Method for predicting mercury injection capillary pressure curve by using machine learning based on nuclear magnetic T2 spectrum

Abstract

The invention discloses a method for predicting a mercury injection capillary pressure curve by using machine learning based on a nuclear magnetic T2 spectrum, and the method comprises the steps: S1, carrying out the preprocessing and data preparation, and screening and sorting a training set and a prediction set; s2, machine learning training: importing a training set, selecting a plurality of machine learning methods for training, comparing advantages and disadvantages of different methods through evaluation indexes, and exporting a model; s3, model prediction and optimization: performing prediction after importing a prediction set, performing data set optimization and domain knowledge post-processing, and finally performing qualitative evaluation and qualitative analysis on a result; the influence of data features and a machine learning method on the prediction effect is explored, and influence factors for predicting the precision of the mercury injection capillary pressure curve are analyzed; according to the method, capillary pressure curves with different peak values of mercury saturation are selected as a prediction set, and the model has universality; according to the method, negative value 0 supplementation and monotonous non-decreasing processing are carried out in combination with domain knowledge, a more reasonable mercury injection capillary pressure curve is obtained, and a prediction result can be applied to reality.

Description

Technical Field

[0001] This invention patent relates to the field of oil and gas exploration and development. Specifically, it is a method for predicting mercury injection capillary pressure curves using machine learning based on nuclear magnetic resonance T2 spectra. Background Art

[0002] In recent years, with the growth of oil and gas resource demand and the improvement of exploration technologies, unconventional reservoirs have become the key points and difficulties in oil and gas development, with great exploration potential and prospects.

[0003] The key to reservoir exploration, development, and evaluation lies in the characterization of the reservoir pore structure. Among them, the mercury injection method, as an accurate method for detecting pore throat distribution, is considered the most widely used indirect measurement method for pore structure. However, the mercury injection method has the disadvantages of high cost, great destructiveness, and inevitable limitations, and some means are needed to construct the mercury injection capillary pressure curve. Nuclear magnetic resonance is non-destructive, and its results contain rich pore structure information, which is widely used in the fine description of pore structure. Since the pore size distribution obtained by nuclear magnetic resonance is correlated with the pore throat distribution obtained by the mercury injection capillary pressure curve, the mercury injection capillary pressure curve can be constructed through the nuclear magnetic resonance T2 spectrum.

[0004] Tight conglomerate also belongs to unconventional reservoirs and has the characteristics of low porosity, low permeability, and strong heterogeneity. However, there are currently few methods and studies on predicting mercury injection capillary pressure curves using nuclear magnetic resonance T2 spectra for tight conglomerate reservoirs. Moreover, the average correlation coefficient R of the prediction accuracy of the piecewise power function used by Song Yong et al. in "Estimation of oil saturation via pseudo capillary pressure curve from nuclear magnetic resonance log data in tight conglomerate reservoirs" is 0.8583, and the accuracy is limited. Summary of the Invention

[0005] The object of the present invention is to improve the accuracy of predicting mercury injection capillary pressure curves using nuclear magnetic resonance T2 spectra in tight conglomerate reservoirs, and to propose a method for predicting mercury injection capillary pressure curves using machine learning based on nuclear magnetic resonance T2 spectra.

[0006] Technical solution of the present invention: A method for predicting mercury injection capillary pressure curve using machine learning based on nuclear magnetic resonance T2 spectrum, comprising: S1: Pretreatment and data preparation: Through data pretreatment, nuclear magnetic resonance samples and mercury injection samples are sorted out, and the training set and prediction set are divided according to a ratio; S2: Machine learning training: Import the training set for machine learning training, use evaluation indicators to test the advantages and disadvantages of different methods, select the optimal method, and export the model; S3: Model prediction and optimization: If the data set is not optimized, import the prediction set to predict mercury saturation; if the data set is optimized, use the interpolation method to change the data characteristics, repeat the processes of S1 and S2, then import the prediction set to predict mercury saturation; combine the prediction results and perform post-processing of domain knowledge; draw a comparison graph of the true-predicted mercury injection capillary pressure curve for qualitative analysis of the prediction effect, and use evaluation indicators to quantitatively evaluate the prediction accuracy.

