Continuous Real-Time Measurement of Drilling Trajectory with New State

144 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 65, NO. 1, JANUARY 2016 Continuous Real-Time Measurement of Drilling Trajectory With New State-Space Models of Kalman Filter Qilong Xue, Henry Leung, Fellow, IEEE, Ruihe Wang, Baolin Liu, and Yunsheng Wu

Abstract— Rotary-steerable drilling provides unique features drillstring attitude (inclination and azimuth) measurement such as an extended reach and accurate well trajectory control. is usually carried out when the drillstring is not rotating. These characteristics can notably increase drilling efficiency However, as drilling technology improves, continuous mea- and safety. One of the main technical difficulties of rotary- steerable drilling is dynamically measuring the spatial attitude surement of the well trajectory becomes increasingly impor- at the bottom of the rotating drillstring as the drillstring rotates. tant. It is also essential in a rotary-steerable system (RSS). We developed a strap-down measurement system, with a triaxial An RSS [5]Ð[7] is a mechatronics tool developed for direc- accelerometer and triaxial magnetometers installed near the bit. tional drilling. It can drill a more economical and smoother The inclination and azimuth can be measured in real time even borehole. Since the introduction of RSS, rotary-steerable as the drillstring rotates. Although the magnetic system is the norm, we can use this system to achieve continuous measurement technology has achieved notable progress in reliability and while drilling; to achieve this, a novel state-space model is has become a standard drilling tool in many worldwide proposed here and the Kalman filter is used to estimate the applications. The application of RSS is restricted to high-cost states. Simulation and experiments show that a continuous-survey offshore sites and is becoming more common in cost-sensitive system with a Kalman filter approach can improve measurement land work, especially in shale-gas and shale-oil drilling [8]. precision and reduce errors produced by drillstring vibration. Despite popular use of the RSS, field-trial results of Index Terms— Continuous measurement while drilling continuous measurement of inclination and azimuth have not (MWD), directional drilling, Kalman filter, state-space model, been well documented in the literature. However, measuring strap down. the posture of downhole tools as the drillstring rotates is I. INTRODUCTION essential because of its closed-loop control structure [9], [10]. IRECTIONAL drilling technology involves directing A bottom-drilling tool shows complex dynamics while rotating Da wellbore along a predefined trajectory, which owing to the combined effects of nonlinear vibrations, such dramatically reduces costs and saves time during drilling as vertical vibration, horizontal vibration, eddy, and sticky operations [1]Ð[3]. During the last several years, more and slip [11], [12]. The effects of such vibrations cause the more attention had been paid to the development of directional measurement sensors to generate large errors. This is a huge well-drilling technologies. Technology for directional- challenge for signal processing [9], which is completely drilling navigation is currently based on an integrated different from the measurement-while-drilling (MWD) survey magnetometer and accelerometer triad [4]. To compute the systems in current oil and gas industry. bottom-hole assembly (BHA) position, data of the earth’s Continuous MWD is studied under laboratory magnetic field and the force of gravity are measured. The conditions using a gyroscope-based system [13]Ð[15]. surveying system is executed along the well trajectory at ElGizawy et al. [13], Elgizawy et al. [14], and stationary survey stations. In drilling engineering, the bottom Jurkov et al. [15] proposed an advanced inclination and direction sensor package based on an inertial navigation Manuscript received April 15, 2015; revised August 3, 2015; accepted system (INS). They verified the reliability of the algorithm August 4, 2015. Date of publication October 6, 2015; date of current version December 7, 2015. This work was supported in part by the Fundamental through simulation, which used INS to achieve continuous Research Funds for the Central Universities under Grant 2652015063 and in MWD with high accuracy. The influences of vibration part by the Public Welfare Fund Project through the Ministry of Land and and temperature on MWD were also analyzed [16]Ð[18]. Resources under Grant 201411054. The Associate Editor coordinating the review process was Dr. George Xiao. Yanshun et al. [19] and Chen et al. [20] conducted a Q. Xue and B. Liu are with the Key Laboratory on Deep GeoDrilling similar study by developing an MWD instrument based Technology, Ministry of Land and Resources, School of Engineering and on a predigested inertial measurement unit. However, they Technology, China University of Geosciences, Beijing 100083, China (e-mail: [email protected]). did not consider the downhole complex situations, severe H. Leung is with the Department of Electrical and Computer Engineering, vibration, and high temperature. These are great challenges University of Calgary, Calgary, AB T2N 1N4, Canada. for measurement of accuracy and sensors’ lifetime. Drillstring R. Wang is with the College of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China. vibration can greatly affect the life of the gyroscope, and an Y. Wu is with State Grid Haixing Power Supply Company, increasing temperature can cause drift error in the gyroscope. Cangzhou 510623, China. The approaches mentioned above can increase the accuracy Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. of measurements to a certain extent. However, effort still needs Digital Object Identifier 10.1109/TIM.2015.2479096 to be made in order to improve the performance of the MWD 0018-9456 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. XUE et al.: CONTINUOUS REAL-TIME MEASUREMENT OF DRILLING TRAJECTORY 145

