dynamic measurement of spatial attitude at bottom rotating ... · stationary surveying). fig. 2...

Qilong Xue1

Key Laboratory on Deep GeoDrilling Technology

of the Ministry of Land and Resources,

School of Engineering and Technology,

China University of Geosciences,

Beijing 100083, China

e-mail: [email protected]

Ruihe WangCollege of Petroleum Engineering,

China University of Petroleum,

Qingdao 266580, China

Baolin LiuKey Laboratory on Deep GeoDrilling Technology

of the Ministry of Land and Resources,

School of Engineering and Technology,

China University of Geosciences,


Leilei HuangSinopec International Petroleum

Service Corporation,


Dynamic Measurement ofSpatial Attitude at BottomRotating Drillstring: Simulation,Experimental, and Field TestIn the oil and gas drilling engineering, measurement-while-drilling (MWD) system is usu-ally used to provide real-time monitoring of the position and orientation of the bottomhole. Particularly in the rotary steerable drilling technology and application, it is a chal-lenge to measure the spatial attitude of the bottom drillstring accurately in real timewhile the drillstring is rotating. A set of “strap-down” measurement system was devel-oped in this paper. The triaxial accelerometer and triaxial fluxgate were installed nearthe bit, and real-time inclination and azimuth can be measured while the drillstring isrotating. Furthermore, the mathematical model of the continuous measurement wasestablished during drilling. The real-time signals of the accelerometer and the fluxgatesensors are processed and analyzed in a time window, and the movement patterns of thedrilling bit will be observed, such as stationary, uniform rotation, and stick–slip. Differ-ent signal processing methods will be used for different movement patterns. Additionally,a scientific approach was put forward to improve the solver accuracy benefit from the useof stick–slip vibration phenomenon. We also developed the Kalman filter (KF) to improvethe solver accuracy. The actual measurement data through drilling process verify thatthe algorithm proposed in this paper is reliable and effective and the dynamic measure-ment errors of inclination and azimuth are effectively reduced.[DOI: 10.1115/1.4031742]

Keywords: strap-down, continuous MWD, rotary steerable, stick–slip vibration, spatialattitude

1 Introduction

Directional drilling is the technology for directing a wellborealong a predefined trajectory, which is essential for many reasons,such as side tracking of an existing well, drilling multiple wellsfrom the same offshore platform, multilateral drilling, and hori-zontal drilling. This dramatically reduces the cost and time of dril-ling operations. Thus, the development of directional drillingtechnologies has gained more attention in recent years. Besidesthe conventional drilling assembly, directional drilling operationsrequire position sensors to provide estimations of the inclination(deviation from the vertical direction) and azimuth (deviationfrom the north direction in the horizontal plane) [1,2]. These sen-sors are part of the MWD tool, which is installed several feetbehind the drill bit to monitor all physical parameters that affectthe drilling operation.

Current MWD survey is performed along the well path at sta-tionary survey stations. That is to say, the bottom drillstring atti-tude (inclination and azimuth) measurement is carried out in thecase that the drillstring does not rotate. But with the developmentof drilling technology, continuous measurement of well trajectorybecomes increasingly important. It also has become essential inrotary steerable system (RSS).

As a booming technology catering the 21st century, rotarysteerable drilling features extended the reach capacity, well trajec-tory control accuracy and flexibility, which can notably increasedrilling efficiency and safety [3–6]. One of the technical difficul-ties in the rotary steerable drilling system is how to dynamically

measure the spatial attitude accurately at the bottom rotating drill-string. The regular wellbore position calculations are typicallyperformed by measuring azimuth and inclination with the MWDsystem in a stationary mode (the drillstring nonrotating). How-ever, the attitude of the bottom rotating drilling tool should beobtained in real time in both the RSS and automatic vertical dril-ling system. In this paper, we developed the methods of dynamicsolving of azimuth and inclination when drillstring is rotatingbased on theoretical analysis and real data of the field test, withregard to the drillstring state of motion. The achievement canimprove the attitude solving accuracy of bottom rotating drill-string and the trajectory guidance capability in automatic verticalor rotary steerable drilling.

