GB2135783A - Borehole inertial guidance system - Google Patents

Abstract

In order to improve the accuracy of borehole survey systems utilizing probes with inertial components including inclinometers, two ring laser gyro units are included to provide rotation information 56, 58 to the system. When the probe is moving in a borehole, inclinometer information 50, 52, 54 is used 78 to produce a synthetic rotation signal 80 to take the place of a third gyro and the earth's rotation OMEGA , 68 is used 66 for a similar purpose in combination with signals from the two ring laser gyros when the probe is stopped (Vp = 0 at 74). Wire line velocity Vp, 60 is used in combination with the inclinometer and gyro information to provide signals representing the probe velocity and position (152). Coordinate transformations 64, 104, 126-130 are provided in the probe to transform the inertial signals and wire line velocity signals into earth reference coordinate system. Kalman filtering 142 incorporates non-inertial velocity data to reduce the effect of errors inherent in the generation of various input signals to the system. <IMAGE>

Description

SPECIFICATION Borehole inertial guidance system Technical Field This invention relates to the field of borehole survey instruments and in particular relates to borehole survey instruments utilizing acceleration and angular dispiacement sensors.

Background of the Invention In many prior art borehole survey systems, a probe is used that includes acceleration or inclinometer measuring instruments in combination with azimuth or direction determining instruments such as magnetometers. Examples of such systems are provided in U.S. patents 3,862,499 and 4,362,054 which disclose borehole surveying instruments using an inclinometer that includes three accelerometers to measure deviation of the borehole from vertical along with a three axis magnetometer for azimuth determination. 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 through which the borehole passes. There have also been a number of systems that have used gimballed or strap-down mechanical gyros in place of the magnetometers for direction or rotation sensing.However, due to sensitivity to shock and vibration, mechanical gyroscopes do not provide the desired accuracy and reliability for borehole systems.

Further, mechanical gyros are subject to drift and precession errors and require substantial settling periods for stabilization. These instruments also tend to be mechanically complex as well as expensive.

One approach for reducing the errors inherent in making inertial type measurements of the probe location in a borehole has been the use of Kalman filtering. However, up to the present time, the use of Kalman filtering has been limited to alignment of the probe when stopped in the borehole and has not been used in a dynamic sense for error reduction in measurements made while the probe is moving within the borehole.

Summary of the Invention It is therefore an object of the invention to provide a borehole survey apparatus that includes a probe suitable for insertion in a borehole; a mechanism for generating a signal representing the movement of the probe in the borehole; and acceleration measurement instruments within the probe for generating three acceleration signals representing components of accleration of the probe with respect to three probe axes and an angular rotation measuring means for generating two rotation signals representing the angular rotation of the probe with respect to two probe axes of rotation.Also included is a first circuit for generating a first synthetic angular rotation signal representing the angular rotation of the probe about a third probe axis when the probe is moving and a circuit responsive to the angular rotation signals for generating a second synthetic angular rotation signal representing 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 rotation signals and synthetic rotation signal for transforming the signals representing movement of the probe in the borehole into coordinates referenced to the earth and computation circuits connected to the transform circuit and the acceleration measuring circuits for converting 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 advantageously further includes a Kalman filter that uses the dynamic constraints of zero motion normal to the borehole to compensate for errors in acceleration, angular rotation and alignment data used to generate the velocity and position signals.

Brief Description of the Drawings Figure 1 is an illustration of an apparatus embodying the invention, including a section through a borehole showing a probe used with the borehole surveying apparatus; Figure la is a perspective drawing of the probe components; and Figure 2 is a logic diagram illustrating the logic for computing the location of the probe in the borehole.

Detailed Description of the Invention In Fig. 1 is illustrated a representative environment for the preferred embodiment of the invention. Extending below the ground 10 is a borehole generally indicated at 1 2 that is lined with a plurality of borehole casings 1 4 and 1 6. Inserted into the borehole 1 2 is a probe 18 connected to a cable reel 20 by means of a cable 22 that runs over an above ground pulley 24.

