Wellbore attitude measurement error analysis method based on double-vector dot product

Abstract

The invention discloses a borehole attitude measurement error analysis method based on a double-vector dot product, and relates to the technical field of oil and gas well engineering, the method comprises the following steps: determining a main error source when a triaxial magnetometer and a triaxial accelerometer are used for borehole attitude measurement; the error source comprises a sensor fixed bias, a geomagnetic field correlation error and a magnetometer scale factor error; constructing a drilling tool coordinate system and an east-north-sky coordinate system during borehole attitude measurement; respectively determining a geomagnetic component and a gravity component under a drilling tool coordinate system and an east-north-sky coordinate system; on the basis of the geomagnetic component, the gravity component and the dot product relation thereof, a borehole attitude error containing a sensor error is obtained; and according to the borehole attitude error containing the sensor error, obtaining borehole attitude errors corresponding to different error sources. The borehole attitude measurement error propagation characteristics of a measurement-while-drilling instrument or a cable inclinometer can be determined, and the borehole attitude precision under the influence of each error can be analyzed accurately.

Description

Technical Field

[0001] This invention relates to the field of oil and gas well engineering technology, and more specifically to a wellbore attitude measurement error analysis method based on double vector dot product. Background Technology

[0002] During oil and gas well drilling and production, attitude measurements need to be performed at various measurement stations along the wellbore. The accuracy of the wellbore attitude directly determines whether the drilling equipment can accurately reach the reservoir. Therefore, theoretical analysis of wellbore attitude errors plays a crucial role in sensor selection, wellbore trajectory design, and wellbore measurement result evaluation. Wellbore attitude information mainly includes: inclination angle (inc), azimuth angle (azi), and gravity tool face angle (tf). Currently, the mainstream measurement instruments used are measurement-while-drilling systems (MWD) consisting of a triaxial magnetometer and a triaxial accelerometer, or continuous cable inclinometers. The error of the triaxial accelerometer affects the measurement accuracy of the inclination angle and gravity tool face angle, while the measurement accuracy of the azimuth angle is determined jointly by the errors of the triaxial magnetometer and accelerometer.

[0003] Internationally, there are two main models in the research on wellbore attitude error: the WdW model proposed by Wolff and De Wardt in 1981 and the ISCWSA model established by the Society of Petroleum Engineers (SPE). However, the focus of these two models is on analyzing the uncertainty of wellbore trajectory measurement, and they lack in-depth analysis and theoretical derivation of the propagation mechanism of wellbore attitude error.

[0004] In China, wellbore attitude error analysis currently relies solely on instrument accuracy specifications for rough estimations of measurement errors, without a systematic analysis of the underlying principles of wellbore attitude measurement. Existing magnetometer and accelerometer-based measuring instruments are selected based on industry experience, which fails to meet the requirements for precise wellbore attitude measurement.

[0005] Therefore, in oil and gas well engineering, how to clarify the propagation characteristics of wellbore attitude measurement errors of measurement-while-drilling instruments or wireline inclinometers and accurately analyze the wellbore attitude accuracy under the influence of various errors is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of the above problems, the present invention provides a wellbore attitude measurement error analysis method based on two vector dot product, so as to at least solve some of the technical problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention provides a wellbore attitude measurement error analysis method based on two vector dot product, comprising the following steps:

[0009] The error sources for wellbore attitude measurement using a triaxial magnetometer and a triaxial accelerometer were identified; the error sources include sensor fixed bias, geomagnetic field correlation error, and magnetometer scaling factor error.

[0010] Construct a drill string coordinate system and a northeast-sky coordinate system for wellbore attitude measurement; and determine the geomagnetic and gravitational components in the drill string coordinate system and the northeast-sky coordinate system, respectively;

[0011] Based on the geomagnetic and gravitational components and their dot product relationship, the wellbore attitude error, including sensor error, is obtained.

[0012] Based on the wellbore attitude error including sensor error, the wellbore attitude error corresponding to different error sources is obtained.

[0013] Furthermore, the fixed bias of the sensor includes: zero bias error of the triaxial magnetometer and the triaxial accelerometer.

[0014] Furthermore, the geomagnetic field related errors include: magnetic declination error, magnetic inclination error, and geomagnetic field strength error.

[0015] Furthermore, the geomagnetic and gravitational components in the northeast-northeast coordinate system are expressed as follows:

[0016] m n =[m E m N m U ] T =[Bcosdipsindec Bcosdipcosdec-Bsindip] T

[0017] f n =[f E f N f U ] T =[00g] T

[0018] Where, m n Indicates the geomagnetic components in the northeast-northeast coordinate system; m E Indicates the eastward geomagnetic component of the northeast-northeast coordinate system; m N Indicates the northward geomagnetic component of the northeast-northeast coordinate system; m U f represents the celestial geomagnetic component in the northeast-northeast coordinate system; n f represents the gravitational components in the northeast-northeast coordinate system; E f represents the eastward component of gravity in the northeast-northeast coordinate system. N f represents the northward gravity component in the northeast-northeast coordinate system. Udenoted by ∠D / ∠, representing the celestial gravity component in the northeast-northeast coordinate system; dec represents magnetic declination; dip represents magnetic inclination; g represents gravity; and B represents magnetic field strength.

