Design of High Accuracy Orientation sensor of MWD

Gong xianfeng , Yang Jing School of Mechanical Engineering, University of Science and

Technology Beijing Beijing, China

xianfenggong@126.com

Wang Wei Drilling Company Jianghan Petroleum Administration of

Sinopec Directional Drilling Service Center Qianjiang of Hubei Province, China

Abstract—This paper proposes to develop an angle measurement system of the orientation sensor based on accelerometers and fluxgate magnetometers. By analyzing temperature error and fix error which affect the orientation accuracy, a new error correcting model has been put forward. Testing results show that the MWD orientation sensor system utilizing the suggested compensation model is more accurate in directional drilling operations, which has considerable values.

Keywords-Orientation sensor; Temperature error; Fix error

I. INTRODUCTION Orientation sensor plays an important role in Measurement-

While-Drilling (MWD) of oil drilling, but the high accuracy is difficult to get, because it works in a harsh condition of strong vibration and high temperature[1][2]. In this paper, an error correcting model and algorithm of accuracy compensation have been put forward to the sensor, and the software and hardware is realized, thus the accuracy is good enough for MWD.

II. MWD MEASUREMENT PARAMETERS The set of orientation sensor is primarily composed of

three-axis accelerometers, three-axis magnetometers, and some basic processing circuits, as the Fig. 1 shows. Three accelerometers are respectively installed in X, Y, and Z directions of the body frame and the three fluxgate magnetometers are installed the same way. Generally, the X, Y, and Z directions are defined as follows:

Z-direction is the axis of the wellbore;

X-direction is set to be perpendicular to the reference plane of the device;

Y-direction is derived from the right-hand rule of X and Z directions.

The outputs of accelerometers in X, Y and Z direction are Gx, GY and Gz respectively, and that of magnetometers is Hx, Hy and Hz.

The desired measurement parameters are the gravity tool face angle (GTF), the magnetic tool face angle (MTF), the inclination (INC), and the azimuth (AZ).

The gravity tool face angle (GTF) is defined to be a clockwise deviation of the X-direction from the high side of the wellbore, obtained when looking down straight at the wellbore.

Tan(GTF)=X

Y

GG

− 1

The magnetic tool face angle (MTF) is an included angle between X-direction and the magnetic North direction. Computation of the MTF is presented in the following equation:

Tan(MTF)=X

Y

HH

− 2

Inclination refers to the deviation of Z-direction from the vertical direction. Computation of it is given as follows:

Tan(INC)=Z

YX

G

GG 22 + 3

Azimuth is a clockwise deviation of the magnetic North from the projection of the Z-direction on the horizontal plane. Computation of it can be expressed as follows:

Tan(AZ)= XZXYZYXYZ

XYYX

GGHGGHGGHGHGHG−−+

+−)(

)(22

4 The accuracy of the MWD system is acceptable when

errors of the above measurement parameters are within the following threshold values, respectively:

Inclination: ±0.1 ; Azimuth: ±1 ; Tool face: ±1.5 .

Figure 1. Definition of X, Y, Z directions about orientation sensor

978-1-4244-8039-5/11/$26.00 ©2011 IEEE

III. ESTABLISHMENT OF THE ERROR CORRECTING MODEL Both the fix error and the variation of operating

temperature have unavoidable effects on sensor accuracy. To obtain a satisfying accuracy under the condition of high vibration and broad temperature range, it is necessary to analyze possible errors and propose solutions to them. The measurement errors of sensors is derived from temperature variation and fix error.

A. Temperature compensation The mathematical model for both the accelerometer and the

fluxgate magnetometer could be expressed in the following equation[3]:

BPSV −•= 5 Where V is the desired voltage outputted from the sensor; P

is the output of the sensors, among which for the accelerometers are GX, GY and GZ (g), the gravity components in X, Y and Z directions, respectively, while for the fluxgate magnetometers are HX, HY and HZ (Gauss), the magnetic components in X, Y and Z directions; B represents the zero drift which is of the same unit as P; S is known as the scale coefficient with a unit of V/g or V/Gauss.

What can be extracted from the above equation is that any factor that has an effect on either S or B does affect the sensor accuracy as well. Practically, the sensors operating temperature disturbs S and B most, mainly in the forms of scale error and zero drift error, respectively, and due to its huge variation, errors caused by the operating temperature must be reduced.

1) Zero drift compensation Zero drift is defined to be an output offset voltage of the

sensor circuit when inputting a zero-value quantity. Due to the fact that zero drift varies with temperature, different one corresponding to different zero drift, error will definitely exist if applying zero drift to each calculation with the same value, which is unacceptable in high accuracy measurements. Hence, it bears great essentiality and significance to make clear of the correlation between zero drift and temperature, so as to maximally eliminate the temperature’s impact on accuracy.

Based on a set of zero drift values measured at different temperatures, a suggested method for the elimination is to construct a best match function f(T), which could optimally approach the true zero drift curve. Thus the zero drift value at any specific temperature, which is a necessity for compensating sensors during practical angles measurement, can be yielded according to the match function f(T).

