Drill bit optimization method based on main factor-three-dimensional golden section

Abstract

The invention discloses a drill bit optimization method based on main factor-three-dimensional golden section. The drill bit optimization method comprises the following steps: finding out main factors representing change characteristics of a data set by utilizing a main factor analysis method; based on the obtained main factor, a golden section is drawn by adopting a three-dimensional golden section method; drawing the main factors, the average drilling speed and the average drilling footage of different drill bits and the golden section in the same coordinate system, and selecting the drill bits above the golden section as a preferable result. The method can effectively guarantee the accuracy and reliability of drill bit model selection, is high in applicability, practicability and universality in practical application, is convenient to popularize and operate, improves the drill bit model selection efficiency, and is wide in application prospect.

Description

Technical Field

[0001] The invention relates to the technical field of oil drilling, in particular to a drill bit optimization method based on a main factor-three-dimensional golden section, which is used for selecting drill bits corresponding to different strata during the drilling process. Background Art

[0002] During the drilling process, the drill bit is a tool used to break the rock to form a wellbore. The eccentricity of a wellbore and its life span are related not only to the characteristics of the formation being drilled and the performance of the drill bit itself, but also to the matching degree between the drill bit and the formation. Therefore, the reasonable selection of the drill bit plays an important role in increasing the drilling speed and reducing the drilling cost.

[0003] At present, in oil drilling projects, the traditional drill bit optimization methods are: (1) Statistical analysis selection method. This method is a selection method based on the drill bit usage database. This method is limited by the quality of the drilling database, the data type and the optimization method, and the optimization effect for a certain section of the formation or a certain wellbore is poor. (2) Rock mechanics parameter method. By comprehensively analyzing the abrasiveness of the block rock, the rock drillability index is obtained, and then the drill bit is selected. However, this method is expensive and has a long cycle, and its economic applicability is poor in actual selection applications. (3) Comprehensive comparative analysis selection method. This method mainly uses logging data to complete the bottom layer drillability analysis, but when optimizing the drill bit that meets the drillability in each area, it is also necessary to use the drill bit application data, which has great limitations. (4) Drill bit optimization methods based on various neural networks. This type of method mainly uses the feedback function of the neural network to make negative feedback judgments on used drill bits and then classify the drill bits in the sample set (point system, the higher the score, the better the use effect). However, this type of method has a common disadvantage: the feedback weight cannot be adjusted and the input layer parameter structure is complex, resulting in inaccurate results and increased computing costs. Therefore, how to efficiently, conveniently and reliably select drill bits and improve drilling speed based on the premise of making full use of drilling big data is of great significance to the digital development of oil fields. Summary of the invention

[0004] In order to solve the problems of insufficient use of field data, unstable model, high calculation cost and poor operability in traditional drill bit selection methods, the present invention provides a drill bit optimization method based on main factor-three-dimensional golden section.

[0005] The present invention discloses a drill bit optimization method based on main factor-three-dimensional golden section, which comprises:

[0006] Step 1: Use the principal factor analysis method to find the main factors that represent the change characteristics of the data set;

[0007] Step 2: Based on the main factors obtained in step 1, use the three-dimensional golden section method to draw the golden section surface;

[0008] Step 3: Plot the main factors, average drilling speed and average footage of different drill bits in the same coordinate system with the golden section plane, and select the drill bit above the golden section plane as the preferred result.

[0009] Furthermore, the step 1 comprises:

[0010] Step 11: Obtain and count the p parameters used in the specified formation, and use the obtained parameters as basic data for optimizing the drill bit; the parameters include mechanical drilling speed, footage, displacement, drilling pressure, rotation speed, mechanical specific energy and pure drilling time;

[0011] Step 12: Standardize the parameter set formed by all the parameters in step 11 to obtain a standardized matrix;

[0012] Step 13: Calculate the covariance matrix of the standardized matrix in step 12, and find the eigenvalues ​​and eigenvectors corresponding to the covariance matrix;

[0013] Step 14: Calculate the principal component contribution rate and cumulative contribution rate, select the principal factor whose cumulative contribution rate is greater than the preset value as the principal factor representing the data set, and find the average principal factor corresponding to different samples.

[0014] Further, the step 12 comprises:

[0015] Assuming there are n drill bit samples and p related parameters of the optimal drill bit, a sample matrix x of size n*p is constructed:

[0016]

[0017] The standardized matrix is ​​obtained by calculating the standard deviation of the sample matrix x, as shown below:

[0018]

[0019] Where: X ij is the standardized data of parameter j.