Mahmoud et al. [7], Noureldin et al. [8], and Pecht and Min-tchev [9] studied the continuous MWD under laboratory condi-tions using gyroscope-based system and proposed an advanceddirection and inclination sensor package based on the inertial nav-igation system (INS). They verified the reliability of the algo-rithm, through simulation, which used INS to achieve thecontinuous MWD with high accuracy. They analyzed the influen-ces of vibration and temperature upon MWD and used KF toimprove the system accuracy. However, they insufficiently con-sidered about the downhole complex situations [10–12]. Thesevere vibration of drillstring causes great challenges for the mea-surement accuracy and lifetime of the sensors, which will greatlyaffect the life of the gyroscope. Moreover, the increasing tempera-ture will give high-rise to the error drift of the gyroscope.

Actually, in the control process, assume that the measured val-ues under stationary state remain unchanged during drilling, andcould still achieve the closed-loop control of rotary steerable.However, the disadvantage is obvious. Figure 1 shows that theactual trajectory of drilling fluctuates with the design trajectory.This phenomenon cannot be avoided because of the hysteresis of

1Corresponding author.Contributed by the Petroleum Division of ASME for publication in the JOURNAL

OF ENERGY RESOURCES TECHNOLOGY. Manuscript received February 27, 2015; finalmanuscript received September 1, 2015; published online October 29, 2015. Editor:Hameed Metghalchi.

Journal of Energy Resources Technology MARCH 2016, Vol. 138 / 022903-1Copyright VC 2016 by ASME

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stationary surveying. Continuous MWD surveying system shouldbe developed but the vibration noises are unavoidable while thedrillstring is rotating. Bottom drilling tool shows complex charac-teristics while rotating, which include vertical vibration, horizon-tal vibration, eddy, sticky slip, and their combined effects.

With the development needs of rotary steerable drilling technol-ogy, this paper studied the dynamic measurement of spatial atti-tude at the bottom rotating drillstring. Based on the theoreticalanalysis and verification of field data measurement during drilling,a new algorithm was proposed through the state of motion analy-sis. The downhole measurement signal processing methods andthe algorithm of dynamic solving of spatial attitude were devel-oped. Initially, a theoretical system of dynamic solving was estab-lished, which laid theoretical and technical foundation for thecontinuous MWD and RSSs development.

2 Systems Solutions

We developed a strap-down rotary steerable drilling system[13] that mainly included two parts: strap-down stabilized plat-form (1) and oriented actuator (2) (as shown in Fig. 2). The stabi-lized platform is composed of measurement and control section(5), power section (4), and servo section (6). Measurement sectionis equipped with triaxial accelerometer and triaxial fluxgate.Power section consists of turbo generator principally, which isdriven by drilling fluid to generate power. For RSS, which is anew form of drilling technology used in directional drilling in theoil and gas industry, the whole drillstring is rotated from the sur-face by a hydraulically driven top drive (typically). It uses pads onthe outside of the tool which press against the well bore therebycausing the bit to press on the opposite side to cause a direction

change. RSS technique has become increasingly important for anextended reach on horizontal and 3D wells. The pads of the RSSwere periodically pushed in a fixed position against the boreholewall in the process of drillstring rotating. This is the main differ-ence between RSS and conventional drilling. Frictional forcebetween the pads and borehole wall will make the drill bit instan-taneous rotational speed reducing.

The surveying tools are installed inside nonmagnetic drill col-lars, which are usually designed from Monel metal to avoid exter-nal interferences with the measurements taken by the magnetic-based surveying tools. In the measurement section, as shown inFig. 2, Ax, Ay, and Az are defined as survey signals of triaxialaccelerometers on the xyz axis, respectively. Bx, By, and Bz aredefined as survey signals of triaxial magnetometers on the xyzaxis, respectively. Assume the Earth’s magnetic field strength as

M. Obviously, M ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2

x þ B2y þ B2

z

q. Under certain sample fre-

quency (100 Hz), measuring signals are time series and can beexpressed as time function. Assume the acceleration of gravity asGtotal. Gx, Gy, and Gz are defined as survey signals of gravityacceleration on the xyz axis, respectively, as follows:

Gtotal ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG2

x þ G2y þ G2

z

q. The survey signals of triaxial acceler-

ometers include not only the acceleration of gravity but also theacceleration of drillstring vibration.

