RU2186966C2 - Method of determination and compensation of inclinometer magnetic deviation - Google Patents

Abstract

FIELD: precision instrumentation engineering; applicable in improved determination of azimuth orientation of movable object using three-axis flux-gate inductive transducers and accelerometers. SUBSTANCE: method is realized with use of three-axis inductive transducer in entire rotation sphere of inclinometer including steps: determination of deviation error of azimuth during calibration, approximation of azimuth deviation error by results of calibration by Fourier harmonic series (including determination of coefficients of series by any suitable method, for instance, by method of least squares), compensation of azimuth deviation error in inclinometer working conditions algorithmically in computer. Azimuth deviation error is determined during calibration depending on all three angles of inclinometer orientation (azimuth, longitudinal rotation and zenith). Approximation is effected by continuous dependence directly on angle of longitudinal rotation by Fourier harmonic series up to 7-th order. Approximation is effected by continuous dependence on azimuth angle by Fourier harmonic series, at least, to 5-th order. Approximation is effected by discontinuous dependence of error on zenith angle. For which purpose, two above described operations are carried out on different zenith angles alternating every 10-15 dwg for determination of dependence on azimuth and angle of longitudinal rotation. In this case, formed on each zenith angle is respective set of coefficients B_0,0, B_1,0...B_10,14, which is stored in configuration file. EFFECT: higher accuracy of azimuth determination.

Description

 The invention relates to precision instrumentation and can be used to improve the determination of the azimuthal orientation of a moving object using triaxial flux-gate induction sensors and accelerometers as sensors.

 Advantageously, the invention can be applied to the examination of oil and geophysical wells. In particular, the method can be used in magnetogravity type inclinometers (hereinafter referred to as the inclinometer), used to determine the curvature and trajectory of uncased drilling (or using non-magnetic LBT pipes) wells during directional drilling.

 A known method of eliminating errors in determining the azimuth (US patent 4,761,889) arising if the Earth's field at the measurement location was distorted by external magnetic fields. The method is based on the assumption that the magnitude of the vector of the magnetic field of the Earth at a given point in the terrain and the angle of inclination of this vector are known in advance. The results of measurements of the magnetic field obtained using magnetometers are compared with a previously known vector, and the required correction to azimuth is determined by the difference in their values. The disadvantage of this method is that it is designed to determine the error only from external distortions of the magnetic field, while modern drilling methods use non-magnetic materials for casing and the influence of external distorting fields becomes insignificant. In addition, when examining open-hole wells, the influence of external fields (from downhole equipment and rigs) also becomes insignificant, therefore, the problem of the intrinsic accuracy of the measuring device (inclinometer) comes to the forefront, due to the intrinsic errors of the sensors, which cannot be eliminated in this method. In addition, this method requires knowledge of the Earth's magnetic field vector, and its determination requires accurate measuring equipment that does not have its own magnetic deviation, with sensors that do not have their own instrumental errors, which is unattainable in practice. Thus, in this method, a methodological error is in advance due to the uncertainty of the Earth's magnetic field vector and the neglect of the intrinsic errors of the measuring device.

 There is another way to improve the determination of the azimuth and dip (zenith angle) of the well (US patent 4,956,921). The method consists in the fact that before starting work, an initial exhibition is made to determine the vectors of the magnetic field and the gravitational field of the Earth, as well as the angle between them. Then, in the process of measuring the well, the uncertainties of the sensor readings are found - according to estimates of the variances of the sources of uncertainty (instrumental errors), estimates of the covariances between the sources of uncertainties and the readings of the sensors. After that, the errors of the sensor readings are compensated by minimizing the conditional function of the total error.