Here is an example of the X-direction fluxgate magnetometer.

The mathematic model based on a third-order polynomial can be utilized to construct the desired match function f(T), shown in expression (6).

32 )3()2()1()0()( TFTFTFFTf +++= 6

The experimental data of the fluxgate magnetometer are listed in Table.1. According to (6), these data points are then fit to the third-order polynomial by the Least Squares method, so

as to generate the mathematic expression of f(T), which could yield a accurate zero drift value at any specific temperature:

32 )1033136.2(72794722.1)50529672.2(45042642.2)(

TeTe

TeeTf

−−+−+

−−+−−=(7)

TABLE I. ZERO-DRIFT EXPERIMENTAL DATA OF THE X-DIRECTION FLUXGATE MAGNETOMETER

Temperature 0 27.10 52.16 77.41

Zero drift (Gauss) -0.0003 -0.0006 -0.0010 -0.0013

Temperature 100.82 126.84 150.00

Zero drift (Gauss) -0.0013 -0.0012 -0.0013

0 50 100 150-14

-12

-10

-8

-6

-4

-2x 10

-4

Temperature(deg C)

Zer

o D

rift V

alue

(Gau

ss)

Zero DriftBest Match Function

Figure 2. Zero Drift and Its Fitting Function Curves of X-direction Fluxgate Magnetometer

As is shown in Fig.2, the pre-compensation error of zero drift is close to 14x10-4 Gauss within the whole operating temperature range, while the error after applying the match function achieves ± 1x10-4 Gauss, which decreases nearly one order of magnitude than before.

2) Scale coefficient compensation Scale coefficient refers to the ratio of sensor output to input,

which varies with temperature, and needs compensating as well. Similar mathematic model can be applied to this scale coefficient, and again, take the X-direction fluxgate magnetometer for example.

TABLE II. SCALE COEFFICIENT EXPERIMENTAL DATA OF X-DIRECTION FLUXGATE MAGNETOMETER

Temperature 0 27.10 52.16 77.41

Relative scale Coefficient 0.9668 0.9651 0.9636 0.9625

Temperature 100.82 126.84 150.00

Relative scale Coefficient 0.9609 0.9586 0.9571

Shown as follows, the temperature experimental data of scale coefficient are listed in Table.2; the match function obtained through mathematic computation is represented in expression (8); Fig.3 describes the correlation curves of scale coefficient and match function corresponding to temperature, respectively.

32 )1003301.8()87786514.8()50288821.6(16678063.9)(

TeTe

TeeTf

−−+−

+−−+−= (8)

As is shown in Fig.3, the pre-compensation error of scale

coefficient is close to 5.3x10-2V/Gauss within the whole operating temperature range, while the error after applying the match function achieves ± 2x10-3Gauss, which also decreases one order of magnitude than before.

0 50 100 1500.956

0.958

0.96

0.962

0.964

0.966

0.968

0.97

Temperature(deg C)

Rel

ativ

e S

cale

Fac

tor

Relative Scale FactorBest Match Function

Figure 3. Scale Coefficient and Its Fitting Function Curves of X-direction

Fluxgate Magnetometer

B. Fix error correcting The fix error generally consists of two types of error[4]: the

non-orthogonal error, caused by the non-orthogonal among sensors installed on X, Y and Z coordinate axes, respectively; the misalignment error, caused by the measurement axis of each sensor misaligning with corresponding axis of the coordinate system. Since neither of the two types of error varies with the temperature, only geometric correction could satisfy the accuracy requirement.

Geometric correction method for the fix error is based on a mathematic model expressed by following equation:

000 ZXZYXYXXXX HKHKHKH ++= (9)

Where HX is the corrected X-axial magnetic component; HX0, HY0 and HZ0 are the pre-correction magnetic components of X, Y, and Z axes, respectively; KMN is the cross-axial acting factor hat represents the influence imposed by N-axis on M-axis (with M or N separately standing for anyone of the X, Y and Z axes), such as the influences Y and Z-axis fluxgate magnetometers have on the correction of X-axis fluxgate magnetometer. By experiments, each KMN is calibrated as

follows: KXY=1.3849286e-3, KXZ= -2.2113571e-3, KXX=1.0000000

After the above error analysis, the sensors integrated models with temperature error compensation and fix error correcting, can be described as following matrixes:

Matrix model for the three-axis accelerometers:

−−−

−−−−

=)()()(

)(/1000)(/1000)(/1

11

1

0

0

0

TG

TG

TG

V

V

V

TSTS

TS

KKKKKK

G

G

G

Z

Y

X

Z

Y

X

Z

Y

X

ZYZX

YZYX

XZXY

Z

Y

X

(10) Matrix model for the three-axis fluxgate magnetometers:

−−−

−−−−

=)()()(

)(/1000)(/1000)(/1

11

1

0

0

0

'

'

'

'

'

'

''

''

''

TH

TH

TH

V

V

V

TSTS

TS

KKKKKK

H

H

H

Z

Y

X

Z

Y

X

Z

Y

X

ZYZX

YZYX

XZXY

Z

Y

X

(11)

Where K and K serve as the fix error correcting coefficients; S and S as the scale coefficients with temperature error compensation; G0 and H0 as zero drifts conducted by the temperature compensation.

