CN112781577B - Novel inclinometer north-seeking calculation method - Google Patents
Novel inclinometer north-seeking calculation method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract
The invention belongs to the technical field of drilling, and particularly relates to a novel inclination measurement north-seeking calculation method which has the following specific modes: on the carrier seatMarker system OX 3 c Y 3 c Z 3 c In the middle, the vector of the gravity acceleration and the rotational angular velocity of the earth is g 3 ＝C 0 3 g 0 ，ω 3 ＝C 0 3 ω 0 The solution method depends only on the time taken for a single measurement, ω x And ω y Relative relationship of
And their specific values ω x And ω y Independent, i.e. independent of the scale factor s of the gyroscope. The scheme can eliminate north-seeking errors generated by the temperature characteristic of the scale factor, thereby improving the resolving precision of the azimuth angle. The method can effectively improve the resolving precision of the azimuth angle and is effective for all non-horizontal plane north-seeking applications. The north-seeking error generated by the temperature characteristic of the scale factor is effectively inhibited.
Description
Technical Field
The invention relates to the technical field of drilling, in particular to a novel inclination measuring and north finding resolving method.
Background
Currently, there are two main types of drilling inclinometers for a while-drilling system: one is to use a fluxgate as an orientation sensor to convert the geographical orientation of the earth by measuring the direction of the earth magnetic field so as to determine the track trend of the borehole. This measurement method requires no ferromagnetic substance within 5 meters around the fluxgate. In the second type, a gyroscope and an accelerometer are used as measuring elements, and the azimuth angle, the inclination angle and the tool face angle are calculated by measuring the rotational angular velocity and the gravitational acceleration of the earth, so that the well track trend is determined. Because the gyro is not influenced by an external magnetic field, the method is suitable for measuring the borehole trajectory under the condition of magnetic interference.
At present, two types of gyros are mainly used at home and abroad as azimuth sensors to sense the rotational angular velocity of the earth, one type is a dynamic tuning gyroscope, and the other type is a fiber optic gyroscope. In contrast, the fiber optic gyroscope is an all-solid-state optical structure, has no moving parts, and has good shock resistance and vibration resistance. The existing testing mode has a large environment temperature change range due to logging application, so that the accuracy of non-horizontal plane north-seeking in a full temperature range is restricted.
Disclosure of Invention
The invention aims to provide a novel inclination measurement north-seeking calculation method to solve the problem that the accuracy of non-horizontal plane north-seeking in the whole temperature range is restricted due to the large environment temperature change range of logging application in the conventional testing mode proposed in the background art.
1. In order to achieve the purpose, the invention provides the following technical scheme: a novel inclinometer north seeking calculation method is characterized by comprising the following steps: the novel inclinometer north seeking calculation method has the following specific mode:
in a carrier coordinate system OX 3 c Y 3 c Z 3 c In the middle, the vector of the gravity acceleration and the rotational angular velocity of the earth is g 3 ＝C 0 3 g 0 ，ω 3 ＝C 0 3 ω 0 Namely:
in the formulas (1.6) and (1.7), x, y and z are carrier coordinate systems, and omega is x And omega y Is the vector omega 3 Component in the x and y axes, g x And g y Is a vector g 3 The carrier coordinate system of the inclinometer consists of three sensitive axes of the gravity accelerometer, the z axisCoincident with the instrument axis, the sensitive axis of the gyroscope being aligned with x or y, C 0 3 For the transformation matrix from the geographical coordinate system to the carrier coordinate system, g 0 Is the acceleration of gravity, omega, in the geographic system 0 Is the angular velocity of rotation of the earth in a geographic coordinate system, g is the acceleration rate of gravity of the earth, omega e The self-rotation angular rate of the earth, A is an azimuth angle, and a is the geographical latitude of a measuring point;