[0019] Furthermore, the geomagnetic and gravitational components in the drill coordinate system are expressed as follows:

[0020]

[0021] Where, m d f represents the geomagnetic components in the drill string coordinate system; d Indicates the gravity component in the drill string coordinate system; This represents the attitude transformation matrix between the northeast-sky coordinate system and the drill coordinate system.

[0022] Furthermore, the wellbore attitude error, which includes sensor error, is expressed as:

[0023]

[0024] Where δazi represents the azimuth error; δinc represents the wellbore inclination error; δtf represents the gravity tool face angle error; δm E δm represents the eastward magnetometer error in the northeast-northeast coordinate system. N δf represents the northward magnetometer error in the northeast-northeast coordinate system. E δf represents the eastward accelerometer error in the northeast-central coordinate system. N δf represents the northward accelerometer error in the northeast-northeast coordinate system. U This indicates the error of the celestial accelerometer in the northeast-central coordinate system.

[0025] Furthermore, the wellbore attitude error corresponding to the fixed bias of the sensor is obtained, specifically including:

[0026] When a fixed sensor bias exists, the outputs of the triaxial magnetometer and triaxial accelerometer are defined as follows:

[0027]

[0028] in, This indicates the actual output of the triaxial magnetometer; This represents the actual output of the triaxial accelerometer; m d and f d These are the theoretical outputs of the triaxial magnetometer and the triaxial accelerometer, respectively; εm d This indicates the fixed bias of the triaxial magnetometer; εf d This indicates the fixed bias of the triaxial accelerometer;

[0029] Incorporating the sensor's fixed bias into the wellbore attitude error, which includes the sensor's error, let δm d =εmd ,δf d =εf d Transform it to the northeast celestial coordinate system, that is Where, εm E This indicates that the eastward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm N This indicates that the northward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm U This indicates that the celestial magnetometer in the northeast-northeast coordinate system is fixedly biased; εf E This indicates that the eastward accelerometer in the northeast-central coordinate system is fixedly biased; εf N This indicates that the northward accelerometer in the northeast-central coordinate system is fixedly biased; εf U This indicates that the celestial accelerometer in the northeast-central coordinate system is fixedly biased.

[0030] The wellbore attitude error under the influence of a fixed sensor offset is then obtained, expressed as:

[0031]

[0032] Furthermore, the wellbore attitude error corresponding to the magnetometer scaling factor error is obtained, specifically including:

[0033] When only the magnetometer scaling factor error exists, the actual output of the magnetometer in each axis is expressed as follows:

[0034]

[0035] in, This represents the actual output of the eastward magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the northbound magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the astronomical magnetometer when only the magnetometer scaling factor error exists; m E This represents the theoretical output of the eastward-directing magnetometer; m N This represents the theoretical output of the northward magnetometer; m U This represents the theoretical output of the astromagnetic meter;

[0036] Based on the outputs of the magnetometers along each axis, the error parameters of the triaxial magnetometer are expressed as follows:

[0037]

[0038] When the accelerometer scaling factor error is zero, based on the wellbore attitude error including sensor error, the wellbore attitude error δzai corresponding to the magnetometer scaling factor error is... I Represented as:

[0039] δazi I=-sindeccosdec·S mE +sindeccosdec·S mN

[0040] Among them, S mE S represents the scale factor error equivalent to the eastward direction; mN S represents the northward equivalent scaling factor error; mU This represents the scaling factor error equivalent to the celestial axis.

[0041] Furthermore, the wellbore attitude error corresponding to the geomagnetic field related error is obtained, specifically including:

[0042] 1) Obtain the wellbore attitude error corresponding to the magnetic declination error:

[0043] When only magnetic declination error exists, the output of each axis component in the Northeast Celestial coordinate system is expressed as follows:

[0044]

[0045] in, This represents the actual output of the eastward magnetometer when only magnetic declination error exists. This represents the actual output of the north-facing magnetometer when only magnetic declination error exists. δdec represents the actual output of the astromagnetic meter when only magnetic declination error exists; δdec represents the magnetic declination error.

[0046] Based on the two-vector attitude determination principle, the attitude transformation matrix including sensor errors is obtained. Represented as:

[0047]

[0048] The wellbore attitude error corresponding to the magnetic declination error is expressed as:

[0049]

[0050] Among them, R z (δdec) represents the Euler matrix for rotation about the z-axis by an angle δdec, corresponding to the azimuth error δazi. II for:

[0051] δazi II =δdec

[0052] 2) Obtain the wellbore attitude error corresponding to the geomagnetic field strength error:

[0053] When only the geomagnetic field strength error exists, the actual magnetic field strength is expressed as:

[0054]

[0055] in, δB represents the actual magnetic field strength; δB represents the error in the geomagnetic field strength.

[0056] The output of the triaxial magnetometer is then expressed as:

[0057]

[0058] in, This represents the actual output of the eastward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the northward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the astromagnetic meter when only the geomagnetic field strength error exists.