[0007] Specifically, the nuclear magnetic resonance samples and mercury injection samples used are from a tight conglomerate reservoir.

[0008] Further, the data pretreatment in S1 includes data cleaning, data integration, data transformation, and data set segmentation.

[0009] Specifically, data integration: The nuclear magnetic resonance T2 spectrum corresponding to the core depth of the mercury injection capillary pressure curve is obtained according to the core depth of the mercury injection capillary pressure curve.

[0010] Specifically, data cleaning: Outliers are deleted, that is, different mercury injection capillary pressure curves measured at different times for the same core are excluded, and noise data with significantly high signals in the nuclear magnetic resonance T2 spectrum is excluded.

[0011] Specifically, data transformation: After the nuclear magnetic resonance T2 spectrum is reversely accumulated and normalized, the non-wetting phase saturation is obtained, and then the mercury injection capillary pressure curve is predicted using the non-wetting phase saturation.

[0012] Specifically, the data normalization formula is:

[0013]

[0014] Where x is a specific value in the data set, max(X) and min(X) are the maximum and minimum values in the data set respectively. After normalization, the range of x norm is between 0 and 1.

[0015] Specifically, data set segmentation: According to a ratio greater than 11:1, 58 groups of training sets and 5 groups of prediction sets are divided. Among the 5 groups of prediction sets, the peak values of the mercury saturation of the mercury injection capillary pressure curve are different, and the peak values are: 33.0070%, 42.1230%, 46.3250%, 47.4100%, 54.3550% respectively, to prove the versatility of the model.

[0016] Further, the machine learning training method in S2 includes: the boosting tree model of conventional machine learning, exponential Gaussian process regression (Exponential GPR), squared exponential Gaussian process regression (Squared Exponential GPR), and the artificial neural network ANN of deep learning.

[0017] Specifically, the boosting tree (BT) used in the present invention is the least squares boosting decision tree (LS-BT), which is a machine learning model combining the decision tree (DT) and the least squares (LS) enhancement technique. The basic principle is as follows:

[0018] First, initialize the model f0(x); secondly, calculate the residual during the process where the iteration number m ranges from 1 to n: r m (x) = y - f m-1 (x), where r m (x) is the residual function in the m-th iteration, y is the true value, and f m-1 (x) is the model prediction value after the (m - 1)-th iteration; then, train the weak learner h m (x) to fit the residual; subsequently, calculate the weight v m to minimize the loss function; finally, update the model: f m (x) = f m-1 (x) + v m h m (x).

[0019] Specifically, Gaussian process regression GPR is a non-parametric Bayesian regression method that can provide the probability distribution of the predicted value, thereby quantifying the uncertainty of the prediction; based on different kernel functions, there will be different types of Gaussian process regression GPR. The present invention uses exponential Gaussian process regression (Exponential GPR) and squared exponential Gaussian process regression (Squared Exponential GPR).

[0020] Specifically, the kernel function formula of exponential Gaussian process regression (Exponential GPR) is:

[0021]

[0022] Specifically, the kernel function formula of squared exponential Gaussian process regression (Squared Exponential GPR) is:

[0023]

[0024] where k E is the exponential kernel function; k SE is the squared exponential kernel function; x is the actual value, x′ is the predicted value, l is the length, and σ 2 is the variance.

[0025] Furthermore, the artificial neural network (ANN) of deep learning includes three training algorithms: Levenberg-Marquardt method (L-M), Bayesian regularization method (BR), and Quantized Conjugate Gradient method (QCG).