 The disadvantage of this method is that only instrumental errors of the sensors are considered, such as the offset of the zero signal, the slope error, the errors of the sensors based; errors arising from the presence of magnetically hard and magnetically soft iron are not considered. In addition, the need for an initial exhibition at the well, firstly, gives an additional error from the influence of metal equipment available at the wellhead, and secondly, it increases the working time at the well, which is economically disadvantageous. And also the fact that errors are compensated not by the azimuthal angle, but directly in the readings of the sensors, which leads to an increase in the total random error according to the readings of the flux gates of the induction sensor, because The correction is introduced into the channel of each fluxgate with some random error, and as a result of the correlation of these errors, the error can increase by a factor of three. In addition, in this method, as in the previous one, it is required to know with high accuracy the vector of the Earth's magnetic field at the point of survey, which is practically impossible under actual operating conditions of inclinometers. In addition, random errors arise due to the fact that random parameters are used, such as estimates of variances of sources of uncertainties and estimates of covariances between them, determined statistically, with a random error; thus, an additional error is introduced when trying to correct the readings of accelerometers and fluxgates by an approximate method.

 Therefore, the above methods are not able to make measurements optimally, with high accuracy.

 A known method of compensating for azimuthal angle errors from magnetic deviation, used in magnetic compasses operating in only one plane (horizontal), is described, for example, in [2]. This method cannot be applied to inclinometers, because in the case of using a triaxial induction sensor, the task is to compensate for deviation in the entire sphere of rotation of the device. The specificity of this problem is that the magnetic field of deviation is not anisotropic in various directions and depends on the orientation of the device in three-dimensional space, which means that this method is not applicable for inclinometers. In addition, compensation is carried out through the use of a special deviation device, which complicates the design of the device, increases the complexity of the settings and gives an error in the settings, because it is done manually.

 The closest prototype is a method of compensating for azimuthal angle errors in an inclinometric transducer (patent RU 2102596, MKI E 21 V 47/02 of 01/20/98). The method consists in the fact that the corrections are formed in the form of continuous functions approximating the dependences of the systematic errors of the converters on the given parameter values represented by the measured parameter values, and also that the corrections are formed in the form of continuous functions approximating the differences between the measured values and the specified parameter values depending on the measured values of the parameters.

 This method has several significant disadvantages. Firstly, continuous functions approximating the measured value of the orientation parameter (or its deviation from the set value) are described as functions of one (of the same name) parameter. Other factors available in the approximating function reflect only the features of the construction and operating conditions of the inclinometer. However, in the case of the actual use of the inclinometer, the task is to compensate for deviation in the entire sphere of its rotation, i.e. depending on all three angles describing the spatial orientation of the inclinometer. Because the magnetic field of deviation is not anisotropic in different directions and depends on the orientation of the inclinometer in three-dimensional space.

 Secondly, to calculate the correction to the parameter, the function describing this correction is substituted with the parameter value measured in the same measure, but since the parameter is measured with an error (moreover, an error depending on the orientation of the inclinometer), it can also an error occurs.

 Thirdly, the method assumes a graphoanalytic (rather than automatic) method for selecting the form of the error function, most suitable for its mathematical description, and also a graphoanalytic method for determining the amplitudes of harmonics.

 In addition, practice shows that the expansion of the error function in a Fourier series to the second and even third order does not provide optimal accuracy for determining the correction.

 The purpose of the invention is to improve the accuracy of determining the azimuthal angle due to the method of calibrating the deviation error of determining the azimuth, which would introduce a correction as a continuous function not in the sensor readings, but in the azimuthal angle, which does not require knowing the Earth's magnetic field vector, which does not require an initial exposure before at the beginning of each well measurement, introducing an amendment to the measurements algorithmically in the calculator in order to eliminate the instrumental error of deviation compensation, which is inevitable during it appears when entering compensation manually.