[0059] The errors in each component caused by the geomagnetic field strength error are as follows:

[0060]

[0061] The magnetometers in the equivalent northeast-northeast coordinate system measured in the actual experiment were fixedly biased by δazi. III Represented as:

[0062]

[0063] Substituting the geomagnetic field strength error into the fixed offset of each magnetometer in the equivalent northeast-northeast coordinate system of the actual measurement, the wellbore attitude error corresponding to the geomagnetic field strength error is obtained, expressed as:

[0064]

[0065] 3) Obtain the wellbore attitude error corresponding to the magnetic inclination error:

[0066] When only magnetic tilt error exists, the actual magnetic tilt angle is expressed as:

[0067]

[0068] in, δdip represents the actual magnetic tilt angle; δdip represents the magnetic tilt angle error.

[0069] The output of the triaxial magnetometer is then expressed as:

[0070]

[0071] in, This represents the actual output of the eastward magnetometer when only magnetic tilt error exists; This represents the actual output of the north-facing magnetometer when only magnetic tilt error exists. This represents the actual output of the astromagnetic meter when only magnetic tilt error exists.

[0072] The errors caused by magnetic inclination are expressed as follows:

[0073]

[0074] Substituting the various error components caused by magnetic inclination into the azimuth error formula, the wellbore attitude error δazi corresponding to the magnetic inclination error is obtained. IIII , is represented as:

[0075]

[0076] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a wellbore attitude measurement error analysis method based on double vector dot product, which has the following beneficial effects:

[0077] This invention addresses the lack of theoretical and systematic analysis of wellbore attitude errors. Taking a common magnetometer + accelerometer wellbore attitude measurement scheme as an example, it derives in detail, from the measurement principle, the influence of sensor error parameters on wellbore attitude accuracy. This provides a theoretical basis for sensor selection, determination of instrument measurement accuracy indicators, and analysis of wellbore trajectory uncertainty. Furthermore, the proposed method allows for qualitative analysis of each error source to determine the relative importance of each source in the attitude error.

[0078] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0080] Figure 1 This is a schematic diagram of the wellbore attitude measurement error analysis method based on double vector dot product provided in an embodiment of the present invention.

[0081] Figure 2 A schematic diagram of the seven geomagnetic elements and the northeast-sky geomagnetic components provided for embodiments of the present invention. Detailed Implementation

[0082] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0083] To address the lack of systematic and theoretical analysis of wellbore attitude measurement errors, this invention, starting from the measurement principles of magnetometers and accelerometers and based on the principle of dual-vector attitude determination, derives and analyzes the sensor error sources affecting wellbore inclination angle, gravity tool face angle, and azimuth angle. An embodiment of this invention discloses a wellbore attitude measurement error analysis method based on dual-vector dot product. (See [link to relevant documentation]). Figure 1 As shown, it includes:

[0084] S1. Identify the error sources when using a triaxial magnetometer and a triaxial accelerometer for wellbore attitude measurement; the error sources include sensor fixed bias, geomagnetic field correlation error, and magnetometer scaling factor error;

[0085] S2. Construct the drill string coordinate system and the northeast-sky coordinate system for wellbore attitude measurement; and determine the geomagnetic and gravitational components in the drill string coordinate system and the northeast-sky coordinate system respectively;

[0086] S3. Based on the geomagnetic component and the gravity component and their dot product relationship, obtain the wellbore attitude error including sensor error;

[0087] S4. Based on the wellbore attitude error including sensor error, obtain the wellbore attitude error corresponding to different error sources;

[0088] S5. Classify and summarize the error sources according to azimuth error, well inclination angle error, and tool face angle error.

[0089] The labels S1-S4 above are for ease of explanation only and do not specify the execution order of the steps. The following sections will provide a detailed explanation of each step.

[0090] In step S1 above, the error sources for wellbore attitude measurement using a triaxial magnetometer and a triaxial accelerometer are identified; the error sources include sensor fixed bias, geomagnetic field correlation error, and magnetometer scaling factor error; wherein:

[0091] (1) Sensor fixed bias: The zero bias error of the magnetometer and the zero bias error of the accelerometer are collectively referred to as sensor fixed bias in this embodiment of the invention. The zero bias error of the magnetometer will cause a measurement deviation in the borehole azimuth angle, and the zero bias error of the accelerometer will affect the measurement accuracy of the borehole inclination angle and the tool face angle.

[0092] (2) Geomagnetic field related errors: Geomagnetic field related errors mainly include magnetic declination error, magnetic inclination error, and geomagnetic field strength error. These errors will be transmitted to the output end of the triaxial magnetometer and ultimately affect the measurement of the wellbore attitude.

[0093] (3) Magnetometer scaling factor error: Due to the magnetometer's weak resistance to magnetic interference and its susceptibility to magnetization, scaling factor error is one of the main calibration error items during periodic calibration. Therefore, this embodiment of the invention considers it as one of the main factors in error source analysis.

[0094] (4) The non-orthogonality error of the triaxial sensor is a secondary factor affecting the accuracy of the wellbore attitude. In this embodiment of the invention, it is not used as the main error source for theoretical analysis, but it can be analyzed using the error source theoretical analysis method introduced in this paper.