Unlike the conventional MWD, the inclination and azimuthshould be solved dynamically when the drillstring is rotating inthe RSS. Accelerometers are hypersensitive to vibration, so theviolent vibration of bottom hole assembly leads the measured sig-nals to submerge into noise signals. In a control process, valve’sposition is set by motor output torque which is controlled by thecurrent density change in control circuit, and the friction resist-ance on the valves is uncertain due to the changing properties of

Fig. 1 Schematic diagram of the trajectory control. (The actualtrajectory of drilling fluctuates with the design trajectory. Thisphenomenon cannot be avoided because of the hysteresis ofstationary surveying).

Fig. 2 Sketch diagram of the structure of rotary steerable drilling system (in the measure-ment section, equipped with triaxial accelerometer and triaxial fluxgate on the xyz axis,respectively): (1) strap-down stabilized platform, (2) oriented actuator, (3) rotor, (4) powersection, (5) measurement and control section, (6) servo section, (7) plate valve, (8) rib, and(9) bit

Fig. 3 Measurement signals exhibit a sine wave during rota-tion (where A indicates the amplitude; x is the rotation speed; uis the initial phase; T is the rotation period)

022903-2 / Vol. 138, MARCH 2016 Transactions of the ASME


drilling fluid, so the motor load is changed all the time, and this isa great challenge on establishment and accuracy of controlalgorithm as well. All of these difficulties need to be coped within realistic experiments.

3 Methods

3.1 Stationary Surveying. The present MWD surveying sys-tems incorporate three-axis magnetometers and three-axis

accelerometers arranged in three mutually orthogonal directions[14–16]. The magnetic surveying tools are installed inside thenonmagnetic drill collars. Noureldin [17] proposed that the non-magnetic drill collar is too expensive and developed the technol-ogy of fiber optic gyroscopes (FOGs), which has been suggestedfor MWD surveying of the directional wells [18,19]. But gyro-scope’s reliability is a problem, say the least, the FOG system alsoneeds accelerometer, utilizing stick–slip vibration method in thispaper is equally applicable to this system. This paper focuses onthe magnetic surveying tools which have a wider range ofapplications.

Theoretically, in measuring subsystem it is enough to have onlythree accelerometers and three fluxgate sensors that were installedin the instrument coordinate system, which additionally requires atemperature sensor and an angular rate gyroscope. In fact, wedesigned a redundancy scheme in order to effectively improve thesystem reliability. Define toolface as uG, inclination as h, and azi-muth as w. Regarding the static algorithm, there are several differ-ent formulas, basically they are the same on the principle

Gx

Gy

Gz

2664

3775 ¼

G cos u sin h

�G sin u sin h

�G cos h

2664

3775 (1)

Bx

By

Bz

2664

3775 ¼

BHðcos w cos u cos h� sin w sin uÞ � BV cos u sin h

�BHðcos w sin u cos hþ sin w cos uÞ þ BV sin u sin h

BH cos w sin hþ BV cos h

2664

3775

(2)

where BH ¼ B cos / is the horizontal component of the earth’smagnetic field and BV ¼ B sin / is the vertical component of theearth’s magnetic field (/ is the local magnetic inclination angle).Then, the toolface, inclination, and azimuth will be obtained

uG ¼ tg�1 �Gy

Gx

� �(3)

h ¼ tg�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG2

x þ G2y

q�Gz

0@

1A

(4)

w ¼ tg�1 G ByGx � BxGyð ÞBz G2

x þ G2y

� �� Gz BxGx þ ByGyð Þ

!(5)

Fig. 4 Analysis of the stick–slip vibration phenomena,as shown in (a), when the surface top drive rotary speed is100 r/min, the speed of drill bit has fluctuated between 0 and200 r/min and the stick–slip phenomenon is very critical. From(b), the stick–slip vibration is always existent throughout thedrilling process. (a) Surface RPM and bit RPM and (b) speedstatistical histogram.