the calculation formula for the well offset angle I derived from equation (1.6) is:
according to (1.6) and (1.7), two new equations are firstly constructed;
the first equation is:
ω x g y -ω y g x ＝-ω e gcosαsinAsinI(1.22)；
the second equation is:
ω x g x +ω y g y ＝-ω e g(cosαcosAsinIcosI+sinαsin2I)(1.23)；
wherein, ω is x And omega y Is the vector omega 3 Component in x and y axes, g x And g y Is a vector g 3 Components in the x-axis and y-axis;
formula (1.22) is divided by formula (1.23) to yield:
the formula (1.24) shows that the solution method depends only on the time taken by a single measurement, omega x And ω y Relative relationship of (2)
And their specific values ω x And ω y Independent, i.e. independent of the scale factor s of the gyroscope;
according to (1.8) and (1.24 Can obtain 2 azimuth angles A) 1 And A 2 Respectively as follows:
A 2 ＝π-A 1 -2γ(1.25)；
wherein γ is given by:
according to formulae (1.25), (1.26), A 1 、A 2 The numerical value of (A) is the ratio of the output rotating speeds of the gyroscope in the x direction and the y direction
Determining absolute value ω of output speed x And ω y Irrelevant, also irrelevant to the scale factor of the gyroscope;
the formula (1.25) shows that the inclination measuring and north finding method can obtain 2 azimuth angles, and the elimination of the added root is the problem to be solved;
first, ω is solved back from (1.8), (1.22) and (1.23) x Or ω y ；
Then, the azimuth angle a calculated from the equation (1.25) is substituted into the equation (1.27) 1 、A 2 Respectively obtain corresponding omega x1 And ω x2 And finally, determining the real azimuth angle A according to the following method:
ω x1 and ω x2 A large difference of a few ω x1 Omega compared with actual output of gyroscope x More closely, then A 1 Is the true azimuth angle a; if omega x2 Omega compared with actual output of gyroscope x More closely, then A 2 Is the true azimuth angle a;
ω x1 and ω x2 Very small difference, true azimuth
Compared with the prior art, the invention has the beneficial effects that:
the scheme can eliminate north-seeking errors generated by the temperature characteristic of the scale factor, thereby improving the resolving precision of the azimuth angle. The method can effectively improve the resolving precision of the azimuth angle and is effective for all non-horizontal plane north-seeking applications. The north-seeking error generated by the temperature characteristic of the scale factor is effectively inhibited.
Drawings
FIG. 1 is a schematic representation of a geographic coordinate system of the present invention;
FIG. 2 is a schematic diagram of the transformation of the geographic coordinate system and the carrier coordinate system according to the present invention;
FIG. 3 is a schematic diagram of the temperature characteristics of a fiber optic gyroscope according to the present invention;
FIG. 4 is a schematic diagram of the temperature characteristics of a dual-axis accelerometer of the present invention;
FIG. 5 is a chart of a comparison of azimuthal angle solution error for a well slope angle of I =10 deg. in accordance with the present invention;
fig. 6 is a comparison of azimuthal error for a well angle of I =30 ° in accordance with the invention;
fig. 7 is a comparison of the azimuth error at a well-off angle I =50 ° in accordance with the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention.
Example (b):
referring to fig. 1-7, the present invention provides a technical solution: a novel inclination measuring and north finding calculation method is characterized in that the specific mode of the novel inclination measuring and north finding calculation method is as follows:
as shown in fig. 1 for a geographical coordinate system OX 0 c Y 0 c Z 0 c (northeast), α is the geographic latitude of the measurement point. In the geographic coordinate system, the acceleration of gravity g 0 Angular velocity omega of rotation with the earth 0 Is composed of
Wherein, ω is e Is the earth rotation angular velocity and g is the earth gravitational acceleration rate.
As shown in fig. 2, a schematic diagram of transformation between a geographic coordinate system and a carrier coordinate system is shown, the geographic coordinate system is subjected to rotation transformation for 3 times to obtain the carrier coordinate system, and the specified rotation direction is: the rotation axis rotates counterclockwise when viewed from the positive direction to the negative direction. The rotation angles corresponding to 3 rotations are the azimuth angle a, the inclination angle I and the tool face angle T (magnetic/high side).
