Well separation coefficient calculation method based on particle swarm optimization algorithm

Abstract

The invention discloses a borehole separation coefficient calculation method based on a particle swarm optimization algorithm, and the method comprises the steps: employing the particle swarm optimization algorithm, taking the distance between two closest points on an ellipsoid as an optimization target, and building an ellipsoid distance solving model through an ellipsoid parameter equation; and carrying out iterative calculation by adopting algorithm parameters in different ranges until the algorithm converges, and determining two nearest points on the surface of the error ellipsoid. And finally, inputting a distance between two points by using a borehole separation coefficient nearest distance algorithm model to obtain a separation coefficient. According to the method, the nearest distance of the error ellipsoid in the three-dimensional space is solved through rapid iteration, the number of needed steps is small, the number of iteration times is small, a complex mathematical optimization constructor function does not need to be solved, the obtained separation coefficient evaluation precision is high, and the intensive cluster well design and anti-collision analysis requirements are better met.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas resource development, and in particular to a method for calculating a wellbore separation coefficient based on a particle swarm optimization algorithm. Background Art

[0002] In the efficient development of oil and gas resources, cluster well technology significantly reduces the initial investment cost, land occupation and environmental pollution, and is widely used in marine and land drilling operations. With the deepening of oil and gas field exploration and development, the wellbore layout has become more and more dense, which puts higher requirements on the accuracy and reliability of anti-collision technology. Wellbore anti-collision technology runs through the pre-drilling design and actual drilling monitoring of cluster wells, infill wells and directional wells. Risk assessment is based on well spacing scanning and trajectory error analysis, and the evaluation indicators include the closest distance to adjacent wells, wellbore separation coefficient and collision probability. Existing methods mainly include traditional separation coefficient method, center vector method, foot line method, directional separation coefficient method and ellipse scaling method. Previous studies have shown that the results of traditional separation coefficient method and foot line method are conservative, and the results of center vector method and directional separation coefficient method are too optimistic. The ellipse scaling method is most in line with reality, but its calculation is complex and difficult to be extended to field applications. Furthermore, the above methods are generally based on the ellipse on the two-dimensional plane to calculate the degree of separation, and cannot truly reflect the degree of separation of the two error ellipsoids in three-dimensional space. Summary of the invention

[0003] In view of the problem that the current method for calculating the wellbore separation coefficient is computationally complex and cannot truly reflect the degree of separation of two error ellipsoids in three-dimensional space, the present invention provides a method for calculating the wellbore separation coefficient based on a particle swarm optimization algorithm.

[0004] This method uses the particle swarm optimization algorithm, takes the distance between the two nearest points on the ellipsoid as the optimization target, and establishes an ellipsoid distance solution model through the ellipsoid parameter equation. Iterative calculations are performed using different ranges of algorithm parameters until the algorithm converges and determines the two nearest points on the error ellipsoid surface. Finally, the borehole separation coefficient nearest distance algorithm model is used to input the distance between the two points to obtain the separation coefficient. This method can provide faster solution speed and higher evaluation accuracy by quickly iterating to solve the nearest distance of the error ellipsoid in three-dimensional space, and better meet the needs of dense cluster well design and anti-collision analysis. Furthermore, since the particle swarm optimization algorithm has the characteristics of simple algorithm and few parameters, this method is easier to promote in on-site construction.

[0005] The method for calculating the wellbore separation coefficient based on the particle swarm optimization algorithm provided by the present invention comprises the following specific steps:

[0006] S1. Use the ISCWSA error model to solve the uncertainty covariance matrix of the wellbore position. Specifically, input the error model parameters, including magnetic inclination, magnetic declination, magnetic field strength, longitude and latitude, 6-degree band number and ellipsoid magnification factor, and input the wellbore trajectory inclination data with well inclination angle, well inclination azimuth and depth as the measurement point elements, and use the ISCWSA error model to calculate the uncertainty covariance matrix.

