IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 6, DECEMBER 2002 1177 Accuracy Limitations of FOG-Based Continuous Measurement-While-Drilling Surveying Instruments for Horizontal Wells Aboelmagd Noureldin, Dave Irvine-Halliday, and Martin P. Mintchev Abstract—Horizontal drilling processes in the oil industry uti- lize directional measurement-while-drilling (MWD) instruments to provide real-time monitoring of the position and the orientation of the bottom hole assembly (BHA). It has been reported that a single fiber optic gyroscope (FOG) can be incorporated with three-axis accelerometers to provide real-time MWD surveying of horizontal wells. However, the long-term performance and the ac- curacy limitations of this FOG-based instrumentation system have not been discussed. This article aims at describing a methodology for quantitative long-term analysis of the various surveying errors while drilling the near-vertical sections of the well. It also offers some techniques to enhance the long-term surveying accuracy in an experimental model of the FOG-based downhole-surveying instrument. The surveying errors are optimally estimated by the Kalman filtering techniques, and their long-term analysis is based on studying the corresponding mean square estimation errors. In order to limit the long-term growth of the surveying errors, we suggest improving the velocity computation provided by the FOG-based system either by continuous velocity update or by zero velocity update at some predetermined surveying stations. These techniques have significantly limited the long-term growth of the position errors (less than 100 m over a more than 2-h experiment). Moreover, the errors associated with the BHA orientation components were kept at less than 1 . Suggested methodology significantly improved the surveying accuracy in an experimental model of the FOG-based MWD surveying system. Index Terms—Borehole surveying, error analysis, fiber optic gy- roscopes (FOG), inertial positioning, oilfield instrumentation. LIST OF ABBREVIATIONS BHA Bottom hole assembly. FOG Fiber optic gyroscope. INS Inertial navigation system. MSEE Mean square estimation error. MWD Measurement-while-drilling. ZUPT Zero velocity update. NOMENCLATURE FOG measurements in degrees/s. Accelerometer measurements along the -direction in m/s . Manuscript received May 11, 2002; revised September 25, 2002. This work was supported in part by International Downhole Equipment, Ltd., Canada, Micronet Centers of Excellence, Canada, Alberta Energy Research Institute, Canada, and the Killam Memorial Fund, Canada. The authors are with the University of Calgary, Department of Electrical and Computer Engineering, Calgary, AB T2N 1N4 Canada (e-mail: anoureld@ucal- gary.ca; halliday@enel.ucalgary.ca; mintchev@enel.ucalgary.ca). Digital Object Identifier 10.1109/TIM.2002.808025 Accelerometer measurements along the -direction in m/s . Accelerometer measurements along the -direction in m/s . Synthetic rotation rate component along the East di- rection in degrees/s. Synthetic rotation rate component along the North direction in degrees/s. Inclination angle in degrees. Roll angle in degrees. Azimuth angle in degrees. Velocity component along the East direction in m/s. Velocity component along the North direction in m/sd. Velocity component along the vertical direction in m/s. Transformation matrix between the b-frame and the local-level frame. Earth gravity in m/s . Latitude angle in degrees. Longitude angle in degrees. Altitude in meters. FOG measurement error in degrees/s. Accelerometer measurement error along the -di- rection in m/s . Accelerometer measurement error along the -di- rection in m/s . Accelerometer measurement error along the -di- rection in m/s . Synthetic rotation rate component error along the East direction in degrees/s. Synthetic rotation rate component error along the North direction in degrees/s. Inclination angle error in degrees. Roll angle error in degrees. Azimuth angle error in degrees. Velocity error along the East direction in meters/s. Velocity error along the North direction in meters/s. Velocity error along the vertical direction in me- ters/s. Latitude angle error in degrees. Longitude angle error in degrees. Altitude error in meters. Position error along the East direction in meters. Position error along the North direction in meters. 0018-9456/02$17.00 © 2002 IEEE