An azimuth angle A: geographic coordinate system OX 0 c Y 0 c Z 0 c Around OZ 0 c The axis rotation A results in a coordinate system OX 1 c Y 1 c Z 1 c Coordinate transformation matrix of C 0 1 Comprises the following steps:
x＝XcosA+YsinA
y＝-XsinA+YcosA
z＝Z
well inclination angle I: coordinate system OX 1 c Y 1 c Z 1 c Around OY 1 c Axis rotation I yielding a coordinate system OX 2 c Y 2 c Z 2 c Coordinate transformation matrix of C 1 2 Comprises the following steps:
x＝XcosI-ZsinI
y＝Y
z＝XsinI+ZcosI
tool face angle T: coordinate system OX 2 c Y 2 c Z 2 c Around OZ 2 c Rotation of the axis T to obtain a coordinate system OX 3 c Y 3 c Z 3 c Coordinate transformation matrix of C 2 3 Comprises the following steps:
x＝XcosT+YsinT
y＝-XsinT+YcosT
z＝Z
transformation matrix C from geographic coordinate system to carrier coordinate system 0 3 Comprises the following steps:
in a carrier coordinate system OX 3 c Y 3 c Z 3 c In the middle, the vector of the gravity acceleration and the rotational angular velocity of the earth is g 3 ＝C 0 3 g 0 ，ω 3 ＝C 0 3 ω 0 Namely:
in the formulas (1.6) and (1.7), x, y and z are carrier coordinate systems, omega x And omega y Is the vector ω 3 Component in x and y axes, g x And g y Is a vector g 3 The carrier coordinate system of the inclinometer consists of the sensitive axes of three gravity accelerometers, wherein the z axis is coincident with the axis of the instrument, and the sensitive axis of the gyroscope is aligned with x or y;
the calculation formula for the angle of inclination I can be derived from equation (1.6) as follows:
according to (1.6) and (1.7), two new equations are firstly constructed;
the first equation is:
ω x g y -ω y g x ＝-ω e gcosαsinAsinI(1.22)；
the second equation is:
ω x g x +ω y g y ＝-ω e g(cosαcosAsinIcosI+sinαsin2I)(1.23)；
wherein, ω is x And omega y Is the vector ω 3 Component in the x and y axes, g x And g y Is a vector g 3 Components in the x-axis and y-axis;
formula (1.22) is divided by formula (1.23) to yield:
the formula (1.24) shows that the solution method depends only on the time taken by a single measurement, omega x And ω y Relative relationship ofIs a system
And their specific values ω x And ω y Independent, i.e. independent of the scale factor s of the gyroscope;
from (1.8) and (1.24), 2 azimuths A can be obtained 1 And A 2 Respectively as follows:
A 2 ＝π-A 1 -2γ(1.25)；
wherein γ is given by:
according to formulae (1.25), (1.26), A 1 、A 2 The numerical value of (A) is the ratio of the output rotating speeds of the gyroscope in the x direction and the y direction
Determining an absolute value ω of the output speed x And omega y Irrelevant, also irrelevant to the scale factor of the gyroscope;
the formula (1.25) shows that the inclination measuring and north finding method can obtain 2 azimuth angles, and the elimination of the added root is the problem to be solved;
first, ω is solved by reverse reaction from (1.8), (1.22) and (1.23) x Or ω y ；
Then, the azimuth angle a calculated from the formula (1.25) is substituted into the formula (1.27) 1 、A 2 Respectively obtain corresponding omega x1 And omega x2 And finally, determining the real azimuth angle A according to the following method:
ω x1 and ω x2 A large difference of a few ω x1 Omega compared with actual output of gyroscope x More closely, then A 1 Is the true azimuth angle a; if omega x2 Omega compared with actual output of gyroscope x More closely, then A 2 Is the true azimuth angle a;
ω x1 and ω x2 Very small difference, true azimuth
According to the theoretical analysis, a classical inclination measuring north-seeking method is adopted, in the Beijing area, the latitude is 39 degrees and 54', when the maximum inclination angle is 50 degrees, in order to realize that the azimuth angle measurement error is better than 2 degrees, the maximum deviation of a scale factor cannot exceed 3.50 percent.
