Shale gas well yield linear and nonlinear mixed automatic classification and prediction method

Abstract

The invention relates to the field of shale gas well yield analysis, and particularly discloses a shale gas well yield linear and nonlinear hybrid automatic classification and prediction method, which comprises the following steps of: selecting geological and engineering factors as characteristic variables, establishing a linear and nonlinear hybrid model, and determining an influence relationship of each variable by minimizing a fitting error; unsupervised automatic classification is carried out on the samples until the number of residual samples is insufficient; and calculating the minimum value of the distance from the prediction sample to each classification, and predicting the yield according to the classification rule. According to the method, unsupervised automatic classification is realized, the prediction problem of unknown classification is solved, the yield prediction precision is improved, the geological complexity is fit, and the method can be expanded and applied.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shale gas well production analysis, in particular to a shale gas well production linear and nonlinear mixed automatic classification and prediction method. BACKGROUND

[0002] In order to achieve a certain production scale, shale gas wells need to be fractured on a large scale. The factors affecting the production of shale gas wells mainly include geological factors and engineering factors. The geological factors mainly include reservoir permeability, porosity, effective thickness, fracture density, and reservoir TOC content. The engineering factors mainly include horizontal section length, fracturing section number, fracture half-length, and flowback rate. Some factors have a linear effect on production, and some factors have a nonlinear effect on production. However, there are many types of nonlinearities. Because the types of reservoirs are different, the characteristic variables affecting the production are also different. Therefore, how to use the current shale gas well production to predict the production of new wells is an urgent technical problem in the field.

[0003] At present, in order to predict the production of new wells based on shale gas well production, a linear and nonlinear mixed model between production and characteristic parameters is established. Generally, a linear model assumes that the relationship between variables is linear, while a nonlinear model allows more complex relationships. A mixed model may refer to a method that combines both characteristics, or a model that can automatically handle linear and nonlinear relationships.

[0004] At present, linear regression is purely linear, while decision trees, LightGBM or XGBoost are nonlinear, and support vector machines (SVM) use kernel tricks to handle nonlinearity, but linear SVM is linear. These models can handle linear or nonlinear models individually, but models that combine both characteristics are relatively rare. Through big data research and analysis, there are currently several combined models: traditional statistical models, ensemble learning, neural networks, Bayesian methods, AutoML, etc. These methods are currently popular classification and prediction methods, and most of them are supervised learning classification. On this basis, prediction is carried out. However, in actual production, it is unknown which samples are classified according to what rules or unsupervised classification, thus posing a challenge to prediction.

[0005] Therefore, there is an urgent need for a shale gas well production linear and nonlinear mixed automatic classification and prediction method to improve the prediction accuracy of the production scale of shale gas well fracturing. SUMMARY

[0006] The present application provides a shale gas well production linear and nonlinear mixed automatic classification and prediction method to effectively solve the prediction problem under unsupervised classification and improve prediction accuracy.

[0007] To achieve the above object, the application provides a shale gas well production linear and nonlinear mixed automatic classification and prediction method, comprising the following steps:

[0008] S1, selecting the influencing factors of shale gas well production as characteristic variables, wherein the influencing factors include geological factors and engineering factors;

[0009] S2, establishing a linear and nonlinear mixed model between the characteristic variables and the production, recording the fitting correlation coefficient R of various nonlinear relationships jk and the main parameter influence coefficient α j,k,1 , and determining the linear or nonlinear influence relationship of each characteristic variable on the production through a target function of minimizing the fitting error sum of squares;

[0010] S3, unsupervised automatic classification of samples based on the mixed model, establishing a fitting error function by randomly selecting samples, and screening out classification parameters meeting the error minimum condition through circulation until the number of remaining samples is less than the number of characteristic variables plus 1;

[0011] S4, calculating the minimum distance of the prediction sample to each classified sample, determining the belonging classification, and predicting the production based on the influence law of the classification.

[0012] Preferably, in S2, the expression of the mixed model is:

[0013] Y = β0 + β1f1(x1) + β2f2(x2) + … + β p f p (x p );

[0014] Wherein, Y is the production, x1...x p is the characteristic variable, β0...β p is the coefficient, f j (x j ) is the linear or nonlinear function of the jth characteristic variable, the linear function is f j (x j ) = x j , and the nonlinear function includes exponential, logarithmic and power exponential.

