NL8400558A - DRILLING HOLE INSERTION GUIDANCE SYSTEM. - Google Patents

Description

jr et υ LN 5560-27 Ned.M / EvF>

• X

Short designation: Borehole inertial guidance system.

The invention is in the field of borehole measuring instruments and in particular to borehole measuring instruments using acceleration and angular displacement sensors.

Many well known borehole measurement systems use a probe that includes accelerometer or inclinometer measuring instruments in combination with azimuth or direction determining instruments such as magnetometers. Examples of such systems are provided in U.S. Pat. Nos. 3,862,499 and 4,362,054, which disclose borehole gauges using an inclinometer, which includes three accelerometer gauges for measuring borehole deviation from the vertical along a three-axis magnetometer for azimuth determination. Such systems are subject to errors due to a number of factors including variations in the geomagnetic field caused by the nature of the material through which the borehole 15 passes. Also, a number of systems have utilized gimbal-suspended or "strap-down" mechanical gyros instead of scanning the direction or rotation magnetometers. However, due to the sensitivity to shock and vibration, mechanical gyroscopes do not provide the desired accuracy and reliability for borehole systems. Furthermore, mechanical gyros are subject to drift and precession errors and require significant periods of time to settle for stabilization. These instruments also tend to be mechanically complex as well as expensive.

A first approach to reducing the errors inherent in taking inertia probe in-borehole measurements has been to use the Kalman filter. However, up to the present time, the use of the Kalman filter has been limited to probe alignment when it was plugged into the borehole and has not been used in a dynamic error reduction scan in measurements made while the probe is moving within the probe. borehole.

The object of the invention is therefore to provide a borehole measuring device comprising a probe suitable for insertion into a borehole; a mechanism for generating a signal showing the displacement of the probe in the borehole? and Accelerometer Measurement Instruments within the Probe to Generate Three Acceleration Signals, which display the acceleration components of the Probe relative to 8400558 - 2 - * *

1 I

of three probe axes and an angular rotation measuring device for generating two rotation signals, which represent the angular rotation of the probe with respect to two probe rotation axes. The device also includes a first circuit for generating a first synthetic angular rotation signal, which displays the angular rotation of the probe about a third probe axis as the probe moves, and a circuit responsive to the angular rotation signals for generating a second synthetic angular rotation signal showing the angular rotation of the probe about the third probe axis when the probe is not moving.

The invention further includes a circuit responsive to the rotational signals and the synthetic rotational signal for transforming the signals representing the movement of the borehole probes in coordinates referring to ground and computational circuits connected to the transform circuit and the acceleration metering circuits for converting the acceleration signals into a first set of speed signals and a first set of position signals representing the speed and position of the probe in the earth coordinate system.

The invention further includes a Kalman filter using the dynamic coercive means of nui displacement perpendicular to the borehole to compensate for acceleration errors, angular rotation and alignment data used to generate the velocity and position signals.

The invention will be explained in more detail below with reference to the figures of the accompanying drawings.

FIG. 1 is an illustration of a device embodying the invention, comprising a cross-section through a borehole, showing a probe used in the borehole measuring device; Fig. la is a perspective drawing of the probe components; and FIG. 2 is a logic circuit illustrating the logic for calculating the location of the probe in the borehole.

In Fig. 1, a representative environment is illustrated for the preferred embodiment of the invention. Borehole 10 extends a borehole, generally indicated with 12, which is lined 35 with a number of borehole formwork 14 and 16. In the borehole 12, a probe 18 is inserted connected to a cable reel 20 by means of a cable 22, which runs over an overhead pulley 24. The cable 22 serves to lower the probe 18 through the borehole 12 and provides 8400558% - 3 - in addition: a transmission medium for transferring data from the probe 18 to an overhead signal processor. Another signal transmission line 28 can be used to provide an indication of the amount of cable 22 being squeezed into the borehole 12 as well as data from the cable 22 to the signal processor 26. Although according to the invention illustrated in Figure 1 transferred to and from the probe 18 by means of the cable 22, data can be transferred upwards by other means, such as pressure pulses, which transmit digital data via a drilling mud, for example, in a measurement during drilling situation. The data can also be stored in a memory in the probe and retrieved at a later time.