Fig. 1. (a) Multimodel measurement system at the drill bit. (b) Construction of measurement system.

TABLE I x, y,andz axes, respectively. Moreover, mx , m y,andmz are CHARACTERISTICS OF SENSORS defined as survey signals of the triaxial magnetometers on the x, y,andz axes, respectively. Assume that the earth’s magnetic = ( 2 + 2 + 2)1/2 field strength is M. Obviously, M mx m y mz . Under a certain sample frequency (100 Hz), the measuring signal can be considered as a time series. Assume that the acceleration of gravity is G,and gx, gy,andgz are defined as survey signals of gravity acceleration on the x, y,andz axes, respectively. Then, = ( 2 + 2 + 2)1/2 , , ) G gx gy gz . The survey signals (ax ay az of the triaxial accelerometers include not only the acceleration of gravity but also the acceleration of the drillstring vibration. Electronic instruments consisting of three-axis accelerometers instrument. Qilong Xue et al. [9] developed a strap-down and three-axis magnetometers are shown to relate to the multimode surveying system. They gave more consideration measured inclination and azimuth. The drillstring posture is to the actual situation of the drilling process and used field determined via the following known equations: test data to study the measurement algorithm. This system is ⎛ ⎞ more conducive to field applications. Moreover, improvement g2 + g2 ⎝ x y ⎠ in accuracy is crucial, especially for the continuous MWD Inc = arctan (1) gz of an RSS, for precise and efficient measurement of wellbores drilled for oil and gas exploration. Within the signal-processing G · (gxm y − gymx ) Azi = arctan . (2) community, Kalman filter still remains a very active topic. This m g2 + g2 − g (g m − g m ) paper is concerned with improving the accuracy and stability z x y z x x y y of inclination and azimuth measurements of the accelerometer The three-axis inclination and six-axis azimuth equa- and magnetometer. We developed new state-space models that tions [22] are used in the static MWD surveys as industry- were applied to the Kalman filter model. The algorithm greatly standard survey methods. The azimuth direction is determined improved the accuracy of well-trajectory measurements and in a stationary mode by using three-axis magnetometers, while is expected to be applied to ordinary magnetic surveying the inclination and the tool face angle are determined using systems, which are more widely used in drilling engineering. three-axis accelerometers. Drilling has to pause frequently at surveying stations in order to allow the inclination and II. MEASUREMENT SYSTEM azimuth to be surveyed. The well trajectory is then computed We develop a strap-down MWD system here that incorpo- between the two surveying stations based on some mathe- rates three-axis magnetometers and three-axis accelerometers matical assumptions; It is assumed that the drilled distance arranged in three mutually orthogonal directions [9], [10], is a smooth arc. In (1) and (2), only the acceleration of as shown in Fig. 1(a). The magnetic measuring tools are gravity is concerned, and the drillstring vibration signals are installed in the interiors of nonmagnetic drill collars. These considered as noise. The determination of azimuth while special drill collars are usually designed from monel metal drilling (while the sensors are rotating) was not demonstrated to avoid external interference with measurements taken by owing to limitations in the capabilities of downhole process- magnetic MWD surveying tools [3], [9]. Fig. 1(b) shows the ing. The survey signals of triaxial accelerometers include not structure of the downhole measurement system, and Table I only the acceleration of gravity but also the acceleration of shows the characteristics of the sensors. ax , ay,andaz are drillstring vibration. Unlike the conventional MWD, the incli- defined as survey signals of the triaxial accelerometers on the nation and azimuth should be dynamically solved when the 146 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 65, NO. 1, JANUARY 2016