The cable 22 serves to lower the probe 1 8 through the borehole 1 2 and additionally provides a transmission medium for transmitting data from the probe 1 8 to a signal processor 26 above ground. Another signal transmission line 28 can be used to provide an indication of the amount of cable 22 that is paid out into the borehole 1 2 as well as data from cable 22 to the signal processor 26. Although in the invention illustrated in Fig. 1 data is transmitted to and from the probe 18 by means of the cable 22, data can be transmitted top-side by other means such as pressure impulses transmitting digital data through drilling mud. The data may also be stored in a memory in the probe and retrieved at a later time.

As shown in Fig. 1 a, secured within the probe 1 8 is a triaxial accelerometer package including 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 the coordinate system shown at 38. In the probe body coordinate system, the x axis as indicated by xb extends along the borehole and the y axis as indicated by yb and the z axis as indicated by Zb are orthogonal with respect to the Xb axis.

Also included in the probe 1 8 is a laser gyro assembly 40 that includes two laser gyros 42 and 44. The first laser gyro 42 is oriented within the probe so as to measure the angular rotation of the probe arround the yb axis wherein the angular rotation so measured is denoted by copy. Similarly the second laser gyro 44 is secured within the probe 18 such that it will measure probe rotation around the zb axis as denoted by fz. Because the diameter of the probe 18 is relatively small, there is not sufficient room to provide a laser gyro that will effectively measure rotation around the Xb axis.

Also included in the preferred embodiment of the probe 1 8 is a microcomputer 46 along with a memory 48. Connected to the microprocessor from the accelerometers 32, 34 and 36 are lines 50, 52 and 54 that serve to transmit acceleration signals a,. a, and a2 representing acceleration of the probe along the xb, yb and zb axes respectively. In a similar manner, the microprocessor 46 is connected to the laser gyro assembly 40 by means of lines 56 and 58 that serve to transmit the angular rotation signal by from the y axis gyro 42 and the angular rotation signal Ubz from the z axis gyro 44.

In the embodiment of the invention illustrated in Fig. 1a, a velocity signal VP is indicated as being transmitted by means of a line 60 to the microprocessor 46. As shown in Fig. 1, this signal would be generated by the rate of rotation of the pulley 24 thereby giving a measure of the speed or velocity of the probe in the borehole 1 2 with the line 60 included in cable 22.

There may be circumstances however when the VP signal could more profitably be generated in a different manner such as counting the pipe sections 14 and 16, down hole.

In determining the location of the probe and hence the location of the borehole, which is of course the ultimate object of the invention, it is necessary to transform the various sensor signals which are generated in the body coordinate system 38 into a coordinate system that is referenced to the earth. Such a coordinate system is illustrated in Fig. 1 as shown generally at 62 wherein the x axis as indicated by xL is parallel to the gravity vector gL and the remaining axis y and z are orthogonal to the x' axis and parallel with the ground. This coordinate system 62 can be termed the level coordinate system with the z' and yL axes respresenting directions such as North and East.

The logic by which the microprocessor 48 converts the acceleration signals on lines 50, 52 and 54, the angular rate signals on lines 56 and 58 and the velocity signal on line 60 to location signals is illustrated in Fig. 2. It should be understood, however, that some of this processing could be accomplished in the computer 26 located top-side. As indicated before, one of the primary problems in generating signal representing the location of the probe 1 8 with respect to the earth coordinate system XL, y' and ZL is to accurately convert signals representing the orientation and movement of the probe 1 8 from the body coordinate system xb, yb and zb into the level or earth coordinate system. One of the primary objects of the logic shown in Fig. 1 is to perform the coordinate transformation as accurately as possible utilizing Kalman filtering to compensate for the errors inherent in the various signal sources.