[0015] Preferably, in S2, the target function of minimizing the fitting error sum of squares is:

[0016]

[0017] Wherein, Y i is the actual production, is the fitting value of the jth characteristic variable to the ith sample, the expression is:

[0018]

[0019] where i is the ith sample number; j is the jth feature variable number; α j,k,0 is the 0th parameter of the nonlinear k type of the jth feature variable on the response variable; α j,k,1 is the 1st parameter of the nonlinear k type of the jth feature variable on the response variable; α j,k,p is the pth parameter of the nonlinear k type of the jth feature variable on the response variable.

[0020] Preferably, in S3, the specific steps of the automatic classification are:

[0021] S31, analyzing the influence type and parameter of each feature variable on the yield;

[0022] S32, randomly selecting p+1 samples to establish a fitting error function, determining the classification parameter through a regression optimization method, and separating out the first type of samples;

[0023] S33, repeating S31-S32 for the remaining samples until the number of the remaining samples is not more than p+1, and each of the remaining samples is of one type.

[0024] Preferably, in S32, the fitting error function is:

[0025]

[0026] where k1 is the number of exponential nonlinear relationships, and k3 is the number of power exponential nonlinear relationships.

[0027] Preferably, in S3, the number of classified samples Nc is not less than p+1 each time to ensure the uniqueness of the solution of the fitting error function; when the fitting error function is repeatedly established, the parameter with the minimum fitting error is selected as the classification parameter.

[0028] Preferably, in S4, the minimum distance is calculated by the following formula:

[0029]

[0030] wherein, is the number of samples of each classification.

[0031] Preferably, in S4, when the distance between the prediction sample and a single classification is the minimum, the expression of the classification is used for prediction, and the expression is:

[0032] Y e = f j (x j ,α j,nj[j],0 ,α j,nj[j],1 ,…,αj,nj[j],p );

[0033] wherein, nj[j] is the nonlinear type of the jth characteristic variable; α j,nj[j],0 is the 0th parameter in the nonlinear type of the jth characteristic variable; α j,nj[j],1 is the 1st parameter in the nonlinear type of the jth characteristic variable; α j,nj[j],p is the pth parameter in the nonlinear type of the jth characteristic variable; Y e is the predicted value of the predicted sample.

[0034] Preferably, in S4, the predicted sample is closest to a single sample, and the yield of the sample is directly taken as the predicted value

[0035] Preferably, the exponential function is the logarithmic function is f j (α j,2,1 , x j ) = ln x j and the power exponential function is

[0036] Therefore, the present application proposes a shale gas well yield linear and nonlinear mixed automatic classification and prediction method, which has the following beneficial effects:

[0037] (1) Unsupervised automatic classification is adopted, and the basic law of different shale gas well influencing factors can be determined without knowing the sample classification law, so that the prediction difficulty caused by unclear classification in actual production is solved.

[0038] (2) The linear and nonlinear mixed model is combined, the influence relationship of each characteristic variable on the yield is accurately fitted, and the prediction accuracy of the shale gas well fracturing yield scale is improved.

[0039] (3) The influence law of the characteristic variable on the yield in each classification is independently determined, which is more suitable for the complexity of geological factors, and can be extended and applied to multiple fields.

[0040] The technical solutions of the present application will be further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is a linear or nonlinear determination schematic diagram of a shale gas well yield linear and nonlinear mixed automatic classification and prediction method of the present application;

[0042] Figure 2 is a first classification fitting curve diagram of a shale gas well yield linear and nonlinear mixed automatic classification and prediction method of the present application;

[0043] Figure 3It is a second classification fitting curve graph of a shale gas well production linear and nonlinear mixed automatic classification and prediction method of the present application;

[0044] Figure 4 It is a third classification fitting curve graph of a shale gas well production linear and nonlinear mixed automatic classification and prediction method of the present application;

[0045] Figure 5 It is a fourth classification fitting curve graph of a shale gas well production linear and nonlinear mixed automatic classification and prediction method of the present application;

[0046] Figure 6 It is a fifth classification fitting curve graph of a shale gas well production linear and nonlinear mixed automatic classification and prediction method of the present application. DETAILED DESCRIPTION

[0047] In order to make the technical scheme, advantages and purposes of the present application clearer, the technical scheme of the embodiments of the present application will be described clearly and completely below. The described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without any creative effort fall within the protection scope of the present application.

