A shale brittleness index prediction method based on principal component analysis and neural network

Abstract

The application discloses a shale brittleness index prediction method based on principal component analysis and neural network, which comprises determining training wells and test wells; performing correlation analysis on each logging variable in the training wells and the brittleness index respectively and comparison, and then combining previous research to select a logging variable which has a connection with the brittleness index and a high absolute value of a correlation coefficient as an independent variable and the shale brittleness index as a dependent variable. The method of combining principal component analysis (PCA) and cuckoo search (CS)-BP neural network is used to predict the shale brittleness index for the first time, and the shale brittleness indexes of two wells Y1 and Y2 in a work area are predicted through a PCA-CSBP shale brittleness index prediction model. The results show that the PCA-CSBP shale brittleness index prediction model can accurately predict the shale brittleness index.

Description

TECHNICAL FIELD

[0001] The present application relates to a shale brittleness index prediction method, in particular to a shale brittleness index prediction method based on principal component analysis and neural network. BACKGROUND

[0002] Unconventional gas such as tight oil and gas, shale oil and gas is a new growth point of today's oil and gas exploration, an important replacement energy, and has become a hot spot of today's oil and gas exploration. The shale gas storage layer usually has the characteristics of relatively low porosity, permeability and other rock physical properties (Hou Bing et al., 2014). Therefore, hydraulic fracturing and transformation of underground reservoirs are often implemented in a timely manner according to needs during the production process (Li Che et al., 2014). Shale brittleness index is an extremely important parameter and one of the research characteristics of rock mechanics. According to the experience of shale fracturing operation in the United States, the gas well with high production after fracturing must be the formation with high fracturing index, not the formation with high fracture pressure (Hou Bing et al., 2014), so the fracturing performance of shale gas reservoir can be characterized by brittleness, that is, shale brittleness index is used to evaluate the fracturing performance of shale gas reservoir (Zou Nengliang et al., 2014). The important research significance of shale reservoir brittleness evaluation lies in that through the design of more reasonable and scientific fracturing operation scheme, the efficiency of fracturing operation and the development cost of equipment can be improved (Li Che et al., 2014). There are various methods for indoor evaluation of shale brittleness at present, which can be divided into three categories in general: (1) brittleness index evaluation method based on mineral properties (Jarvie et al., 2007); (2) brittleness index evaluation method based on elastic properties (Rickman et al., 2008); (3) brittleness index evaluation method based on rock strength (Altindag et al., 2003). There are some problems in the indoor evaluation of these methods: (1) dependence on core samples, which will cause difficulties in experimental testing when the samples are not complete or incomplete; (2) inability to obtain continuous data; (3) high cost and time-consuming of laboratory measurement.

[0003] To solve these problems, some scholars propose to calculate rock brittleness based on logging data. Wood (2021) proposes to apply an optimized data matching algorithm to predict the brittleness index of the Lower Barnett Shale based on logging data; Lai et al. (2015) established a brittleness index prediction model based on the ratio of gamma ray to photoelectric absorption cross-section index (GR / Pe); Jin et al. (2014) pointed out that porosity is negatively correlated with brittleness, and compressional slowness is related to rock porosity, and then established the relationship between brittleness and compressional slowness. The above methods use logging data sets as input and brittleness index as output to obtain the brittleness index of the entire well section. Considering that the main components of rock minerals, various mechanical properties of rock layers under primary rock conditions, etc. also affect the brittleness of shale rock mass, therefore, it is necessary to use various rock logging parameters to establish a prediction model of shale surrounding rock brittleness index. SUMMARY

[0004] The present application aims to provide a shale brittleness index prediction method based on principal component analysis and neural network, which can solve the above problems and realize continuous, rapid and high-precision prediction of shale brittleness index based on neural network.