Fig. 2. Energy spectrum of lateral vibration signals (left) and longitudinal vibration signals (right). drillstring rotates. Accelerometers are hypersensitive to vibrations, so the violent vibration of a BHA leads the measured signals to be submerged in noise signals. The continuous MWD in this paper is based on a strap-down multimodel surveying system [9]. According to the data of field test, we completed a Fig. 3. Solving process for the system. frequency analysis of the vibration signals to evaluate if the white noise hypothesis. Frequency analysis is indispensable The measurement equation of the system is given by when discussing the most advanced approach that involves dynamic spectral analysis and analyzing how the spectrum zk = Hk xk + ηk (5) of a signal evolves in time. This analysis is performed with Gabor transforms [25], which are close relatives of wavelet where zk is the measurement vector of the system output, η transforms. Gabor transforms are particularly useful in ana- Hk is the observation or design, and k is the measurement η lyzing drillstring vibration signals. The transform is employed noise. The system noise wk and the measurement noise k here to determine the sinusoidal frequency and phase are unassociated zero-mean white-noise processes with deter- content of local sections of a signal as it varies with time. The mined autocovariance functions. function is first multiplied by a Gaussian window function. The We developed an algorithm with new state-space models resulting function is then transformed by the Fourier transform. by analyzing drillstring dynamics. In the solution system, we define the input vector of KF-1 as We use a timeÐfrequency box to express the energy distribution of the Gabor function. The timeÐfrequency spectrum of a a a X = x y z the vibration signal is plotted in Fig. 2. The Gabor transform mx m y mz can help us discriminate the rotational movement pattern. which is measured by the three-axis magnetometers and Define Gu,ξ (t) as the time window function, where u is center three-axis accelerometers. The input vector of KF-2 is the point, σ is the width, and the Fourier transform of Gu,ξ (t) can = I be expressed as inclination and azimuth, defined as M A ,whereI is ˆ ˆ iu(ω−ξ) the inclination of the borehole and A is the azimuth of the Gu,ξ (ω) = G(ω − ξ)e . (3) borehole. Using the solving process as shown in Fig. 3, we As shown in Fig. 2, from the energy spectrum of develop two KFs for the entire drilling process. After KF-1, lateral vibration signals (left) and longitudinal vibration we can obtain the more precise signals of gravity acceleration signals (right), we find that the spectrum does not particularly gx, gy,andgz, that defined as the output of KF-1. Using have the energy concentration point, and the signals can be the gravity accelerations, we can obtain the inclination and considered as random. Therefore, the hypothesis of white azimuth by the equation developed when the drillstring rotates. noise in the new Kalman filter is satisfied. KF-2 is then used to further smooth the drilling trajectory. The output of KF-2 is defined as M =[I A]T ,whichismore III. NEW KALMAN FILTER APPROACH precise. The application of KF [23], [24] requires that both the system and the measurement models of the underlying process be A. State-Space Model for KF-1 linear. A discrete-time linear state-space system is described by The sensors installed at the center of the drillstring, and x = , − x − + G − w − k k k 1 k 1 k 1 k 1 (4) the measurement signals of the x and y axes, will exhibit where k,k−1 is the state transition matrix, xk is the state a sine wave during rotation. Theoretically, accelerometer vector, Gk−1 is the noise distribution matrix, wk−1 is the and magnetometer signals have the same rule. In the actual process noise vector, and k is the measurement epoch. drilling process, the vibration of the drillstring affects less XUE et al.: CONTINUOUS REAL-TIME MEASUREMENT OF DRILLING TRAJECTORY 147 on the magnetometer signals. That is, the magnetometer as follows: signals are used to calibrate the accelerometer signals. 2Np 2 2Np 2 From the laboratory testing, we can conclude that the = gx dTM + = gydTM − TM 0 TM 0 changes of signals of fluxgate in line with signals of gravity I = tg 1 (9) − 2Np g dT acceleration, as shown in Fig. 6, will be provided in the TM =0 z M following. A = tg−1 Assuming that the angular velocity is ωx,y,z and the 2Np = G(m y gx − mx gy)dTM sampling interval is t,then × TM 0 2Np 2 + 2 − 2Np ( + ) = mz gx gy dTM = gz mx gx m y gy dTM mx,y(k) M sin ωx,yt TM 0 TM 0 = (10) mx,y(k − 1) M sin ωx,y(t − t) = G sin ωx,yt gx,y(k) where TM is the magnetic toolface angle: TM = = . (6) −1 tg (−m y/mx ). Toolface angle used for near-vertical wells. G sin ωx,y(t − t) gx,y(k − 1) Magnetic toolface is the angle, or azimuth, of the borehole