где γ - угол продольного вращения инклинометра, град;
Δψ - поправка азимута, град;
A₀, A₁ ... A₁₄ - коэффициенты аппроксимации, определяемые методом наименьших квадратов; для чего инклинометр устанавливают на заданный азимут и обеспечивают его вращение вокруг продольной оси, при этом производят непрерывную регистрацию результатов измерений для последующей обработки, далее аппроксимируют неявной непрерывной зависимостью от азимутального угла гармоническим рядом Фурье не менее чем пятого порядка

где ψ_y - истинный азимут инклинометра, определенный по шкале установки;
В_0,0, B_1,0 . .. B_10,14 - коэффициенты аппроксимации, описывающие зависимость коэффициентов А₀, A₁ ... А₁₄, а следовательно, и ошибки азимута от азимутальной ориентации инклинометра, определяемые методом наименьших квадратов,
для определения последних инклинометр устанавливают на различные азимуты, чередующиеся через 30^o, и производят вышеописанную операцию по определению зависимости ошибки от угла продольного вращения, при этом также производят непрерывную регистрацию измерений для последующей обработки, далее аппроксимируют релейной или ступенчатой зависимостью ошибки от зенитного угла, для чего на различных зенитных углах производят две вышеописанные операции по определению зависимости от азимута и угла продольного вращения, при этом на каждом зенитном угле формируют соответствующий набор коэффициентов В_0,0, B_1,0 . . . B_10,14, хранящийся в файле конфигурации, с помощью которых во время рабочих измерений вводят поправку к определяемому азимуту в зависимости от зенитного угла посредством выбора набора коэффициентов В_0,0, B_1,0 . . . В_10,14 из файла конфигурации, после чего зависимость от азимута определяют посредством подстановки коэффициентов В_0,0, B_1,0 ... B_10,14 в формулы

где ψ_и - азимут, измеренный инклинометром, взятый с предыдущего такта, скорректированный на предыдущем такте,
далее зависимость от угла продольного вращения определяется посредством подстановки коэффициентов A₀, A₁ ... А₁₄ формулу

найденную поправку Δψ далее учитывают в показаниях инклинометра.The goal is achieved by the method proposed in this application. A method for determining and compensating for the intrinsic magnetic deviation of an inclinometer using a triaxial induction sensor in the entire scope of the inclinometer rotation, including determining the azimuth deviation error during calibration, approximating the azimuth deviation error from the results of calibration with the Fourier harmonic series, including determining the coefficients of the series using the least squares method, and compensating for the deviation error azimuth in the operating mode of the inclinometer algorithmically on a computer. In this case, the azimuth deviation error is determined during calibration, depending on all three angles of orientation of the azimuth inclinometer, longitudinal rotation and zenith, and is approximated by a continuous dependence directly on the longitudinal rotation angle by the Fourier harmonic series up to the seventh order

where γ is the angle of longitudinal rotation of the inclinometer, deg;
Δψ - azimuth correction, degrees;
A ₀ , A ₁ ... A ₁₄ - approximation coefficients determined by the least squares method; why the inclinometer is set to a given azimuth and its rotation around the longitudinal axis is provided, while the measurement results are continuously recorded for subsequent processing, then they are approximated by an implicit continuous dependence on the azimuthal angle of not less than fifth order Fourier harmonic series

where ψ _y is the true azimuth of the inclinometer, determined on the scale of the installation;
B _0.0 , B _1.0 . .. B _10.14 - approximation coefficients describing the dependence of the coefficients A ₀ , A ₁ ... A ₁₄ , and therefore the azimuth errors from the azimuthal orientation of the inclinometer, determined by the least squares method,
to determine the latter, the inclinometer is set to different azimuths, alternating through 30 ^o , and the above operation is performed to determine the dependence of the error on the angle of longitudinal rotation, while also continuously recording measurements for subsequent processing, then approximate the relay or stepwise dependence of the error on the zenith angle, for which, at different zenith angles, carry out the two operations described above to determine the dependence on the azimuth and the angle of longitudinal rotation, with each zenith ohm carbon form a corresponding set of coefficients B _0,0, B _1,0. . . B _10.14 , stored in the configuration file, by which, during operational measurements, a correction is made to the determined azimuth depending on the zenith angle by selecting a set of coefficients B _0,0 , B _1,0 . . . _10.14 from the configuration file, after which the dependence on the azimuth is determined by substituting the coefficients B _0,0 , B _1,0 ... B _10,14 in the formula

where ψ _and is the azimuth measured by the inclinometer, taken from the previous measure, adjusted at the previous measure,
further, the dependence on the angle of longitudinal rotation is determined by substituting the coefficients A ₀ , A ₁ ... A _{14 the} formula

the found correction Δψ is then taken into account in the inclinometer readings.

