CN110807234A - Method for evaluating borehole trajectory error on any section - Google Patents
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Abstract
The invention discloses a method for evaluating borehole trajectory errors on any section, which comprises the following steps: obtaining inclination measurement data of a well track by using a measuring instrument, and solving a covariance matrix at each measurement point under a wellhead coordinate system, wherein the covariance matrix represents an error ellipsoid group; selecting an amplification factor to uniquely determine an error ellipsoid; intercepting the error ellipsoid by using an arbitrary plane through the spherical center of the error ellipsoid to obtain an error ellipse; characterizing the spatial attitude of the plane by the normal direction of the plane; determining a covariance matrix of an error ellipse based on the covariance matrix of the error ellipsoid; determining the size and the posture of the error ellipse on the plane based on the covariance matrix of the error ellipse; the uncertainty of the well track on the plane is represented based on the size and the posture of the error ellipse, so that the feasibility and the rationality of the drilling engineering design are evaluated, the implementation effect of the well track on the plane is monitored and controlled, the hit rate and the reservoir drilling rate of the well track are improved, and the yield of oil and gas single wells and the exploitation and recovery rate are improved.
Description
Technical Field
The invention relates to the field of oil and gas well engineering, in particular to a method for evaluating borehole trajectory errors on any section in oil and gas well engineering.
Background
The basic goal of wellbore trajectory monitoring and control is to determine the spatial location of any point on the wellbore trajectory, i.e., the wellbore trajectory location. However, due to measurement, calculation, etc. errors, the borehole trajectory positioning may not be absolutely accurate. Although the positioning accuracy of the borehole trajectory can be improved by means of error correction and the like, the errors cannot be completely eliminated, so that the borehole trajectory has an uncertainty problem.
Error ellipsoids at the measuring points can be obtained based on the borehole trajectory error model, and the error ellipsoids are used for representing uncertainty of the spatial position of the borehole trajectory. In order to analyze uncertainty of a well track in the horizontal direction, an evaluation method of a horizontal section error ellipse (Liu Gong Hui, Dongbin, Gao Deli. error ellipsoid (circle) and well collision probability analysis [ J ]. drilling and production process, 2000,23(3):5-12.) has been proposed, and can meet the requirement of well track error analysis of a common directional well. However, for wells with complex structures such as horizontal wells and extended reach wells, borehole trajectory errors on vertical sections, normal sections and even arbitrary sections need to be analyzed, and at this time, the prior art cannot meet the requirements.
Therefore, there is a need for an evaluation method that can establish borehole trajectory errors on arbitrary cross sections.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for evaluating borehole trajectory errors on an arbitrary section, the method comprising:
acquiring inclination measurement data of a well track by using a measuring instrument according to industrial regulations, and solving a covariance matrix at each measuring point under a wellhead coordinate system NEH based on an ISCSSA standard and a model, wherein the covariance matrix represents an error ellipsoid group, and the probability that each different error ellipsoid in the error ellipsoid group contains a well track error is different;
selecting an amplification factor to uniquely determine the error ellipsoid according to the probability required by the actual drilling engineering;
intercepting the error ellipsoid by using an arbitrary plane through the spherical center of the error ellipsoid to obtain an error ellipse on the plane, and representing the spatial attitude of the plane by using the normal direction of the plane;
determining a covariance matrix of an error ellipse on the plane based on the covariance matrix of the error ellipsoid;
determining the size and the posture of the error ellipse on the plane based on a covariance matrix of the error ellipse, wherein the size and the posture of the error ellipse are respectively represented by two main shaft radiuses and a deflection angle;
and characterizing the uncertainty of the well track on the plane based on the size and the posture of the error ellipse on the plane, so as to evaluate the feasibility and the reasonableness of the drilling engineering design, monitor and control the implementation effect of the well track on the plane, improve the hit rate and the reservoir drilling rate of the well track, and further improve the yield and the exploitation and recovery rate of oil and gas single wells.
In a method for evaluating borehole trajectory errors in arbitrary cross-sections, the inclinometry data includes a borehole angle, an azimuth angle, a borehole depth, and a toolface angle, and the covariance matrix of error ellipsoids is a 3 x 3 matrix C under a borehole coordinate system NEH]NEHWherein: n is north coordinate, m; e is the east coordinate, m; h is the vertical depth coordinate, m.