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

TABLE I CL, = Probe body to level coordinate transformation matrix C,b = Pipe to probe body coordinate transform abX = Acceleration along 'x' axis of body aby = Acceleration along 'y' axis of body azb = Acceleration along 'z' axis of body a(1)b = Accleration vectors in probe body coordinates at a first time = = Acceleration vectors in probe body coordinates at a second time = = Angular rotation about 'x' axis of probe body = = Angular rotation about 'y' axis of probe body = = Angular rotation about 'z' axis of probe body VP = Velocity of the probe along the pipe Vm = Velocity of the probe in level coordinates as measured Vil = Velocity of the probe in level coordinates derived inertially = = Angular rotation of the earth = Angular rotation of the earth-North component = = Angular rotation of the earth-Down component p = Angular velocity of the level relative to the earth R = Position vector with following three components: RN = North position coordinate RE = East position coordinate RD = Down position coordinate # = Latitude # = Error in body to level transformation CbL # = Probe body misalignment in pipe K = Suboptional Kalman gain coefficients gL = Gravity vector g'(RD) = Ws(RE-RD) l = Identity matrix RE = Radius of the earth GVL = Velocity errors in level coordinates = = Accelerometer errors eg = Gyro errors V3 = Gyro bias errors v = White measurement noise q1 = 'y' gyro white noise power spectral density in (degree/root hour)2 q2 = 'z' gyro white noise power spectral density in (degree/root hour)2 q3 = Uncertainty of twisting (roll wX ) of probe along the borehole whilte probe is in motion QL = Gyro random walk variance matrix in level coordinates Xe = Error states Xe = Error dynamics between discrete measurements # = Time mapping for error equations F = Dynamic error model matrix H = Velocity measurement matrix P = Covariance of error states R = Covariance of white measurement raise Ws =

Schuler oscillation rate (about 1/34 min.) X = Body-path misalignment time constant { } = Denotes the skew symmetric matrix representation of the enclosed vector Logic for updating the coordinate transformation matrix C, is indicated within the box 64 of Fig. 2. Inputs to this logic include the angular rotation signals #by and #zb on lines 56 and 58.

Since it is necessary to have a signal representing the rotation of the probe around the x axis a,b to update the transformation logic in box 64, it is necessary to generate a synthetic a;xb signal.

This is accomplished when the probe 18 is stopped in the bore hole 12 by means of the logic enclosed within box 66. Two of the inputs to the logic in box 66 are the angular rotation signals Coyb and C9zb on lines 56 and 58 and the third input is a signal that represents the rotation of the earth . The origin of the S2 signal is indicated in box 68 wherein as shown the signal Q is composed of three vectors including uN and uD which represents the rotation of the earth about North and in a down direction respectively.Also as shown within box 68 the value of S1 is dependent upon the latitude A of the probe 1 8. To facilitate operation of the logic of Fig. 2 in the probe microprocessor 46, the latitude A of the borehole can be stored in the memory 48 and transmitted to box 68 by means of line 69. The Sl signal is then transmitted over line 70 to logic 66 which generates a first synthetic eb signal on line 72. When the probe is stopped in the borehole a logic signal indicating that VP is equal to zero is transmitted by means of a dashed line 74 thereby being effective to connect the signal on line 72 to the 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 sensed acceleration.

Alternatively when the probe is in motion through the borehole 12, a second synthetic 9eb signal is generated on line 78 by means of the logic shown in box 80. When the probe is in motion in the borehole 12, a logic signal on line 74 will serve to close the switch 76 thereby connecting line 80 with the line 73. As shown in Fig. 2, the acceleration signals on line 50, 52 and 54 representing acceleration of the body a are transmitted over a bus 82 to the logic 78 and a delay circuit 84. The first input into the logic 78 over a bus 82 may be termed abi which represents the body acceleration of the probe 1 8 at a first time. The delay circuit 84 provides a second body acceleration signal a(b2) over a bus 86 to the logic 78.An acceptable time delay for the delay circuit 84 is 1/600th of a second. In this manner, synthetic angular rotation signals about the probe x axis are produced both for the case when the probe 1 8 is in motion and when it is stopped.

Along with the S2 signal on line 70, the change in transformation logic in box 64 receives a signal on line 90 which represents the angular velocity of the probe relative to the earth as indicated by box 92. The output of logic 64 C,on bus 94 represents the time rate of change of the probe body to level coordinate transform resulting from the acceleration signals ab and the angular rotation signals wb. This signal is then integrated as indicated at 96 thereby producing on bus 98 a signal C, that represents the transformation matrix required to convert signals generated in the body coordinate system 38 into the level coordinate system 62. The signals on line 98 representing the coordinate transform matrix C are transmitted through a summing junction 100 to a bus 102.