[0007] S2, determining two error ellipsoid parameters to be solved;

[0008] Solve the eigenvalues ​​and eigenvectors of the wellbore position uncertainty covariance matrix obtained in step S1 to determine the ellipsoid parameters. This mainly includes the following steps:

[0009] The probability density of wellbore position error is expressed as follows:

[0010]

[0011] Where Δr is the increment of wellbore trajectory position error; |C K | is the matrix C K The determinant of ;

[0012] The equal probability density surface of the well trajectory error distribution is:

[0013] (Δr) T C K -1 (Δr)=k 2

[0014] Where k is the confidence factor; each different confidence factor value corresponds to a three-dimensional confidence ellipsoid, and the relationship between its three semi-axes and k is as follows:

[0015]

[0016] Where: λ1, λ2 and λ3 are the covariance matrix C K The three eigenvalues ​​of; r1, r2 and r3 represent the lengths of the three semi-axes of the ellipsoid respectively; the covariance matrix C K The three eigenvectors v1, v2 and v3 represent the principal axis directions of r1, r2 and r3 respectively.

[0017] S3, establishing an error ellipsoid distance solution model;

[0018] Through the ellipsoid parameter equation and the 4×4 affine transformation matrix, a point on the local coordinate system of the ellipsoid is rotated and translated to the wellhead coordinate system, and then the distance between the two points in the wellhead coordinate system is calculated.

[0019] The specific method is as follows:

[0020] Express the ellipsoid as a parametric equation:

[0021]

[0022] Written in the form of a 3×1 vector:

[0023]

[0024] Thus, the mapping between the two error ellipsoids and the particles is constructed:

[0025] X=(θ M ,φ M ,θ P ,φ P )

[0026] In the formula, X represents the position of the particle. In solving the problem of the closest distance to the ellipsoid, the dimension of the search space is 4, so it has 4 components; θ M and φ M Respectively represent the angle θ and angle φ of the reference point error ellipsoid in the parametric equation, rad; θ P and φ P They represent the angle θ and the angle φ of the error ellipsoid of the scanning point in the parametric equation, rad;

[0027] The fitness function of the particle swarm optimization algorithm is expressed as:

[0028] fitness=|T M v M -T P v P |

[0029] In the formula, fitness represents the fitness value; the || symbol represents the modulus of the vector; v M and v P Respectively represent a point on the reference point ellipsoid and the scanning point ellipsoid, located in the local coordinate system of the ellipsoid; T M It represents the affine transformation from the local coordinate system of the reference point ellipsoid to the wellhead coordinate system of the reference well. The point is first rotated according to the ellipsoid posture and then translated to the reference point. It is a 4×4 matrix. M The expansion formula is as follows:

[0030]

[0031] Where M E 、M V and M N Respectively represent the East, Vertical, and North coordinate values ​​of the reference point, m; M vector is a 3×3 matrix, each column of which is the three eigenvectors of the reference point uncertainty covariance matrix.

[0032] S4, use the particle swarm optimization algorithm to iteratively search for the two points closest to each other;

[0033] Using the particle swarm optimization algorithm, the error ellipsoid parameters are input, the particle swarm dimension, scale, and number of iterations are initialized, and the iteration is repeated until the maximum number of times or the minimum difference between the distances of two iterations is reached to obtain two points that meet the shortest distance.

[0034] It includes the following four sub-steps:

[0035] S41, using the particle swarm optimization algorithm, inputting the error ellipsoid parameters, the error ellipsoid parameters including the coordinate vector, the attitude matrix and the lengths of the three semi-axes, through the T of step S3 M The expansion formula establishes the transformation matrix from the ellipsoid local coordinate system to the wellhead coordinate system;

[0036] S42, initialize the particle swarm dimension, quantity, number of iterations, individual learning factor c1 and group learning factor c2, and randomly initialize the position and velocity of each particle;

[0037] S43, the algorithm starts, and the velocity and position of the particle are updated in each iteration. When the position is updated, the points on the two ellipsoids are calculated according to the mapping relationship between the two error ellipsoids and the particles constructed in step S3, and v is obtained. M and v P ; Then the distance between the two points is calculated by the fitness function of the particle swarm optimization algorithm in step S3 as the fitness value of the particle swarm optimization algorithm;

[0038] S44, update the optimal fitness value of each particle, update the optimal fitness value of the group, and end the algorithm when the minimum difference in the number of iterations or the distance between two iterations is reached.