According to an embodiment of the present invention, in the method for evaluating borehole trajectory errors on an arbitrary section, in the step of uniquely determining the error ellipsoid according to the probability, an amplification factor is found by a relation between the probability and the amplification factor as follows, and the error ellipsoid is determined:
wherein: k is an amplification factor and has no dimension; p is the error probability, decimal, of the borehole trajectory. The above formula can be solved by a numerical integration method, so that the probability P that the borehole trajectory is positioned in the error ellipsoid is obtained. When the amplification factor k is 1.0 to 4.0 and the step size is 0.5, the probabilities P are 19.87%, 47.78%, 73.85%, 89.99%, 97.07%, 99.34%, and 99.89%, respectively.
According to one embodiment of the method for evaluating borehole trajectory errors on arbitrary cross sections, in the step of characterizing the spatial attitude of the plane with the normal direction of the plane, the method comprises the following sub-steps:
based on a unit vector m of the plane normal direction, using a skew angle α of the unit vector mmAnd azimuth angle phimTo characterize the spatial pose of the plane;
and establishing a rectangular coordinate system XYZ by taking the spherical center of the error ellipsoid as an origin, wherein the Z axis points to the normal direction of the plane, the X axis is the intersection line of the plane and a vertical plane passing through the Z axis and points to the direction of the high side, and the Y axis points to the right side horizontally.
According to the method for evaluating borehole trajectory errors on arbitrary cross sections of the present invention, in the step of determining the covariance matrix of the error ellipse on the plane based on the covariance matrix of the error ellipsoid, the following sub-steps are included:
based on the transformation relation between the coordinate system XYZ and the coordinate system NEH, based on the covariance matrix [ C ] under the coordinate system NEH]NEHCalculating covariance matrix [ C ] under coordinate system XYZ]XYZThe concrete calculation formula is
[C]XYZ＝[T][C]NEH[T]T
Wherein
In the formula αmIs the well angle, (°) in the direction of the plane normal; phi is amAzimuth, in the direction of the plane normal, (°);
intercepting the error ellipsoid through the plane of the spherical center of the error ellipsoid to obtain the error ellipsoid, and obtaining a covariance matrix [ C ] of the error ellipsoid under the coordinate system XYZ]XYZPartitioning, and reserving relevant items of parameters X and Y to obtain a covariance matrix [ C ] of the error ellipse on the plane]XYIs composed of
In the formula: sigmaX 2、σY 2Variance in X-axis direction and Y-axis direction respectively; sigmaXYIs the covariance between the X-axis and the Y-axis.
According to the method for evaluating the borehole trajectory error on any section, in the step of determining the size and the posture of the error ellipse on the basis of the covariance matrix of the error ellipse on the plane, the size and the posture of the error ellipse are represented by two main shaft radiuses and a deflection angle of the error ellipse, wherein the deflection angle is an included angle between two main shafts of the error ellipse and an X axis and a Y axis respectively;
calculating the radius of the main shaft and the deflection angle of the error ellipse according to the following formulas:
wherein
In the formula: r is the radius of the main axis of the error ellipse, m; λ is the covariance matrix [ C ]]XYCharacteristic value of (1), m2(ii) a θ is the deflection angle, (°) of the error ellipse.
According to the method for evaluating the error of the borehole trajectory on any section, the inclination angle α of the normal direction of the plane is usedmAnd azimuth angle phimTo characterize the arbitrary plane for evaluation of borehole trajectory errors in an arbitrary spatial attitude plane, wherein commonly used spatial planes include horizontal, vertical, and normal, when the normal to the plane is at a well angle αmAngle of well deviation phimThe values of (A) are respectively as follows:
when the plane is horizontal, α is takenm＝φm＝0；
When the plane is vertical, α is takenmTaken phi at 90 DEGmThe azimuth angle is the normal direction of the vertical plane;
when the plane is a normal plane, α is takenmAnd phimRespectively, the angle α and the azimuth angle phi of the wellbore trajectory.