 Initially, it is assumed that the instrumental errors of the accelerometers (zero offset, slope error, nonlinearity, baseline error) are determined in laboratory conditions with high accuracy, as is done with the MINK 42-100 / 60 inclinometer manufactured by Aras-plus LLC, Arzamas [1]. So, we can be sure of the accuracy of the accelerometers and, therefore, the correct determination of the zenith angles and longitudinal rotation. Instrumental errors of flux gates (zero offset, slope error, nonlinearity, base error) can also be determined during the calibration process (if possible) - this will reduce the total error of the induction sensor and generally improve the accuracy of measurements. Thus, the error in determining the azimuth will be due only to magnetic deviation from the presence of current systems, magnetically soft and magnetically hard iron in the inclinometer design.

где γ - угол продольного вращения прибора;
A₀, A₁, А₂ ... A₁₄ - коэффициенты аппроксимации.In accordance with the classical concept of the structure of magnetic deviation [2], it is divided into circular, semicircular, quarter circular (or quarter). In this case, circular deviation is understood as the zero offset of the error, semicircular as the first harmonic of the error, and the fourth as the second harmonic. Based on this, one can imagine the dependence of the error in determining the azimuth Δψ in the form of a harmonic Fourier series, and the error will depend on the orientation angles of the inclinometer. In the inventive method, it is proposed that the order of the series should exceed the second (in contrast to the classical concepts of deviation described in [2]), and the third (in contrast to the method proposed in patent RU 2102596, MKI E 21 B 47/02), because Studies have shown that higher-order harmonics of deviation are also significant and must also be taken into account. It is advisable to introduce harmonics into the dependence, for example, on the angle of longitudinal rotation (as studies have shown), at least up to the 7th order. In this case, the dependence is introduced directly (error from the angle), as shown in equation (1):

where γ is the angle of longitudinal rotation of the device;
A ₀ , A ₁ , A ₂ ... A ₁₄ - approximation coefficients.

 To determine the approximation coefficients, you can use the method of "least squares" (see reference: Korn G., Korn T. "Handbook of mathematics for scientists and engineers" M. Nauka, 1974 [3]). It is proposed that the data array necessary for this can be obtained by setting the inclinometer on the calibration unit at a given azimuth (and zenith) and rotating it on this unit around its longitudinal axis (i.e., at least one full revolution along the angle γ), continuously recording while the readings of the sensors. The process of collecting and processing measurement data can be automated using appropriate software. Thus, the dependence of the error in azimuth on the angle of longitudinal rotation at one azimuth and one zenith angle can be approximated.

При этом азимут (указанный в скобках) задается по шкале установки, на которой производится калибровка инклинометра и поэтому его можно считать истинным.By placing the inclinometer at different azimuths (for example, alternating through 30 ^o from 0 to 330 ^o ) and repeating the above operation on the same zenith angle, you can get a set of coefficients A ₀ , A ₁ ... A ₁₄ for different azimuths:

In this case, the azimuth (indicated in brackets) is set on the installation scale on which the inclinometer is calibrated and therefore it can be considered true.

где ψ - истинный азимут инклинометра, определяемый по шкале установки;
B_0,0, B_1,0 . .. B_10,14 - коэффициенты аппроксимации, описывающие зависимость коэффициентов А₀, A₁ ... A₁₄, а следовательно, и ошибки азимута от азимутальной ориентации инклинометра.Next, the dependence of the azimuth error on the azimuthal orientation of the inclinometer is determined. The decomposition order (i.e., the number of harmonics) in determining this dependence should also exceed two. For example, when alternating azimuths through 30 ^{o, it is} possible to determine up to five harmonics. This dependence is not described explicitly, but as the dependence of the coefficients A ₀ , A ₁ ... A ₁₄ on the azimuth ψ, which is approximated by the Fourier series, similarly to the dependence (1)

where ψ is the true azimuth of the inclinometer, determined by the installation scale;
B _0.0 , B _1.0 . .. B _10,14 - approximation coefficients describing the dependence of the coefficients A ₀ , A ₁ ... A ₁₄ , and therefore the azimuth error from the azimuthal orientation of the inclinometer.

