CH658296A5 - APPARATUS FOR MEASURING WELL HOLES. - Google Patents

Description

The invention relates to the field of instruments for measuring boreholes, and it relates to an apparatus for measuring boreholes using probes which work on acceleration and angular displacement.

In many systems for the measurement of boreholes according to the state of the art, a probe is used comprising instruments for measuring acceleration or inclinometers in combination with instruments for determining azimuth or direction , such as magnetometers. Examples of such systems are found in US Pat. Nos. 3,862,499 and 4,362,054 which describe instruments for measuring boreholes using an inclinometer comprising three accelerometers to measure the deviation of the borehole from the vertical, and also a three-axis magnetometer for determining the azimuth. Such systems can provide erroneous results due to a number of factors, for example variations in the Earth's magnetic field caused by the nature of the material through which the borehole passes. A number of such systems are also known which have used mechanical gyros with cardanic mounting or with strap-down mounting in place of magnetometers in order to detect direction or rotation. However, mechanical gyroscopes do not guarantee the precision and reliability necessary for borehole systems, due to their sensitivity to shock and vibration. In addition, mechanical gyros are subject to drift and precession errors, and they require fairly long periods for their stabilization. These instruments also tend to be mechanically complicated and, at the same time, very expensive.

One attempt to reduce the errors involved in inertia measurement of the position of a probe in a borehole was the use of Kaiman filtering. However, to date, the use of Kaiman filtering has been limited to alignment of the probe when stopped in the borehole, and this filtering has not been used in a dynamic sense for reduction errors during the measurements which are carried out by a moving probe inside the borehole.

The apparatus according to the invention is defined in claim 1, while special embodiments and executions are the subject of the dependent claims.

The invention will now be described in more detail, by way of example of execution, in the description which follows and with reference to the drawing, in which:

fig. 1 is an illustration of an apparatus according to the invention, comprising a section of a borehole and showing a probe used in conjunction with the apparatus for measuring the borehole;

fig. 1a shows a perspective view of the components of the probe, and FIG. 2 is a logic diagram illustrating the logic used to calculate the position of the probe inside the borehole.

Fig. 1 shows an illustration of a preferred arrangement of the apparatus according to the invention. A borehole 12 extends below the ground 10; the borehole is surrounded by a number of jackets 14, 16. In the borehole 12 is a probe 18 connected by a cable 22 to a winch 20; the cable 22 is guided by a pulley 24 above the ground. The cable 22 serves to lower the probe 18 into the hole 12 and at the same time serves as a means of transmission for the data which is supplied by the probe 18 to a signal processor 26 also located above the ground. Another signal transmission line 28 can also be used to obtain an indication of the length of the cable 22 fed into the borehole 12, and also to transmit data by the cable 22 to the signal processor 26. Although the data are transmitted according to fig. 1 between the processor and the probe via the cable 22, this data can also be transmitted to the surface by other means such as pressure pulses transmitting digital data via the drilling mud as and as the hole advances, during drilling. It is also possible to store the data in the probe and work on it at another time.

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658296

As shown in fig. la, the probe 18 contains a triaxial acceleration measurement group comprising three accelerometers 32, 34 and 36. These 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 around reference 38. In this coordinate system of the probe, the X axis indicated by Xb extends along the borehole, the Y axis indicated by Yh and the Z axis, indicated by Zb, being orthogonal to the X axis \

The probe 18 also includes a gyrometric assembly 40 which comprises two laser gyros 42 and 44. The first laser gyro 42 is oriented inside the probe so that it measures the angular rotation of the probe around the axis Yb where the angular rotation thus measured is designated by cob. Similarly, the second laser gyro 44 is mounted in the probe 18 in such a way that it can measure the rotation of the probe around the axis Zb, which is designated by a> b. Since the diameter of the probe 18 is relatively small, there is not enough space to mount a laser gyro which effectively measures the rotation around the axis Xb.

The probe 18 preferably also comprises a microcomputer 46 and a memory 48. The accelerometers 32, 34 and 36 are connected by conductors 50, 52 and 54 to the microprocessor, and these conductors are used to transmit acceleration signals to X, at Y and Z representing the acceleration of the probe along the axes Xb, Yb and Z \ respectively. Similarly, the microprocessor 46 is connected to the gyrometric assembly 40 by the lines 56 and 58 which serve to transmit the angular rotation signal to "coming from the gyro of the Y axis 42, and the angular rotation signal ce> b coming from the gyro of the Z axis 44.