Fig. 5 Dynamic measurement algorithm flowchart, when the drillstring is not rotating, real-time signals on three-axis were all used for calculation, at the same time, signals on x- and y-axis were stored in the memory block. When the drillstring is rotating, signals on z-axis andstored signals of x- and y-axis were adopted to solve the inclination and azimuth. Then,based on the trajectory model, to improve the solver accuracy, KF was developed.

Journal of Energy Resources Technology MARCH 2016, Vol. 138 / 022903-3


Fig. 6 Discrete KF model

Fig. 7 Dynamic solution error at a different inclination and azimuth: (a) accelerometer: 20 dB and flux-gate: 30 dB, (b) accelerometer: 5 dB and fluxgate: 30 dB, and (c) accelerometer: 1 dB and fluxgate: 30 dB



DiPersio and Cobern [20] gave the following calculation for-mulas from another perspective. They provide useful inclinationand azimuth equations, which can be computed with the axial ac-celerometer and magnetometer readings. The azimuth can beobtained as follows:

k ¼ arcsinGxBx þ GyBy þ GzBz

GtotalM

� �(6)

w ¼ cos /ð Þ � cos hð Þsin kð Þsin hð Þcos kð Þ

(7)

3.2 Dynamic Algorithm for Uniform Rotary (DAU). Whenthe drillstring rotated, the equations mentioned above were no lon-ger applicable. The sensors are installed in the center of the drill-string and the measurement signals of x and y axes will exhibit asine wave during rotation, as shown in Fig. 3.

For Eqs. (4) and (5), integration throughout the cycle for mag-netic toolface angle can be obtained by the continuous formulaunder rotation condition. Computational formulas of deflection hr

and azimuth wr are given as follows:

hr ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2Np

TM¼0

GxdTM

!2

þð2Np

TM¼0

GydTM

!2vuut

�ð2Np

TM¼0

GzdTM

(8)

wr¼ tg�1

ð2Np

TM¼0

Gtotal GxBy�GyBxð ÞdTMð2Np

TM¼0

Bz G2xþG2

y

dTM�

ð2Np

TM¼0

Gz GxBxþGyByð ÞdTM

0BBBB@

1CCCCA

(9)

wherein TM is magnetic toolface angle, defined asTM ¼ tg�1ð�By=BxÞ.

This algorithm is theoretically to calculate the borehole inclina-tion and azimuth while the drillstring is rotating. We defined thisalgorithm as “DAU” method.

3.3 Dynamic Algorithm for Stick–Slip Motion (DAS). Inthe actual drilling process, the drillstring will appear as torsional

Fig. 8 Laboratory experiment: (a) is an experimental equipment, when the string continuous rotation with a constant speedand be located at a particular borehole inclination and azimuth, accelerometer (x, y, and z axes) and fluxgate (x, y, and z axes)measurement data will be obtained, (b) is the accelerometer measurement signals, and (c) is the fluxgate measurement signals



vibration and stick–slip phenomenon but not always presents uni-form rotating [21]. As shown in Fig. 4(a), by extracting a periodof underground data, the rotary table speed is maintained at 100r/min, the drill bit speed has fluctuated between 0 and 200 r/min,and the stick–slip phenomenon is very critical. In this situation,the theoretical models based on the drillstring uniform rotatingwill not be practicable.