As shown in Figure 1a, within the probe 18 is a triaxial accelerometer package comprising three accelerometers 32, 34 and 15 36. The accelerometers 32, 34 and 36 are oriented with their sensitive axes corresponding to the body of the probe as indicated by the coordinate system shown at 38. In the probe body coordinate system, the x axis indicated by x extends along the borehole and the y axis indicated by y and the z axis indicated by 3b Jb 20 through z are perpendicular to the x axis. Probe 18 also includes a laser gyros assembly 40, which includes two laser gyros 42 and 44. The first laser gyro 42 is oriented within the probe to measure the angular 1b rotation of the probe about the y axis, the angular rotation thus measured is indicated by. Similarly, the second laser gyro 44 is mounted within the probe 18 such that it the probe rotation will measure around the z axis indicated by φ. Since z the diameter of the probe 18 is relatively small, there is not enough space to provide a laser gyro, which will effectively measure rotation around the xbas.

The preferred embodiment of the probe 18 also includes a microcomputer 46 along with a memory 48. Connected to the microprocessor from accelerometers 32, 34 and 36 are lines XV z 50, 52 and 54, which serve to transmit acceleration signals a, a and a, representing the acceleration of the probe along the 35 x, y and z axes, respectively. Similarly, the microprocessor 46 is connected to the laser gyro assembly 40 by 1b lines 56 and 58, which serve to transmit the angular rotation signal vanuit from the y-axis gyro 42, and the angular rotation signal 8400558 from> 4. the z-axis gyro 44.

In the embodiment of the invention shown in Fig. 1a, a speed signal is indicated as being transferred by a line 60 to the microprocessor 46. As shown in Fig. 1, this signal will be generated by the rotational speed of the pulley 24, which is a measure of the velocity of the probe in the borehole 12, the line 60 being included in the cable 22. However, there may be circumstances when the V signal could be generated more profitably in another manner such as counting the 10 pipe sections 14 and 16 down into the hole.

In determining the location of the probe and thus the location of the borehole, which is of course the end object of the invention, it is necessary to transform the different sensor signals generated in the body coordinate system 38 into a coordinate system, which is referred to as earth. Such a coordinate system is shown in Fig. 1 as generally indicated by 62, wherein the x axis, as indicated by xL, is parallel to the

gravity vector gL and the other axes y and z are perpendicular to L.

the X: axis and parallel to the earth. This coordinate system 62 can be called the level coordinate system with the and y ** axes representing directions such as north and east.

The logic with which the microprocessor 48 converts the acceleration signals on lines 50, 52 and 54, the angular speed signals on lines 56 and 58 and the speed signal on line 60 to 25 positioning signals is illustrated in FIG. 2. However, it will be apparent. that part of this operation could be performed in the top 26 computer. As previously indicated, one of the major problems in generating signals which represent the location of the probe 18 relative to the

L L L

30 Earth coordinate system .X, y and z is to accurately convert signals showing the orientation and displacement of the probe 18 from the body.

Jd - jb £) display coordinate system x, y and z to the level or ground coordinate system. One of the primary objectives of the logic shown in Figure 1 is. performing the coordinate transformation as accurately as possible using the Kalman filter technique to compensate for the errors inherent in the various signal sources.

Definitions of the various symbols used in Figure 2 are provided in Table I below.

8400558 «*

- 5 TABLE I

c £ = Probe body to equalize the coordinate transformation matrix

C ° = Pipe to probe body coordinates transform P

a ^ = Acceleration along 'x' axis of the body a '= Acceleration along' y 'axis of the body 5 a = Acceleration along' z 'axis of the body z 1b a ^ = Acceleration vectors in probe body coordinates at a first time & a ^ = Acceleration vectors in probe body coordinates at a second time = Angular rotation about the 'x' axis of the probe body oi = Angular rotation about the 'y' axis of the probe body 10 oi = Angular rotation about the 'zT axis of the probe body z VP = Speed of the probe along the pipe V1, = Speed of the probe in level coordinates as measured m V ^ = Speed of the probe in level coordinates derived from the inertia 15 Ω = Angular rotation of the earth Ω ^ = Angular rotation of the Earth - North component '8 ^ = Angular rotation of the Earth Down (Down) component p = Angular velocity of the level relative to the Earth R = Position vector with the following three components: 20 = North position coordinate