[0039] S5. Determine the wellbore separation coefficient by using the wellbore separation coefficient closest distance algorithm model; the calculation formula is as follows:

[0040]

[0041] Where NDSF is the separation factor; R s is the distance between the two error ellipsoids, m; AB is the shortest distance between the two error ellipsoids.

[0042] Compared with the prior art, the present invention is beneficial in that:

[0043] (1) Compared with the prior art which mostly adopts the method of calculating on a two-dimensional plane projection, the borehole separation coefficient calculation method based on the particle swarm optimization algorithm provided by the present invention can calculate the closest distance of the error ellipsoid in three-dimensional space, and can more accurately reflect the degree of separation of the two error ellipsoids in space; the calculation requires fewer steps and fewer iterations, and there is no need to solve complex mathematical optimization constructors. The obtained separation coefficient evaluation accuracy is high, and a higher evaluation accuracy can be obtained.

[0044] (2) The borehole separation coefficient calculation method of the present invention solves the shortest distance of the error ellipsoid in three-dimensional space through rapid iteration, which is used to optimize the borehole collision prevention index, thereby reducing the real-time collision risk during the drilling process with more accurate evaluation results, and providing a better choice for drilling collision prevention design.

[0045] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The present invention is a flow chart of a method for calculating a wellbore separation coefficient based on a particle swarm optimization algorithm.

[0047] Figure 2 The present invention is a flow chart of using the particle swarm optimization algorithm to solve the error ellipsoid shortest distance.

[0048] Figure 3 This is a three-dimensional position relationship diagram of the closest distance points A and B of the error ellipsoid obtained by the particle swarm optimization algorithm of the present invention.

[0049] Figure 4 It is a comparison chart of the separation coefficient optimized by the particle swarm optimization algorithm of the present invention and the separation coefficient obtained by the existing method. DETAILED DESCRIPTION

[0050] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0051] like Figure 1-3 As shown, the method for calculating the wellbore separation coefficient based on the particle swarm optimization algorithm provided by the present invention has the following detailed steps:

[0052] Step S1, using the ISCWSA error model to solve the wellbore position uncertainty covariance matrix. The details are as follows:

[0053] S11: Solving the wellbore position uncertainty covariance matrix using the ISCWSA error model can be described by the following equation:

[0054]

[0055] In the formula, e i is the position error in the NEH coordinate system caused by the error source i at the current measuring point; σ i represents the magnitude of error source i; It represents the influence of error source i on well depth, well inclination angle and well inclination azimuth; It shows the influence of well depth, well inclination angle and well inclination azimuth on N coordinate, E coordinate and H coordinate.

[0056] S12: Use Δr k represents the displacement between k-1 and k measuring points, and the error caused by the ith error source at the kth survey station in the lth survey section is expressed as the sum of the effects on the displacements calculated before and after:

[0057]

[0058] Among them, e i,l,k represents the position error caused by error source i at measuring point k in the lth measuring segment; σ i,l is the error magnitude of error source i in the lth measurement segment; It represents the influence of error source i on the well depth, well inclination angle and well inclination azimuth at the measuring point k; and They respectively represent the influence of the measurement error at measuring point k on the displacement vector from measuring point k-1 to k and from measuring point k to k+1.

[0059] At the last measuring point, since there is no k+1 measuring point, equation (2) can be simplified to:

[0060]

[0061] S13: Different error sources can be divided into random error, systematic error, single well error and global error according to their influence on the subsequent measurement point position error. The accumulation method is as follows:

[0062]

[0063] in,

[0064]

[0065] in,

[0066]

[0067] in,

[0068]

[0069] In the formula, and are the covariance matrices of random error, systematic error, single well error and global error respectively; K l Indicates the last measurement point in the measurement segment numbered l. L indicates the total number of measurement segments.