[0005] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a shale brittleness index prediction method based on principal component analysis and neural network, comprising the following steps:

[0006] 1. A shale brittleness index prediction method based on principal component analysis and neural network, characterized by comprising the following steps:

[0007] (1) The original logging data of a plurality of wells are known, and the original logging data includes logging parameters and shale brittleness index BI at n different depths in the well; the logging parameters include acoustic time difference AC, neutron porosity CNL, compensated density DEN, shear wave time difference DTS, natural gamma ray GR and resistivity RT; one well is selected as a training well, and the rest are test wells;

[0008] (2) Correlation analysis is performed on each logging parameter in the training well and the shale brittleness index, and the absolute values of the correlation coefficients are sorted in descending order, and then the logging parameters used by predecessors to calculate the shale brittleness index are combined, and finally four logging parameters with correlation coefficient absolute value greater than 0.4 are selected as the input parameters of principal component analysis PCA combined with cuckoo CS-BP neural network, which are marked as independent variable A, independent variable B, independent variable C and independent variable D respectively, and the brittleness index is used as the output parameter;

[0009] (3) Constructing training samples and training database;

[0010] The four independent variables at the same depth of the training well form a training sample x i ={x Ai ,x Bi ,x Ci ,x Di},i represents the ith depth, i = 1 ~ n, x Ai , x Bi , x Ci , x Di respectively represent the values of the independent variable A, the independent variable B, the independent variable C and the independent variable D at the ith depth, and the shale brittleness index corresponding to the depth is y i , y i is used as the label of the training sample, and all training samples form a training database;

[0011] (4) using principal component analysis PCA combined with cuckoo CS-BP neural network training database to construct a PCA-CSBP shale brittleness index prediction model; comprising steps (41)-(46);

[0012] (41) all training samples are composed into a matrix X={X A , X B , X C , X D}, wherein X A , X B , X C , X D are column vectors composed of all x Ai , x Bi , x Ci , x Di , and column vector Y is composed of all shale brittleness indexes according to depth; the matrix X is input into the principal component analysis PCA algorithm, and the principal components with a combined contribution greater than 90% are used as new input parameters;

[0013] (42) two components with a contribution greater than 90% in the combined principal components are composed into training samples x′ i ={x′ 1i , x′ 2i}, i represents the ith depth, i=1~n, x′ 1i , x′ 2i respectively represent the values of the first principal component and the second principal component at the ith depth, and the matrix X′={X′1, X′2} is composed of all principal components, wherein X′1, X′2 are column vectors composed of all x′ 1i , x′ 2i , column vector Y is composed of all shale brittleness indexes according to depth; 80% of the data in the column vector Y is divided into training data of the PCA-CSBP shale brittleness index prediction model, and the PCA-CSBP shale brittleness index prediction model is established; 20% of the data in the column vector Y is divided into test data for self-training prediction;

[0014] (43) the elements in the matrix X′ are normalized respectively to obtain a normalized matrix X″;

[0015] (44) calculating the predicted value of the matrix Y, including (a1)-(a2);

[0016] (a1) the matrix X″ data corresponding to 80% of the data in the column vector Y is input into the principal component analysis PCA combined with cuckoo CS-BP neural network algorithm, and the algorithm is trained to establish the PCA-CSBP shale brittleness index prediction model;

[0017] (a2) The remaining 20% ​​of the data in column vector Y is predicted using the established PCA-CSBP shale brittleness index prediction model, and this 20% of data is recorded as the true value y. zi The column vector formed by them is Y z The obtained predicted value y ti The resulting column vector is denoted as Y. t ;

[0018] (45) Calculate the predicted value Y t Compared with the true value Y z The mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to determine the accuracy of prediction, and it is required that MAE is less than 0.1 and MAPE is less than 15% to achieve high-precision prediction.

[0019] (46) If the established PCA-CSBP shale brittleness index prediction model satisfies (45), then the established prediction model meets the requirements for predicting the shale brittleness index.

[0020] (5) Select a well to be logged, obtain the logging data corresponding to matrix X from its original logging data, input it into the PCA-CSBP shale brittleness index prediction model, and output its predicted value.

[0021] 2. In step (1), the method for selecting training wells is as follows: compare the amount of shale brittleness index data for each well and select the well with the larger amount of shale brittleness index data as the training well.