[0095] In step S2 above, the drill string coordinate system and the northeast-sky coordinate system are constructed for wellbore attitude measurement; and the geomagnetic and gravitational components under the drill string coordinate system and the northeast-sky coordinate system are determined respectively; specifically:

[0096] Two Cartesian coordinate systems are defined: the drill string coordinate system (d) and the northeast-central coordinate system (n). The d system refers to the coordinate system in which the three-axis magnetometer and the three-axis accelerometer are located, and the n system is the reference coordinate system. That is, the d system can coincide with the n system by rotating the Euler angle three times. The three angles rotated are the three wellbore attitude angles.

[0097] See Figure 2 As shown, based on the seven elements of geomagnetism and local geographical information, the geomagnetic and gravitational components in the northeast-northeast coordinate system can be determined to be m respectively. n and f n The specific form is as follows:

[0098] m n =[m E m N m U ] T =[Bcosdipsindec Bcosdipcosdec-Bsindip] T

[0099] f n =[f E f N f U ] T =[00g] T

[0100] Where, m n Indicates the geomagnetic components in the northeast-northeast coordinate system; m E Indicates the eastward geomagnetic component of the northeast-northeast coordinate system; m NIndicates the northward geomagnetic component of the northeast-northeast coordinate system; m U f represents the celestial geomagnetic component in the northeast-northeast coordinate system; n f represents the gravitational components in the northeast-northeast coordinate system; E f represents the eastward component of gravity in the northeast-northeast coordinate system. N f represents the northward gravity component in the northeast-northeast coordinate system. U denoted by ∠D / ∠, representing the celestial gravity component in the northeast-northeast coordinate system; dec represents magnetic declination; dip represents magnetic inclination; g represents gravity; and B represents magnetic field strength.

[0101] Based on the attitude transformation matrix between the northeast-northeast coordinate system (n) and the drill string coordinate system (d) In the drill string coordinate system, the outputs of the magnetometer and accelerometer can be represented by the attitude matrix as follows:

[0102]

[0103] Where, m d f represents the geomagnetic components in the drill string coordinate system; d Indicates the gravity component in the drill string coordinate system; This represents the attitude transformation matrix between the northeast-sky coordinate system and the drill coordinate system.

[0104] In step S3 above, the wellbore attitude error, including sensor error, is obtained based on the geomagnetic component and the gravity component and their dot product relationship; specifically:

[0105] Considering the measurement error of the sensor, the attitude matrix and the sensor output can be expressed as:

[0106]

[0107] in, This indicates the actual output of the triaxial magnetometer; This represents the actual output of the triaxial accelerometer; δm d Indicates the error of the triaxial magnetometer; δf d Triaxial accelerometer error;

[0108] Based on the two-vector attitude determination principle, the attitude transformation matrix including sensor errors can be obtained. The specific format is as follows:

[0109]

[0110] In the formula: |f n |=g,|f n ×m n |=gBcosdip,|f n ×m n×f n |=g 2 Bcosdip.

[0111] Combining the above attitude matrices, we can simplify to obtain:

[0112]

[0113] Therefore, the attitude calculation method based on the magnetometer first rotates the magnetometer around the Z-axis by a magnetic declination angle dec before transforming from the drill string coordinate system to the northeast-central coordinate system. To simplify the error analysis, the denominator in the drill string coordinate system is approximated as follows:

[0114]

[0115] Therefore, the attitude matrix can be represented as:

[0116]

[0117] Since the attitude error is small, and can be represented as an inaccuracy angle error, the error vector can be expressed as: Right now, The calculated attitude matrix and the theoretical attitude matrix can be represented as:

[0118] The calculation of the attitude matrix is ​​simplified as follows:

[0119]

[0120] in,

[0121]

[0122]

[0123] make:

[0124]

[0125] This allows us to obtain the expressions for each element in the matrix:

[0126]

[0127]

[0128] Since the elements that determine the wellbore attitude error are: These correspond to azimuth angle error, gravity tool face angle error, and well inclination angle error, respectively. The error expression for the influence of sensor measurement errors on wellbore attitude can be obtained as follows:

[0129]

[0130] Where δazi represents azimuth error; δinc represents wellbore inclination error; δtf represents gravity tool face angle error; dec represents magnetic declination; g represents gravity; δm E δm represents the eastward magnetometer error in the northeast-northeast coordinate system. N δf represents the northward magnetometer error in the northeast-northeast coordinate system. E δf represents the eastward accelerometer error in the northeast-central coordinate system. N δf represents the northward accelerometer error in the northeast-northeast coordinate system. U This indicates the error of the celestial accelerometer in the northeast-central coordinate system.