[0070] By adding the covariance matrices of random error, systematic error, single well error and global error, we can get the general form of the error accumulation equation:

[0071]

[0072] In the formula, C K It is the covariance matrix at the measuring point K; R, S, W, and G represent random error, systematic error, single well error, and global error, respectively.

[0073] Step S2: Determine the two error ellipsoid parameters to be solved

[0074] After the wellbore position uncertainty covariance matrix is ​​solved by the ISCWSA error model in step S1, the eigenvalues ​​and eigenvectors of the covariance matrix are solved in step S2 to determine the ellipsoid parameters; the steps are as follows:

[0075] S21: Since the borehole position error obeys the normal distribution, according to the theory of mathematical statistics, the probability density of the borehole position error can be described by the following formula:

[0076]

[0077] Where Δr is the increment of wellbore trajectory position error; |C K | is the matrix C T The determinant of .

[0078] S22: From the above formula, the equal probability density surface of the well trajectory error distribution can be obtained as:

[0079] (Δr) T C K -1 (Δr)=k 2 (12)

[0080] In the formula, k is the confidence factor. Each different confidence factor value can correspond to a three-dimensional confidence ellipsoid, and the relationship between its three semi-axes and k is as follows:

[0081]

[0082] Where: λ1, λ2 and λ3 are the covariance matrix C K The three eigenvalues ​​of; r1, r2 and r3 represent the lengths of the three semi-axes of the ellipsoid respectively; the covariance matrix C KThe three eigenvectors v1, v2 and v3 can represent the principal axis directions of r1, r2 and r3 respectively.

[0083] Step S3: Establishing an error ellipsoid distance solution model

[0084] By using the ellipsoid parametric equation and combining it with a 4×4 affine transformation matrix, a point on the local coordinate system of the ellipsoid is rotated and translated to the wellhead coordinate system; the detailed steps are as follows:

[0085] S31: Express the ellipsoid in the form of a parametric equation:

[0086]

[0087] S32: written in the form of a 3×1 vector:

[0088]

[0089] S33: From this, the mapping between the two error ellipsoids and the particles can be constructed:

[0090] X=(θ M ,φ M ,θ P ,φ P )(16)

[0091] In the formula, X represents the position of the particle. In solving the problem of the closest distance to the ellipsoid, the dimension of the search space is 4, so it has 4 components; θ M and φ M Respectively represent the angle θ and angle φ of the reference point error ellipsoid in the parametric equation, rad; θ P and φ P They represent the θ angle and φ angle of the scanning point error ellipsoid in the parametric equation representation, rad.

[0092] S34: The fitness function of the particle swarm optimization algorithm can be expressed as:

[0093] fitness=|T M v M -T P v P | (17)

[0094] In the formula, fitness represents the fitness value; the || symbol represents the modulus of the vector; v M and v P Respectively represent a point on the reference point ellipsoid and the scanning point ellipsoid, located in the local coordinate system of the ellipsoid; T M It represents the affine transformation from the local coordinate system of the reference point ellipsoid to the wellhead coordinate system of the reference well. The point is first rotated according to the ellipsoid posture and then translated to the reference point. It is a 4×4 matrix. MThe expanded form is as follows:

[0095]

[0096] Where M E 、M v and M N Respectively represent the East, Vertical, and North coordinate values ​​of the reference point, m; M vector is a 3×3 matrix, each column of which is the three eigenvectors of the reference point uncertainty covariance matrix.

[0097] T P The expanded form is as follows:

[0098]

[0099] Where P E , P V and P N Respectively represent the East, Vertical, and North coordinate values ​​of the scan point, m; P vector are the three eigenvectors of the uncertainty covariance matrix of the scan point, column-wise and M vector Consistent.