[0048] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meanings understood by those of ordinary skill in the art to which the present application belongs.

[0049] The present application provides a shale gas well production linear and nonlinear mixed automatic classification and prediction method, comprising:

[0050] S1, selecting factors affecting shale gas well production as characteristic variables, the factors affecting shale gas well production including geological factors and engineering factors;

[0051] S2, establishing a linear and nonlinear mixed model Y = β0 + β1f1(x1) + β2f2(x2) + … + β p f p (x p ) between the characteristic variables and the production; wherein Y is the production, x1...x p is the characteristic variable, β0...β p is the coefficient, f j (x j ) is a linear or nonlinear function of the jth characteristic variable;

[0052] Recording various nonlinear relationship fitting correlation coefficients R jk and main parameter influence coefficients α j,k,1The linear or nonlinear influence of each feature variable on output is determined by minimizing the sum of squared fitting errors as the objective function.

[0053] The linear function is f j (x j )=x j Nonlinear functions include exponential, logarithmic, and power functions. The exponential function is... The logarithmic function is f j (α j,2,1 ,x j )=lnx j The power function is

[0054]

[0055] Among them, Y i For actual output, Let be the fitted value of the j-th feature variable for the i-th sample. The expression is:

[0056]

[0057] In the formula, i is the number of the i-th sample; j is the number of the j-th feature variables; α j,k,0 Let α be the 0th parameter of the k-th type of nonlinearity of the effect of the j-th feature variable on the response variable; j,k,1 Let α be the first parameter of the k-th type of nonlinearity of the effect of the j-th feature variable on the response variable; j,k,p Let p be the p-th parameter of the nonlinear k-type influence of the j-th feature variable on the response variable; k=0 indicates a linear relationship, k=1 indicates an exponential relationship, k=2 indicates a logarithmic relationship, and k=3 indicates a power relationship.

[0058] S3. Based on the hybrid model, perform unsupervised automatic classification of samples. By randomly selecting samples, establish a fitting error function, and iteratively filter out classification parameters that meet the minimum error condition until the number of remaining samples is less than the number of feature variables plus 1.

[0059] The specific steps for automatic classification are as follows:

[0060] S31. Analyze the type and parameters of the impact of each characteristic variable on output;

[0061] S32. Randomly select p+1 samples to establish a fitting error function, determine the classification parameters through regression optimization, and separate the first class of samples; wherein, the fitting error function is:

[0062]

[0063] Wherein, k1 is the exponential nonlinear relationship quantity, k3 is the power index nonlinear relationship quantity;

[0064] S33, repeat S31-S32 for the remaining samples until the number of remaining samples is not greater than p+1, and each of the remaining samples is a class.

[0065] In S3, the number of classified samples Nc is not less than p+1 to ensure the uniqueness of the solution of the fitting error function; when the fitting error function is established, the parameters with the minimum fitting error are selected as the classification parameters.

[0066] S4, calculate the minimum distance of the prediction sample to each classification sample, determine the belonging classification, and perform yield prediction based on the influence law of the classification.

[0067] The minimum distance is calculated by the following formula:

[0068]

[0069] In the formula, Nc1…Nc n is the number of samples of each classification.

[0070] When the prediction sample is closest to a single classification, the expression of the classification is used for prediction, and the expression is:

[0071] Y e =f j (x j ,α j,nj[j],0 ,α j,nj[j],1 ,…,α j,nj[j],p );

[0072] In the formula, nj[j] is the nonlinear type of the jth characteristic variable; α j,nj[j],0 is the 0th parameter of the nonlinear type of the jth characteristic variable; α j,nj[j],1 is the 1st parameter of the nonlinear type of the jth characteristic variable; α j,nj[j],p is the pth parameter of the nonlinear type of the jth characteristic variable; Y e is the predicted value of the prediction sample.