[0026] Specifically, the artificial neural network (ANN) is a class of computational models inspired by biological neural networks, consisting of a large number of artificial neurons, including an input layer, a hidden layer, and an output layer. The neurons in the hidden layer and the output layer first receive signals, then perform weighted summation and add a bias, and finally output through an activation function. The specific formula is as follows:

[0027]

[0028] α = σ(z)

[0029] In the formula, x i is the i-th input signal; w i is the corresponding weight; b is the bias; z is the result of the linear combination; σ(z) is the activation function, which is the Sigmoid activation function in the hidden layer and the ReLU activation function in the output layer; α is the final output.

[0030] Specifically, the optimization algorithms of the artificial neural network include the Levenberg-Marquardt method (L-M), the Bayesian regularization method (BR), and the Quantized Conjugate Gradient method (QCG), that is, they constitute LM-ANN, BR-ANN, and QCG-ANN.

[0031] Specifically, the Levenberg-Marquardt method (L-M), also known as the damped least squares method, is used to solve the nonlinear least squares problem. The algorithm has a high convergence speed and good numerical stability during iteration. The specific formula is as follows:

[0032]

[0033] In the formula, x k is the parameter estimation vector of the current iteration; J k is the Jacobian matrix (first derivative matrix) of the objective function at x k ; f(x k ) is the residual vector of the objective function at x k ; μ k is a positive scaling parameter; I is the identity matrix.

[0034] Specifically, the Bayesian regularization method (BR) is an optimization algorithm used to solve the problems of model selection and avoiding overfitting, reducing overfitting and improving the generalization ability of the model; its formula is:

[0035]

[0036] Where x are model parameters, D is the training dataset, α and β are hyperparameters related to the regularization term, and M represents the model structure; P(D|x,β,M) is the likelihood function; P(x|α,M) is the prior probability distribution; P(D|α,β,M) is the model evidence, which is a normalization factor that ensures the sum of the probability distribution is 1.

[0037] Specifically, the Quantized Conjugate Gradient method (QCG) is a numerical algorithm for solving large-scale sparse linear systems or least squares problems, with the advantages of fast convergence speed and low memory occupancy; its iterative formula is:

[0038] |x> k+1 =|x> k +α k |p> k+1

[0039] |p> k+1 =|r> k +β k |p> k

[0040]

[0041] Where |x> k is the solution at the k-th iteration; p> k is the conjugate gradient direction at the k-th iteration; |r> k is the residual at the k-th iteration; α k is the step size determined by quantum linear search; β k is a scalar used to update the conjugate gradient direction; A is a quantum operator related to the problem; b> is the target vector.

[0042] Furthermore, the evaluation metrics for training and prediction in S2 and S3 include: correlation coefficient R, root mean square error RMSE, and mean absolute error MAE.

[0043] Specifically, the correlation coefficient R: also known as the Pearson correlation coefficient, which is used to measure the linear correlation degree between two variables; the specific formula is:

[0044]

[0045] Where n is the number of data points; x i and y i are the values of the two variables of the i-th data point respectively; are the means of x and y respectively.

[0046] Specifically, the root mean square error (RMSE): Also known as the squared L2 loss, it measures the average magnitude of the error and focuses on the deviation from the actual value. It is simple to calculate and easy to understand. The specific formula is:

[0047]

[0048] where n is the number of data points; y i is the actual value of the i-th data point; is the predicted value of the i-th data point.

[0049] Specifically, the mean absolute error (MAE): Also known as the L1 loss, it is a commonly used metric to measure the difference between the predicted value and the actual value. It can effectively avoid high errors caused by punishing data outliers; the specific formula is:

[0050]

[0051] where n is the number of data points; y i is the actual value of the i-th data point; is the predicted value of the i-th data point.

[0052] Specifically, the nearest neighbor interpolation method is used to optimize the dataset in S3; Interpolation feature quantities: The interpolation features of the mercury injection samples are 26, 52, and 104 features, and the interpolation features of the nuclear magnetic resonance samples are 30, 100, 300, and 400 features.