[0100] Step S4, using the particle swarm optimization algorithm to iteratively search for the two points with the closest distance;

[0101] Using the particle swarm optimization algorithm, input the error ellipsoid parameters, initialize the particle swarm dimension, scale, and number of iterations, and iterate until the maximum number of times or the minimum difference between two iterations is reached to obtain two points that meet the shortest distance. Figure 2 The detailed steps are as follows:

[0102] S41: Input the reference point and scanning point error ellipsoid parameters (coordinate vector, attitude matrix, three semi-axis lengths), and establish the transformation matrix from the ellipsoid local coordinate system to the wellhead coordinate system through equation (18).

[0103] S42: Initialize the particle swarm dimension to 4, the number to 100, the maximum number of iterations to 50, the individual learning factor c1 and the group learning factor c2 to 1.49445, and randomly initialize the position and velocity of each particle. In order to avoid the algorithm from finding the local optimal solution, an adaptive strategy is used to adjust the inertia weight. First, a larger inertia weight is used for global search to make the search space converge quickly to a certain area, and then a smaller inertia weight is used for local fine search to obtain a high-precision solution. The adjustment strategy of the inertia weight can be expressed by the following formula:

[0104]

[0105] In the formula, ωmin and ω max are the minimum inertia weight and the maximum inertia weight, which are set to 0.5 and 1.2 respectively; iter is the current iteration number; iter max is the maximum number of iterations.

[0106] S43: The algorithm starts, and the velocity and position of the particle are updated in each iteration. When the position is updated, the points on the two ellipsoids are calculated according to the mapping relationship of formula (16) to obtain v M and v P , and then the distance between the two points is calculated by formula (17) as the fitness value of the particle swarm optimization algorithm.

[0107] S44: Update the optimal fitness value of each particle and the optimal fitness value of the group. When the number of iterations or the minimum difference between the distances of two iterations is reached, the algorithm ends. The obtained three-dimensional position relationship diagram of the closest distance points A and B of the error ellipsoid Figure 3 shown.

[0108] Step S5, determine the separation coefficient by using the borehole separation coefficient closest distance algorithm model; the formula is as follows:

[0109]

[0110] Where NDSF is the separation factor; R s is the distance between the two error ellipsoids, m; AB is the shortest distance between the two error ellipsoids.

[0111] The comparison effect between the separation coefficient obtained by the particle swarm optimization algorithm of the present invention and the separation coefficient of the existing method is as follows: Figure 4 As shown in the figure, it can be seen that the separation coefficient obtained by the calculation method of the present invention is between the traditional separation coefficient and the directional separation coefficient; the traditional separation coefficient calculation result is conservative, and the directional separation coefficient result is optimistic, while the method of the present invention is between the two and has a higher evaluation accuracy.

[0112] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating wellbore separation coefficient based on particle swarm optimization algorithm, characterized in that: The following steps are involved: S1. Solve the wellbore position uncertainty covariance matrix using the ISCWSA error model; S2, determining two error ellipsoid parameters to be solved; S3, establish the error ellipsoid distance solution model, the method is as follows: Express the ellipsoid as a parametric equation: Written in the form of a 3×1 vector: Thus, the mapping relationship between the two error ellipsoids and the particles is constructed: X=(θ M ,f M ,i P ,f P ) In the formula, X represents the position of the particle. In solving the problem of the closest distance to the ellipsoid, the dimension of the search space is 4, so it has 4 components; θ M and φ M Respectively represent the angle θ and angle φ of the reference point error ellipsoid in the parametric equation, rad; θ P and φ P They represent the angle θ and the angle φ of the error ellipsoid of the scanning point in the parametric equation, rad; The fitness function of the particle swarm optimization algorithm is expressed as: fitness=|T M in M -T P in P | In the formula, fitness represents the fitness value; the || symbol represents the modulus of the vector; v M and v P Respectively represent a point on the reference point ellipsoid and the scanning point ellipsoid, located in the local coordinate system of the ellipsoid; T M It represents the affine transformation from the local coordinate system of the reference point ellipsoid to the wellhead coordinate system of the reference well. The point is first rotated according to the ellipsoid posture and then translated to the reference point. It is a 4×4 matrix. M The expansion formula is as follows: Where M E 、M v and M N Respectively represent the East, Vertical, and North coordinate values ​​of the reference point, m; M vector is a 3×3 matrix, each column of which is the three eigenvectors of the reference point uncertainty covariance matrix; S4, use the particle swarm optimization algorithm to iteratively search for the two points closest to each other; Specifically, the particle swarm optimization algorithm is used, the error ellipsoid parameters are input, the particle swarm dimension, scale, and number of iterations are initialized, and the iteration is performed until the maximum number of times or the minimum difference between the distances of two iterations is reached, and two points that meet the shortest distance are obtained; S5. Determine the separation coefficient through the borehole separation coefficient closest distance algorithm model.