In the exemplary embodiment of the invention illustrated in FIG. 1a, a speed signal Vp is indicated as being transmitted by line 60 to the microprocessor 46. As shown in FIG. 1, this signal will be generated by the speed of rotation of the pulley 24, thus giving a measurement of the speed of the probe inside the borehole 12 by the line 60 which is in the cable 22. However, it there may be circumstances where the signal Vp could be created more advantageously in a different way, for example by counting the sections of the tube 14 and 16 towards the bottom of the hole.

By determining the position of the probe and, consequently, that of the borehole, which is naturally the true aim of the invention, it is necessary to transform the various detection signals which are generated in the coordinate system of the probe. 34 into a coordinate system that refers to the earth. Such a coordinate system is illustrated in FIG. 1, bearing the reference number 62, in which the axis X as indicated by XL is parallel to the gravity vector gL, and the other axes Y and Z are orthogonal to the axis X1 'and parallel to the ground. This coordinate system 62 can be called the surface coordinate system where the axes ZL and YL represent directions such as north and east.

The logic by which the microprocessor 48 transforms the acceleration signals on lines 50, 52 and 54, the angular displacement signals on lines 56 and 58, and the speed signal on line 60 into position signals, is illustrated. in fig. 2. It goes without saying that, however, part of the signal processing can be carried out in the computer 26 on the surface. As already mentioned, one of the first problems, when generating the signals which represent the position of the probe 18 relative to the coordinate system with reference to the earth XL, YL and ZL, consists in the precise conversion of the signals representing the orientation and movement of the probe 18 from the coordinate system of the probe Xb, Yb and Zb in this surface coordinate system (with reference to the earth). One of the primary objectives of the logic shown in fig. 2 is to perform this coordinate transformation as precisely as possible using Kaiman filtering to compensate for the errors inherent in the different signal sources.

In the following table, we give the definition of the different symbols used in fig. 2.

Table 1

at

=

Matrix for transforming probe coordinates

in surface coordinates

cbp

=

Transformation of the coordinates of the tube to the body of the probe

5

have

=

Acceleration along the "X" axis of the probe

ay

=

Acceleration along the "Y" axis of the probe

azb

=

Acceleration along the "Z" axis of the probe

Ç \ b

=

Acceleration vectors in coordinates of the probe in the

initial stage

10

ab d [2)

=

Acceleration vectors in coordinates of the probe in a

second phase

© Ì

=

Angular rotation around the "X" axis of the probe

(Ùy

=

Angular rotation around the "Y" axis of the probe

=

Angular rotation around the "Z" axis of the probe

15

vp

=

Probe speed along the hole

yL v m

=

Probe speed in surface coordinates, according to measurement

VI

=

Speed of the probe in surface coordinates, derived by

inertia measurement

Q

=

Angular rotation of the earth

20

£ 2n

=

Angular rotation of the earth: north component

=

Angular rotation of the earth: component down

P

=

Angular velocity of the surface relative to the earth

R

=

Position vector having the following three components:

Rn

=

north position coordinates

25

Re

=

east position coordinates

Rd

=

vertical position coordinates

X

=

Latitude

V

=

Error in probe transformation: surface Cb

4

=

Probe alignment error in the hole, w and t represent

30

both the physical conditions

K

=

Subsequent Kaiman gain coefficients

gL

=

Gravity vector: gL (RD) = Ws (Re — RD)

I

=

Identity matrix

R "

=

Earth radius

35

5VL

=

Speed errors in surface coordinates

Her

-

Accelerometer errors

=

Gyro error

P-3

=

Gyro preload errors

v

=

White measurement noise

40

11

=

Spectral density of the white noise power "Y" of gyro,

in (degree / root hour) 2

q?