To determine the approximation coefficients B _0,0 , B _1,0 ... B _10,14 , you can also use the well-known method of least squares. It is proposed that the process of collecting and processing measurement data can also be automated using appropriate software. Thus, it is possible to approximate the dependence of the azimuth error together on the azimuthal orientation and the angle of longitudinal rotation of the inclinometer at one zenith angle.

которые подставляются в уравнение (2), в зависимости от текущего зенитного угла.The dependence of the azimuth error on the zenith angle (angle of inclination of the well) is also not described explicitly, but through the dependence of the approximation coefficients B _0.0 , B _1.0 . . . At _10.14 from the zenith. The introduction of the dependence of the azimuth error on the zenith angle is complicated by the fact that it can have a non-harmonic character, therefore, in the method described here it is introduced as follows. All the above operations to determine the dependence of the error on the angle of longitudinal rotation and azimuth (i.e., the determination of the coefficients В _0,0 , B _1,0 ... В _10,14 ) are performed at several zenith angles. In this case, we obtain a series of coefficients B _0,0 (Θ _i ), B _1,0 (Θ _i ), ... B _10,14 (Θ _i ), which will be different at different zenith angles Θ _i (where Θ is the zenith angle , i = 1, 2, ...). Then, during working measurements of the well with an inclinometer using this method, stepwise or relay switching of the coefficient array is introduced

which are substituted into equation (2), depending on the current zenith angle.

в диапазоне 20^°<Θ≤40^° будет использоваться набор

в диапазоне 40^°<Θ≤60^° будет использоваться набор

в диапазоне 60^°<Θ будет использоваться набор

Эти наборы коэффициентов могут храниться в специальном файле конфигурации, а переключение с одного набора на другой будет происходить автоматически, если создать соответствующее программное обеспечение (например, как сделано в инклинометре МИНК 42-100/60 производства ООО "Арас-плюс", г. Арзамас, [1]).For example, the coefficients B _0,0 (Θ _i ), B _1,0 (Θ _i ), ... B _10,14 (Θ _i ) at the zenith angles of 10, 30, 50 and 70 ^{o are} obtained. Then in the zenith range Θ≤20 ^{° the} set will be used

in the range of 20 ^° <Θ≤40 ^{° the} set will be used

in the range of 40 ^° <Θ≤60 ^{° the} set will be used

in the range 60 ^° <Θ the set will be used

These sets of coefficients can be stored in a special configuration file, and switching from one set to another will happen automatically if you create the appropriate software (for example, as done with the MINK 42-100 / 60 inclinometer manufactured by Aras-plus LLC, Arzamas , [1]).

The algorithm in accordance with this method will be performed in the following sequence:
1) Determination of the zenith angle Θ from the readings of accelerometers previously calibrated with the necessary accuracy.

2) The selection, in accordance with the zenith angle Θ defined in the previous step, of the necessary set of coefficients B _0,0 (Θ _i ), B _1,0 (Θ _i ), ... B _10,14 (Θ _i ) from the configuration file and the calculation of the coefficients A ₀ , A ₁ ... A ₁₄ according to the formula (2). In this case, the azimuth ψ can be taken from the previous measurement step (after correction by this method), because the azimuthal angle of the well usually varies slowly in depth. And at the first measure, you can take the uncompensated angle ψ, then in this measure the correction will be determined not exactly, but with each subsequent measure everything will be more accurate, and will approach the real azimuth error for 3-4 measures (which at a sufficiently high clock frequency of the inclinometer is ≤ 1 second).