[0131] In step S4 above, the wellbore attitude error corresponding to different error sources is obtained based on the wellbore attitude error including sensor error; specifically including:

[0132] (1) Obtain the wellbore attitude error corresponding to the fixed bias of the sensor, specifically including:

[0133] When a fixed sensor bias exists, the outputs of the triaxial magnetometer and triaxial accelerometer are defined as follows:

[0134]

[0135] in, This indicates the actual output of the triaxial magnetometer; This represents the actual output of the triaxial accelerometer; m d This represents the theoretical output of the triaxial magnetometer; f d This represents the theoretical output of the triaxial accelerometer; εm d This indicates the fixed bias of the triaxial magnetometer; εf d This indicates the fixed bias of the triaxial accelerometer;

[0136] Incorporating the sensor's fixed bias into the wellbore attitude error, which includes the sensor's error, let δm d =εm d ,δf d =εf d Transform it to the northeast celestial coordinate system, that is Where, εm E This indicates that the eastward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm N This indicates that the northward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm U This indicates that the celestial magnetometer in the northeast-northeast coordinate system is fixedly biased; εf E This indicates that the eastward accelerometer in the northeast-central coordinate system is fixedly biased; εf N This indicates that the northward accelerometer in the northeast-central coordinate system is fixedly biased; εf U This indicates that the celestial accelerometer in the northeast-central coordinate system is fixedly biased.

[0137] The wellbore attitude error under the influence of a fixed sensor offset is then obtained, expressed as:

[0138]

[0139] Generally, the accelerometer error is much smaller than the magnetometer error, meaning the accelerometer error term in the orientation error formula can be omitted. However, when there are significant deviations in the magnetometers along each axis, these terms should be retained. Thus, the attitude error caused by the fixed bias of the magnetometer and accelerometer can be obtained.

[0140]

[0141] (2) Obtain the wellbore attitude error corresponding to the magnetometer scaling factor error, specifically including:

[0142] Scale factor error is measured as a percentage in the specifications of triaxial magnetometers, typically as a percentage of full scale. Therefore, scale factor error can also be characterized, to some extent, as the bias caused by the scale factor error. In the northeast-northeast coordinate system, if only the sensor scale factor error is considered, the actual output of the magnetometer in each axis can be expressed as:

[0143]

[0144] in, This represents the actual output of the eastward magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the northbound magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the astronomical magnetometer when only the magnetometer scaling factor error exists; m E This represents the theoretical output of the eastward-directing magnetometer; m N This represents the theoretical output of the northward magnetometer; m U This represents the theoretical output of the astromagnetic meter;

[0145] Based on the outputs of the magnetometers along each axis, the error parameters of the triaxial magnetometer are expressed as follows:

[0146]

[0147] Based on the above formula derivation, the formula can be rewritten as follows. Assuming the accelerometer scale factor error is zero, the terms containing accelerometer error can be omitted. Finally, the orientation error under the influence of the magnetometer scale factor error can be obtained as follows:

[0148] δazi I =-sindeccosdec·S mE +sindeccosdec·S mN

[0149] Among them, S mE S represents the scale factor error equivalent to the eastward direction; mN S represents the northward equivalent scaling factor error; mU This represents the scaling factor error equivalent to the celestial axis.

[0150] (3) Obtain the wellbore attitude error corresponding to the geomagnetic field related error, specifically including:

[0151] 1) Obtain the wellbore attitude error corresponding to the magnetic declination error:

[0152] When only magnetic declination error exists, the output of each axis component in the Northeast Celestial coordinate system is expressed as follows:

[0153]

[0154] in, This represents the actual output of the eastward magnetometer when only magnetic declination error exists. This represents the actual output of the north-facing magnetometer when only magnetic declination error exists. This represents the actual output of the astromagnetic meter when only magnetic declination error exists; δdec represents the magnetic declination error; δdec represents the magnetic declination error;

[0155] Based on the two-vector attitude determination principle, the attitude transformation matrix including sensor errors can be obtained. The specific format is as follows:

[0156]

[0157] The wellbore attitude error corresponding to the magnetic declination error is expressed as:

[0158]

[0159] Among them, R z (δdec) represents the Euler matrix for rotation about the z-axis by an angle δdec, corresponding to the azimuth error δazi. II for:

[0160] δazi II =δdec

[0161] As can be seen from the formula, the error caused by magnetic declination can be attributed to the rotational attitude error angle generated by rotating around the Z-axis, where the Z-axis corresponds to the azimuth angle.

[0162] 2) Obtain the wellbore attitude error corresponding to the geomagnetic field strength error:

[0163] When only the geomagnetic field strength error exists, the actual magnetic field strength is expressed as:

[0164]

[0165] in, δB represents the actual magnetic field strength; δB represents the error in the geomagnetic field strength.

[0166] The output of the triaxial magnetometer is then expressed as:

[0167]

[0168] in, This represents the actual output of the eastward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the northward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the astromagnetic meter when only the geomagnetic field strength error exists.

[0169] As can be seen from the expression, the error caused by the geomagnetic field strength can be attributed to an additive error, which can be equivalent to a fixed zero bias for each component. Therefore, similar to the aforementioned analysis method, this error term will generate a small-angle attitude error term. However, a more concise expression is needed. Let the azimuth error δazi be... III Rewritten as:

[0170]

[0171] The above equation represents the fixed bias of each magnetometer in the equivalent northeast-northeast coordinate system of actual measurements. Substituting the components of the geomagnetic field strength error along each axis into the above equation, it can be simplified to:

[0172]

[0173] Since the accelerometer's fixed bias is much smaller than the magnetometer's fixed bias, the azimuth error caused by the geomagnetic field strength error can be approximated as zero. This shows that, ideally, the magnetometer measurement results are error-free. When there is an error in the total magnetic field strength, each of the three-axis components will increase the error proportionally, without affecting the azimuth measurement. However, in reality, the total magnetic field strength error will always be reflected in the magnetometer measurement results of each axis. When we use the theoretical total field strength as the reference vector, the error in the total magnetic field strength can be attributed to the sensor's fixed bias.