gx(k) survey instrument within the wellbore measured clockwise In the KF-1, we define the state vector as xg(k) = gy(k) , relative to magnetic north and in the plane perpendicular to ( ) gz k the wellbore axis; the north, east, south, and west directions as shown in Fig. 2, from the vibration signals of a , a ,anda , x y z have magnetic toolface angles of 0¡, 90¡, 180¡, and 270¡, we can obtain the signals of gravity acceleration x (k). Thus g respectively. Magnetic toolface may be corrected to reference ax the measurement vector of the system output as z(k) = ay , either grid north or true north. az Although the drillstring rotational speed is a way to deter- when the drillstring rotates, the measurement signals of the mine whether the string is rotating or not, it reliability of this x-andy-axis will exhibit a sine wave except the signal of the approach is not high. Instead, using the standard-deviation z-axis. So the transformation matrix is defined as statistical methods to determine the drillstring movement is ⎡ ⎤ m (k) more effective because it reflects the degree of dispersion x 00 ⎢ m (k − 1) ⎥ among the individuals within the group. Using 50 data points ⎢ x ( ) ⎥ , ,..., , Hk = ⎢ m y k ⎥. as a time window, assumed them to be x1 x2 x49 x50,we ⎣ 0 0 ⎦ σ = (( / ) N ( −¯)2)1/2 m y(k − 1) get the standard deviation 1 N i=1 xi x . 001 The drillstring can be considered static when the standard deviation σ is close to zero. The system noise wk and the measurement noise ηk are uncorrelated zero-mean white-noise processes. Therefore, we obtain the state-space model of the KF-1 as follows: C. State-Space Model for KF-2 ⎡ ⎤ In the drilling process, the movement states that σ = 0or m (k) x σ = 0 will appear alternately. When σ = 0, the results are ⎢ ( − ) 00⎥ ⎢ mx k 1 ⎥ more accurate because the vibration is slight when the drill- x (k) = ⎢ m y(k) ⎥ x (k − 1) g ⎣ 0 0 ⎦ g string is not rotating. We develop another Kalman filter (KF-2), m (k − 1) y as shown in Fig. 2, to smooth the trajectory of the drilling. 001 ⎡ ⎤ (KF-2 was divided into KF-2.1 and KF-2.2, respectively, as ( − ) wx k 1 showninFig.5.) + ⎣ ( − ) ⎦ wy k 1 (7) In a normal drilling process, the drilling operation has to ( − ) wz k 1 frequently stop at measurement stations in order to measure the z(k) = Hk xg(k) + η(k). (8) inclination and azimuth. The well trajectory is then computed between the two surveying stations based on mathematical assumptions. For instance, it may be assumed that the drilled B. Calculating the Inclination and Azimuth distance is a straight line, smooth arc, or polygonal line; each When the drillstring rotates, the above equations are not requires a different calculating method. Assuming that the applicable. The sensors installed at the center of the drillstring, 3-D coordinates of the measuring Nth point of the actual and the measurement signals of the x-andy-axis, will exhibit drilling trajectory are (xN , yN , zN ), the measuring (N + 1)th a sine wave during rotation. point is (xN+1, yN+1, zN+1), and the well depth, vertical Through KF-1, we obtain gx , gy,andgz which are defined depth, inclination, and azimuth are L N , HN , θN ,andψN , as survey signals of gravity acceleration on the x, y,andz and L N+1, HN+1, θN+1,andψN+1, respectively. The well axes, respectively. Then define the input vector of the system trajectory between the two points can then be defined as as X = gx gy gz . follows: mx m y mz ⎧ = ⎪ = − Define the rotational speed as R.IfR 0, ⎨⎪L L N+1 L N (1) and (2) are used to calculate the inclination and azimuth. H = HN+1 − HN = ⎪θ = (θ + θ )/ (11) R 0 indicates that the drillstring is rotating, and compu- ⎩⎪ N N+1 2 tational formulas of inclination I and azimuth A are given ψ = (ψN + ψN+1)/2. 148 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 65, NO. 1, JANUARY 2016

