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Comparison of the bit–torque models for estimating bit-rock interaction parameters in real-time using an adaptive observer
Abstract. Obtaining real-time estimates of the bit-rock interaction (BRI) parameters and real-time formation pose significant challenges in developing an automated closed-loop geo-steering system for drilling operations. A major challenge for the same is the prohibitively expensive high bit-rate and low latency downhole telemetry systems. Drilling dynamics can be broadly divided into off-bottom and on-bottom dynamics. Recent results have successfully captured the significant dynamics for off-bottom dynamics and have been validated against the field data . However, developing an on-bottom dynamics field validated model is faced with significant challenges in accurately estimating the bit-rock interaction parameters, which in turn aid in estimating formation detection in real-time. A simulation-validated on-bottom dynamics model was recently proposed by Auriol et al. . The model was developed based on the understanding of bit-rock interaction as proposed by Detournay and Defourny . The BRI law, proposed by Detournay and Defourny, is dependent on friction coefficient at the rock contact, bit constant, depth of cut, intrinsic specific energy of the rock, drilling strength, and weight-on-bit (WOB). Auriol et al.  modified the BRI law by simplifying the model whose BRI parameters are dependent on WOB and depth of cut. The variations in the BRI parameters give insights into the happenings of drilling at the interface of the drillstring. However, this model doesn’t give a direct insight into the changes in the rock strength. To address the same, a mechanical specific energy (MSE) based law is proposed to obtain the bit torque. The changes in the bit-torque obtained using the MSE-based approach give direct insights into the changes in the rock strength, which is helpful for formation change detection.
The off-bottom dynamics field validated model is based on the distributed drillstring model and uses only the surface parameters, RPM, and torque. In the proposed work, the on-bottom dynamics model as proposed by Auriol et al. and the MSE-based bit-torque models are combined with the field-validated off-bottom dynamics model. Coupled with the surface RPM and surface torque, the proposed model uses additional surface measurements, weight-on-bit, differential pressure, and flow rate to estimate the downhole RPM, downhole torque, and the BRI parameters. In proposed model assumes the torsional motion of the drill string to be the dominating dynamics behavior, a constant rate-of-penetration (ROP) and therefore a steady axial velocity of the bit, no distributed axial dynamics, and the friction coefficients along the drillstring are known. The proposed models are field validated against the field data obtained for an unconventional well drilled in North America.
The soft sensor developed in this work is the extension of the same developed for the off-bottom dynamics field validated model that provides estimates for downhole torque and the BRI parameters along with the downhole RPM by using only the surface measurements. Once the bit tags the bottom, the estimation of the friction coefficients is stopped, and the BRI parameters and the downhole torque are estimated. The main reason behind adopting such an approach is that the observer used in the model cannot distinguish between friction coefficients and the bit-rock interaction parameters. By using such an approach, the friction coefficients and the BRI parameters are estimated separately, without the need for any further complex mathematical model. The estimates provided by the proposed soft sensor were found to be robust to poor initial estimates. The vital feature of the observer is its ability of adaptive estimation. Convergence of the friction parameters is aided by the adaptive estimation nature of the soft sensor, which otherwise is computationally expensive using other techniques that include the industry-standard friction tests where the pipe is raised and then lowered. The model used in this work is computationally efficient, which is a result of its simplistic nature. This makes the proposed model an appealing candidate for online, real-time sensing systems for drilling applications.
Keywords: Bit-rock interaction (BRI), depth-of-cut, weight-on-bit, observer estimation
 S. S. Kandala, and R. J. Shor, “Evolution of static and kinetic friction in a horizontal well using an adaptive model-based observer: Field validation,” Journal of Petroleum Science and Engineering, vol. 208, part D, 2022.
 J. Auriol, U. J. F. Aarsnes, and R. Shor, “Self-tuning torsional drilling model for real-time Applications,” ACC 2020.
 E. Detournay and P. Defourny, “A phenomenological model for the drilling action of drag Bits,” International journal of rock mechanics and mining sciences & geomechanics abstracts, vol. 29, pp. 13–23, 1992.
Biography. Shanti Swaroop Kandala received a Ph.D. degree in Mechanical and Aerospace Engineering from the Indian Institute of Technology Hyderabad, in 2020. He has been a postdoctoral associate with Dr. Roman Shor in the Geothermal Energy Laboratory at the University of Calgary since January 2020. His research interests include modeling, analysis, and control of dynamical systems, optimization, biomechanics, robotics, cyber-physical systems, data-driven modeling, and geothermal energy.