3) Calculation of the azimuthal correction Δψ according to the formula (1) using the coefficients A ₁ , A ₂ . .. And ₁₄ are found in the previous step. In this case, the angle of longitudinal rotation γ is determined from the readings of the accelerometers.

Of course, when finding the zenith angle near the switching point (in the above example, the angles 20, 40 and 60 ^o ), the inclinometer readings will be the worst, but the ranges of zenith angles and switching points can be selected in such a way that even in the worst case, the error in determining the azimuth is not will go beyond tolerance. Thus, it is possible to achieve very high accuracy in azimuth measurements by increasing the number of zenith angles at which the inclinometer is calibrated, reducing, accordingly, the switching ranges (i.e., increasing the number of switching points). Or you can reduce the complexity of the calibration process, reduce the calibration time, if you reduce the accuracy requirements (by reducing the number of zenith angles at which calibration is performed).

Sources of information
1. Continuous magnetic inclinometer cable MINK 42-100 / 60. Operation manual MINK 402115.001 OM.

 2. Mikhailov O.I., Kozlov I.M., Gergel F.S. Aviation devices. M. Engineering, 1949

 3. Korn G., Korn T. Handbook of mathematics for scientists and engineers. M. Science, 1974

 4. US Patent 4,761,889, MKI E 21 B 33/312, 1988

 5. US Patent 4,956,921, MKI E 41 B 47/22, 1990

 6. Patent RU 2102596, MKI E 21 V 47/02 of 01/20/98.

Claims (1)

A method for determining and compensating for the intrinsic inclinometer’s own magnetic deviation using a triaxial induction sensor in the entire inclinometer rotation area, including determining the azimuth deviation error during calibration, approximating the azimuth deviation error from the results of calibration with the Fourier harmonic series, including determining the coefficients of the series using the least squares method, and compensating for the deviation error azimuth in the operating mode of the inclinometer algorithmically on a computer, characterized in that the deviation error The azimuth curve is determined during calibration, depending on all three inclinometer orientation angles: longitudinal rotation, azimuth and zenith, and is approximated by a continuous dependence directly on the longitudinal rotation angle by the Fourier harmonic series to the seventh order

where γ is the angle of longitudinal rotation of the inclinometer, deg;
Δψ - azimuth correction, degrees;
A ₀ , A ₁ , A ₂ .... A ₁₄ - approximation coefficients determined by the least squares method,
why the inclinometer is set to a given azimuth and its rotation around the longitudinal axis is provided, while the measurement results are continuously recorded for subsequent processing, then they are approximated by an implicit continuous dependence on the azimuthal angle of the Fourier harmonic series of no less than fifth order

where ψ _y is the true azimuth of the inclinometer, determined on the scale of the installation;
B _0,0 , B _1,0 , ... B _10,14 - approximation coefficients describing the dependence of the coefficients A ₀ , A ₁ , ... A ₁₄ , and therefore the azimuth errors from the azimuthal orientation of the inclinometer, determined by the least squares method ,
to determine the latter, the inclinometer is set to various azimuths alternating through 30 ^o and the above operation is performed to determine the dependence of the error on the angle of longitudinal rotation, while also continuously recording measurements for subsequent processing, then approximate the relay or stepwise dependence of the error on the zenith angle, for which at the different zenith angles, the two operations described above are carried out to determine the dependence on the azimuth and the angle of longitudinal rotation, with each zenith m carbon form a corresponding set of coefficients B _0.0, B _1.0, B ... _10.14, stored in a configuration file in which the measurements during working administered correction to the azimuth determined depending on the inclination angle by selecting a set of coefficients B _0.0 , B _1.0,. . . B _10.14 from the configuration file, after which the azimuth dependence is determined by substituting the coefficients B _0,0 , B _1,0 , ... B _10,14 in the formula

where ψ _and is the azimuth measured by the inclinometer, taken from the previous measure, adjusted on the previous measure, then the dependence on the angle of longitudinal rotation is determined by substituting the coefficients A ₀ , A ₁ , ... A ₁₄ , in the formula

the found correction Δψ is then taken into account in the inclinometer readings.