We first analyzed the movement of the drillstring, actually tofigure out how often the stick–slip phenomenon emerges through-out the drilling process. The RSS we have developed has con-ducted a number of field tests [13], the measurement data showthat the stick–slip vibration will frequently occur in drilling. Werandomly selected the speed data of 2 hrs utilizing the reservoirsampling principle [22] and estimated the overall characteristicsfrom the characteristics of the sample. First, select the top of datapoints of 1 hr; suppose there are k data points; from the k þ 1 datapoint to the last data point is reached; Select the ith data point inthe probability of 1/i (i¼ kþ 1, kþ 2,…,N), and randomly replacea previously selected elements. This traversal time can guaranteedata points of 1 hr to be completely randomly selected. As shownin Fig. 4(b), speed at vicinity of zero represents the emergence ofstick–slip. Stick–slip vibration is always existent throughout thedrilling process, so the application of the stick–slip vibrationmethod to improve the measurement accuracy is feasible.

3.3.1 Utilizing Stick–Slip Vibration to Improve MeasurementAccuracy. Dynamic solution approach to the bottom of the rotat-ing drillstring attitude was shown in Fig. 5. When the drillstring isnot rotating, filtered real-time signals on the three-axis were allused for calculation, and at the same time, filtered signals on x-and y-axis were stored in the memory block. When the drillstringis rotating, real-time filtered signals on z-axis and stored signals ofx- and y-axis with nonrotating drillstring were adopted for solvingthe inclination and azimuth. In addition, when the bottom drill-string appears in the stick–slip vibration, the stick of the downholedrilling tool can be regarded as a nonrotating “stationary” state.Real-time judgment method of drillstring rotation state was pro-posed based on the downhole survey data.

The standard deviation statistical methods can be used to deter-mine the drillstring movement, since it reflects the degree of dis-

persion among the individuals within the group. Using 50 datapoints as a time window, defined as the time seriesx1; x2;…; x49; x50, the average value is u, then

u ¼ 1

N

XN

i¼1

xi (10)

The standard deviation r can be obtained

r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XN

i¼1

xi � uð Þ2vuut (11)

wherein N¼ 50.

3.3.2 KF Approach. KF is an optimal recursive data-processing algorithm. It is optimal in the sense that it uses allavailable information to minimize the errors in the state variablesof a given system. It is recursive, because it does not require allprevious data to be kept in storage. It is also a data-processingalgorithm since it is not an electrical filter, but rather a computerprogram [23]. In order to implement a discrete KF, the error mod-els have to be given in state-space form

xk ¼ Fk;k�1 þ Gk�1wk�1 (12)

yk ¼ Hkxk þ vk (13)

Equation (11) is called the dynamics equation and Eq. (12) isthe observation or update equation [24]. Here, xk is the processstate vector, Fk,k�l is a square matrix relating xk to xk�1 beingcalled the state transition matrix, and wk�1 is a random functionconsidered the white noise with Gk�1 as its coefficient vector. InEq. (12), yk is the measurement vector at the kth moment, Hk isthe design matrix giving the ideal noiseless relationship betweenthe observations vector and the state vector, and vk is the observa-tion random noise. It is assumed that vk has no correlation withwk�1. The KF model used in this paper is shown in Fig. 6.

When toolface is defined as uG, inclination as h, and azimuthas w, transformation matrix Rn

b can be defined as follows:

Rnb ¼

cos w cos /þ sin w sin h sin / sin w cos h cos w sin /� sin w sin h cos /�sin w cos /þ cos w sin h sin / cos w cos h �sin w sin /� cos w sin h cos /

�cos h sin / sin h cos h cos /

24

35 (14)

Assuming that Gb ¼ ½Gx Gy Gz�T, the rotary speed is defined as xx, xy, xz on the xyz axis, respectively, xbib ¼ ½xx xy xz�T. Then,

the rotary angle will be obtained

hbib ¼

Dhx

Dhy

Dhz

24

35

b

ib

¼xx

xy

xz

24

35Dt (15)

Using quaternion Q ¼ ½q1 q2 q3 q4�T to express the coordinate system transformation, then Rnb can be redefined as follows:

Rnb ¼

R11 R12 R13

R21 R22 R23

R31 R32 R33

264

375 ¼

q21 � q2

2 � q23 þ q2

4 2ðq1q2 � q3q4Þ 2ðq1q2 þ q3q4Þ2ðq1q2 þ q3q4Þ �q2

1 þ q22 � q2

3 þ q24 2ðq2q3 � q1q4Þ

2ðq1q3 � q2q4Þ 2ðq2q3 þ q1q4Þ �q21 � q2

2 þ q23 þ q2

4

264

375 (16)



Then, the dynamics equation in the inclination and azimuthsolving will be obtained

Qkþ1 ¼

1 � 1

2xxdt � 1

2xydt � 1

2xzdt

1

2xxdt 1

1

2xzdt � 1

2xydt

1

2xydt � 1

2xzdt 1

1

2xxdt

1

2xzdt

1

2xydt � 1

2xxdt 1

2666666666664

3777777777775

Qk (17)

When the drillstring appears torsional or stick–slip vibration inthe actual drilling process, we use the algorithm defined as “DAS”method.

4 Results

4.1 Simulation Result. A program was developed with theDAU method using MATLAB software, assuming that drillstringcontinuously rotates with a constant speed and be located at a par-ticular borehole inclination and azimuth. The measurement sig-nals were simulated and were added to the triaxial accelerometersignals with signal-to-noise ratio of 20 dB, 5 dB, and 1 dB whiteGaussian noise, to the three-axis fluxgate signals with signal-to-noise ratio of 30 dB white Gaussian noise (due to the actual dril-ling process, fluxgate signals are less affected by the vibration ofthe drillstring).

Continuous change in the values of inclination and azimuth andthe error under different inclinations and azimuths are observed.Simulation results are shown in Fig. 7, the theoretical models canbe verified entirely feasible when the drillstring uniform isrotating.

4.2 Laboratory Experiment. We have done the experimen-tal study using the DAS method. Put the entire system to the labo-ratory bench (Fig. 8(a)) for testing the accuracy of the measuringsystem. Figures 8(b) and 8(c) show the accelerometer (x, y, and zaxes) and fluxgate (x, y, and z axes) measurement data. It can beseen that the accelerometer measurement noises are larger thanfluxgate measurement signals relatively. The main reason is thataccelerometers are hypersensitive to the drillstring vibrations.

Finally, when the experimental equipment is at the inclination of5 deg, the test results are shown in Table 1.

Through laboratory tests, the theoretical models can be verifiedentirely feasible when the drillstring is rotating. Simulation andexperiments collectively show that the dynamic solver methods inthis paper can meet the engineering requirements.

4.3 Field Data Analysis. The simulation results in Fig. 7show that the final solver results are seriously interfered by thenoise signals. Furthermore, the measurement signals in the prac-tice drilling engineering subject to interference are much largerthan that in the simulation. We have adopted low-pass filter andmoving average filter for noise reduction. Accelerometer signal ofz-axis is also subjected to the influence of drillstring vibration thatwas smaller relatively. We used moving average filter for furtherprocessing, as shown in Eq. (17)

Gzn¼X10

i¼1

aiGznþi�9; ai ¼

1

10(18)

We also used the finite impulse response (FIR) filter eliminationfor signal-to-noise. Noise signals of fluxgate have been consideredto be high-frequency component since it is not affected by vibration.

Assuming that an FIR filter has length of M, the input is xðnÞ,output is yðnÞ, yðnÞ can be described by the differential equation

yðnÞ ¼XM�1

k¼0

bkxðn� kÞ (19)

where bk are the filter coefficients. It can also be used for systemfunction characterization

HðzÞ ¼XM�1

k¼0

hðkÞz�k (20)

After the preprocessing, we use the DAS method for dynamicmeasurement of spatial attitude at bottom rotating drillstring. Weset a time window to judge the state of motion of the drillstring inreal time.