[0053] Specifically, the formula for the nearest neighbor interpolation method is:

[0054] f(x) = y i

[0055] where f(x) is the interpolation result at point x, x i is the abscissa of the known data point closest to x, y i is the ordinate corresponding to x i of.

[0056] Furthermore, the domain knowledge post-processing in S3 includes: filling negative values with 0 and monotonic non-decreasing processing.

[0057] Specifically, filling negative values with 0: Let the i-th mercury saturation be y i , if the predicted mercury saturation y i < 0, then let y i = 0, i ∈ [1, 13].

[0058] Specifically, monotonic non-decreasing processing: Among the results that do not conform to monotonic non-decreasing, if y i-1 = 0 and y i+1 = 0, y i > 0, then let y i= 0; If y i-1 > y i then let y i-2 be the first term of the arithmetic sequence and y i+1 be the last term of the arithmetic sequence, and fill y i-1 and y i with the equal common difference; If y 12 > y 13 then do not adopt this mercury injection capillary pressure curve and re-predict.

[0059] The beneficial effects of the present invention are as follows:

[0060] (1) Application of the method of the present invention: Using machine learning, especially LM-ANN, can realize the prediction of mercury injection capillary pressure curve based on nuclear magnetic T2 spectrum, with low cost, non-destructive, fast and high precision.

[0061] (2) Optimization of the prediction set of the method of the present invention: Selecting capillary pressure curves with different peak values of mercury saturation as the prediction set indicates the universality of the model.

[0062] (3) Exploration of the method of the present invention: Explore the influence of data characteristics and machine learning methods on the prediction effect, and analyze the influencing factors of the accuracy of predicting mercury injection capillary pressure curve.

[0063] (4) Optimization of the method of the present invention: Combining domain knowledge to fill 0 for negative values and perform non-decreasing monotonicity processing to obtain a more reasonable mercury injection capillary pressure curve, so that the prediction results can be applied to practice. Description of the Drawings

[0064] Figure 1 is a schematic flow chart provided by an embodiment of the present invention.

[0065] Figure 2 is a nuclear magnetic T2 spectrum and non-wetting phase saturation curve diagram of a training set provided by an embodiment of the present invention.

[0066] Figure 3 is a mercury injection capillary pressure curve diagram of a prediction set provided by an embodiment of the present invention.

[0067] Figure 4 is a coincidence diagram of the non-wetting phase saturation curve and the mercury injection capillary pressure curve of a training set provided by an embodiment of the present invention.

[0068] Figure 5 is a schematic diagram of post-processing of domain knowledge provided by an embodiment of the present invention.

[0069] Figure 6 is a statistical chart of ANN prediction results provided by an embodiment of the present invention.

[0070] Figure 7ANN error comparison chart provided by an embodiment of the present invention.

[0071] Figure 8 Statistical chart of prediction results of conventional machine learning provided by an embodiment of the present invention.

[0072] Figure 9 Conventional machine learning error comparison chart provided by an embodiment of the present invention.

[0073] Figure 10 Statistical chart of prediction results of LM-ANN after interpolation of nuclear magnetic resonance samples provided by an embodiment of the present invention.

[0074] Figure 11 Error comparison chart of characteristic quantities of nuclear magnetic resonance sample interpolation provided by an embodiment of the present invention.

[0075] Figure 12 Statistical chart of prediction results of LM-ANN after interpolation of mercury injection samples provided by an embodiment of the present invention.

[0076] Figure 13 Error comparison chart of characteristic quantities of mercury injection sample interpolation provided by an embodiment of the present invention. Detailed implementation manners

[0077] In order to enable those skilled in the art to more fully understand the technical solutions of this specification, the embodiments of this specification will be described in detail and completely based on the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments in this specification, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on one or more embodiments in this specification without creative efforts shall fall within the scope of protection of the embodiments of this specification.