[0073] In S4, the prediction sample is closest to a single sample, and the yield of the sample is directly taken as the predicted value

[0074] Example one

[0075] Since there are many geological factors and engineering factors that affect the yield of shale gas wells, the following geological factors and engineering factors are mainly selected for analysis according to the ease of data acquisition and data source, as shown in Table 1. Eight geological factors and five engineering factors are selected as characteristic factors for classification, and a total of 77 classification samples are selected.

[0076] Table 1 shale gas well production impact factor statistics table

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] The specific classification steps are as follows:

[0084] First step: first judge the nonlinear type of the characteristic factor on the production impact, use the regression analysis method in Figure 1 , the influence type of each characteristic variable on the production is shown in Table 2, of which 3 are linear, 2 are nonlinear exponential, 3 are logarithmic, and 4 are power index, that is, p = 12, record the nonlinear type and the main influence coefficient.

[0085] Table 2 influence type of characteristic variable on production

[0086]

[0087] Second step: randomly select 12+2 samples from 77 input samples, establish the fitting error function of 12+2 samples, record the fitting error each time, assume the cycle number is 1000 times, select the minimum fitting error as the standard, use multidimensional optimization to get the corresponding classification parameters, the parameters are shown in Table 3, and the classification expression is:

[0088]

[0089] Use the expression to predict the production of samples that meet the first classification, and the fitting curve is shown in Figure 2 .

[0090] Table 3 first classification parameter table

[0091]

[0092] Third step: repeat the first step and the second step from the remaining 77-14 sample data, and the influence type of the second classification characteristic variable on the production is shown in Table 4.

[0093] Use multidimensional optimization to get the corresponding classification parameters, the parameters are shown in Table 5, and the second classification prediction expression is:

[0094]

[0095] The fitting curve is shown in Figure 3 .

[0096] Table 4 Influence type of second classification characteristic variable on yield

[0097]

[0098] Table 5 Second classification parameter table

[0099]

[0100] The influence law of the second classification characteristic variable on yield is completely different from the first classification, which fully embodies that different geological characteristics have different influences on yield.

[0101] By analogy, until the remaining sample number is less than 13, the influence type of the third classification characteristic variable on yield is shown in Table 6.

[0102] Table 6 Influence type of third classification characteristic variable on yield

[0103]

[0104] The third classification table parameters are shown in Table 7. The third classification prediction expression is:

[0105]

[0106] The fitting curve is shown in Figure 4 . The influence law of the third classification characteristic variable on yield is completely different from the first classification and the second classification.

[0107] Table 7 Third classification parameter table

[0108]

[0109] The influence type of the fourth classification characteristic variable on yield is shown in Table 8, and the fourth classification table parameters are shown in Table 9. The fourth classification prediction expression is:

[0110]

[0111] The fitting curve is shown in Figure 5 . The influence law of the fourth classification characteristic variable on yield is also completely different from the first three classifications.

[0112] Table 8 Influence type of fourth classification characteristic variable on yield

[0113]

[0114] Table 9 Fourth classification parameter table

[0115]

[0116] The fifth classification characteristic variable impact on yield type is shown in Table 10, and the fourth classification table parameter is shown in Table 11. The fifth classification prediction expression is:

[0117]

[0118] The fitting curve is shown in Figure 6 The fifth classification characteristic variable impact on yield is completely different from the first four classifications.

[0119] Table 10 Fifth classification characteristic variable impact on yield type

[0120]

[0121] Table 11 Fifth classification parameter table

[0122]

[0123] Finally, there are 7 single samples left, which do not meet the sample number ≥ p+1, so each of the 7 samples is a class, as shown in Table 12. Thus, the 77 samples can be automatically divided into 12 classes.

[0124] Table 12 Sixth-twelfth classification sample table

[0125]

[0126]

[0127] Next, the average value of all samples is taken as the prediction sample to compare the prediction results. The average value of the sample is shown in Table 13. The minimum distance of the prediction sample to each classification sample is calculated to determine the classification of the prediction sample. The calculation result is that the prediction sample is closest to the first sample of the third classification, i.e. Nck=3, so the third classification sample is used for prediction, and the predicted yield is 1958000 cubic meters / day, which is very close to the statistical average value of 2089000 cubic meters / day, indicating that the classification and prediction method is reliable.