Fig. 4. Trajectory prediction using method of inclined plane cirque.

If the vertical depth H is a known, the 3-D coordinates of the measuring (N + 1)th point can be deﬁned as ⎧ ⎨ + = + θ ψ xN 1 xN H tan cos Fig. 5. Solving process for KF-2. = + θ ψ ⎩yN+1 yN H tan cos (12) zN+1 = zN + H. We can obtain the spatial coordinates of each point by during t). As shown in Fig. 4, we can use the measurement recursive calculation, thereby obtaining the entire drilling of acceleration on the z-axis to calculate the displacement. trajectory. az is the signal of the triaxial accelerometers on the z-axis, As shown in Fig. 4, we can use the wellbore trajectory which is combined with the gravitational acceleration and extrapolation method to establish a recursive relationship vibration acceleration. The measurement of acceleration on between two adjacent measurement points. Assume L is the the z-axis time series is deﬁned as az(k). depth of the drilling, γ is the angle of the drilling trajectory So before calculating the displacement L, we should and its tangent. Then exclude the impact of gravity as follows: ( ) = ( ) − · ( ) L(k) = L(k − 1) + L(k) (13) fgz k az k G cos Ik−1 (18)

γ = arccos [cos(Ik− ) cos(Ik− ) + sin(Ik− ) ( ) 2 1 2 where fgz k , the acceleration time series function by remov- ( ) × sin(Ik−1) cos(Ak−1 − Ak−2)] (14) ing the acceleration of gz, can be calculated from az k and γ inclination I − corresponding to the same time. γ(k) = L(k). (15) k 1 L(k − 1) Then, we can calculate the depth (L) of drilling using ( ) From (13) to (15), we can use two points to estimate the acceleration on the z-axis time series fgz k . Define the state ( ) next point, so the well trajectory can be smoothed. As shown in L k vector as L(k) = L˙ (k) , the measurement vector of Fig. 5, we can calibrate the drilling trajectory using Kalman L¨ (k) filter 2.2, wherein the kth measurement point is defined as the system output as z(k) = f (k), we develop a state-space ( ) =[ gz P k Ik Ak]. The system inputs are P(k-2) and P(k-1), model for KF-2.1 as follows: KF-2.2 estimated P(K) combined with measured values and ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ( ) 1 2 ( − ) ε( ) the theoretical calculation values. L k ⎢1 t t ⎥ L k 1 k ⎣ ˙ ( ) ⎦ = ⎣ 2 ⎦ ⎣ ˙ ( − )⎦ + ⎣ε(˙ )⎦ KF-2.2 can smooth the well trajectory using inclination L k 01 t L k 1 k (19) ¨ ( ) ¨ ( − ) ε(¨ ) and azimuth as inputs. Assume that the state vector is L k 00 1 L k 1 k I ⎡ ⎤ x(k) = k and the measurement vector of the system ( ) Ak L k ⎣ ˙ ( ) ⎦ Ik fg (k) = 001 L k + η(k). (20) output is y(k) = , which is calculated from (8) and (9). z ¨ Ak m L(k) ( ) = 10 The transformation matrix is defined as H k 01 . By preprocessing the measured signals, a dynamic azimuth- According to (12)Ð(14), the state-space model for KF-2.2 can and inclination-solving algorithm is established based on be obtained in (16) and (17), as shown at the bottom of this dynamic analysis of the bottom rotating drilling tool. Based page. on the theoretical model, we develop a Kalman filter to As shown above, we should determine L as the improve the solver accuracy as well; the state-space equations KF-2.2 input (the distance that the drill bit moves forward used for the Kalman filter have been established based on

