NO840482L - DEVICE FOR BOREHOLE MEASUREMENT - Google Patents

Description

The present invention relates to instruments for measuring boreholes and particularly relates to such instruments which use acceleration and angular displacement sensors.

In many previously known borehole surveying systems

a probe is used which includes acceleration or inclinometer measuring instruments in combination with azimuth or direction determining instruments, such as magnetometers. Examples of such systems are given in US Patent Nos. 3,862,499 and 4,362,054 which describe borehole surveying instruments that use an inclinometer comprising three accelerometers to measure the borehole's deviation from the vertical along with a three-axis magnetometer for azimuth decision. Such systems are subject to errors due to a number of factors including variations in the earth's magnetic field caused by the nature of the material the borehole passes through. There have also been a number of systems that have used mechanical gyros with sway bars or gimbal suspension instead of the magnetometers for direction or rotation sensing. Due to sensitivity to shock and vibration, however, mechanical gyroscopes do not provide the desired accuracy and reliability in borehole systems. Furthermore, mechanical gyros are subject to drift and precession errors and require significant periods for stabilization. These instruments also tend to be mechanically complicated as well as expensive.

One method to reduce the inherent errors in inertial-type measurements of probe position in a borehole has been the use of Kalman filtering. Until now, the use of Kalman filtering has been limited to aligning the probe when it has stopped in the borehole, and has not been used in a dynamic sense for error reduction in measurements made while the probe is moving inside the borehole.

It is therefore an object of the invention to provide

a borehole surveying apparatus comprising a probe suitable for insertion into a borehole, a mechanism for generating a signal representing the movement of the probe in the borehole and acceleration measurement instruments in the probe for generating three acceleration signals representing components of the probe's acceleration with respect to three probe axes and a device for measuring angular rotation to generate two rotational

signals representing the angular rotation of the probe with respect to two axes of rotation of the probe. It also includes a first circuit for generating a first synthetic angular rotation signal that represents the angular rotation of the probe about a third probe axis when the probe moves, and a circuit that responds to the angular rotation signals by generating a second synthetic angular rotation signal that represents the angular rotation of the probe about the third probe axis when the probe not moving. The invention further comprises a circuit that responds to the rotation signals and the synthetic rotation signal by converting the signals representing the probe's movement in the borehole into coordinates that refer to the Earth, and calculation circuits connected to the conversion circuit and the acceleration measurement circuits to convert the acceleration signals into a first set of velocity signals and a first set of position signals representing the velocity and position of the probe in the Earth coordinate system.

The invention further includes a Kalman filter that uses the dynamic constraints of zero motion normal to the borehole to compensate for errors in the acceleration, angular rotation, and alignment data used to generate the velocity and position signals.

Reference is made to the attached drawings where:

figure 1 is an illustration of an apparatus embodying the invention, including a section through a borehole showing a probe used in connection with the apparatus for surveying the borehole;

figure 1a is a perspective drawing of the probe components; and

Figure 2 is a logic diagram illustrating the logic for calculating the position of the probe in the borehole.

Figure 1 shows representative surroundings for the preferred embodiment of the invention. Beneath the ground 10 extends a borehole which is generally denoted by the reference number 12, which is lined with a series of casing pipes 14 and 16. Inserted in the borehole 12 is a probe 18 connected to a cable coil 20 by means of a cable 22 which runs over a pulley 24 above the ground. The cable 22 serves to lower the probe 18 through the borehole 12 and also constitutes a transmission medium for transmitting data from the probe 18 to a signal processor 26 above ground. Another signal transmission line 28 can be used to provide an indication of the amount of cable being fed down the borehole 12, as well as data from the cable 22 to the signal processor 26. Although data in the invention illustrated in Figure 1 is sent to and from the probe 18 using the cable 22, data can be transferred to the equipment above ground using other devices, such as pressure pulse transmission of digital data through drilling mud such as used when measuring during drilling. The data can also be stored in a memory in the probe and retrieved at a later time.

As shown in Figure 1a, in the probe 18 there is an accelerometer unit with three axes comprising three accelerometers 32, 34 and 36. The accelerometers 32, 34 and 36 are oriented with their sensitive axes corresponding to the probe body as indicated by means of the co-ordinate system shown at 38. In the probe body coordinate system, the x-axis as indicated by x extends along the borehole and the y-axis as indicated by y b and the z-axis as indicated by z Ider orthogonal with respect to the x-axis.

