the following steps:

[0051] Step 1: Extract the logging data of a well from the petroleum reservoir geological model and perform data preprocessing on it; specifically:

[0052] Step 1.1: Load the extracted LAS format logging data through the lasio library in Python and convert it into CSV format for saving;

[0053] Step 1.2: First load the CSV format logging data saved in step 1.1, calculate the mean of water saturation and the mean of other logging parameters, and finally fill and replace missing values ​​and outliers by the mean filling method and mean replacement method respectively;

[0054] Step 1.3: The CSV format logging data processed in step 1.2 is used as a group of 16 data as time series data, and the remaining 10 logging parameters excluding water saturation are used as features. The batch size is set to 32 to construct a training data set.

[0055] Step 2: The well logging data preprocessed in step 1 is fed into a three-layer one-dimensional convolutional neural network (CNN), which is amplified to extract the features of the input data and perform nonlinear activation; specifically:

[0056] Step 2.1: Adjust the number of input features of the first convolution layer to 10 to fit the 32×16×10 data set obtained at the end of step 1. Then, the next convolution layer first enlarges the feature size to 128, and the last convolution layer reduces it to 64.

[0057] Step 2.2: Send the data set obtained at the end of step 1 into the 3-layer convolutional network and perform ReLu nonlinear activation on it to extract the data features after convolution.

[0058] Step 3: Reshape the data features extracted in step 2 and send them to the 2-layer long short-term memory cell (LSTMCell) containing the ordinary differential equation (ODE) solution to calculate the output of the last time step; specifically:

[0059] Step 3.1: Reshape the data feature shape extracted in step 2 into a shape suitable for LSTMCell through the permute function;

[0060] Step 3.2: Traverse the 16 time series in the data set, and use the long short-term memory network (LSTM) to calculate the reshaped data in step 3.1 in each time series to obtain the hidden layer state h and cell state c in the tensor format of the current time series;

[0061] Step 3.3: Input the hidden layer state h obtained in step 3.2 into the fourth-order Runge-Kutta method with a fixed step size to numerically solve the differential equation. The calculated result is used as the new hidden layer state new_h after smoothing. The calculation formula is as follows:

[0062]

[0063] in:

[0064] k 1 =f(t n ,y n )

[0065]

[0066] k 4 =f(t n +Δt,y n +Δtk 3 )

[0067] In the formula, y n is the function value of the current state; y n+1represents the function value of the next time step state; Δt is the time step; k 1 , k 2 , k 3 , k 4 Represents the differential value at different time points and states, used to update the state of y;

[0068] Step 3.4: Combine the new hidden layer state new_h obtained in step 3.3 with the cell state c obtained in step 3.2, and continue to input them into LSTM for calculation. Correspondingly, a new set of hidden layer states and cell states are generated. After traversing and calculating all 16 time series, the output of the last time step is obtained.

[0069] Step 4: Calculate the mean square error loss function for the output of the last time step obtained in step 3 to train the overall neural network and save the optimal network model parameters; specifically:

[0070] Step 4.1: Calculate the mean square error loss function between the output of the last time step obtained in step 3 and the true value. The formula is:

[0071]

[0073] In the formula, n is the number of samples, y is i is the true value of the i-th sample, is the predicted value of the i-th sample;

[0074] Step 4.1: Train the entire network model, stop when the loss rate converges and save the current model parameters, see Figure 2 This is the curve of the overall number of training rounds and the determination coefficient. It can be clearly seen that the determination coefficient reaches the highest and optimal level at 500 rounds.

[0075] Step 5: Load the optimal network model parameters saved in step 4 to predict the water saturation of a section of the well logging data to obtain the result; specifically:

[0076] Step 5.1: Load the optimal network model parameters saved at the end of step 4 and cancel the calculation of the loss function;

[0077] Step 5.2: Take any segment of the well logging data, and send the other 10 characteristic parameters except water saturation into the network model loaded with the optimal parameters in step 5.1 for calculation, and the predicted value is obtained;

[0078] The predicted value obtained in step 5.2 was fitted with the true value, and the determination coefficient was calculated to be 0.9821. Figure 3, the prediction effect is better than the actual value, as can be seen from the scatter plot of the predicted water saturation values. Figure 4 By comparing the curves of the predicted water saturation values ​​with their true values, we can clearly observe the degree of fit between the predicted values ​​and the true values ​​and the prediction effect.