Fig. 3 is a temperature characteristic of the fiber optic gyroscope, in which the maximum change in the scale factor reaches about 8.93% in a high temperature environment.
Figure 4 is a temperature profile of a two-axis accelerometer with a test time of 3 hours. The temperature of the incubator rises from room temperature to 60 c and the temperature inside the accelerometer should be above 60 c. Because the accelerometer does not contain a temperature sensor inside, fig. 4 shows a time curve of the output data of the accelerometer in the X-axis and the Y-axis. It can be seen that the zero drift is greater for the Y-axis than for the X-axis.
Based on fiber optic gyroscope scale factor temperature drift, zero point temperature drift and angle random walk data, and biaxial accelerometer random noise temperature drift data, azimuth angle solution errors for the case of tilt angles I =10 °, I =30 ° and I =50 ° are analyzed, and for each tilt angle, four cases of azimuth angles a =0 °, a =90 °, a =180 ° and a =270 ° are considered.
Figure 5 shows the comparison of the azimuthal solution error at a skew angle I =10 °. At the moment, the azimuth angle resolving errors of the classical method and the new method are small and are smaller than +/-1 degrees. According to an error formula of the classical inclination measurement north-seeking method, the measurement error of the azimuth angle is in direct proportion to the tangent value of the well inclination angle I, when I is small, the temperature characteristic of the scale factor has little influence on the calculation precision of the azimuth angle, and the classical method can also achieve good north-seeking precision.
Fig. 6 shows the azimuthal error at a well angle I =30 °. As can be seen from the error formula of the classical method, the azimuth resolving error is proportional to the sine value of the azimuth a, so that the north-seeking error of the classical method is smaller when the azimuths a =0 ° and a =180 °, which is consistent with the data analysis results shown in fig. 6 (a) and 6 (c). When a =90 ° and a =270 °, sinA = ± 1 is the maximum positive or negative, and the azimuth angle error of the classical method is large. As shown in fig. 6 (b) and 6 (d), as the temperature increases, the scale factor temperature deviation becomes larger, and the azimuth angle resolving error of the classical method increases, and when a =90 °, the azimuth angle maximum error is 2.010 °, and when a =270 °, the azimuth angle maximum error is-1.702 °. In contrast, the azimuth angle resolving error of the new method is kept stable all the time, the maximum measurement error is only 0.549 degrees, and the azimuth angle resolving error generated by the deviation of the scale factor is effectively inhibited.
Fig. 7 shows the comparison of the azimuth angle error when the inclination angle I =50 °, and it can be seen that as the inclination angle I increases, the azimuth angle solution error of the classical inclinometer north seeking method also increases, which is consistent with the theoretical analysis result of the error formula of the classical method. As shown in fig. 7 (b) and 7 (d), as the temperature increases, the scale factor deviation becomes larger, and the azimuth angle resolving error of the classical method increases, and when a =90 °, the azimuth angle maximum error is 3.966 °, and when a =270 °, the azimuth angle maximum error is 3.543 °. In contrast, the azimuth angle resolving error of the new method is kept stable all the time, the maximum resolving error is only 0.833 degrees, and the azimuth angle resolving error generated by the deviation of the scale factor is effectively inhibited.