=

Spectral density of the white noise power "Z" of gyro,

in (degree / root hour) 2

q3

=

Improbability of torsion (wb roll) of the probe along the

45

borehole during movement of the probe

QL

=

Variance matrix of the random gyro drift, in coordon

surface born

X "

=

Error states

Xc

=

Error dynamics between discrete measurements

50

=

Time mapping for error equations

F

=

Matrix of a dynamic error model

H

=

Speed measurement matrix

P

=

Covariance of error states

R

=

Covariance of the increase in the white measurement

ws

=

Schüler oscillation speed (approx. Vìa min)

T

=

Time constant for misalignment along the path

of the probe

{•}

=

Designates the representation of the antisymmetric matrix of the vector between braces

The logic for updating the coordinate transformation matrix Cb is given in box 64, see fig. 2. The inputs of this logic are the angular rotation signals <ab and 65 <ob on the conduits 56 and 58. Since it is necessary to have a signal which represents the rotation of the probe around the X axis ( cob) to update the transformation logic in box 64, a synthetic signal cob must be generated. This is done when the

658,296

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probe 18 is stopped in the borehole 12, by means of the logic which is in the box 66. Two of the inputs of the logic in the box 66 are the angular rotation signals coj and rab on lines 56 and 58, and the third input is a signal representing Earth's rotation Q. The origin of this signal Q is indicated in box 68, in which, as shown, the signal £ 1 is composed of three vectors, including fìN and fìD which represent the rotation of the earth around north and, respectively, in a downward direction. It is also shown in box 68 that the value of Q depends on the latitude X of the probe 18. In order to facilitate the operation of the logic according to FIG. 2 in the microprocessor 46 of the probe, the latitude X of the borehole can be stored in the memory 48 and transmitted to the box 68 by the line 69. The signal Q is then transmitted by the line 70 to the logic 66 which generates a first synthetic signal <Bb on line 72. When the probe is stopped in the borehole, a logic signal which indicates that Vp is equal to zero is transmitted by means of the dotted line 74; at the same time, the signal on line 72 is connected to logic 64 via line 73.

Accelerometer errors are calibrated while the probe is stopped, and the acceleration due to gravity is set to be equal and opposite to the detected acceleration.

Alternatively, when the probe is moving in the borehole 12, a second synthetic signal cob is generated on the line 80 by means of the logic represented in the box 78. When the probe moves in the borehole 12, the logic signal on line 74 serves to close the switch 76 which connects line 80 with line 73. As can be seen in FIG. 2, the acceleration signals on lines 50, 52 and 54 and which represent the acceleration of the probe, are transmitted by a bus 82 to the logic 78 and a timing circuit 84. The first input of the logic 78 by the bus 82 can be designated as au) which represents the acceleration of the probe 18 to a first phase. The delay circuit 84 creates a second acceleration signal from the probe a} ,, which is transmitted by a bus 86 to the logic 78. For example, a good delay made by the delay circuit 84 is Vaoo second. In this way, synthetic signals of angular rotation around the axis X of the probe are produced both for the case where the probe 18 is in motion and for the case where it is stopped.

The transformation logic which is in the box 64 receives, next to the signal Q on the line 70, a signal on the line 90 which represents the angular speed of the probe compared to the ground, as it is indicated in the box 92. The output of logic 64, Cb, on bus 94 represents the speed of movement of the probe, expressed in surface coordinates, resulting from calculations from the acceleration signals ab and the angular rotation signals cob. This output signal is then integrated as indicated at 96, and a signal Q is produced on the bus 98 which represents the transformation matrix necessary for converting the signals generated in the probe coordinate system 34 in the surface coordinate system 62 The signals on line 98, which represent the transformation matrix of coordinates C, are transmitted via an addition junction 100 to a bus 102.

The accelerations ab are converted from the coordinates of the probe to the surface coordinates by the logic 104 which received the coordinate transformation matrix updated by the bus 102. The resulting output on the bus 106 represents the acceleration of the probe 18 in surface coordinates which is transmitted to an addition junction 108. A signal g1- on line 110 is subtracted in addition junction 108 and represents acceleration by gravity, and a signal is obtained on a bus 112 representing the acceleration vL of the probe 18 in surface coordinates. As indicated by the box 113, g1- is a function of the depth Rd of the probe 18. This signal is then integrated as indicated at 114 to produce a signal on line 116 which represents the speed vL on the bus 116.

The signal for the resulting speed VL is then fed back to line 118 in logic 120 which, in turn, generates signals on the bus 122 representing the centripetal acceleration resulting from the Coriolis force which is created by the rotation of the Earth. The resulting signal on the bus 122 is in turn subtracted from the acceleration signals aL in the addition junction 108. It will be appreciated that the resulting signal on the bus 112 represents the acceleration of the probe 18 in the hole drilling, having taken into consideration the gravity and the acceleration created by the rotation of the earth.