As shown in Fig. 9, using the DAU method, inclination and azi-muth show great fluctuations when the drillstring is rotating.Whereas the fluctuations are significantly smaller when momen-tarily at rest, this prompts us to seek a new way such as DAS

Fig. 9 The solving results of DAU method (inclination and azimuth show great fluctuationswhen the drilling string is rotating, whereas the fluctuations are significantly smaller whenmomentarily at rest)



method using the measurement signals when the drillstring is mo-mentarily at rest to improve the accuracy of the whole process.Time series is used to, as shown in Fig. 9, calculate the inclinationand azimuth every 10 s. When the drillstring appears as torsionalvibration and stick–slip phenomenon, we playback the measure-ment signals as shown in Fig. 10. In the sticky area, fluxgate sig-nals maintain at a fixed value, accelerometer signals show somefluctuations but much smaller than the performance when thedrillstring is rotating. Through the installation structure of mea-surement system, it can be inferred that the y-axis signal and thex-axis are similar except the phase difference of 90 deg. Obvi-ously, accelerometer signals should also be presented in the sinewave like fluxgate signals when the drillstring is rotating, if thereis no vibration noise.

The solving results of inclination and azimuth are shown inFig. 11, our algorithm of DAS with KF approach could effectivelyenhance the measurement precision and deduce the effect ofvibration to resolve results.

5 Conclusions

In the oil and gas drilling engineering, MWD system is usuallyused to provide real-time monitoring of the position and orienta-tion of the bottom hole. Particularly in the rotary steerable drillingtechnology and application, it is a challenge to measure the spatialattitude of the bottom drillstring accurately in real time while thedrillstring is rotating. The regular wellbore position calculationsare typically performed by measuring azimuth and inclinationwith the MWD system in a stationary mode (the drillstring nonro-tating). However, the attitude of the bottom rotating drilling toolshould be obtained in real time in both RSS and automatic verticaldrilling system.

The drillstring vibration seriously affected the accuracy ofdynamic solving. Through statistical analysis of field measurementdata, we found that the stick–slip phenomenon is always existent

throughout the drilling process, so the application of the stick–slipvibration method to improve the measurement accuracy is feasible.A dynamic algorithm was developed using the stick–slip state andKF. It can improve the accuracy of bottom drillstring inclinationand azimuth solving. All the results of simulation, experimental,and field test show that the algorithms developed in this paper havegood practicability.

Although magnetic-based surveying system is classical in theMWD, we will also use this system to achieve continuous meas-urements relying on the software algorithms. With the developingneeds of rotary steerable drilling technology, this paper studies thedynamic measurement of spatial attitude at the bottom rotatingdrillstring. Based on the theoretical analysis and verification offield data MWD, we propose a new algorithm through the state ofmotion analysis and develop the downhole measurement signalprocessing methods and the algorithm of dynamic solving of spa-tial attitude at the bottom rotating drillstring. Initially, a theoreti-cal system of dynamic solving was established and laid thetheoretical and technical foundation for the continuous MWD andRSS development.

Fig. 10 Accelerometer and fluxgate x-axis measurement data (sampling frequency 100 Hz)

Table 1 The test results of inclination with 5 deg

No. Rotary speed Azimuth Inclination Inclination error

1 0 255.5 5.48 0.482 0 256.6 5.67 0.673 0 259.0 3.42 �1.584 0–60 259.0 3.42 �1.585 0–60 253.7 4.97 �0.036 60 252.9 4.98 �0.027 60 253.9 4.98 �0.028 60–120 254.2 5.09 0.099 60–120 253.8 5.04 0.0410 60–120 252.2 4.94 �0.06



Acknowledgment

The authors express their appreciation to Drilling TechnologyResearch Institute, Shengli Petroleum Administration of SinopecCorp. for providing data and materials. In addition, we acknowl-edge the support of the Fundamental Research Funds for the Cen-tral Universities (2652015063) and the Public Welfare FundProject from The Ministry of Land and Resources (201411054).

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Fig. 11 Contrast inclination and azimuth dynamic measure-ment results with the DAU and DAS methods: (a) is the resultsof inclination and (b) is the results of azimuth, algorithm of DASwith KF approach could effectively enhance measurement pre-cision and deduce the effect of vibration on resolve results



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