[0022] 3. In step (2), the formula for calculating the correlation coefficient is:

[0023]

[0024] In the formula: inx q y is the input logging variable; y is the shale brittleness index value; inx q,i The i-th depth value of the input logging variable; The average value of the input logging variables; y i This represents the brittleness index of shale at the i-th depth. This represents the average value of the shale brittleness index.

[0025] 4. In step (43), normalization is performed using the following formula:

[0026]

[0027] x represents an element in the vector, and x′ represents the element after normalization. max and x min These represent the maximum and minimum values ​​in the vector, respectively.

[0028] 5. In step (45), calculate the predicted value Y.t Compared with the true value Y z The mean absolute error (MAE) and mean absolute percentage error (MAPE) are calculated using the following formulas:

[0029]

[0030] In equations (1) and (2), y zi For Y in step (a2) z The brittleness index value of the shale at the i-th depth, y ti For the predicted value Y t The i-th element, where N is the amount of prediction data.

[0031] Compared with the prior art, the advantages of the present invention are as follows:

[0032] For the first time, a predictive model for shale brittleness index was established by using principal component analysis (PCA) combined with the Cuckoo CS-BP neural network algorithm, with multiple logging parameters as inputs, to train the neural network.

[0033] By further dividing the training database into 80% as training data for Principal Component Analysis (PCA) combined with the Cuckoo CS-BP neural network algorithm and 20% as test data for training effect, self-prediction can be performed.

[0034] Finally, calculate the predicted value Y. t Compared with the true value Y z The mean absolute error (MAE) and mean absolute percentage error (MAPE) are calculated, with MAE less than 0.1% and MAPE less than 15%, thus obtaining a PCA-CSBP shale brittleness index prediction model. This invention provides a method for continuous, rapid, and high-precision prediction of shale brittleness index. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 A distribution of the original BI values ​​of the training wells as a function of depth;

[0037] Figure 3a This is a plot of the intersection of acoustic time differences AC and BI.

[0038] Figure 3b This is a cross-plot of neutron porosity (CNL) and BI.

[0039] Figure 3c Cross plot of DTS and BI to compensate for density;

[0040] Figure 3d This is the intersection plot of Poisson's ratio RT and BI;

[0041] Figure 4 A comparison chart of test prediction results and true values for training wells;

[0042] Figure 5 A comparison chart of predicted values and true values of shale brittleness index for well Y1 in the work area;

[0043] Figure 6 A comparison chart of predicted values and true values of shale brittleness index for well Y2 in the work area. DETAILED DESCRIPTION

[0044] The application will be further described below with reference to the accompanying drawings.

[0045] Example 1:

[0046] 1. Referring to Figures 1-4 A shale brittleness index prediction method based on principal component analysis and neural network, comprising the following steps:

[0047] (1) The original logging data of a plurality of wells are known, the original logging data including logging parameters at n different depths in the well and shale brittleness index BI; the logging parameters include acoustic time AC, neutron porosity CNL, compensated density DEN, shear wave time DTS, natural gamma GR and resistivity RT; one well is selected as a training well, and the rest are test wells;

[0048] (2) Correlation analysis is performed on each logging parameter in the training well and the shale brittleness index, and the absolute values of the correlation are sorted by size, then the logging parameters used by the predecessors to calculate the shale brittleness index are combined, and finally four logging parameters with an absolute value of the correlation coefficient greater than 0.4 are selected as input parameters of the principal component analysis PCA combined with the cuckoo CS-BP neural network, which are respectively marked as independent variable A, independent variable B, independent variable C and independent variable D, and the brittleness index is used as an output parameter;

[0049] (3) Training samples and a training database are constructed;

[0050] The four independent variables at the same depth of the training well form a training sample x i ={x Ai , x Bi , x Ci , x Di}, i represents the ith depth, i = 1 ~ n, x Ai , x Bi , x Ci , x Di respectively represent the values of the independent variable A, the independent variable B, the independent variable C and the independent variable D at the ith depth, and the shale brittleness index corresponding to the depth is y i , y iAs the label of the training sample, all the training samples constitute a training database;