In addition to the speed signals generated by the inertia means as described above, speed signals are also produced by the actual measurement of the movement of the probe 18 in the borehole. As already described, the signal Vp on line 60 can represent the speed of the cable from which the probe is suspended in the borehole. This signal is transformed by means of the logic represented in the box 124 into a speed signal on a bus 126, a signal which represents the speed of the probe in probe coordinates is Vb. As indicated in box 124, the transformation matrix Cp comprises an identity matrix I plus a matrix i; which represents in matrix form the misalignment of the probe 18 in the tubes 14 and 16. The resulting speed signal Vb on the bus 126 is then transformed by means of the transformation matrix of coordinates 20 C ^, represented by 128, into speed signals V „in surface coordinates on the bus 130. These speed signals are then transmitted by an addition junction 132 to a bus 134 and integrated as shown in 136 to generate on the bus 138 signals representing the coordinates of position R of the probe relative to north, east and down, as expressed by the surface coordinates 62 (fig. 1).

As would be expected, the speed signals on the bus 134, resulting from the actual measurements on the suspension cable, and the speed signals on the line 118, resulting from the sources of inertia signals, are subjected to different sources of errors. In order to be able to create a 5VL signal representing the relative error between the speed signals on buses 118 and 134, these signals on buses 118 and 134 are applied to an addition junction 140 which gives a speed error signal 8VL in surface coordinates on the bus 141. In order to compensate for the various sources of errors which appear during the generation of the speed signals and, consequently, of the position signals, Kaiman filtering is used to estimate signals error correction.

One of the main purposes of using a reduced order Kaiman 40 filter is to compensate for missing or distorted inertia data. This technique takes advantage of the fact that, over a significant distance in the borehole, the probe 18 is forced to follow the axis of the borehole, which can be translated into equivalent speed information, and a improvement of the measurement accuracy of the borehole. The use of dynamic obligations of this nature gives a significant advantage over the prior art systems. The complexity of the calculation in the Kaiman filtering operation is reduced when we are content to model only the most significant error orders. For example, the attitude of the probe 18 is used to resolve the external speed Vp into surface coordinates to produce position coordinates.

The Kaiman filtering process is indicated by a logic block 142 which receives as an input the error signal of the speed 8VL by the 55 bus 141. As indicated in the logic block, the Kaiman K gain coefficients are multiplied by the signal speed error 5VL and added to the quantities indicated in the matrix 144. The revised values indicated in the matrix 146 are then applied to different parts of the logic, shown in fig. 2, so to perform error compensation. For example, the error compensation terms for position coordinates R are applied via bus 148 to an addition junction 150 to create updated position coordinates, see reference 152. Similarly, error terms for speed are applied by the bus 154 to 65 the addition junction 132 to carry out the error compensation of the speed signals V „. The error terms y for the transformation matrix of coordinates C |; are on bus 158 and arrive at addition junction 100, and the error terms are applied

5

658,296

via line 160 to correct the misalignment Ç in the transformation logic 124.

In order to improve the efficiency of this process, the Kaiman K coefficients can be stored in memory 48 inside the probe instead of being calculated each time at the bottom of the hole, as indicated by the box. 162. When the Kaiman K coefficients are placed in memory 48, the transformation methods can be corrected dynamically inside the probe 18 while the latter is in the borehole 12.

In a discrete linear Kaiman filter, the calculations at the level of the covariance finally give the Kaiman gain positions K which are then used in the calculation of the expected values of the error states Xc. These error states are defined by:

X, =

SR SV V

In the system model, the error states are a function of 4>, namely the temporal mapping of the error equations. The time © is equal to:

€> =; I- | -F At

Eq (2)

in which the matrix F represents the error dynamics between discrete measures:

SR sY v

L t

= F

8R 8V V

. \ J

+ noise

Eq (3)

Equation (3) can be detailed as follows: SR = {VL} V - 8 V + C! R {Vb} Ç + Clv

—Ws 0 0

8V =

0 —Ws 0 0 0 -Ws.

Eq (4)

8R— {2fì} 8V— {A} 1? + ChEa Eq (5)

K = P (-) HT [HP (-) HT + R] 1 Eq (10)

in which the discount of error covariance is equal to:

P (+) = [I-KHP] H Eq (11)

The noise covariance matrix of the gyro operation is defined as follows:

Eq (1)

QL = CE

q, 0 0 0q20 .0 Oqs.

this

Eq (12)

The variance q3 and the preload of the gyro | i3, based on the nonlinear reconstruction of the missing gyro cox, are given as follows:

q, = 3.6 ^

R3 =

-4.5 ^ / q

Eq (13)

20 in which q = q, = q2.