Rg - East position coordinate Rjj - Down position coordinate X = latitude

L

ψ = Error in body to CT transformation level

b 25 ξ = Misalignment of the probe body in the pipe K = SuB optional Kalman amplification coefficients L lg - == Gravity vector g (R ^ l = 30 8400558 a. I- - 6 - I = Unit matrix Rg = Radius of the Earth (SVL = Speed errors in level coordinates ea = Accelerometer errors 5 ε · = Gyro errors g μ ^ = Gyro control voltage errors v = White noise measurement 2 q ^ = 'y' gyro white noise power spectral density in (degree / root hour) 2 - 'z' gyro white noise power spectral density in (degree / root hour) 10 q_ = Uncertainty of twisting (roll w) of probe along the borehole,

«J X

while the probe is moving QL = Gyro random-way variance matrix in level coordinates X = Error states e = Error dynamics between discrete measurements 15 φ = Time mapping for error comparisons F = Dynamic error model matrix H = Speed measurement matrix P = Covariance of error states R = Cocariance of white noise measurement

fK

20 W = -i / rr * Hinge oscillation speed (approx. 1/34 min.) S V Rs X - Body-cock misalignment time constant

Means the tilt symmetrical matrix representation of the oras locks vector 8400558 - 7 - V%

Logic for updating the coordinate transformation matrix C? 1 is indicated within block 64 of Fig. 2. Inputs 3d to this logic include the angular rotation signals m and ω on 3Γ 2 lines 56 and 58, since it is necessary to have a signal 5 showing the rotation of the probe about the x-axis ω3 in order to update the transformation logic in the block 64, it is necessary 3d to generate a synthetic ω signal. This is accomplished,

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when the probe 18 is plugged into the borehole 12 by the logic trapped within the block 66. Two of the inputs to the logic 3d 3d 10 in the block 66 are the angular rotational signals and ωζ over lines 56 and 58 and the third input is a signal that shows the rotation of the earth Ω. The origin of the Ω signal is indicated in block 68, in which, as shown, the signal Ω is composed of three vectors, including 0 ^. and Ωβ, which represents the rotation of Earth 15 around the north, respectively. in a downward direction. Also, as shown, within the block 68, the value of Ω depends on the geographic width λ of the probe 18. To facilitate the operation of the logic of Fig. 2 in the probe microprocessor 46, the width X of the borehole can be stored in memory 48 and transmitted to block 68 by line 69. The Ω signal is then transmitted over line 70 to logic 66, which generates a first synthetic b αχχ signal over line 72. When the probe is plugged into the borehole, a logic signal indicating VP equal to zero is emitted through a dotted line 74, making it effective to connect the signal over line 72 to logic 64 over line 73.

The accelerometer errors are calibrated while the probe is stopped and the acceleration due to gravity is reset to be equal and opposite to the scanned gear.

On the other hand, as the probe is moving through the borehole 12, a second synthetic signal is generated on line 78 by the logic shown in block 80. When the probe is moving in the borehole 12, the logic signal over line 74 will serve to close switch 76, connecting line 80 to line 73. As shown in Figure 2, the acceleration signals on lines 50, 52 and 54, representing acceleration of the body a, sent over a rail 82 to logic 78 and a delay chain 84. The first input in logic 78 via a rail 82 8400558-8 can be called , which represents the body acceleration of the probe 18 at a first time. The delay circuit 84 provides a second

The body acceleration signal a ^ through a rail 86 to the logic 78. An acceptable time delay for the delay circuit 84 is 1 / 600th of a second. In this way, synthetic angular rotation signals about the x-axis of the probe are produced both when the probe 18 is moving and when it is stopped.

Together with the Ω signal over line 70, the change in transform logic in block 64 receives a signal over line 90, which represents the angular velocity of the probe relative to Earth as

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indicated by the block 92. The output of the logic 64 on the rail 94 gives the time change speed of the probe body to level coordinate transformation resulting from the acceleration signals] d b 15 a and the angular rotation signals ω. This signal is then integrated as indicated at 96 thereby producing over the rail 98 a signal representing the transformation matrix required to convert signals generated in the body coordinate system 38 into the level coordinate system 62. The signals over the line 98, representing the coordinates-20 transformation matrix C are transmitted from an adder node 100 to a rail 102.

The gears a are converted from body coordinates to level coordinates by logic 104, which has received the updated coordinate transformation matrix through rail 102. The resulting output over the rail 106 represents the acceleration of the probe 18 in level coordinates and is transmitted to an addition node 108. From the addition node 108, a signal gL is subtracted over line 110, which represents acceleration due to gravity, resulting in a signal over a rail 112, showing acceleration 30 ^ of probe 18 in level coordinates. As indicated by block 113, gL is a function of the depth of the probe 18.