[0051] (4) Constructing a PCA-CSBP shale brittleness index prediction model by using principal component analysis PCA combined with a cuckoo CS-BP neural network training database; comprising steps (41)-(46);

[0052] (41) All training samples constitute a matrix X = {X A , X B , X C , X D}, wherein X A , X B , X C , X D are column vectors composed of all x Ai , x Bi , x Ci , x Di , and all shale brittleness indexes are column vectors according to depth Y; input the matrix X into the principal component analysis PCA algorithm, and combine the principal components with a contribution greater than 90% as new input parameters;

[0053] (42) Two components with a contribution greater than 90% in the combined principal components constitute a training sample x′ i = {x′ 1i , x′ 2i}, i represents the ith depth, i = 1 ~ n, x′ 1i , x′ 2i respectively represent the values of the first principal component and the second principal component at the ith depth, all principal components constitute a matrix X′ = {X′1, X′2}, wherein X′1, X′2 are column vectors composed of all x′ 1i , x′ 2i , and all shale brittleness indexes are column vectors according to depth Y; divide 80% of the data in the column vector Y as training data for the PCA-CSBP shale brittleness index prediction model to establish the PCA-CSBP shale brittleness index prediction model; divide 20% of the data in the column vector Y as test data for self-training prediction;

[0054] (43) Normalize the elements in the matrix X′ respectively to obtain a normalized matrix X″;

[0055] (44) Calculate the predicted value of the matrix Y, including (a1)-(a2);

[0056] (a1) Input the matrix X″ data corresponding to 80% of the data in the column vector Y into the principal component analysis PCA combined with the cuckoo CS-BP neural network algorithm, train the algorithm, and thus establish the PCA-CSBP shale brittleness index prediction model;

[0057] (a2) using the established PCA-CSBP shale brittleness index prediction model to predict the remaining 20% data of column vector Y, and recording the 20% data as true value y zi , the column vector formed by y z is Y ti ; t the column vector formed by the obtained prediction value y t is Y z ;

[0058] (45) calculating the mean absolute error (MAE) and the mean absolute percentage error (MAPE) of the prediction value Y t and the true value Y z , and requiring that the MAE is less than 0.1 and the MAPE is less than 15% to meet the high-precision prediction effect;

[0059] (46) if the established PCA-CSBP shale brittleness index prediction model meets (45), the established prediction model meets the requirements of predicting shale brittleness index;

[0060] (5) selecting a well to be tested, obtaining the logging data corresponding to the matrix X in the original logging data, inputting the PCA-CSBP shale brittleness index prediction model, and outputting the prediction value.

[0061] 2. In step (1), the method for selecting the training well is: comparing the shale brittleness index data amount of each well, and selecting the well with large shale brittleness index data amount as the training well.

[0062] 3. In step (2), the calculation formula of the correlation coefficient is:

[0063]

[0064] In the formula, inx q is the input logging variable; y is the shale brittleness index value; inx q,i is the i-th depth value of the input logging variable; is the average value of the input logging variable; y i is the i-th depth value of the shale brittleness index; is the average value of the shale brittleness index.

[0065] 4. In step (43), normalization processing is performed using the following formula:

[0066]

[0067] x represents an element in the vector, x' represents an element after normalization processing, x max and x min represent the maximum value and the minimum value in the vector, respectively.

[0068] 5. In step (45), the predicted value Y t is calculated. z The mean absolute error MAE and the mean absolute percentage error MAPE of the predicted value Y zi and the true value Y z are calculated using the following formulas:

[0069]

[0070] In formulas (1) and (2), y ti is the shale brittleness index value at the i-th depth in step (a2), y t is the i-th element of the predicted value Y , and N is the amount of predicted data.