[0078] An embodiment of a method for predicting mercury injection capillary pressure curve using machine learning based on nuclear magnetic resonance T2 spectrum provided by this specification, as Figure 1 shown, the method includes the following steps:

[0079] (1) S1 Pretreatment and data preparation:

[0080] (2) Further, S1-1 Data integration: Since the acquisition cost of indoor mercury injection capillary pressure curve data is high, the acquisition process is destructive and harmful to the environment, and the inherent limitation of obtaining discontinuous well sections is difficult to avoid, resulting in a small amount of data; while a large amount of continuous nuclear magnetic resonance T2 spectra can be obtained during actual logging of nuclear magnetic resonance logging. Therefore, the corresponding nuclear magnetic resonance T2 spectra are selected according to the core depth of the mercury injection capillary pressure curve.

[0081] (3) Further, S1-2 data cleaning: Since there are dirty data in the data, which have an adverse effect on the model prediction, the present invention adopts a method of removing outliers, that is, eliminating different mercury injection capillary pressure curves measured at different times for the same core, and eliminating noisy data with obviously high nuclear magnetic T2 spectra.

[0082] (4) Specifically, the present invention collects a total of 63 sets of valid data: the nuclear magnetic T2 spectrum is obtained through nuclear magnetic resonance logging, with a total of 200 features, whose X-axis is the transverse relaxation time T2, in ms; the Y-axis is the signal intensity, dimensionless; the mercury injection capillary pressure curve is obtained through indoor mercury injection experiment, with a total of 13 features, whose X-axis is the mercury injection pressure, in MPa, and the Y-axis is the mercury saturation, dimensionless.

[0083] (5) Further, S1-3 data transformation: the non-wetting phase saturation is obtained by reversely accumulating and normalizing the NMR T2 spectrum, and then the non-wetting phase saturation is used to predict the mercury injection capillary pressure curve; the X-axis of the non-wetting phase saturation curve is the reverse transverse relaxation time T2, and the Y-axis is the non-wetting phase saturation.

[0084] (6) Further, the S1-4 data set was segmented: after obtaining 63 groups of NMR samples and mercury injection samples, 58 training sets and 5 prediction sets were segmented at a ratio greater than 11:1. In the 5 prediction sets, the peak values ​​of mercury saturation of the mercury injection capillary pressure curves were different, and the peak values ​​were 33.0070%, 42.1230%, 46.3250%, 47.4100%, and 54.3550%, respectively, to prove the versatility of the model.

[0085] (7) Further, S2 machine learning training: using computer software MATLAB, select conventional machine learning and deep learning artificial neural network ANN training.

[0086] (8) Further, S2-1 conventional machine learning: conventional machine learning is to use multiple nuclear magnetic T2 spectrum features to predict a single mercury saturation, and then draw a mercury injection capillary pressure curve after prediction. The methods selected by the present invention include: boosting tree, exponential Gaussian process regression (exponential GPR), and squared exponential Gaussian process regression (squared exponential GPR).

[0087] (9) Further, S2-2 artificial neural network ANN:

[0088] (10) Specifically, the parameters during training are: training-validation ratio: 9:1, number of neural network layers: 10, training algorithms: Levenberg-Marquardt method (LM), Bayesian regularization method (BR), quantized conjugate gradient method (QCG).

[0089] (11) Further, after both conventional machine learning and artificial neural network ANN are tested by evaluation metrics R and RMSE, the best machine learning method is selected to derive the prediction model.

[0090] (12) Further, S3 model prediction and optimization:

[0091] (13) Further, S3-1 dataset optimization: The nearest neighbor interpolation method is used to change the data features: the interpolation features of the mercury injection samples are 26, 52, and 104 features, and the interpolation features of the nuclear magnetic resonance samples are 30, 100, 300, and 400 features;

[0092] (14) Further, S3-2 model prediction: The prediction set is input, and the trained model is used for prediction.