This signal is then integrated as indicated at 114 to generate a signal over line 116 representing velocity vL over rail 116.

The resulting velocity signal is then fed back through a line 118 to logic 120, which in turn generates signals across the rail representing centripedal acceleration resulting from the eoriolis force generated by the earth's rotation. The 8400558-9 signal resulting over the rail 122 is in turn subtracted from the acceleration signals a1 at the addition node 108. As a result, it will be understood that the resulting signal over the rail 112 represents the acceleration of the probe 18 in the borehole, taking into account gravity and acceleration generated by the earth's rotation.

In addition to the velocity signals generated by the inertial means as described above, velocity signals are also produced by actually measuring the displacement of the probe 18 in the p10 borehole. As previously described, signal V over line 60 may represent the wireline speed of the downhole probe. This signal is transformed by logic shown in the block 124 into a speed signal over a rail 126, which represents the speed of the solid in body coordinates V * 3. As indicated in block 24, the transformation matrix C comprises a unit matrix X plus one

P

matrix ξ, which in matrix form represents the misalignment of probe 18 in pipes 14 and 16. The resulting velocity signal V * 3 on rail 126 is then transformed by means of the coordinate transformation matrix displayed at 128 in velocity signals 20 in the level coordinate system to the rail 130. These velocity signals are then transferred via an addition node 132 to a rail 134 and integrated as shown at 136 to generate signals on the rail 138, which represent the position coordinates R of the probe to the north, east and down as expressed in the level coordinates 62.

As may be expected, the speed signals on the rail 134 resulting from actual wireline measurements as well as the speed signals on the line 118 resulting from inertial signal sources are subject to various error sources. To provide a signal SV ^, which represents the relative error between speed signal over rails 118 and 134, the signals over rails 118 and 134 are applied to an addition node 140 leading to the speed error signal in level coordinates on rail 141 To compensate for the various error sources present in the generation of the speed signals and thus position signals, Kalman filtering technique is used to estimate the error correction signals,

One of the primary purposes for using a Kalman reduced order filter is to compensate for the missing 8400558 -10 or deterioration in quality data. This technique takes advantage of the fact that the probe 18 is forced to track the borehole axis over a considerable distance in the borehole, which can be translated into equivalent velocity information, thereby improving the accuracy of the borehole measurement. The use of dynamic coercive means of this nature provides an important advantage over the systems disclosed in the prior art. The calculation burden in the Kalman filter technique is reduced by modeling only the most important error conditions, for example the behavior of the

P

Probe 18 is used to resolve the external velocity V into level coordinates to produce position coordinates.

The Kalman filtering process is indicated by a logic block 142, which receives the speed error signal 5VL via the rail 141 as input. As indicated in the logic block, the Kalman gain 15 coefficients K are multiplied by the speed error signal 5VL and applied to the amounts indicated in the matrix 144. The revised values indicated in the matrix 146 are then applied to various parts of the diagram shown in FIG. 2. displayed logic to provide error compensation. For example, error compensation terms for the position-20 coordinates R are applied by a rail 148 to an addition node 150 to provide updated position coordinates as shown at 152. Similarly, velocity error terms are applied to an addition node 156 via the rail 154. addition node 132 to provide error compensation for the speed signals 25 v1, and v ^. Error terms ψ for the body by level transformation matrix S 1

Cb are provided via the rail 158 to the addition node 100, while error terms are applied over the line 160 to correct misalignment in the transformation logic 124.

In order to improve the efficiency of the process, the Kalman coefficients K can be stored in the memory 48 within the probe instead of being calculated "down", as indicated by the block 162. By placing the Kalman coefficients K in the memory 48 , the transformation processes can be dynamically corrected within the probe 118 as it occurs. located in the borehole 12.

In a linear discrete Kalman filter, calculations at the covariance level ultimately provide the Kalman gain coefficients K, which are then used in calculating expected values of the error states X. These error conditions include: e 8400558 - il - r

SR

x 4 «y (i) e ψ ξ

^ J

5 In the system model, the error states are a function of φ, i.e. mapping the time for error comparisons. The term φ is equal to: φ »I + F Δ t (2) 10 in which the matrix F represents the error dynamics between discrete measurements: * 6ff] SR ~ -F + noise- (3) Φ Φ.

. y Ll.