The accelerations ab are converted from body coordinates to level coordinates by means of logic 104 which has received the updated coordinate transformation matrix over bus 102. The resulting output on bus 106 represents the acceleration of the probe 1 8 in level coordinates and is transmitted to a summing junction 1 08. Subtracted in the summing junction 108 is a signal gL on line 110 that represents acceleration due to gravity resulting in a signal on a bus 11 2 representing the acceleration vL of the probe 1 8 in level coordinates. As indicated by box 113, go 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 11 6 representing the velocity v' on bus 11 6.

The resulting velocity VL is then fed back by means of a line 11 8 to logic 1 20 that in turn generates signals on bus 1 22 representing the centripedal acceleration resulting from the coriolis force generated by the earth's rotation. The resulting signal on bus 1 22 is in turn subtracted from the acceleration signals aL in summing junction 108. As a result, it may be appreciated that the resulting signal on bus 11 2 represents the acceleration of the probe 1 8 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 movement of the probe 1 8 in the borehole.

As previously described, the signal VP on line 60 can represent the wire line speed of the probe in the borehole. This signal is transformed by means of logic shown in box 1 24 into a velocity signal on a bus 1 26 representing the velocity of the probe in body coordinates Vb As indicated in box 24, the transform matrix Cpb includes an identity matrix I plus a matrix e that represents in matrix form the misalignment of the probe 18 in the pipes 14 and 16.The resulting velocity signal Vb on bus 126 is then transformed by means of the coordinate transform matrix C, shown at 1 28 into velocity signals V' in the level coordinate system on bus 1 30. These velocity signals are then transmitted through a summing junction 1 32 to a bus 1 34 and integrated as shown at 1 36 to generate on bus 1 38 signals representing the position coordinates R of the probe with respect to North, East and down as expressed in the level coordinates 62.

As may be expected, the velocity signals on bus 1 34 resulting from actual wire line measurements and the velocity signals on line 11 8 resulting from inertial signal sources are subject to sundry sources of errors. In order to provide a signal 6VL representing the relative error between velocity signal on busses 11 8 and 134, the signals on busses 11 8 and 1 34 are applied to a summing junction 140 resulting in the velocity error signal 6VL in level coordinates on bus 141. To compensate for the various sources of errors that are present in the generation of the velocity signals and hence position signals, Kalman filtering is used to estimate the error correction signals.

One of the principal objects of using a reduced order Kalman filter is to compensate for the missing or degraded inertial data. This technique makes use of the fact that over significant distance in the borehole, the probe 1 8 is constrained to follow the borehole axis which can be translated into equivalent velocity information thereby enhancing the borehole survey accuracy.

The use of dynamic constraints of this nature provides a significant advantage over the systems disclosed in the prior art. Computational burden in the Kalman filtering operation is reduced by modeling only the most significant error states. For example, the attitude of the probe 18 is used to resolve the external velocity VP into level coordinates for producing position coordinates.

The Kalman filter process is indicated by a logic block 142 which receives as input the velocity error signals 6VL over bus 141. As indicated in the logic block, the Kalman gain coefficients K are multiplied by the velocity error signals 6VL and added to the quantities indicated in the matrix 144. The revised values indicated in matrix 146 are then applied to various portions of the logic shown in Fig. 2 in order to provide for error compensation. For example, error compensation terms for the position coordinates R are applied by means of a bus 148 to a summing junction 1 50 to provide updated position coordinates as shown at 1 52.

Similarly, velocity error terms are applied over bus 1 54 to a summing junction 1 56 and the summing junction 1 32 in order to provide error compensation for the velocity signals vmL and v:.

Error terms + for the body to level transform matrix C, are provided on bus 1 58 to the summing junction 100 and error terms are applied over line 1 60 to correct for misalignment 5 in the transformation logic 1 24.

In order to enhance the efficiency of the process, the Kalman coefficients K may be stored in memory 48 within the probe rather than computed downhole, as indicated by box 1 62. By placing the Kalman coefficients K in memory 48, the transformation processes can be dynamically corrected within the probe 11 8 while it is in the borehole 1 2.