IV. SYSTEM HARDWARE MSP430F149, an enhanced 16-bit MCU produced by TI

Company, is selected as the control core for the downhole sensor. The device features a large memory space, various interfaces, ISP capability, and a wide operating temperature range of -40~125 C , all of which perfectly satisfy the requirement of the downhole environment.

ADS1216, a successive approximation Analog-to-Digital converter(ADC) produced by Analog Devices, Inc., with 24-bit resolution and 8 input channels, is selected as the A/D module for signal acquisition. The device has a combined features of high precision, high integration, and a wide temperature range of -40~125 C . Data transmission between ADC and MCU is realized through the serial peripheral interface (SPI), while MCU receives and transmits orders through the serial communication interface (SCI).

The overall system is composed of the following parts: voltage matching module, hardware filter, signal acquisition, MCU minimum system, power conversion, and SCI module, etc. With the application of modular design, the system is open to debugging and maintenance. The whole system block diagram is shown in Fig. 4.

Figure 4. Block Diagram of the system

V. SYSTEM SOFTWARE In order to assure the efficiency, readability and portability

of the procedures, the system adopts C as its programming language. With the help of the ISP function on the MSP430F149 chip, it becomes more convenient either to write codes into MCU through the USB port, without getting devices off the PCB board, or to modify the programs downloaded to MCU in real-time just under the PC environment. The system flow chart and error compensation flow chart are both shown in Fig.5.

start

Configure error compensation coefficients for the accelerometers,

magnetometers and temperature sensor

A/D sampling for N times

Low-pass filtering

1) Calculate compensation value for temperature and fix error2) Get GTF, MTF, INC and AZ

Binary code to g or gauss conversion

Save results

End

start

initialization

Transmit command ?

Data aquisition

Error compensation

Angle computation

Data transmission

Y

N

(a) (b) Figure 5. Main program (a) and Error Compensation program (b) flow chart

VI. TEST RESULTS AND DISCUSSIONS When the sequential steps of hardware filtering, software

filtering and error compensations have been completed, take a test of the newly-designed device on a standard test table. Test results are listed in Table.3.

TABLE III. STATISTIC TESTING RESULTS OF THE MWD SYSTEM

GTF (degree)

Theoretical AZ(degree)

Measurement AZ(degree)

Theoretical INC(degree)

Measurement INC(degree)

0 0 0.0 15 15.0 90 45 44.8 30 30.0 180 90 90.0 45 45.0 270 135 135.2 60 60.0 0 180 180.3 75 75.1 90 225 225.4 90 90.0 180 270 270.3 120 119.9 270 315 315.2 145 145.0

As is shown in Table.3, when measuring in different attitudes at room temperature, the maximal error range for the inclination, azimuth and tool face angle is 0.1 , 1 and

1.5 respectively, all of which has achieved the design requirements.

At room temperature, the attitude measured by the orientation device are of a 205.4 tool face angle, a 89.5inclination, a 271.2 azimuth and a 1.001 integrated gravity. Next put the device into the high temperature test chamber, and carry out high temperature experiment within the range of 25 to 150 . Results are listed in Table.4. Until now we can conclude that the system has properly met the accuracy demands on the whole temperature range.

TABLE IV. HIGH TEMPERATURE TESTING RESULTS OF THE MWD SYSTEM

Temperature

GTF (degree)

INC (degree)

AZ (degree)

Gravity (g)

25 205.4 89.5 271.2 1.0011 50 205.4 89.5 270.8 1.0012

75 205.4 89.5 270.6 1.0013 100 205.3 89.6 270.7 1.0017

110 205.3 89.6 270.8 1.0018 120 205.3 89.6 270.8 1.0017 130 205.4 89.6 270.7 1.0014

135 205.3 89.6 270.8 1.0014

150 205.4 89.6 270.8 1.0015

Fix the orientation device to a vibration table and gradually raise the vibration intensity. Results show that the system could still satisfy the target accuracy requirements, even imposed with a 10g vibration.

From the above, it can be obviously concluded that the software compensation, based on the error correcting model proposed in this paper, has achieved acceptable effects, which not only satisfies the requirements of practical measurements but also accomplishes the accuracy target raised by this design.

REFERENCES

[1] Wang Ruo. Developing history of Logging While Drilling technology, PETROLEUM INSTRUMENTS, Vol.15, No 2, pp.35-47, 2001(In Chinese)

[2] Zhang Yubo and Bi Hongbo. Design of the high accuracy MWD, Measurement Control Technology and Instruments, No 7, pp.78-80, 2007(In Chinese)

[3] Sun Huiqing and Guo Zhiyou. Technology of Error Compensation on Sensors, CHINESE JOURNAL OF SENSORS AND ACTUATORS, No 1, pp.90-92, 2004(In Chinese)

[4] Paul E, Radzinski, Michael L Larronde, Jian-Qun Wu, Calculating Directional Drilling Tool Face Offset, US7555398B2 2003-01-01