[0093] (15) Further, S3-3 domain knowledge post-processing:

[0094] (16) Specifically, according to geophysical knowledge, the mercury saturation cannot be negative, and as the mercury injection pressure increases, the mercury saturation gradually increases from 0, showing a non-decreasing monotonic change. Based on this, the present invention performs post-processing on the prediction results:

[0095] (17) Further, negative value filling with 0: Let the mercury saturation of the i-th be y i , if the predicted mercury saturation y i < 0, then let y i = 0, i ∈ [1, 13].

[0096] (18) Further, non-decreasing monotonicity processing: Among the results that do not conform to the non-decreasing monotonicity, if y i-1 = 0 and y i+1 = 0, y i > 0, then let y i = 0; if y i-1 > y i , then let y i-2 be the first term of the arithmetic sequence, y i+1 be the last term of the arithmetic sequence, and fill y i-1 and y i with the equal common difference; if y 12 > y 13 , then this mercury injection capillary pressure curve is not adopted and re-predicted.

[0097] (19) Further, S3-4 result analysis:

[0098] (20) Further, qualitative analysis: Corresponding to the logarithmic coordinates, connect the points into a line, draw a comparison graph of the true - predicted mercury injection capillary pressure curve, and observe the prediction effect.

[0099] (21) Further, for quantitative evaluation: using the correlation coefficient R, root mean square error RMSE, and mean absolute error MAE as evaluation indicators, calculate the error between the actual mercury saturation and the predicted mercury saturation, and analyze the prediction accuracy of different methods and different interpolation features.

[0100] Those skilled in the art should understand that the above one or more embodiments are only used to describe the technical solutions of the present invention, rather than limiting it. One or more embodiments of this specification can have various modifications and changes without departing from the essence of the corresponding technical solutions from the scope of the technical solutions of each embodiment of the present invention.

Claims

1. A method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic resonance T2 spectrum using machine learning, characterized in that: include: S1: Preprocessing and data preparation: Through data preprocessing, NMR samples and mercury injection samples were sorted out, and the training set and prediction set were divided according to the proportion; S2: Machine Learning Training: Import the training set for machine learning training, use evaluation indicators to test the advantages and disadvantages of different methods, select the best method, and export the model; S3: Model prediction and optimization: If the data set is not optimized, the prediction set is imported to predict mercury saturation; If the data set is optimized, the interpolation method is used to change the data characteristics, and the S1 and S2 processes are repeated, and then the prediction set is imported to predict the mercury saturation; Combine the prediction results and perform domain knowledge post-processing; A comparison chart of the actual and predicted mercury injection capillary pressure curves was drawn to qualitatively analyze the prediction effect, and the prediction accuracy was quantitatively evaluated using evaluation indicators.

2. The method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic T2 spectrum using machine learning according to claim 1, characterized in that: The nuclear magnetic resonance samples and mercury injection samples are derived from tight conglomerate reservoirs.

3. The method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic T2 spectrum using machine learning according to claim 1, characterized in that: The data preprocessing includes data cleaning, data integration, data transformation, and data set segmentation, and the ratio of the training set to the prediction set is not less than 11:

1.

4. The method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic T2 spectrum using machine learning according to claim 1, characterized in that: The machine learning training methods include: conventional machine learning boosting tree model, exponential Gaussian process regression, squared exponential Gaussian process regression, and deep learning artificial neural network (ANN) method.

5. The method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic T2 spectrum using machine learning according to claim 1, characterized in that: The evaluation indicators include correlation coefficient R, root mean square error RMSE, and mean absolute error MAE.

6. The method for predicting mercury intrusion capillary pressure curve based on nuclear magnetic T2 spectrum using machine learning according to claim 1, characterized in that: The optimized data set uses the nearest neighbor interpolation method, the interpolation features of the mercury injection sample are 26, 52, and 104 features, and the interpolation features of the nuclear magnetic resonance sample are 30, 100, 300, and 400 features.

7. The method for predicting mercury intrusion capillary pressure curve based on T2 spectrum using machine learning according to claim 1, characterized in that: The domain knowledge post-processing includes: filling negative values ​​with 0 and monotonic non-decreasing processing.

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