[0020] Further, the step 13 comprises:

[0021] Based on the standardized matrix, the covariance matrix of the standardized matrix is ​​obtained:

[0022]

[0023] Where: r ij is the covariance after parameter standardization; R is the covariance matrix of the data set;

[0024] Based on R, calculate the corresponding eigenvalues ​​and eigenvectors:

[0025] Compute eigenvalues:

[0026] λ1≥λ2≥…≥λ p ≥0, since R is a semi-positive definite matrix, and the trace of the covariance matrix is:

[0027]

[0028] Compute the eigenvectors:

[0029]

[0030] Where: i is the eigenvalue of the covariance matrix; a p are the eigenvectors of the covariance matrix.

[0031] Furthermore, in step 14:

[0032] The principal components are:

[0033]

[0034] The cumulative contribution rate of the principal components is:

[0035]

[0036] Where: Ctribution is the principal component; Ctribution_sum is the cumulative contribution rate of the principal component; λ i is the matrix eigenvalue;

[0037] The main factors are:

[0038]

[0039] The average main factors corresponding to different samples are:

[0040]

[0041] Where: F i is the main factor of parameter i; is the weighting factor of all main factors; a ij is the matrix of eigenvectors.

[0042] Furthermore, the step 2 comprises:

[0043] The average mechanical drilling speed V i , average footage L i and the average principal factor As the XYZ axis in the three-dimensional rectangular coordinate system, the average mechanical drilling speed V of each drill bit is i , average footage L i and the average principal factor Presented in a coordinate system to obtain the golden section surface.

[0044] Furthermore, the average mechanical drilling speed V i :

[0045]

[0046] Among them, V m is the drilling speed of the mth drill bit of the same model in the specified formation, and N is the total number of drill bits of the same model used;

[0047] Average footage L i :

[0048]

[0049] Where: L m is the drilling footage of the mth drill bit of the same model in the specified formation; N is the total number of drill bits of the same model used;

[0050] Weighted principal factors

[0051]

[0052] Where: F i is the main factor of parameter i.

[0053] Furthermore, the expression of the golden section plane is:

[0054]

[0055] Where: F is the three-dimensional golden section judgment surface; F a is the average main factor of the drill bit; v a is the average mechanical drilling speed of the drill bit; l a is the average penetration of the drill bit; v is the drilling speed required for the three-dimensional golden section judgment surface; l is the penetration required for the three-dimensional golden section judgment surface.

[0056] Due to the adoption of the above technical solution, the present invention has the following advantages:

[0057] The present invention is based on the use parameters of the drill bit (mechanical drilling speed, footage, well diameter, drilling pressure, torque, displacement, rotation speed, mechanical specific energy and pure drilling time), finds the main factors of the parameter set through the main factor analysis method, and uses the drilling speed, footage and main factors of the drill bit as three core evaluation indicators, applies the three-dimensional golden section method containing the main factors to obtain the golden section surface to optimize the drill bit, and finally intuitively reflects the drill bit optimization result through the three-dimensional rectangular coordinate system. In practical applications, the present invention can effectively evaluate the potential of the drill bit, and will not exclude the drill bit with the potential for speed increase due to the single evaluation parameter, and can effectively ensure the accuracy and reliability of the drill bit selection, and has strong applicability, practicability and universality in practical applications, is easy to promote and operate, improves the efficiency of drill bit selection, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0059] Figure 1 Flow chart of the main factor-three-dimensional golden section drill bit optimization method;

[0060] Figure 2 An example of calculating the main factors for a drill bit;

[0061] Figure 3 An example of calculating the main factors for a drill bit;

[0062] Figure 4 An example of the optimal selection of a three-dimensional golden section drill bit as the main factor;

[0063] Figure 5(a) and Figure 5(b) are comparison diagrams of the effects of the two-dimensional golden section method and the principal factor-three-dimensional golden section method, respectively. DETAILED DESCRIPTION

[0064] The present invention is further described in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field should fall within the scope of protection of the embodiments of the present invention.

[0065] See also Figure 1The present invention provides an embodiment of a drill bit optimization method based on principal factor-three-dimensional golden section. The technical solution of this embodiment is: first, the principal factor analysis method is used to find the principal factors representing the characteristics and changes of the data set, and then the three-dimensional golden section method containing the principal factors of the data set is used to draw the golden section surface, and finally the relevant parameters of the drill bit (principal factors, average drilling speed and average penetration) and the golden section surface are drawn in a three-dimensional rectangular coordinate system, and the drill bit above the golden section surface is selected as the optimization result. Specifically, the following operation steps are included:

[0066] S1: Obtain and count the multiple use parameters (mechanical drilling speed, footage, displacement, drilling pressure, rotation speed, mechanical specific energy and pure drilling time) of p types of drill bits used in a specified formation;

[0067] In this embodiment, based on the relevant data of completed drilling of a specified formation in a certain work area, the usage parameters (mechanical drilling rate, footage, well diameter, drilling pressure, torque, displacement, rotation speed, mechanical specific energy and pure drilling time) of different types of drill bits in the specified formation can be obtained, and the obtained parameters can be used as the basic data for the preferred drill bit.