In a linear discrete Kalman filter, calculations at the covariance level ultimately provide the Kalman gain coefficients K, which are then used in the calculation of expected values of the error states Xe. These error states include:

In the system model, the error states are a function of +, that is the time mapping for error equations.The term + is equal to: + = I + Flvt Eq (2) where F matrix represents the error dynamics between discrete measurements:

6Fi 1 SR sy = F L 4 1 + noise Eq = F + noise Eq (3) Equation (3) is detailed as follows: 6R= (vlF - dV + CL,)Vb(S + CbV Eq (4)

The measurement model can be expressed as: SVb = HXe + y (Eq (8) where H represents the velocity measurement matrix: #Vb = CLb {VL}# - {V}# + CbdV + # Eq (9) The Kalman gain coefficients K can be represented by: K = P( - )HT[H P( - )HT + R] - 1 Eq (10) where the error covariance update is:: P(+)= [1-KH]P Eq (11) The gyro process noise covariance matrix is defined as:

The variance Q3 and gyro bias ,U3 based on the nonlinear reconstruction of the missing Cox gyro are given below as: Q3=3.6q Eq(13) 3 = - 4-5A/q where q = q1 = q2 During motion q3 becomes the variance associated with the logic of block 78.

As may be seen from the above discussion the constraints inherent in a borehole survey system where the probe 18 has substainally zero motion perpendicular to the pipe casing 14 and 16 of Fig. 1 are used to facilitate error estimation and correction. For example, an error signal is generated to correct probe roll attitude by differencing the expected acceleration signals on the body y and z axes with the sensed accelerations ay and az on lines 52 and 54.

Additionally as the error signals are processed over time the estimate of body to path misalignment 5 improves.

The stored gravity Model 11 3 can be reset in order to cancel the sensed acceleration ax, ay and a2 using the following relation: 9L(RD) = Ws(Re - RD) Eq (14) where Wx represents the Schuler oscillations.

The techniques described above can be used in a number of different borehole applications.

For example in a measure while drilling environment the described survey method can be used for drill guidance without the necessity of transmitting data to the surface. In this case the attitude of the probe 18 is determined using the logic illustrated at 66 to provide leveling, azimuth and tool face information.

Well surveying on the other hand can make use of the attitude data developed while the prove 18 is moving as provided by the logic in block 78 along with the attitude data generated when the probe is stopped as provided by the logic in block 66.

Claims (9)

1. A borehole survey apparatus comprising: a borehole probe for insertion in a borehole; control means for controlling the movement of said probe in the borehole; means operatively connected to said control means and said probe for generating a signal representing the movement of said probe in the borehole; acceleration means secured within said probe for generating three acceleration signals representing the components of acceleration of said probe with respect to three axes; first angular means secured within said probe for generating two rotation signals representing the angular rotation of said probe with respect to two axes of rotation;; means responsive to said acceleration signals and to said movement signal for generating when said probe is moving a first synthetic angular rotation signal representing the angular rotation of said probe about a third axis of rotation different from said two axes of rotation; means responsive to said angular rotation signals and said movement signal for generating when said probe is not moving a second angular rotation signal representing the angular rotation of said probe about said third axis of rotation; transform means responsive to said rotation signals and said synthetic rotation signal for transforming signals representing probe movement in a probe referenced coordinate system to an earth referenced coordinate system; and first computation means operatively connected to said transform means and acceleration means for converting said acceleration signals into a first set of velocity signals representing the velocity of said probe and a first set of position signals representing the position of the probe in said earth referenced coordinate system.

2. The apparatus of Claim 1 additionally including second computation means operatively connected to said transform means for converting said movement signal into a second set of velocity signals representing the velocity of said probe and a second set of position signals representing the position of the probe in said earth referenced coordinate system.

3. The system of Claim 2 including means for comparing said first set of velocity signals with said second set of velocity signals and generating an error signal.

4. The system of Claim 3 additionally including Kalman filter means operatively connected to said transform means and said first and second computation means for correcting said velocity signals.

5. The apparatus of Claim 4 wherein said probe includes memory means for storing Kalman gain coefficients for said Kalman filter means.

6. The apparatus of Claim 4 wherein said probe includes means of calculating Kalman gain coefficients for said Kalman filter means.

7. The apparatus of Claim 1 wherein said second synthetic angular rotation signals means includes a source of signals representing the angular rotation of the earth.

8. The apparatus of Claim 1 wherein said transform means includes a source of signals representing the angular rotation of the earth.

9. A borehole survey apparatus substantially as described herein with reference to the drawings.