The invention provides a concept and a characterization method of any cross section error ellipse by defining and characterizing any space plane, and further provides an evaluation method of borehole trajectory errors on any space plane. The method can evaluate the borehole track errors on the vertical section, the normal section and even any section, thereby realizing high-precision monitoring and control of the borehole track, reducing the drilling operation risk and improving the development effect of oil and gas fields.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 shows a flow diagram of a method for evaluating borehole trajectory error over an arbitrary section according to one embodiment of the present invention; and
fig. 2 shows a technical schematic of a method for evaluating borehole trajectory errors on arbitrary cross sections according to one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to FIG. 1, a flow chart of a method for evaluating borehole trajectory error for arbitrary cross-sections is shown in accordance with one embodiment of the present invention.
The method comprises steps S1-S4The method is used for obtaining inclination measurement data of the well track by adopting a measuring instrument according to industrial regulations, and solving a covariance matrix at each measuring point under a wellhead coordinate system NEH based on an ISCSSA standard and a model. The covariance matrix characterizes a family of error ellipsoids, wherein each different error ellipsoid in the family of error ellipsoids has a different probability of containing a borehole trajectory error. In a method for evaluating borehole trajectory errors on arbitrary sections, the inclinometry data includes the borehole angle, azimuth, depth, and toolface angle, and the covariance matrix of the error ellipsoid is a 3 x 3 matrix [ C ] under the borehole coordinate system NEH]NEHWherein: n is north coordinate, m; e is the east coordinate, m; h is the vertical depth coordinate, m.
Specifically, in step S1, measurements are performed according to industry regulations, the measurement steps comprise ① strict and regular instrument check, ② slope measurement distance does not exceed 30m, ③ field check of gravity field, geomagnetic field and magnetic dip angle, gyro drift and the like is carried out, ④ non-magnetic distance of MWD is determined according to industry specifications, and ⑤ MWD is used to be far away from a casing and an adjacent well.
In step S2, various error sources are identified and characterized. Including the magnitude and weight functions of the various error sources.
Next, in step S3, an error propagation equation is established.
In the formula: e.g. of the typeiError for north coordinate N, east coordinate E, and vertical depth coordinate H (a 3 x 1 vector) caused by error source i; epsiloniIs the ith error source; sigmaiAn error magnitude (scalar) that is an error source i;as a weight function, the influence of the error source i on the well depth, the well inclination angle and the azimuth angle (3 x 1 vector) is represented;
the effect of well depth, well offset angle and azimuth measurement errors on the N, E and H coordinates (3 x 3 matrix) is shown.
In step S4, error accumulation is performed in the propagation mode. Considering the correlation among various error sources, the error accumulation is respectively carried out according to error propagation modes such as random error, system error, single well and global error, and the like, and a 3 multiplied by 3 covariance matrix [ C ] at each measuring point under a wellhead coordinate system NEH is obtained]NEH。
Then, in step S5, based on the probability of the actual drilling engineering requirement, the magnification factor is selected to uniquely determine the error ellipsoid. The covariance matrix at each survey point characterizes a family of ellipsoids, with different ellipsoids containing different probabilities of borehole trajectory error. According to the requirement of the error probability of the well track, a large coefficient k can be selected and taken, so that 1 error ellipsoid is uniquely determined.
Generally, the amplification factor has a value k of 1 to 4, and the borehole trajectory error is usually evaluated with k of 2. For a well with high requirements on the borehole trajectory monitoring and control precision, the large coefficient k is preferably taken and placed to be not less than 2.8, and the probability that the borehole trajectory is located in the error ellipsoid is more than 95%.
In one embodiment, the probability-based unique determination of the error ellipsoid is determined by finding the amplification factor with the following probability-to-amplification factor relationship:
wherein: k is an amplification factor and has no dimension; p is the error probability, decimal, of the borehole trajectory. The above formula can be solved by a numerical integration method, so that the probability P that the borehole trajectory is positioned in the error ellipsoid is obtained. When the amplification factor k is 1.0 to 4.0 and the step size is 0.5, the probabilities P are 19.87%, 47.78%, 73.85%, 89.99%, 97.07%, 99.34%, and 99.89%, respectively.
In step S6, an error ellipsoid is cut from an arbitrary plane through the center of the error ellipsoid to obtain an error ellipsoid on the plane, and the spatial attitude of the plane can be represented by the normal direction of the plane, and based on the unit vector m of the normal direction of the plane, the inclination angle α of the unit vector m is usedmAnd azimuth angle phimTo characterize the spatial pose of the plane;
further, as shown in FIG. 2, taking the error ellipsoid through an arbitrary plane at the center of the sphere will result in a cross-sectional error ellipse to characterize the spatial attitude of the plane, its normal direction is represented by the unit vector m and is represented by αmAnd phimRepresenting the angle of inclination and azimuth of the plane normal. And establishing a coordinate system XYZ by taking the sphere center of the error ellipsoid as an origin, wherein the Z axis points to the normal direction of the plane, the X axis is the intersection line of the plane and the plumb surface passing through the Z axis and points to the direction of the high side, and the Y axis points to the right side horizontally.