⎡ ⎤ sin(γ + γ(k)) ⎢ arccos cos(Ik−2) cos(γ + γ(k)) − (cos(Ik−2) cos γ − cos(Ik−1)) ⎥ Ik ⎢ sin (γ ) ⎥ wI (k) = ⎣ (γ ( )) − ( ) ( ) ⎦ + (16) Ak cos k cos Ik−1 cos Ik wA(k) Ak−1 + (Ak−1 − Ak−2) · arccos sin(Ik−1) sin(Ik) y(k) = H (k)x(k) + v(k) (17) XUE et al.: CONTINUOUS REAL-TIME MEASUREMENT OF DRILLING TRAJECTORY 149

Fig. 6. (a) Laboratory bench. (b) 3-D simulation model of the test bench. (c) Experimental equipment at inclinations of −5¡, −2¡, 0¡, 2¡, and 5¡ (shown by the red line). the drilling trajectory predicted. The dynamic measurement When the drillstring continuously rotates with a con- algorithm with the Kalman filter is a new model that can stant speed and is located at a particular borehole inclina- greatly reduce the solution errors. tion and azimuth, accelerometer (x, y, z axes) and fluxgate (x, y, z axes) measurement data are obtained as shown in IV. EXPERIMENTAL RESULTS Fig. 7(b) and (c), respectively. We put the entire system on a laboratory bench [Fig. 6(a)] Dynamic measurement algorithms developed in this paper to conduct an accuracy test of the measurement system. were tested through laboratory bench and field measurement Fig. 7(b) and (c) shows the measurement data for the mag- data, respectively. netometers (x, y, z axes) and accelerometers (x, y, z axes). Here, we can calculate the signals of the magnetometers A. Laboratory Testing and accelerometers if we know the inclination according The combined measurement system was tested first in a to (9) and (10). Assumed that the reference of the measure- laboratory environment, as shown in Fig. 6. Measurement data ments data is the reverse theoretical calculation results, the were obtained under different inclination and rotating speed relative errors of measurement data as shown in Fig. 8, it can conditions. In the experimental system, we used the encoder be seen that the accelerometer noises are relatively much larger to measure the drillstring rotational speed and positioned the than the magnetometer signal noises, the peaks in Fig. 8 show inclination mechanically. that the measurement error increases when drillstring appear As shown in Fig. 6(b), the power simulation motor (with stick-slip vibration. The main reason is that accelerometers digital 1 representation), will work to provide electricity, are hypersensitive to drillstring vibrations. In the field test, although this time the drillstring not continuously rotates, the the vibration of the drillstring is more violent. Using the power simulation motor will generate vibration making the sta- components of gravity acceleration on the x, y,andz axes can tic solver results as above are not very accurate. The platform help us calculate the inclination and then combine the fluxgate rotating motor (with digital 7 representation) working makes measurement signals to obtain the azimuth [Fig. 7(d)]. the drillstring continuously rotates, we could use (1) and (2) In engineering applications, the inclination error of 0.1 to dynamically solve the inclination and azimuth. In the will suffice. As shown in Fig. 6(c), when the experimental experiment, we set the laboratory test at different inclinations equipment is at inclinations of −5¡, −2¡, 0¡, 2¡, and 5¡, and different rotational speeds, as shown in Fig. 6(c). the test results are shown in Table II. Through laboratory tests, 150 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 65, NO. 1, JANUARY 2016

Fig. 7. Measurement system. (a) Construction of measurement system. (b) Laboratory survey signals of triaxial magnetometers on the x, y, and z axes. (c) Laboratory survey signals of triaxial accelerometers on the x, y, and z axes. (d) Continuous survey method, gx , gy, and gz are the gravity accelerations on the x, y, and z axes, in (8) and (9), we are only concerned about the acceleration of gravity.