In the probe 18 is also a laser gyro device 40 which comprises

two laser gyros 42 and 44. The first laser gyro 42 is oriented in the probe so that it measures the angular rotation of the probe around the y-axis, as this measured angular rotation with (Jj^,. Likewise, the second laser gyro 44 is fixed inside the probe 18 so that it will measure the probe's rotation about the z -axis which is denoted by <t>z. Because the diameter of the probe 18 is relatively small, there is not enough space to provide a laser gyro which will effectively measure the rotation about the x -axis.

Included in the preferred embodiment of the probe 18 is also a microcomputer 46 together with a memory 48. From the accelerometers 32, 34 and 36 are connected lines 50, 52 and 54 to the microprocessor which serves to transmit acceleration signals a , a and a which represent the probe's acceleration along the x b -, y b - and z b -axes. Similarly, the microprocessor 46 is connected to the alsergyro device 40 by means of lines 56 and 58 which serve to transmit the angular rotation signal cj from the y-axis-b y

the gyro 42 and the angular rotation signal u)z from the z-axis gyro 44.

In the embodiment of the invention illustrated in Figure 1a, a speed signal V"<P> is implied to be transmitted by means of a line 60 to the microprocessor 46. As shown in Figure 1, this signal would be generated by means of the rotational speed of the pulley 24 for thereby providing a measure of the speed or speed of the probe in the borehole 12 with line 60 included in the cable 22. However, there may be cases when the V^ signal can be more appropriately generated in another way, such as by counting pipe sections 14 and 16 down through the hole.

When determining the position of the probe and thus the position of the borehole, which is of course the real purpose of the invention, it is necessary to transform the various sensor signals generated in the probe body coordinate system 38 into a coordinate system that refers to the earth. Such a coordinate system is illustrated in figure 1 as shown generally at 62 where the x-axis as indicated by x<L>, is parallel to the gravity vector gL and the remaining axes y and z are orthogonal to the x^-axis and parallel to the ground . This coordinate system 62 can be called the level coordinate system where the z<L-> and y<L-> axes represent directions such as north and east.

The logic circuits by which the microprocessor 48 converts the acceleration signals on lines 50, 52 and 54, the angular velocity signals on lines 56 and 58 and the velocity signal on line 60 into position signals are illustrated in Figure 2. However, it will be understood that some of this processing can be carried out in the computer 26 which is located on the ground. As indicated above, one of the main problems in generating signals representing the position of the probe 18 relative to the Earth coordinate system x^, y^ and z^ is to accurately transform signals representing the orientation and motion of the probe from the probe body coordinate system x Id , y Id and z b to the level or ground coordinate system. One of the main purposes of the logic circuit shown in Figure 1 is to perform the coordinate transformation as accurately as possible by using Kalman filtering to compensate for the errors inherent in the various signal sources.

Definitions of the various symbols used in Figure 2 are given in Table 1 below.

Logic for updating the coordinate array information matrix

clfo" geikr kean ntyomdeft attiennr evnfinokr erlurotten asj6o4 npså sigfnigauler ne 2. co foInong gatuknz )gper to tliinl the jdenens 56 and 58. Since it is necessary to have a signal representing the rotation of the probe about the x-axis, w , to update the transformation logic in box 64, it is necessary to generate a synthetic wxfø signal. This is done when the probe 18 is stopped in the borehole 12 by means of the logic in box 66. Two of the inputs to the logic in box 66 are the angular rotation signals æ fø and u)føz on lines 56 and 58, and the third input is a signal representing the earth's rotation Q. The origin of the fi signal is indicated in line 68 where the signal as shown is composed of three vectors including Q^, and fiD representing the earth's rotation about a north direction respectively and a down direction.Also as shown in box 68, the value of fi depends on the probe's 18 latitude X.

To facilitate the operation of the logic of Figure 2 in the probe's microprocessor 46, the borehole longitude X can be stored in memory 48 and transferred to route 68 by means of line 69. The ft signal is then sent over line 70 to logic circuit 66 which generates a first synthetic CO feed signal on line 72. When the probe is stopped in drill-

xP

hole, a logic signal indicating that V is equal to zero is transmitted by means of a dotted line 74 which acts to connect the signal on line 72 to the logic 64 above line 73.

The accelerometer errors are calibrated while the probe is stopped, and the acceleration due to gravity is reset to equal and opposite the sensed acceleration.

Alternatively, when the probe is in motion through the borehole 12, another synthetic co^ signal is generated on line 78 using the logic shown in line 80. When the probe is in motion in the borehole 12, the logic signal on line 74 serve to close the switch 76 to thereby connect line 80 with line 73. As shown in Figure 2, the acceleration signals on line 50,

52 and 54 which represent the body's acceleration a, transferred above

a common line or bus 82 to the logic 78 and a delay circuit 84. The first input to the logic 78 over a common line 82 can be called fø which represents the acceleration of the probe body 18 at a first point in time. The delay circuit 84 provides another acceleration signal afø(<2>) ^or le9em over a collector line 86 to the logic 78. An acceptable time delay for the delay circuit 84 is 1/600 of a second.