The postures of the common space plane mainly comprise three types of horizontal plane, plumb plane and normal plane, and the horizontal section ellipse, the vertical section ellipse and the normal section ellipse are respectively obtained by intercepting an error ellipsoid through the center of a sphere at the moment αmAnd phimThe values of (A) are respectively as follows:
(1) ellipse with horizontal cross-section, taken as αm＝φm＝0；
(2) Ellipse with vertical cross-section, taken as αm＝90°，φmTaking a normal azimuth angle of a plumb plane;
(3) normal section ellipse, αmAnd phimTaken as the borehole trajectory's inclination α and azimuth φ, respectively.
The invention can characterize and evaluate borehole trajectory errors on any spatial plane, and the three situations are only special cases.
Then, in step S7, a covariance matrix on an arbitrary plane is found.
Specifically, the present invention further includes, in the step of determining the covariance matrix of the error ellipse on the plane based on the covariance matrix of the error ellipsoid, the following substeps:
based on the transformation relation between the coordinate system XYZ and the coordinate system NEH, based on the covariance matrix [ C ] under the coordinate system NEH]NEHCalculating covariance matrix [ C ] under coordinate system XYZ]XYZThe concrete calculation formula is
[C]XYZ＝[T][C]NEH[T]T(3)
Wherein
In the formula αmIs the well angle, (°) in the direction of the plane normal; phi is amAzimuth, in the direction of the plane normal, (°);
intercepting the error ellipsoid through the plane of the spherical center of the error ellipsoid to obtain the error ellipsoid, and obtaining a covariance matrix [ C ] of the error ellipsoid under the coordinate system XYZ]XYZPartitioning, and reserving relevant items of parameters X and Y to obtain a covariance matrix [ C ] of the error ellipse on the plane]XYIs composed of
In the formula: sigmaX 2、σY 2Variance in X-axis direction and Y-axis direction respectively; sigmaXYIs the covariance between the X-axis and the Y-axis.
Finally, as shown in FIG. 1, in step S8, a cross-sectional error ellipse is characterized.
Specifically, the size and attitude of an error ellipse on an arbitrary plane are determined based on a covariance matrix of the error ellipse, wherein the size and attitude of the error ellipse are characterized by two major axis radii and one deflection angle, respectively.
In the step of determining the size and the posture of the error ellipse based on the covariance matrix of the error ellipse on the plane, the size and the posture of the error ellipse are represented by two main shaft radiuses and a deflection angle of the error ellipse, wherein the deflection angle is an included angle between the two main shafts of the error ellipse and an X axis and a Y axis respectively;
calculating the radius of the main shaft and the deflection angle of the error ellipse according to the following formulas:
wherein
In the formula: r is the radius of the main axis of the error ellipse, m; λ is the covariance matrix [ C ]]XYCharacteristic value of (1), m2(ii) a θ is the deflection angle, (°) of the error ellipse.
And characterizing the uncertainty of the well track on the plane based on the size and the posture of the error ellipse on the plane, so as to evaluate the feasibility and the reasonableness of the drilling engineering design, monitor and control the implementation effect of the well track on the plane, improve the hit rate and the reservoir drilling rate of the well track, and further improve the yield and the exploitation and recovery rate of oil and gas single wells.
The present invention is further described below with reference to examples. The scope of the invention is not limited by the examples, which are set forth in the following claims.
And (3) carrying out measurement and borehole trajectory calculation on a certain horizontal well according to industrial regulations to obtain a calculation result taking true north as a reference standard, and referring to table 1. The geomagnetic field intensity of the well is 56356.51nT, the magnetic declination angle is-10.60 degrees, the magnetic dip angle is 64.72 degrees, and the meridian convergence angle is 0.876 degrees. The large coefficient k of the picking and placing was 2, and the evaluation results shown in table 2 were obtained by using the method for evaluating the borehole trajectory error on an arbitrary section according to the present invention. Table 1 and Table 2 list only a portion of the data, to be limited by space.