[0174] 3) Obtain the wellbore attitude error corresponding to the magnetic inclination error:

[0175] When only magnetic tilt error exists, the actual magnetic tilt angle is expressed as:

[0176]

[0177] in, δdip represents the actual magnetic tilt angle; δdip represents the magnetic tilt angle error.

[0178] The northeast celestial component of the magnetometer is then expressed as:

[0179]

[0180] in, This represents the actual output of the eastward magnetometer when only magnetic tilt error exists; This represents the actual output of the north-facing magnetometer when only magnetic tilt error exists. This represents the actual output of the astromagnetic meter when only magnetic tilt error exists.

[0181] The errors caused by magnetic inclination are expressed as follows:

[0182]

[0183] Therefore, the magnetic inclination error can be equivalent to a fixed offset in the northeast-northeast coordinate system. Substituting this into the azimuth error formula, we can obtain the wellbore attitude error δazi corresponding to the magnetic inclination error. IIII ,Right now:

[0184]

[0185] In step S5 above, the error sources are classified, organized, and summarized according to azimuth angle error, well inclination angle error, and tool face angle error; specifically:

[0186] For simplicity, the simplified trigonometric functions are: sd = sindec, cd = cosdec, cdip = cosdip, tdip = tandip. These can be used to obtain the wellbore attitude error caused by the errors of the magnetometer and accelerometer in the geomagnetic scheme, as shown in Table 1.

[0187] Table 1. Distribution of Wellbore Attitude Errors in Magnetometer Measurement Scheme

[0188]

[0189] Next, a specific embodiment will be used to illustrate the wellbore attitude measurement error analysis method based on the two-vector dot product provided in the above-described embodiments of the present invention.

[0190] Combining the wellbore attitude measurement error analysis method based on dual vector dot product proposed in this invention, the attitude measurement accuracy of inclinometers or measurement-while-drilling subs, composed of triaxial magnetometers and triaxial accelerometers, can be estimated by combining the accuracy indicators of sensors. For example, the accuracy indicators of a magnetometer can be obtained from the manual of a certain type of magnetometer, and the accuracy indicators of an accelerometer can be obtained from a certain type of accelerometer. The errors related to the geomagnetic field can be obtained from the geomagnetic model. The geomagnetic model is not limited to the "Zhang Heng-1" satellite global geomagnetic field model CGGM 2020.0 and the International Geomagnetic Reference Field (IGRF).

[0191] The error parameters are as follows:

[0192] ① Fixed bias of the magnetometer: X: 100nT, Y: 100nT, Z: 100nT;

[0193] ②Magnetometer scaling error: X: 0.01, Y: 0.02, Z: 0.03;

[0194] ③ Magnetic inclination error of the geomagnetic field: 0.5°;

[0195] ④ Magnetic declination error of the Earth's magnetic field: 0.2°;

[0196] ⑤ Fixed bias of the accelerometer: X: 0.1mg, Y: 0.1mg, Z: 0.1mg;

[0197] For example, considering only error parameter ①, the fixed bias of the magnetometer is substituted into the formula:

[0198]

[0199] The accelerometers in the east, north, and sky directions are all fixed with an offset of 0. The azimuth angle error, well inclination angle error, and tool face angle error are calculated respectively.

[0200] When considering only error parameter ②, the scaling error is substituted into the formula:

[0201] δazi I =-sindeccosdec·S mE +sindeccosdec·S mN

[0202] The well inclination angle error and tool face angle error are not affected by the magnetometer scaling error; therefore, only the azimuth angle error needs to be calculated.

[0203] When considering only error parameter ③, the magnetic tilt error is substituted into the following formula, and the accelerometer is fixed at 0, so that the azimuth error can be solved.

[0204]

[0205] When only considering error parameter ④, the magnetic declination error can be directly added to the azimuth error without additional calculation.

[0206] When considering only error parameter ⑤, the fixed bias of the accelerometer is substituted into the formula:

[0207]

[0208] The magnetometers for the east, north, and sky directions are all fixed with an offset of 0. The azimuth error, well inclination angle error, and tool face angle error are calculated respectively.

[0209] By substituting various errors into the corresponding attitude error expressions, the quantitative values ​​of the impact of each error source on the wellbore attitude measurement accuracy can be calculated. Table 2 below directly presents the calculation results:

[0210] Table 2 Calculation results of the influence of different error sources on attitude error

[0211]

[0212] The influence of different error sources on the attitude angles can be estimated from the error distribution of each attitude angle. For example, the main factor affecting the azimuth angle error is the fixed bias of the magnetometer, while the influence of the accelerometer bias on the azimuth angle is negligible. The magnetic declination error is the direct source of error affecting the azimuth angle accuracy, and it depends entirely on the accuracy of the geomagnetic model. Secondly, the scaling error of the magnetometer also has a certain impact on the azimuth angle. The accuracy of the well inclination angle and tool face angle is mainly determined by the accuracy of the accelerometer, while the accuracy of the magnetometer has no effect on the two horizontal angles.