During the movement, q3 becomes the variance associated with the logic of block 78.

As emerges from the above discussion, the constraints ap-25 starting from a borehole measurement system where the probe 18 makes a practically zero movement perpendicular to the lining tube 14 and 16 (fig. 1) are used to facilitate the estimation of the error and its correction. For example, an error signal is generated to correct the roll attitude of the probe by differentiating the acceleration signals expected on the Y and Z axes of the probe by the accelerations detected ay and az on the lines. 52 and 54.

In addition, as the error signals are worked over time, the estimate of the misalignment Ç of the probe on its way is improved.

35 The module 113, where gravity has been stored, can be zeroed in order to suppress the detected accelerations ax, ay and az, using the following relation:

V = {ï2} \ | / + Cfeg

= -lç + w

Eq (7)

The measurement model can be expressed as follows:

8Vb = HX = + v Eq (8)

in which H represents the speed measurement matrix:

5Vb = Cb {VL} \ | / - {v} £ + Cb8V + v Eq (9)

The Kaiman K gain coefficients can be represented by the expression:

gL (RD) = Ws (Re-RD) Eq (14)

Eq (6) in which Ws represents the Schüler oscillations.

The techniques described above can be used in a number of different applications in boreholes. For example, when you want to measure during drilling, the 45 measurement method described can be used to guide the drill without the need to transmit data to the surface. In this case, the attitude of the probe 18 is determined using the logic illustrated at 66 to obtain information on the leveling, the azimuth and the surface of the tool.

n / a Good measurement, on the other hand, can use the attitude data developed while the probe 18 is in motion, as provided by the logic in block 78, simultaneously with the attitude data generated when the probe is stopped , which is obtained in logic block 66.

2 sheets of drawings

Claims (8)

658,296 2 1. Apparatus for measuring boreholes, comprising: - a probe adapted to be inserted into the borehole; - control means for controlling the movement of the probe in the borehole; - Means in functional relation with the probe and the control means, adapted to generate a signal representing the movement of the probe inside the borehole; - acceleration means fixed inside the probe, to generate three acceleration signals representing the components of the acceleration of the probe along three axes; - first angular means fixed inside the probe to generate two rotation signals representing the angular rotation of the probe along two axes of rotation; Means responding to the acceleration signals and to the movement signal to generate, when the probe is in motion, a first synthetic signal of angular rotation representing the angular rotation of the probe around a third axis of rotation which is different from said axes two axes of rotation; - Means responding to the angular rotation signals and the movement signal to generate, when the probe is not in motion, a second angular rotation signal representing the angular rotation of the probe around said third axis of rotation; Transformation means responding to the rotation signals and to the synthetic rotation signal to transform signals representing the movement of the probe in a coordinate system with reference to the probe, into a coordinate system with reference to the earth, and - first calculation means (104) functionally connected to the transformation means (64) and to the acceleration means (32, 34, 36) for converting said acceleration signals (50, 52, 54) into a first series of speed signals, representing the speed of the probe (18). 2. Apparatus according to claim 1, comprising in addition second calculation means in functional relation to the transformation means for converting the movement signal into a second series of speed signals representing the speed of the probe, and a second series of signals position representing the position of the probe, in the coordinate system with reference to earth. 3. Apparatus according to claim 2, comprising means for comparing the first series of speed signals with the second series of speed signals, and for generating an error signal. 4. Apparatus according to claim 3, further comprising a Kaiman filtering device (142) whose input is a source (141) of speed error signals and whose output (158) is functionally connected to the transformation means (64) and the first (104) and second (128) calculation means, for correcting the speed signals. 5. Apparatus according to claim 4, characterized in that the probe comprises memories for memorizing the Kaiman gain coefficients of the Kaiman filters. 6. Apparatus according to claim 4, characterized in that the probe comprises means for calculating the Kaiman gain coefficients for said Kaiman filters. 7. Apparatus according to claim 1, characterized in that the means generating said second synthetic angular rotation signal comprise a source of signals representing the angular rotation of the earth. 8. Apparatus according to claim 1, characterized in that the transformation means comprise a source of signals representing the angular rotation of the earth.