TABLE 1 borehole trajectory calculation results of the examples
| Well depth (m) | Oblique angle (degree) | Azimuth (°) | North coordinate (m) | East coordinate (m) | Vertical depth (m) |
| 0.00 | 0.00 | Is absent from | 0.00 | 0.00 | 0.00 |
| 900.00 | 0.00 | Is absent from | 0.00 | 0.00 | 900.00 |
| 1800.00 | 0.00 | Is absent from | 0.00 | 0.00 | 1800.00 |
| 2700.00 | 0.00 | Is absent from | 0.00 | 0.00 | 2700.00 |
| 3600.00 | 0.00 | Is absent from | 0.00 | 0.00 | 3600.00 |
| 4500.00 | 0.00 | Is absent from | 0.00 | 0.00 | 4500.00 |
| 5400.00 | 0.00 | Is absent from | 0.00 | 0.00 | 5400.00 |
| 6300.00 | 0.00 | Is absent from | 0.00 | 0.00 | 6300.00 |
| 7200.00 | 0.00 | Is absent from | 0.00 | 0.00 | 7200.00 |
| 7660.00 | 0.00 | (29.71) | 0.00 | 0.00 | 7660.00 |
| 7831.77 | 45.81 | 41.16 | 51.74 | 39.36 | 7814.05 |
| 8028.73 | 45.81 | 51.01 | 149.57 | 140.96 | 7951.35 |
| 8161.32 | 90.00 | 55.43 | 221.10 | 237.05 | 8000.00 |
| 8400.00 | 90.00 | 57.02 | 353.79 | 435.44 | 8000.00 |
| 8700.00 | 90.00 | 59.02 | 512.67 | 689.90 | 8000.00 |
| 9000.00 | 90.00 | 61.02 | 662.57 | 949.75 | 8000.00 |
| 9300.00 | 90.00 | 63.02 | 803.32 | 1214.67 | 8000.00 |
| 9600.00 | 90.00 | 65.02 | 934.73 | 1484.34 | 8000.00 |
| 9900.00 | 90.00 | 67.02 | 1056.65 | 1758.43 | 8000.00 |
| 10161.32 | 90.00 | 68.76 | 1155.00 | 2000.52 | 8000.00 |
TABLE 2 results of elliptical evaluation of borehole trajectory section errors for the present invention
In this embodiment, the method for characterizing the error ellipse of any section of the borehole trajectory obtains the error ellipse ellipsoid section error ellipses of the borehole trajectory on the horizontal plane, the plumb plane and the normal plane, and calculates the radius of the main axis (R) of each section error ellipseU,RV) And an attitude angle theta. Therefore, the uncertainty of the borehole trajectory on various planes is represented by the section error ellipse, the physical significance is clear and definite, and the method is convenient to be applied to the aspects of borehole trajectory monitoring, control and the like.
It is to be understood that the disclosed embodiments of the invention are not limited to the particular structures, process steps, or materials disclosed herein but are extended to equivalents thereof as would be understood by those ordinarily skilled in the relevant arts. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase "one embodiment" or "an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
Although the embodiments of the present invention have been described above, the above description is only for the convenience of understanding the present invention, and is not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A method for evaluating borehole trajectory error over an arbitrary cross-section, the method comprising:
acquiring inclination measurement data of a well track by using a measuring instrument according to industrial regulations, and solving a covariance matrix at each measuring point under a wellhead coordinate system NEH based on an ISCSSA standard and a model, wherein the covariance matrix represents an error ellipsoid group, and the probability that each different error ellipsoid in the error ellipsoid group contains a well track error is different;
selecting an amplification factor to uniquely determine the error ellipsoid according to the probability required by the actual drilling engineering;
intercepting the error ellipsoid by using an arbitrary plane through the spherical center of the error ellipsoid to obtain an error ellipse on the plane, and representing the spatial attitude of the plane by using the normal direction of the plane;
determining a covariance matrix of an error ellipse on the plane based on the covariance matrix of the error ellipsoid;
determining the size and the posture of the error ellipse on the plane based on a covariance matrix of the error ellipse, wherein the size and the posture of the error ellipse are respectively represented by two main shaft radiuses and a deflection angle;
and characterizing the uncertainty of the well track on the plane based on the size and the posture of the error ellipse on the plane, so as to evaluate the feasibility and the reasonableness of the drilling engineering design, monitor and control the implementation effect of the well track on the plane, improve the hit rate and the reservoir drilling rate of the well track, and further improve the yield and the exploitation and recovery rate of oil and gas single wells.