[0213] The above process completes the independent analysis of the impact of each error source on the wellbore attitude accuracy. The estimation results show the proportion of each error source in the attitude error.

[0214] In addition, it is necessary to evaluate the overall accuracy of wellbore attitude measurement by the inclinometer or measurement-while-drilling system to determine whether the instrument can meet the needs of actual engineering applications under this index. A comprehensive judgment can be made by combining the attitude error at different angles. Table 3 below shows the attitude error results at different attitude angles.

[0215] Table 3. Comprehensive error of wellbore attitude at different attitude angles

[0216]

[0217] First, the attitude matrix can be calculated based on the various attitude angles. The main formula is as follows:

[0218]

[0219] Taking the transpose of the above attitude matrix transforms the sensor error components to the northeast-northeast coordinate system. Substituting these components into the attitude error expressions for each error allows us to solve for the wellbore attitude angle error. Taking the magnetometer's fixed offset as an example, the fixed offset for the three axes is given as 100nT. This value represents the fixed offset of the three-axis magnetometer in the drill string coordinate system, denoted as εm. d By combining the attitude matrix, it can be converted into error components in the northeast-northeast coordinate system, which is... Furthermore, εm n =[εm E εm N εm U ] T Substitute the error components into the attitude error expression:

[0220]

[0221] The wellbore attitude error generated by this single error source can be obtained.

[0222] Next, each error parameter is processed using the same method, converted into error components in the northeast-northeast coordinate system, and substituted into the attitude error expressions.

[0223] Finally, the sum of the wellbore attitude errors generated by each error source is calculated as the comprehensive error. The comprehensive error is then calculated sequentially for different attitude angles.

[0224] It should be noted that the nine attitude angles listed in the table above are one example and are not intended to limit the implementation conditions. If a more accurate estimate of the overall attitude error is required, the overall attitude error under multiple attitude angles can be added for analysis.

[0225] It should be noted that the evaluation method for attitude angle comprehensive error can be selected according to the actual engineering situation, using different error analysis probability methods, such as the root mean square value of the error, standard deviation, etc.

[0226] It should be noted that in the method provided by the above embodiments of the present invention, random noise can be added to each attitude error in combination with the noise level of the sensor to obtain a more accurate comprehensive error estimation result.

[0227] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0228] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A wellbore attitude measurement error analysis method based on two vector dot product, characterized in that, Includes the following steps: The error sources for wellbore attitude measurement using a triaxial magnetometer and a triaxial accelerometer were identified; the error sources include sensor fixed bias, geomagnetic field correlation error, and magnetometer scaling factor error. Construct a drill string coordinate system and a northeast-sky coordinate system for wellbore attitude measurement; and determine the geomagnetic and gravitational components in the drill string coordinate system and the northeast-sky coordinate system, respectively; Based on the geomagnetic and gravitational components and their dot product relationship, the wellbore attitude error, including sensor error, is obtained. Based on the wellbore attitude error including sensor error, the wellbore attitude error corresponding to different error sources is obtained.

2. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 1, characterized in that, The fixed bias of the sensors includes the zero bias error of the triaxial magnetometer and the triaxial accelerometer.

3. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 1, characterized in that, The geomagnetic field related errors include: magnetic declination error, magnetic inclination error, and geomagnetic field strength error.

4. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 1, characterized in that, The geomagnetic and gravitational components in the northeast celestial coordinate system are expressed as follows: m n =[m E m N m U ] T =[Bcosdipsindec Bcosdipcosdec-Bsindip] T f n =[f E f N f U ] T =[00g] T Where, m n Indicates the geomagnetic components in the northeast-northeast coordinate system; m E Indicates the eastward geomagnetic component of the northeast-northeast coordinate system; m N Indicates the northward geomagnetic component of the northeast-northeast coordinate system; m U f represents the celestial geomagnetic component in the northeast-northeast coordinate system; n f represents the gravitational components in the northeast-northeast coordinate system; E f represents the eastward component of gravity in the northeast-northeast coordinate system. N f represents the northward gravity component in the northeast-northeast coordinate system. U denoted by ∠D / ∠, representing the celestial gravity component in the northeast-northeast coordinate system; dec represents magnetic declination; dip represents magnetic inclination; g represents gravity; and B represents magnetic field strength.

5. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 4, characterized in that, The geomagnetic and gravitational components in the drill string coordinate system are expressed as follows: Where, m d f represents the geomagnetic components in the drill string coordinate system; d This represents the gravity component in the drill string coordinate system; This represents the attitude transformation matrix between the northeast-central coordinate system and the drill coordinate system.

6. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 4, characterized in that, The wellbore attitude error, which includes sensor errors, is expressed as: Where δazi represents the azimuth error; δinc represents the wellbore inclination error; δtf represents the gravity tool face angle error; δm E δm represents the eastward magnetometer error in the northeast-northeast coordinate system. N δf represents the northward magnetometer error in the northeast-northeast coordinate system. E δf represents the eastward accelerometer error in the northeast-central coordinate system. N δf represents the northward accelerometer error in the northeast-northeast coordinate system. U This indicates the error of the celestial accelerometer in the northeast-central coordinate system.

7. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 6, characterized in that, Obtaining the wellbore attitude error corresponding to the fixed sensor offset, specifically including: When a fixed sensor bias exists, the outputs of the triaxial magnetometer and triaxial accelerometer are defined as follows: in, This indicates the actual output of the triaxial magnetometer; This represents the actual output of the triaxial accelerometer; m d This represents the theoretical output of the triaxial magnetometer; f d This represents the theoretical output of the triaxial accelerometer; εm d This indicates the fixed bias of the triaxial magnetometer; εf d This indicates the fixed bias of the triaxial accelerometer; Incorporating the sensor's fixed bias into the wellbore attitude error, which includes the sensor's error, let δm d =εm d ,δf d =εf d Transform it to the northeast celestial coordinate system, that is Where, εm E This indicates that the eastward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm N This indicates that the northward magnetometer in the northeast-northeast coordinate system is fixedly biased; εm U This indicates that the celestial magnetometer in the northeast-northeast coordinate system is fixedly biased; εf E This indicates that the eastward accelerometer in the northeast-central coordinate system is fixedly biased; εf N This indicates that the northward accelerometer in the northeast-central coordinate system is fixedly biased; εf U This indicates that the celestial accelerometer in the northeast-central coordinate system is fixedly biased. The wellbore attitude error under the influence of a fixed sensor offset is then obtained, expressed as:

8. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 6, characterized in that, Obtain the wellbore attitude error corresponding to the magnetometer scaling factor error, specifically including: When only the magnetometer scaling factor error exists, the actual output of the magnetometer in each axis is expressed as follows: in, This represents the actual output of the eastward magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the northbound magnetometer when only the magnetometer scaling factor error exists. This represents the actual output of the astronomical magnetometer when only the magnetometer scaling factor error exists; m E This represents the theoretical output of the eastward-directing magnetometer; m N This represents the theoretical output of the northward magnetometer; m U This represents the theoretical output of the astromagnetic meter; Based on the outputs of the magnetometers along each axis, the error parameters of the triaxial magnetometer are expressed as follows: When the accelerometer scaling factor error is zero, based on the wellbore attitude error including sensor error, the wellbore attitude error δzai corresponding to the magnetometer scaling factor error is... I Represented as: δazi I =-sindeccosdec·S mE +sindeccosdec·S mN Among them, S mE S represents the scale factor error equivalent to the eastward direction; mN S represents the northward equivalent scaling factor error; mU This represents the scaling factor error equivalent to the celestial axis.

9. The wellbore attitude measurement error analysis method based on double vector dot product according to claim 6, characterized in that, Obtain the wellbore attitude error corresponding to the geomagnetic field related error, specifically including: 1) Obtain the wellbore attitude error corresponding to the magnetic declination error: When only magnetic declination error exists, the output of each axis component in the Northeast Celestial coordinate system is expressed as follows: in, This represents the actual output of the eastward magnetometer when only magnetic declination error exists. This represents the actual output of the north-facing magnetometer when only magnetic declination error exists. This represents the actual output of the astromagnetic meter when only magnetic declination error exists; δdec represents the magnetic declination error. Based on the two-vector attitude determination principle, the attitude transformation matrix including sensor errors is obtained. Represented as: The wellbore attitude error corresponding to the magnetic declination error is expressed as: Among them, R z (δdec) represents the Euler matrix for rotation about the z-axis by an angle δdec, corresponding to the azimuth error δazi. II for: δazi II =δdec 2) Obtain the wellbore attitude error corresponding to the geomagnetic field strength error: When only the geomagnetic field strength error exists, the actual magnetic field strength is expressed as: in, δB represents the actual magnetic field strength; δB represents the error in the geomagnetic field strength. The output of the triaxial magnetometer is then expressed as: in, This represents the actual output of the eastward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the northward magnetometer when only the geomagnetic field strength error exists. This represents the actual output of the astromagnetic meter when only the geomagnetic field strength error exists. The errors in each component caused by the geomagnetic field strength error are as follows: The magnetometers in the equivalent northeast-northeast coordinate system measured in the actual experiment were fixedly biased by δazi. III Represented as: Substituting the geomagnetic field strength error into the fixed offset of each magnetometer in the equivalent northeast-northeast coordinate system of the actual measurement, the wellbore attitude error corresponding to the geomagnetic field strength error is obtained, expressed as: 3) Obtain the wellbore attitude error corresponding to the magnetic inclination error: When only magnetic tilt error exists, the actual magnetic tilt angle is expressed as: in, δdip represents the actual magnetic tilt angle; δdip represents the magnetic tilt angle error. The output of the triaxial magnetometer is then expressed as: in, This represents the actual output of the eastward magnetometer when only magnetic tilt error exists; This represents the actual output of the north-facing magnetometer when only magnetic tilt error exists. This represents the actual output of the celestial magnetometer when only magnetic tilt error exists. The errors caused by magnetic inclination are expressed as follows: Substituting the various error components caused by magnetic inclination into the azimuth error formula, the wellbore attitude error δazi corresponding to the magnetic inclination error is obtained. IIII , represented as:

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