[0079] In summary, the present invention inputs the well logging data that has undergone data preprocessing into a convolutional neural network for feature extraction and amplification, and then inputs the enhanced features into a long short-term memory network that contains ordinary differential equation solutions to calculate the evolution of hidden states, perform training, optimize the overall network model, and finally achieve accurate prediction of water saturation. This method effectively captures the dynamic change law of hidden states by introducing ordinary differential equation solutions, improves the water saturation prediction accuracy and stability of the model, and can also provide a more accurate basis for the decision-making process of oil and gas field development. It has significant theoretical value and broad application prospects, especially in complex underground reservoir environments.

Claims

1. A method for predicting reservoir water saturation by combining ordinary differential equations with neural networks, characterized in that: The following steps are involved: Step 1: Extract the logging data of a well in the oil reservoir geological model and perform data preprocessing on it; Step 2: The well logging data preprocessed in step 1 is fed into a three-layer one-dimensional convolutional neural network (CNN), which is amplified to extract the features of the input data and perform nonlinear activation; Step 3: Reshape the data features after nonlinear activation in step 2 and send them to a 2-layer long short-term memory cell (LSTMCell) that contains an ordinary differential equation (ODE) solution to calculate the output of the last time step; Step 4: Calculate the mean square error loss function for the output of the last time step obtained in step 3 to train the overall neural network and save the optimal network model parameters; Step 5: Load the optimal network model parameters saved in step 4 to predict the water saturation of a section in the logging data to obtain the result.

2. The method for predicting reservoir water saturation by combining ordinary differential equations and neural networks according to claim 1, characterized in that: The specific process of step 1 is: Step 1.1: Convert the extracted LAS format well logging data into CSV format; Step 1.2: Fill and replace missing values ​​and outliers by using the mean method; Step 1.3: Use the CSV format file with 16 data as a time series, the remaining 10 logging parameters excluding water saturation as features, and the batch size set to 32 to construct the training data set.

3. The method for predicting reservoir water saturation by combining ordinary differential equations and neural networks according to claim 2, characterized in that: The specific process of step 2 is: Step 2.1: Adjust the number of input features of the first convolution layer to 10 to fit the 32×16×10 dataset obtained at the end of step 1; Step 2.2: Send the dataset into a 3-layer convolutional network and perform ReLu nonlinear activation on it.

4. The method for predicting reservoir water saturation by combining ordinary differential equations and neural networks according to claim 1, characterized in that: The specific process of step 3 is: Step 3.1: Reshape the data feature shape after nonlinear activation in step 2 into a shape adapted to LSTMCell; Step 3.2: Traverse the 16 time series, and use the long short-term memory network (LSTM) to calculate the reshaped data in each time series to obtain the hidden layer state h and cell state c of the current time series; Step 3.3: Input the hidden layer state h obtained in step 3.2 into the fourth-order Runge-Kutta method with a fixed step size to numerically solve the differential equation. The calculated result is used as the new hidden layer state new_h after smoothing. The calculation formula is as follows: in: k1=f(t n ,y n ) k4=f(t n +Δt,y n +Δtk3) In the formula, y n is the function value of the current state; y n+1 Indicates the function value of the state in the next time step; Δt is the time step; k1, k2, k3, k4 represent the differential values ​​at different time points and states, which are used to update the state of y; Step 3.4: The new hidden layer state new_h obtained in step 3.3 is input into the network for calculation. After all 16 time series are calculated, the output of the last time step is obtained.

5. The method for predicting reservoir water saturation by combining ordinary differential equations and neural networks according to claim 1, characterized in that: The specific process of step 4 is: Step 4.1: Calculate the mean square error loss function for the output of the last time step obtained in step 3. The formula is: In the formula, n is the number of samples, y is i is the true value of the i-th sample, is the predicted value of the i-th sample; Step 4.2: Train the entire network model, stop when the loss rate converges and record and save the current model parameters.

6. The method for predicting reservoir water saturation by combining ordinary differential equations and neural networks according to claim 1, characterized in that: The specific process of step 5 is: Step 5.1: Load the network model parameters saved at the end of step 4 and cancel the loss function calculation; Step 5.2: Take out any segment of the logging data and feed it into the network model loaded with the optimal parameters in step 5.1 to obtain the predicted value.

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