Fig. 8. Relative errors of accelerometers and magnetometers measurement Fig. 9. Schematic of field test. The electronic circuit is installed on a data. compressive cylinder and placed in the axis of the drill collar, the sampling frequency of measurement and the control system is 100 Hz, and the TABLE II measurement data can be stored in real time. ERROR OF INCLINATION satisfactory when the drillstring rotates. The accelerometer signals of the field tests are completely different from those obtained via laboratory survey. The azimuth is determined using three-axis magnetometers, while the inclination is determined using three-axis accelerometers. Therefore, the drillstring vibration dramatically amplifies the error of the continuous survey when the drillstring rotates. The algorithms developed in this paper will solve this problem by improving the accuracy of continuous MWD with the proposed state- space models. Fig. 9 shows the schematic of the field test. the theoretical models can be verified as entirely feasible when From the measurement data stored in real time, we can the drillstring rotates. Experiments show that the dynamic obtain the vibration signals measured by the accelerometer solving methods in this paper meet engineering requirements. (x, y,andz axes), which contain the gravity acceleration on the x, y,andz axes. B. Field-Drilling Testing We use the real field-test data to demonstrate the feasibility In the field, a few methods such as a low-pass filter and of our algorithm. The results are shown in Fig. 10. During moving average filter are considered, but the results are not the first step of the solving process for the system (Fig. 3), XUE et al.: CONTINUOUS REAL-TIME MEASUREMENT OF DRILLING TRAJECTORY 151

Fig. 10. Signals of triaxial accelerometers on the x, y,andz axes, as shown in subparts (a), (b), and (c) respectively, before KF-1 and after KF-1.

Fig. 11. Solving results of inclination and azimuth at XuanYe 1. the signals of the triaxial accelerometers (ax , ay, az) going though KF-1 get the gravity acceleration (gx, gy, gz). The results of KF-1 are shown in Fig. 10. The red line is the output of KF-1, that is, the gravity acceleration. Because the accelerometer on the z-axis is not influenced by the rotation of the drillstring, the curve tends to be a straight line when the inclination does not change [Fig. 10(c)]. We cannot estimate the error of this process, because the data came from the field test, which impossible to know the exact measurements. In the actual drilling process, we need to find a way to measure how good the measurement accuracy is. For a continuous drilling trajectory, there is no method that Fig. 12. Inclination error of solving results. could be used to accurately measure the wellbore trajectory. So we could only use the MWD static measuring points for measurement system was deployed at multiple formations. comparison. It should be feasible to evaluate the advantages The field tests were carried out on wells using automatic of the dynamic measurement algorithm. Tests of more than vertical or rotary steerable drilling. Three- and four-rib ten wells were conducted throughout China. The dynamic actuators were adopted. A lot of raw measurement data 152 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 65, NO. 1, JANUARY 2016