2. The method of claim 1, wherein the inclination data comprises a borehole angle, an azimuth angle, a borehole depth, and a toolface angle, and wherein the error ellipsoid has a covarianceThe difference matrix is a 3 x 3 matrix C under the wellhead coordinate system NEH]NEHWherein: n is north coordinate, m; e is the east coordinate, m; h is the vertical depth coordinate, m.
3. The method for evaluating borehole trajectory errors in arbitrary sections according to claim 2, wherein in the step of uniquely determining the error ellipsoid according to the probabilities, an amplification factor is found by using the relationship between the probabilities and the amplification factor as follows to determine the error ellipsoid:
wherein: k is an amplification factor and has no dimension; p is the error probability, decimal, of the borehole trajectory.
4. A method for evaluating borehole trajectory error on arbitrary sections according to claim 3, wherein in the step of characterizing the spatial attitude of the plane with the normal direction to the plane, the sub-steps of:
based on a unit vector m of the plane normal direction, using a skew angle α of the unit vector mmAnd azimuth angle phimTo characterize the spatial pose of the plane;
and establishing a rectangular coordinate system XYZ by taking the spherical center of the error ellipsoid as an origin, wherein the Z axis points to the normal direction of the plane, the X axis is the intersection line of the plane and a vertical plane passing through the Z axis and points to the direction of the high side, and the Y axis points to the right side horizontally.
5. The method for evaluating borehole trajectory errors in arbitrary cross-sections according to claim 4, wherein in the step of determining the covariance matrix of the error ellipse on the plane based on the covariance matrix of the error ellipsoid, the sub-steps of:
based on the transformation relation between the coordinate system XYZ and the coordinate system NEH, based on the covariance matrix [ C ] under the coordinate system NEH]NEHCalculating covariance matrix [ C ] under coordinate system XYZ]XYZThe concrete calculation formula is
[C]XYZ＝[T][C]NEH[T]T
Wherein
In the formula αmIs the well angle, (°) in the direction of the plane normal; phi is amAzimuth, in the direction of the plane normal, (°);
intercepting the error ellipsoid through the plane of the spherical center of the error ellipsoid to obtain the error ellipsoid, and obtaining a covariance matrix [ C ] of the error ellipsoid under the coordinate system XYZ]XYZPartitioning, and reserving relevant items of parameters X and Y to obtain a covariance matrix [ C ] of the error ellipse on the plane]XYIs composed of
In the formula: sigmaX 2、σY 2Variance in X-axis direction and Y-axis direction respectively; sigmaXYIs the covariance between the X-axis and the Y-axis.
6. The method for evaluating borehole trajectory errors in arbitrary sections according to claim 5, wherein in the step of determining the size and attitude of the error ellipse based on the covariance matrix of the error ellipse on the plane, the size and attitude of the error ellipse are characterized by two major axis radii of the error ellipse and a deflection angle, wherein the deflection angle is an angle between the two major axes of the error ellipse and the X-axis and the Y-axis, respectively;
calculating the radius of the main shaft and the deflection angle of the error ellipse according to the following formulas:
wherein
In the formula: r is the radius of the main axis of the error ellipse, m; λ is the covariance matrix [ C ]]XYCharacteristic value of (1), m2(ii) a θ is the deflection angle, (°) of the error ellipse.
7. The method for evaluating borehole trajectory error on any section as recited in any of claims 1 to 6, wherein a well-angle α of normal direction of said plane is usedmAnd azimuth angle phimTo characterize the arbitrary plane for evaluation of borehole trajectory errors in an arbitrary spatial attitude plane, wherein commonly used spatial planes include horizontal, vertical, and normal, when the normal to the plane is at a well angle αmAngle of well deviation phimThe values of (A) are respectively as follows:
when the plane is horizontal, α is takenm＝φm＝0；
When the plane is vertical, α is takenmTaken phi at 90 DEGmThe azimuth angle is the normal direction of the vertical plane;
when the plane is a normal plane, α is takenmAnd phimRespectively, the angle α and the azimuth angle phi of the wellbore trajectory.
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