[0071] Example 2:

[0072] For a better understanding of the present application, we will further describe the embodiment 1. Figures 1-6 In step (1), the selection of the training well is described in

[0073] , Figure 2 In the graph, the horizontal axis is the shale brittleness index value BI, and the vertical axis is the depth. As can be seen from the graph, the well has a large amount of brittle data and suitable data, which can be used as training data for the prediction model. Figure 2 Figure 2 In step (2), after correlation analysis of each logging parameter in the training well with the shale brittleness index and combining the logging parameters used by previous calculations of the shale brittleness index, we found that the acoustic time difference AC, neutron porosity CNL, shear wave time difference DTS, and resistivity RT have strong correlation with the shale brittleness index (the absolute values of the correlation coefficients are 0.44285, 0.54188, 0.53108, and 0.57849, respectively), which meets the requirements for selecting input parameters. Therefore, we selected these four logging parameters as the independent variables of the prediction model. The cross-plot of the four logging parameters and the shale brittleness index BI is shown in

[0074] In the four graphs, the vertical axis is the shale brittleness index BI, and the horizontal axis is the acoustic time difference AC, the neutron porosity CNL, the shear wave time difference DTS, and the resistivity RT, respectively. Figures 3a-3d

[0075] See Figure 4 , 20% of the data in the training well is used as test data, and the predicted value of the test data is compared with the true value. The comparison graph of the predicted value and the true value of the BI is shown in Figure 4 . Figure 4 In the graph, the horizontal axis is the test sample data number, and the vertical axis is the shale brittleness index BI. As can be seen from the graph, the predicted value of the test data is very close to the true value, which shows that the prediction model has good prediction accuracy.​It can be seen that the predicted value of the PCA-CSBP shale brittleness index prediction model is basically consistent with the true value, and the change trend is the same. In addition, the MAE and MAPE of the prediction result of the PCA-CSBP shale brittleness index prediction model are 0.060039 and 11.2464%, respectively, and the prediction error is small. In view of the above results, it can be seen that the self-prediction effect of the in-well shale brittleness index is excellent, and the prediction result of the prediction model meets the requirements of (46).

[0076] In order to verify the effect of the present application, see Figure 5 , Figure 6 : We select two wells to be tested, obtain the same logging parameters as the training wells in the original logging data, input these logging parameters into the PCA-CSBP shale brittleness index prediction model of the present application, and the distribution of the predicted BI value with depth is as shown in Figure 5 , Figure 6 , in which the abscissa is the shale brittleness index BI, and the ordinate is the depth. It can be seen from Figure 5 that the prediction result is basically consistent with the true value, and the predicted value is between 0.3 and 0.7. It can be seen from Figure 6 that the predicted value is basically consistent with the true value, and the predicted value is between 0.2 and 1. Through the prediction of the shale brittleness index of other wells in the work area, the good performance of the established PCA-CSBP shale brittleness index prediction model is confirmed.

[0077] It is worth mentioning that the training well and the well to be tested are located in the same work area.