[0128] Table 13 Average value of all samples

[0129]

[0130]

[0131] Therefore, the present application provides a shale gas well production linear and nonlinear mixed automatic classification and prediction method, realizes unsupervised automatic classification, determines the influence factor law of different wells without knowing the sample classification law, solves the prediction problem of unknown classification in actual production, accurately fits the influence of characteristic variables on production through a linear and nonlinear mixed model, improves the prediction accuracy, and each classification has an independent influence law, fits the geological complexity, and can be extended and applied.

[0132] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for automatic classification and prediction of shale gas well production using a hybrid linear and nonlinear approach, characterized in that, include: S1. Select the influencing factors of shale gas well production as characteristic variables, including geological factors and engineering factors; S2. Establish a hybrid linear and nonlinear model between characteristic variables and output, and record the fitting correlation coefficients R for various nonlinear relationships. jk and the influence coefficient α of the main parameters j,k,1 The linear or nonlinear influence of each feature variable on output is determined by minimizing the sum of squared fitting errors as the objective function. S3. Based on the hybrid model, perform unsupervised automatic classification of samples. By randomly selecting samples, establish a fitting error function, and iteratively filter out classification parameters that meet the minimum error condition until the number of remaining samples is less than the number of feature variables plus 1. S4. Calculate the minimum distance from the predicted sample to each category sample, determine the category, and then predict the yield based on the influence pattern of that category.

2. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach as described in claim 1, characterized in that, In S2, the expression for the hybrid model is: Y=β0+β1f1(x1)+β2f2(x2)+…+β p f p (x p ); Where Y represents output, x1......x p Let β0, ..., β be the characteristic variables. p f is a coefficient j (x j Let f be a linear or nonlinear function of the j-th characteristic variable, where the linear function is f. j (x j )=x j Nonlinear functions include exponential, logarithmic, and power functions.

3. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S2, the objective function for minimizing the sum of squared fitting errors is: Among them, Y i For actual output, Let be the fitted value of the j-th feature variable for the i-th sample. The expression is: In the formula, i is the number of the i-th sample; j is the number of the j-th feature variables; α j,k,0 Let α be the 0th parameter of the k-th type of nonlinearity of the effect of the j-th feature variable on the response variable; j,k,1 Let α be the first parameter of the k-th type of nonlinearity of the effect of the j-th feature variable on the response variable; j,k,p Let p be the p-th parameter of the nonlinear k-type influence of the j-th feature variable on the response variable.

4. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S3, the specific steps of the automatic classification are as follows: S31. Analyze the type and parameters of the impact of each characteristic variable on output; S32. Randomly select p+1 samples to establish a fitting error function, determine the classification parameters through regression optimization, and separate the first class of samples. S33. Repeat S31-S32 for the remaining samples until the number of remaining samples is no greater than p+1, and each of the remaining samples belongs to one class.

5. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 4, characterized in that, In S32, the fitting error function is: Where k1 represents the number of exponential nonlinear relationships, and k3 represents the number of power-law nonlinear relationships.

6. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S3, each classification must satisfy the condition that the number of classification samples Nc is not less than p+1 to ensure the uniqueness of the solution of the fitting error function; when iteratively establishing the fitting error function, the parameter with the smallest fitting error is selected as the classification parameter.

7. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S4, the minimum distance is calculated using the following formula: In the formula, Nc1…Nc n The number of samples for each category.

8. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S4, when the distance between the predicted sample and a single class is minimized, the expression for that class is used for prediction. The expression is: Y e =f j (x j ,a j,nj[j],0 ,a j,nj[j],1 ,…,a j,nj[j],p ); In the formula, nj[j] represents the nonlinear type of the j-th characteristic variable; α j,nj[j],0 α is the 0th parameter in the nonlinear type of the j-th feature variable; j,nj[j],1 α is the first parameter in the nonlinear type of the j-th characteristic variable; j,nj[j],p Y is the p-th parameter in the nonlinear type of the j-th characteristic variable; e This is the predicted value for the predicted sample.

9. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 1, characterized in that, In S4, if the predicted sample is closest to a single sample, then the output of that sample is directly used as the predicted value.

10. The automatic classification and prediction method for shale gas well production using a hybrid linear and nonlinear approach according to claim 2, characterized in that, The exponential function is: The logarithmic function is f j (α j,2,1 ,x j )=lnx j The power function is

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