2. The method for calculating the wellbore separation coefficient based on the particle swarm optimization algorithm according to claim 1, characterized in that: The specific method of step S1 is: input error model parameters, including magnetic inclination, magnetic declination, magnetic field strength, longitude and latitude, 6-degree band number and ellipsoid magnification factor, and input wellbore trajectory inclination data with well inclination angle, well inclination azimuth and depth as measuring point elements, and use the ISCWSA error model to calculate the uncertainty covariance matrix.

3. The method for calculating the wellbore separation coefficient based on the particle swarm optimization algorithm according to claim 1, characterized in that: In step S2, the eigenvalues ​​and eigenvectors of the wellbore position uncertainty covariance matrix obtained in step S1 are solved to determine the ellipsoid parameters.

4. The method for calculating the wellbore separation coefficient based on the particle swarm optimization algorithm according to claim 3, characterized in that: The step S2 comprises the following steps: The probability density of wellbore position error is expressed as follows: Where Δr is the increment of wellbore trajectory position error; |C K | is the matrix C K The determinant of ; The equal probability density surface of the well trajectory error distribution is: (Δr) T C K -1 (Δr)=k 2 Where k is the confidence factor; each different confidence factor value corresponds to a three-dimensional confidence ellipsoid, and the relationship between its three semi-axes and k is as follows: Where: λ1, λ2 and λ3 are the covariance matrix C K The three eigenvalues ​​of; r1, r2 and r3 represent the lengths of the three semi-axes of the ellipsoid respectively; the covariance matrix C K The three eigenvectors v1, v2 and v3 represent the principal axis directions of r1, r2 and r3 respectively.

5. The method for calculating wellbore separation coefficient based on particle swarm optimization algorithm according to claim 1, characterized in that: The step S4 includes the following four sub-steps: S41, using the particle swarm optimization algorithm, inputting the error ellipsoid parameters, the error ellipsoid parameters including the coordinate vector, the attitude matrix and the lengths of the three semi-axes, through the T of step S3 M The expansion formula establishes the transformation matrix from the ellipsoid local coordinate system to the wellhead coordinate system; S42, initialize the particle swarm dimension, quantity, number of iterations, individual learning factor c1 and group learning factor c2, and randomly initialize the position and velocity of each particle; S43, the algorithm starts, and the velocity and position of the particle are updated in each iteration. When the position is updated, the points on the two ellipsoids are calculated according to the mapping relationship between the two error ellipsoids and the particles constructed in step S3, and v is obtained. M and v P ; Then the distance between the two points is calculated by the fitness function of the particle swarm optimization algorithm in step S3 as the fitness value of the particle swarm optimization algorithm; S44, update the optimal fitness value of each particle, update the optimal fitness value of the group, and end the algorithm when the minimum difference in the number of iterations or the distance between two iterations is reached.

6. The method for calculating wellbore separation coefficient based on particle swarm optimization algorithm according to claim 1, characterized in that: In step S5, the calculation formula of the wellbore separation coefficient is as follows: Where NDSF is the separation factor; R s is the distance between the two error ellipsoids, m; AB is the shortest distance between the two error ellipsoids.

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