[0068] S2: Standardize the parameter set in S1 to obtain the standardized matrix X;

[0069] The specific calculation process of the standardized matrix is ​​as follows:

[0070] First Compute column-wise means:

[0071]

[0072] Where: is the mean of variable j; x is a sample matrix of size nxp consisting of n samples and p indicators;

[0073] Then calculate the standard deviation:

[0074]

[0075] Where: p is the number of parameters; S j is the standard deviation of parameter j;

[0076] Data Standardization:

[0077]

[0078] Where: X ij is the standardized data of variable j;

[0079] Therefore, the original sample matrix becomes after standardization:

[0080]

[0081] S3: Calculate the covariance matrix of the standardized matrix in S2, and find the eigenvalues ​​and eigenvectors corresponding to the covariance matrix;

[0082] On the basis of the standardized matrix, the covariance matrix of the standardized matrix is ​​further obtained:

[0083]

[0084] Written in matrix form, it is the covariance matrix (R) of the standard matrix:

[0085]

[0086] Where: r ij is the covariance of the standardized variables; R is the covariance matrix of the data set

[0087] Based on R, calculate the corresponding eigenvalues ​​and eigenvectors:

[0088] Compute eigenvalues:

[0089] λ1≥λ2≥…≥λ p ≥0, since R is a positive semidefinite matrix, and

[0090] Compute the eigenvectors:

[0091]

[0092] Where: i is the eigenvalue of the matrix; a p is the eigenvector of the matrix.

[0093] It should be noted that the matrix in this embodiment is a large matrix. If manual calculation takes a long time, the solution tool in MATLAB can be used to find the covariance matrix corresponding to the standard matrix and the eigenvalues ​​and eigenvectors of the covariance matrix.

[0094] S4: Calculate the principal component contribution rate and cumulative contribution rate, select the principal factor with a cumulative contribution rate greater than 80% as the principal factor of the representative data set, and calculate the average principal factor corresponding to different samples;

[0095] Based on the covariance matrix and the corresponding eigenvalues ​​and eigenvectors, the principal components, the cumulative contribution rates of the principal components and the main factors can be obtained.

[0096] Principal component:

[0097]

[0098] Cumulative contribution rate of principal components:

[0099]

[0100] Main factors:

[0101]

[0102] Average principal factors corresponding to different samples:

[0103]

[0104] It should be noted that the principal component is obtained by calculating the eigenvalue of the covariance matrix, which indicates the degree of influence of a certain parameter on the sample (drill bit). The cumulative contribution rate of the principal component indicates how many principal factors can represent the variation characteristics of the entire data set. Therefore, all principal factors with a cumulative contribution rate greater than 80% are generally selected as the overall representative of the data set. Figure 2 and Figure 3 As shown in the figure, the main factor calculation examples of single well drill bit and multi-well drill bit in a certain work area are given.

[0105] S5: Average mechanical drilling speed V i , average footage L i and the average principal factor As the XYZ axis in the three-dimensional rectangular coordinate system, the average mechanical drilling speed V of each drill bit is i , average footage L i and the average principal factor Presented in a coordinate system;

[0106] Average mechanical drilling speed V i :

[0107]

[0108] Among them, V m is the drilling speed of the mth drill bit of the same model in the specified formation, and N is the total number of drill bits of the same model used;

[0109] Average footage L i :

[0110]

[0111] Where: is the drilling footage of the mth drill bit of the same model in the specified formation; N is the total number of drill bits of the same model used;

[0112] Weighted principal factors

[0113]

[0114] Where: F i is the main factor of parameter i.

[0115] It should be noted that the average mechanical penetration rate of each drill bit is the arithmetic mean of the penetration rates of multiple drill bits of the same model in a specified formation, the average footage of each drill bit is the arithmetic mean of the footage of multiple drill bits of the same model in a specified formation, and the average main factor of each drill bit is the arithmetic mean of the main factors of a single well of the same model of drill bits in a specified bottom layer, such as Figure 3 shown.

[0116] S6: Based on the three-dimensional golden section method, draw a three-dimensional golden section surface, present the golden section surface in the coordinate system, and select the drill bit model corresponding to the point above the golden section surface as the preferred drill bit model.

[0117] Three-dimensional golden section judgment surface:

[0118]

[0119] Where: F is the three-dimensional golden section judgment surface, dimensionless; F a is the average main factor of the drill bit, dimensionless; v a is the average mechanical drilling speed of the drill bit, m / h; l a is the average penetration of the drill bit, m; v is the drilling speed required for the three-dimensional golden section judgment surface, and the value is a range, m / h; l is the penetration required for the three-dimensional golden section judgment surface, and the value is a range, m.