While there have been shown and described the fundamental principles and essential features of the invention and advantages thereof, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof; the present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein, and any reference signs in the claims are not intended to be construed as limiting the claim concerned.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. A novel inclinometer north-seeking calculation method is characterized in that: the novel inclinometer north-seeking calculation method has the following specific mode:
in a carrier coordinate system OX 3 c Y 3 c Z 3 c In the middle, the vector of the gravity acceleration and the rotational angular velocity of the earth is g 3 ＝C 0 3 g 0 ，ω 3 ＝C 0 3 ω 0 That is to say:
in the formulas (1.6) and (1.7), x, y and z are carrier coordinate systems, omega x And omega y Is the vector omega 3 Component in x and y axes, g x And g y Is a vector g 3 Component in x-axis and y-axis, the carrier coordinate system of the inclinometer consists of three sensitive axes of the gravity accelerometer, where the z-axis coincides with the instrument axis, the sensitive axis of the gyroscope is aligned with x or y, C 0 3 For a transformation matrix from the geographic coordinate system to the carrier coordinate system, g 0 For acceleration of gravity, ω, in geographic landmarks 0 Is the rotational angular velocity of the earth in a geographic coordinate system, g is the acceleration rate of the earth gravity, omega e For rotational angular velocity of the earthThe ratio A is an azimuth angle, and a is the geographical latitude of the measuring point;
the calculation formula for the well offset angle I derived from equation (1.6) is:
according to (1.6) and (1.7), two new equations are firstly constructed;
the first equation is:
ω x g y -ω y g x ＝-ω e gcosαsinAsinI(1.22)；
the second equation is:
ω x g x +ω y g y ＝-ω e g(cosαcosAsinIcosI+sinαsin2I)(1.23)；
wherein, ω is x And omega y Is the vector omega 3 Component in the x and y axes, g x And g y Is a vector g 3 Components in the x-axis and y-axis;
formula (1.22) is divided by formula (1.23) to yield:
the formula (1.24) shows that the solution method depends only on the time taken by a single measurement, omega x And ω y Relative relationship of
And their specific values ω x And ω y Independent, i.e. independent of the scale factor s of the gyroscope;
according to (1.8) and (1.24), 2 azimuths A can be obtained 1 And A 2 Respectively as follows:
A 2 ＝π-A 1 -2γ(1.25)；
wherein γ is given by:
according to the formulae (1.25), (1.26), A 1 、A 2 The numerical value of (2) is the ratio of the output rotating speeds of the gyroscope in the x direction and the y direction
Determining an absolute value ω of the output speed x And ω y Irrelevant, also irrelevant to the scale factor of the gyroscope;
the formula (1.25) shows that the inclination measuring and north finding method can obtain 2 azimuth angles, and the elimination of the added root is the problem to be solved;
first, ω is solved back from (1.8), (1.22) and (1.23) x Or ω y ；
Then, the azimuth angle a calculated from the formula (1.25) is substituted into the formula (1.27) 1 、A 2 Respectively obtain corresponding omega x1 And omega x2 And finally, determining the real azimuth angle A according to the following method:
ω x1 and ω x2 A large difference of a few ω x1 Omega compared with actual output of gyroscope x More closely, then A 1 Is the true azimuth angle a; if omega x2 Omega compared with actual output of gyroscope x More closely, then A 2 Is the true azimuth a;
ω x1 and ω x2 Very small difference, true azimuth
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| GB2369188B (en) * | 1997-12-04 | 2002-07-17 | Baker Hughes Inc | Measurement-while-drilling assembly using gyroscopic devices and methods of bias removal |
| CN102071924B (en) * | 2011-02-28 | 2012-12-12 | 重庆华渝电气仪表总厂 | Omnibearing continuous measurement method of gyroscopic clinometer |
| CN105134171B (en) * | 2015-07-29 | 2017-12-15 | 北京航空航天大学 | A kind of implementation method of the continuous inclination measurement system of two axles optical fibre gyro |
| CN105909238B (en) * | 2016-06-07 | 2023-04-25 | 北京科技大学 | Inertia measurement unit and single-axis servo continuous inclinometry method |
| CN107829721B (en) * | 2017-09-21 | 2018-10-30 | 中国科学院地质与地球物理研究所 | A kind of dynamic checkout unit suitable for drilling tool attitude measurement module |
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