[0078] The above only describes the preferred embodiments of the present application and does not limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for predicting the brittleness index of shale based on principal component analysis and neural networks, characterized in that: Includes the following steps; (1) The original logging data of several wells are known. The original logging data includes logging parameters at n different depths in the well and shale brittleness index BI. The logging parameters include sonic transit time AC, neutron porosity CNL, compensated density DEN, shear wave transit time DTS, natural gamma ray GR and resistivity RT. One well is selected as the training well and the rest are test wells. (2) Correlation analysis was performed on each logging parameter in the training well with the shale brittleness index, and the absolute values ​​of the correlation were sorted by size. Then, the logging parameters used by previous researchers to calculate the shale brittleness index were combined, and finally, four logging parameters with an absolute correlation coefficient greater than 0.4 were selected as input parameters for principal component analysis (PCA) combined with the Cuckoo CS-BP neural network, and labeled as independent variable A, independent variable B, independent variable C and independent variable D, respectively. The brittleness index was used as the output parameter. (3) Construct training samples and training database; The training sample x is composed of four independent variables at the same depth of the training well. i ={x Ai x Bi x Ci x Di }, where i represents the i-th depth, i = 1 to n, x Ai x Bi x Ci x Di Let y represent the values ​​of independent variables A, B, C, and D at the i-th depth, and let y be the shale brittleness index corresponding to that depth. i , will y i As labels for the training samples, all training samples constitute the training database; (4) Construct a PCA-CSBP shale brittleness index prediction model using principal component analysis (PCA) combined with the Cuckoo CS-BP neural network training database; including steps (41)-(46); (41) Construct a matrix X = {X} from all training samples. A X B X C X D }, where X A X B X C X D For all x Ai x Bi x Ci x Di The column vectors formed are used to construct column vectors Y for all shale brittleness indices according to depth; the matrix X is input into the principal component analysis (PCA) algorithm, and the principal components with a combined contribution greater than 90% are used as new input parameters; (42) The two components that contribute more than 90% in the combined principal components form the training sample x′. i ={x′ 1i , x′ 2i }, where i represents the i-th depth, i = 1 to n, x′ 1i , x′ 2i Let X' and X'' represent the values ​​of principal component 1 and principal component 2 at the i-th depth, respectively. All principal components form a matrix X' = {X'1, X'2}, where X'1 and X'2 are the values ​​of all x'' values. 1i , x′ 2i The column vector is formed by dividing all shale brittleness indices into column vector Y according to depth; 80% of the data in column vector Y is divided into training data for the PCA-CSBP shale brittleness index prediction model, which is used to establish the PCA-CSBP shale brittleness index prediction model; 20% of the data in column vector Y is divided into test data for self-training prediction. (43) Normalize the elements in matrix X′ to obtain the normalized matrix X”; (44) Calculate the predicted values ​​of matrix Y, including (a1)-(a2); (a1) Input the matrix X” corresponding to 80% of the data in column vector Y into the principal component analysis method PCA combined with the Cuckoo CS-BP neural network algorithm to train the algorithm, thereby establishing the PCA-CSBP shale brittleness index prediction model; (a2) The remaining 20% ​​of the data in column vector Y is predicted using the established PCA-CSBP shale brittleness index prediction model, and this 20% of data is recorded as the true value y. zi The column vector formed by them is Y z The obtained predicted value y ti The resulting column vector is denoted as Y. t ; (45) Calculate the predicted value Y t Compared with the true value Y z The mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to determine the accuracy of prediction, and it is required that MAE is less than 0.1 and MAPE is less than 15% to achieve high-precision prediction. (46) If the established PCA-CSBP shale brittleness index prediction model satisfies (45), then the established prediction model meets the requirements for predicting the shale brittleness index. (5) Select a well to be logged, obtain the logging data corresponding to matrix X from its original logging data, input it into the PCA-CSBP shale brittleness index prediction model, and output its predicted value.

2. The method for predicting shale brittleness index based on principal component analysis and neural networks according to claim 1, characterized in that: In step (1), the method for selecting training wells is as follows: compare the amount of shale brittleness index data for each well and select the well with the larger amount of shale brittleness index data as the training well.

3. The method for predicting shale brittleness index based on principal component analysis and neural networks according to claim 1, characterized in that: In step (2), the formula for calculating the correlation coefficient is: In the formula: inx q y is the input logging variable; y is the shale brittleness index value; inx q,i The i-th depth value of the input logging variable; The average value of the input logging variables; y i This represents the brittleness index of shale at the i-th depth. This represents the average value of the shale brittleness index.

4. The method for predicting shale brittleness index based on principal component analysis and neural networks according to claim 1, characterized in that: In step (43), normalization is performed using the following formula: x represents an element in the vector, and x′ represents the element after normalization. max and x min These represent the maximum and minimum values ​​in the vector, respectively.

5. The method for predicting shale brittleness index based on principal component analysis and neural networks according to claim 1, characterized in that: In step (45), the predicted value Y is calculated. t Compared with the true value Y z The mean absolute error (MAE) and mean absolute percentage error (MAPE) are calculated using the following formulas: In equations (1) and (2), y zi For Y in step (a2) z The brittleness index value of the shale at the i-th depth, y ti For the predicted value Y t The i-th element, where N is the amount of prediction data.

Images