[0120] It should be noted that the three-dimensional golden section surface involves the main factors of the drill bit parameters, drilling speed and penetration, and takes into account more factors and a more comprehensive range. Figure 4 The main factor-three-dimensional golden section drill bit optimization example diagram is given. Compared with the traditional two-dimensional golden section method, the main factor-three-dimensional golden section method can effectively evaluate the potential of the drill bit, so that it will not be misjudged and eliminated during the optimization process. As shown in Figure 5 (a) and Figure 5 (b), the S1665FAG drill bit obviously does not meet the standard in the selection of the traditional two-dimensional golden section method, but using the method of the present invention, it is above the golden section surface, indicating that the drill bit has the potential to increase speed. Facts have proved that in the operation of a certain work area, after strengthening the mechanical parameters of the drill bit, the speed-up effect is obvious compared with the wells using the same drill bit on the same platform.

[0121] In summary, the above method is effective in drill bit selection, the results are reliable, and it plays a substantial and intuitive role in optimizing drill bits in actual drilling.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A drill bit optimization method based on main factor-three-dimensional golden section, characterized in that: include: Step 1: Use the principal factor analysis method to find the main factors that represent the change characteristics of the data set; Step 2: Based on the main factors obtained in step 1, use the three-dimensional golden section method to draw the golden section surface; Step 3: Plot the main factors, average drilling speed and average footage of different drill bits in the same coordinate system with the golden section plane, and select the drill bit above the golden section plane as the preferred result.

2. The method according to claim 1, characterized in that: The step 1 comprises: Step 11: Obtain and count the p parameters used in the specified formation, and use the obtained parameters as basic data for optimizing the drill bit; the parameters include mechanical drilling speed, footage, displacement, drilling pressure, rotation speed, mechanical specific energy and pure drilling time; Step 12: Standardize the parameter set formed by all the parameters in step 11 to obtain a standardized matrix; Step 13: Calculate the covariance matrix of the standardized matrix in step 12, and find the eigenvalues ​​and eigenvectors corresponding to the covariance matrix; Step 14: Calculate the principal component contribution rate and cumulative contribution rate, select the principal factor whose cumulative contribution rate is greater than the preset value as the principal factor representing the data set, and find the average principal factor corresponding to different samples.

3. The method according to claim 2, characterized in that The step 12 comprises: Assuming there are n drill bit samples and p related parameters of the optimal drill bit, a sample matrix x of size n*p is constructed: The standardized matrix is ​​obtained by calculating the standard deviation of the sample matrix x, as shown below: Where: X ij is the standardized data of parameter j.

4. The method according to claim 3, characterized in that The step 13 comprises: Based on the standardized matrix, the covariance matrix of the standardized matrix is ​​obtained: Where: r ij is the covariance after parameter standardization; R is the covariance matrix of the data set; Based on R, calculate the corresponding eigenvalues ​​and eigenvectors: Compute eigenvalues: λ1≥λ2≥…≥λ p ≥0, since R is a semi-positive definite matrix, and the trace of the covariance matrix is: Compute the eigenvectors: Where: i is the eigenvalue of the covariance matrix; a p are the eigenvectors of the covariance matrix.

5. The method according to claim 4, characterized in that In step 14: The principal components are: The cumulative contribution rate of the principal components is: Where: Ctribution is the principal component; Ctribution_sum is the cumulative contribution rate of the principal component; λ i is the matrix eigenvalue; The main factors are: The average main factors corresponding to different samples are: Where: F i is the main factor of parameter i; is the weighting factor of all main factors; a ij is the matrix of eigenvectors.

6. The method according to claim 1, characterized in that The step 2 comprises: The average mechanical drilling speed V i , average footage L i and the average principal factor As the XYZ axis in the three-dimensional rectangular coordinate system, the average mechanical drilling speed V of each drill bit is i , average footage L i and the average principal factor Presented in a coordinate system to obtain the golden section surface.

7. The method according to claim 6, characterized in that Average mechanical drilling speed V i : Among them, V m is the drilling speed of the mth drill bit of the same model in the specified formation, and N is the total number of drill bits of the same model used; Average footage L i : Where: L m is the drilling footage of the mth drill bit of the same model in the specified formation; N is the total number of drill bits of the same model used; Weighted principal factors Where: F i is the main factor of parameter i.

8. The method according to claim 1, characterized in that The expression of the golden section surface is: Where: F is the three-dimensional golden section judgment surface; F a is the average main factor of the drill bit; v a is the average mechanical drilling speed of the drill bit; l a is the average penetration of the drill bit; v is the drilling speed required for the three-dimensional golden section judgment surface; l is the penetration required for the three-dimensional golden section judgment surface.

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