TABLE III BASIC PARAMETERS OF FIELD TEST

Fig. 13. Solving result of inclination at Anshun1. were accumulated. These data were input into our algorithm are all used for calculation, and at the same time, filtered for authentication. Conclusions on bit movement rules were signals on the x and y axes were stored; on condition of drawn by analyzing and summarizing large amounts of data. rotation string, real time filtered signals on the z-axis and Two wells in China (Xuanye1 and Anshun1) are selected stored signals of the x and y axes with nonrotating string are here to evaluate the algorithm. The results for inclination adopted. In addition, stick-slip state of the down-hole drilling and azimuth are shown in Figs. 11 and 12. The basic para- tool is considered as a nonrotating stationary state. meters of field tests are shown in Table III. The proposed Inclination and azimuth show great fluctuations when the Kalman filter method can significantly improve the precision drilling string rotates. The results obtained using the method of the survey and reduce vibration interference in the solution we developed are shown again in Figs. 11 and 12. Comparing results. static measurement points, it can be seen that the dynamic We can also use the periodic static measurements to improve measurement inclination error is less than 1¡, and the azimuth the dynamic solver accuracy. Dynamic solution approach to error is relatively large, between 5¡ and 20¡, because it is the bottom of the rotating drillstring attitude is proposed in [9]. calculated under small inclination angles. When the angle of With nonrotating string, filtered real time signals on three axes inclination is small, accelerometer signals of Gx and G y are XUE et al.: CONTINUOUS REAL-TIME MEASUREMENT OF DRILLING TRAJECTORY 153 small as well; this leads to an increased impact of noise. The dynamic measuring algorithm proposed is analyzed Moreover, the error accumulated in formula (2) causes the through downhole measurement instance data. The results azimuth error to become larger. show that the algorithm can effectively reduce inclination- 1) Drilling at Xuanye1: This drilling field test was and azimuth-solving errors. Field measurement data analysis conducted on May 19, 2010. We use the static measurement shows that the algorithm can effectively solve the dynamic data to evaluate the continuous solving results. From inclination and azimuth when the inclination is large. Figs. 11 and 12, we can see that the inclination error is less than 1¡, additionally, the error is gradually reduced. ACKNOWLEDGMENT Unfortunately, we did not get the static field measurement The authors would like to thank the Drilling Technol- data of azimuth. ogy Research Institute, Shengli Petroleum Administration of 2) Drilling at Anshun1: This drilling field test was Sinopec Corp, for providing data and materials. conducted on January 23, 2012. We use the static measurement data to evaluate the continuous solving results. From Fig. 13, REFERENCES we can see that the inclination error is less than 1¡, and that [1] S. Brzezowski and J. Fagan, “Analysis of alternate borehole survey the azimuth error is between 5¡ and 20¡. systems,” in Proc. 39th Annu. Meeting Inst. Navigat., Houston, TX, USA, 1983, pp. 71Ð78. V. C ONCLUSION [2] S. D. Joshi and W. Ding, “The cost benefits of horizontal drilling,” in Proc. Amer. Gas Assoc., Arlington, VA, USA, 1991, pp. 679Ð684. In the directional drilling and rotary-steerable drilling [3] W. A. Rehm, A. Garcia, and S. A. 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Qilong Xue was born in 1983. He received the bachelor’s degree in electrical engineering and the Ph.D. degree in drilling engineering from the Baolin Liu was born in 1959. He received the China University of Petroleum, Beijing, China, Ph.D. degree in engineering from the China Uni- in 2006 and 2014, respectively. versity of Geosciences, Beijing, China. He was with PetroChina, Beijing, from 2006 to He is currently a Professor and the Director of the 2008. He was a Joint Researcher with the University Key Laboratory on Deep GeoDrilling Technology of Calgary, Calgary, AB, Canada, from 2012 to of the Ministry of Land and Resources, China Uni- 2013, where he was involved in real time measure- versity of Geosciences. His current research inter- ment of bottom drilling tool’s attitude and rotary ests include scientiﬁc drilling, environmental science steerable drilling system. He is currently an Assistant drilling, computer controlled drilling, and new tech- Professor with the China University of Geosciences, Beijing. His current nology drilling engineering. research interests include measurement and control technology of drilling Dr. Liu is a member of the Professional Committee engineering. of Mineral Exploration Engineering.

Henry Leung (F’15) received the Ph.D. degree in electrical and computer engineering from McMaster University, Hamilton, ON, Canada. He was with Defence Research Establishment Ottawa, Ottawa, ON, Canada, where he was involved in the design of automated systems for air and maritime multisensor surveillance. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Calgary, Yunsheng Wu was born in 1977. He received the bachelor’s degree in electric Calgary, AB, Canada. His current research system and automatism from Hebei Radio and Television University, Hebei, interests include chaos, computational intelligence, China, in 1999. information fusion, data mining, robotics, sensor networks, and wireless He has been with State Grid Haixing Power Supply Company, Cangzhou, communications. China, since 2000.