15 Equation (3) is detailed as follows:

Sk = (Λψ - dV + <ξ {ν ^ ξ + c £ v (4) “W2 0 0 20 s <SV - Q -W2 0 <5R- {2Ω} SV- {&} φ + C? E SO cl y 5 / oo -w2 _ s 25 i - (nk + c £ eg (6) (7) 30

The carbon model can be expressed as: SVb = HX + v (8) e 35 where H represents the velocity measurement matrix: dvb “° L + cb <aV + υ (9) 8400558 - 12 - 1 τ

The Kalman gain coefficients K can be represented by: k = p (-) ht £ hp (-) ht + r] "1 (10) 5 where the updated error covariance is: p (+) = [ï-kh] P (11 ) 10 The covariance matrix of the gyroprocess noise is defined as: qj oo “'eL = C ^ 0 q2 0 C * (12) 0 0 q,

15 J

The variance q ^ and gyro control voltage based on the non-linear reconstruction of the missing ω gyro are given below x as: 20 q3 = 3.6 / i ”(13) 3 --4.5 / -5 where q = q ^^ = q2 -25

During displacement, q ^ the variance becomes interacting with the logic of block 78.

As can be seen from the discussion above, the coercive features inherent in a borehole survey system, where probe 18 30 has substantially zero displacement perpendicular to pipe formwork 14 and 16 of FIG. 1, are used to estimate and correct errors to ease. Thus, an error signal is generated to correct the probe roll behavior by making the expected acceleration signals on the y and z axes of the body different from the scanned gears eh a ^ on lines 52 and 54.

In addition, as the error signals are processed over a period of time, the estimate of misalignment ξ from the body to the track improves.

8400558 * »* t - 13 -

The stored gravity model 113 can be reset to omit the scanned accelerations a ^, a ^ and a ^ using the following relationship: 5 gL <V - Ws (Ee - V <U1 where W represents the Hinge oscillations, s

The technique described above can be used in a number of different borehole applications. For example, in an environment where the measurement takes place during drilling, the described survey method can be used for drilling guidance without the need to transfer data to the earth's surface. In this case, the behavior of the probe 18 is determined by using the logic illustrated at 66 to provide information on leveling, azimuth 15 and tool plane.

Wellhead measurement, on the other hand, can use the developed behavioral data, while the probe 18 moves as provided by the logic in the block 78 along with the behavioral data generated when the probe is stopped as provided by the logic in the block 66.

8400558

Claims (8)

1. Borehole measuring device comprising -a borehole probe for insertion into a borehole; control means for controlling the displacement of the probe in the borehole; - means operatively connected to the control means and the probe to generate a signal indicating the displacement of the probe in the borehole; acceleration means mounted within the probe: for generating three acceleration signals representing the acceleration components of the probe relative to the three axes; first angular means mounted within the probe to generate two rotational signals representing the angular rotation of the probe relative to two axes of rotation; Means responsive to the acceleration signals and to the displacement signal to generate a first synthetic angular rotation signal representing the angular rotation of the probe about a third axis of rotation different from the other two axes of rotation as the probe moves; Means responsive to the angular rotation signals and the displacement signal to generate, when the probe is not moving, a second angular rotation signal representing the angular rotation of the probe about the third axis of rotation; transforming means responsive to the rotation signals 25 and the synthetic rotation signal for transforming signals representing the probe displacement in a probe-referenced coordinate system to a ground-referenced coordination system; and first calculating means operatively connected to the transforming means and accelerating means for converting the accelerating signals into a first set of velocity signals; and a first set of speed signals representing the speed of the probe; and a first set of position signals representing the position of the probe in the ground-referring coordinate system. 2. Device as claimed in claim 1, characterized by second calculating means, operatively connected to the transforming means for converting the displacement signal into a second set of speed signals, which represent the speed of the probe, and a second set of position signals, which indicate the position of display the probe in the Earth-referenced coordinate system. 8400558 * w - 15 - System according to claim 2, characterized by means for comparing the first set of speed signals with the second set of speed signals and for generating an error signal. System according to claim 3, further characterized by a Kalman 5 filter operatively connected to the transforming means and the first and second calculating means for correcting the speed signals. Device according to claim 4, characterized in that the probe comprises a memory for storing Kalman gain coefficients for the Kalman filter. Device as claimed in claim 4, characterized in that the probe comprises means for basing the Kalman gain coefficients intended for the Kalman filter. 7. Device according to claim 1, characterized in that the second synthetic angular rotation signal comprises a source of signals representing the angular rotation of the earth. Device according to claim 1, characterized in that the transforming means comprises a source of signals representing the angular rotation of the earth. 8400558