In this way, synthetic angular rotation signals about the x-axis of the probe can be produced both for the case when the probe 18 is in motion and when it is stopped.

Along with the fi signal on line 70, the change in transformation logic in box 64 receives a signal on line 90 representing the angular velocity of the probe relative to the earth, as indicated by route 92. The output of the logic circuit 64 on bus 94 represents the time rate of change of the probe body to the level-coordinate transformation as a result of the acceleration signals a<*3>and the angular rotation signals w . This signal is then integrated as indicated at 96 to thereby produce a signal on bus 98 representing the transformation matrix necessary to transform signals generated in the probe body coordinate system 38 into the level coordinate system 62. The signals on line 98 representing the coordinate transformation matrix C, is transmitted through a summation node 100 to a bus line 102.

The accelerations a fø are transformed from probe body coordinates to level coordinates by means of a logic circuit 104 which has received the updated coordinate transformation matrix over busbar 102. The resulting output on busbar 106 represents the acceleration of the probe 18 in level coordinates and is transferred to a summing node 108. In the summing node 108, a signal gL on line 110 representing the acceleration due to gravity is subtracted, resulting in a signal on a bus 112 representing the probe 18 acceleration v<L>i level -coordinates. As indicated by route 113, gL is a function of probe 18 depth R^. This signal is then integrated as indicated at 114 to produce a signal on line 116 representing the velocity vL on common line 116.

The resulting velocity signal V<L> is then fed back via line 118 to logic circuit 120 which then generates signals on bus line 122 representing the centripetal acceleration resulting from the coriolis force generated by the earth's rotation. The resulting signal on header 122 is then subtracted from the acceleration signals aL in the summing node 108. As will be understood, the result is a The resulting signal on header 112 represents the acceleration of the probe 18 in the borehole taking into account gravity and acceleration generated due to the earth's rotation .

In addition to the speed signals generated by means of the inertia devices as described above, speed signals are also generated by actually measuring the movement of the probe 18 in the borehole. As previously described, the signal V<P> on line 60 may represent the probe cable speed in the borehole. This signal is transformed by the logic shown in block 124 into a velocity signal on a bus line 126 representing the velocity of the probe in probe body coordinates V . As indicated in box 24, the transformation matrix C includes an identity

P

matrix I plus a matrix £ which in matrix form represents the probe misalignment in tubes 14 and 16. The resulting velocity signal V<b>on header 126 is then transformed by

using the coordinate transformation matrix C, shown at 128, to velocity signals in the level coordinate system on busbar 130. These velocity signals are then sent through a summing node 132 to a busbar 134 and integrated as shown at 136, to generate signals on busbar 138 which represent the position coordinates R of the probe with respect to north, east and down as expressed in the level coordinates 62.

As expected, the speed signals on busbar 134 are as

is the result of real cable measurements, and the velocity signals on line 118 which are the result of inertial signal sources, are subject to various sources of error. To provide a signal 6V<L> that represents the relative error between the velocity signal on busbars 118 and 134, the signals on busbars 118 and 134 are applied to a summing node 140 which results in the velocity error signal 6V<L> in level coordinates on busbar 141 In order to compensate for the various error sources present in the generation of the velocity signals and thus the position signals, Kalman filtering is used to estimate the error correction signals.

One of the main purposes of using a reduced-order Kalman filter is to compensate for the missing or reduced inertial data. This technique makes use of the fact that over a considerable distance in the borehole, the probe 18 is forced to follow the borehole axis which can be translated into equivalent velocity information and thereby enhance the accuracy of the borehole survey. The use of dynamic constraints of this nature provides a significant advantage over the systems described in the prior art. The computational burden in the Kalman filtering operation is reduced by modeling only the most significant fault conditions. For example, the position of the probe 18 is used to resolve the external velocity VP into level coordinates to produce position coordinates.

The Kalman filter process is indicated by means of a logic block 142 which receives as input the velocity error signal 6V<L>

across busbar 141. As indicated in the logic block, the Kalman gain coefficients K are multiplied by velocity error signals 6V<L> and added to the quantities indicated in array 144. The revised values indicated in array 146 are then applied to various parts of the logic shown on

figure 2, to ensure error compensation. For example, error-compensating expressions for the position coordinates R are fed by means of a bus line 148 to a summing node 150 to provide updated position coordinates as shown at 152. Similarly, expressions for velocity errors are fed via bus line 154 to a summing node 156 and the summing node 132 to provide error compensation for the velocity signals v^ and v^. Error expression W for probe body-

to the level transform matrix C, is provided on bus 158 to summing node 100, and error expression is applied across line 160 to correct for misalignment in transform logic 124.

To enhance the efficiency of the process, the Kalman coefficients K may be stored in the memory 48 of the probe instead of being calculated downhole, as indicated by block 162.

By placing the Kalman coefficients K in the memory 48, the transformation processes can be dynamically corrected inside the probe 118 while it is in the borehole 12.

In a linear discrete Kalman filter, calculations at the covariance level eventually provide the Kalman gain coefficients K, which are then used in the calculation of expected

values of the error states y • These error states include:

^e

In the system model, the error states are a function of $, that is, the time mapping for error equations. The expression $ is equal to: where the F matrix represents the error dynamics between discrete measurements:

Equation (3) can be specified as follows:

The measurement model can be expressed as: where H represents the matrix of speed measurements:

The Kalman gain coefficients K can be represented by: where the updated error covariance is:

The matrix for noise covariance in the gyro process is defined as:

The variance q_ and gyro bias based on the non-linear reconstruction of the missing oo^ gyro is given below as:

During motion, the q^variance is assigned to the logic in block 78.

As can be seen from the discussion above, the limitations found in a wellbore surveying system where the probe 18 has substantially no movement perpendicular to the casing 14 and 16 of Figure 1 are used to facilitate error estimation and correction. . For example, an error signal is generated to correct the probe's roll orientation by differentiating the expected acceleration signals on the probe body's y- and z-axes with the sensed accelerations a and a on lines 52 and 54.

y z

As the error signals are processed over time, they improve

in addition, the estimate of the probe body-to-orbit misalignment £.

The saved gravity model 113 can be reset for

to cancel the sensed acceleration a , a and a by using

x' y z

following relation:

where Wg represents the Schuler oscillations.

The techniques described above can be used in a number of different downhole applications. For example, when measuring during drilling, the described measurement method can be used to control the drilling without it being necessary to send data to the surface. In this case, the orientation of the probe 18 is determined using the logic shown at 66 to provide level, azimuth, and device face information.

Well surveying, on the other hand, can make use of the orientation data that is developed while the probe 18 is in motion, as shown by the logic in block 78 together with the position or orientation data that is generated when the probe is stopped as shown by the logic in block 66.

Claims (8)

1. Apparatus for measuring boreholes comprehensively a borehole probe for insertion into a borehole, a control device for controlling the movement of the probe in the borehole, a device operatively connected to the control device and the probe for generating a signal representing the movement of the probe in the borehole, acceleration devices fixed inside the probe for generating three acceleration signals representing the probe's acceleration components with respect to three axes, characterized by a first angular device fixed in the probe for generating two rotation signals representing the angular rotation of the probe with respect to two axes of rotation, a device that responds to the acceleration signals and the movement signal by, when the probe is in motion, generating a first synthetic angular rotation signal representing the angular rotation of the probe about a third axis of rotation different from the two axes of rotation mentioned, a device that responds to the angular rotation signals and the movement signal by generating, when the probe is not in motion, another angular rotation signal representing the angular rotation of the probe about the third axis of rotation, a transformation device responsive to the rotation signals and the synthetic rotation signal for transforming signals representing probe motion in a probe-referenced coordinate system to an Earth-referenced coordinate system, and a first computing device operatively connected to the transforming device and the acceleration devices to transform the acceleration signals into a first set of velocity signals and a first set of velocity signals representing the velocity of the probe and a first set of position signals representing the position of the probe in the coordinate system with reference to the Earth. 2. Apparatus according to claim 1, characterized by another calculation device which is operatively connected to the transformation device to transform the movement signal into another set of speed signals representing the probe's speed and another set of position signals representing the probe's position in the coordinate system that refers to the earth . 3. System according to claim 2, characterized by a device for comparing the first set of speed signals with the second set of speed signals and generating an error signal. 4. System according to claim 3, characterized by a Kalman filter device which is operatively connected to the transformation device and the first and second calculation device for correcting the speed signals. 5. Apparatus according to claim 4, characterized in that the probe comprises a memory device for storing Kalman amplification coefficients for the Kalman filter device. 6. Apparatus according to claim 4, characterized in that the probe comprises a device for calculating Kalman amplification coefficients for the Kalman filter device. 7. Apparatus according to claim 1, characterized in that the device for producing the second synthetic angular rotation signal comprises a signal source representing the earth's angular rotation. 8. Apparatus according to claim 1, characterized in that the transformation device comprises a signal source that represents the earth's angular rotation.