Simulation and Measurement of High-Frequency Torsional Oscillation (HFTO)/High-Frequency Axial Oscillation (HFAO) and Downhole HFTO Mitigation: Knowledge Gains Continue Using Embedded High-Frequency Drilling Dynamics Sensors

High-torque, low-speed drilling mud motors are typically used to drive rotary-steerable systems (RSS) to improve the rate of penetration (ROP) of the RSS bottomhole assemblies (BHA). Downhole drilling dysfunctions are common when powered RSS BHAs are pushed to the limit for maximum drilling performance. High-frequency (HF) continuous recording compact drilling dynamics sensors were embedded into the bit, bit box of the RSS, slow-rotating housing (SRH) of the RSS, bit box of the mud motor, and top subassembly (sub) of the mud motor to better understand drilling conditions in different shale plays throughout North America. Embedded sensors placed on the outer diameter of the BHA vs. centerline-mounted sensors give a different measurement response and a different vision of the actual dynamics being experienced in the BHA. The HF sensors were deployed in the in-house developed push-the-bit RSS and mud motors, allowing us to model the motor-assist RSS BHAs with analytical models and finite-element analysis models to predict the HF torsional oscillation (TO) and axial oscillation (AO) frequencies. The derivation of the high-frequency axial oscillation (HFAO) and TO analytical equations is detailed in the paper. In one of the example motor-assist RSS BHA analyses, the simulation results reveal that the fundamental high-frequency torsional oscillation (HFTO) frequency is 11.1 Hz whereas the fundamental HFAO frequency is 32.9 Hz, which is approximately three times higher than the fundamental-mode HFTO frequency. A good correlation was observed between the simulation result and the field data gathered from the HF accelerometer and gyro sensors embedded in the RSS and mud motors. Two new types of HF axial drilling dynamics with a polycrystalline diamond compact (PDC) bit—(1) the third-order-mode HFAO and (2) the harmonics of the HFTO coupled to the longitudinal axis—were discovered and reported in detail. One example in this paper shows that the dominant HFTO frequency shifts occurred in the middle of drilling a stand with no connection involved and no surface parameter changes. The examination of the time-domain signal reveals that (1) the “baseline” HFTO-induced tangential accelerations are due to the mud motor output revolutions per minute (RPM) (2) the variation of the HFTO-induced peak tangential accelerations comes from the drillstring stick/slip, which is transmitted to the drill bit through the mud motor, and (3) the 76 and 114 Hz HFTO-induced accelerations are both approximately in a sinusoidal waveform, except in the 3-second transition period, where the mixture of both frequencies is observed. The 114 Hz-HFTO-induced tangential acceleration measured at the bit box is coupled with the 0.16 Hz drillstring stick/slip oscillation. The analytical equation is provided to describe the HFTO coupled with stick/slip as an analogy to communication theory. In addition, the extensive modeling and field measurement of the HFTO and HFAO lead to the mitigation measure of the harmful HF drilling dynamics in motor-assist RSS BHAs. The proposed HFTO mitigation mechanism is modeled, simulated, and demonstrated in the paper. The latest-generation embedded HF drilling dynamics sensors are placed on the outside diameter of the BHA, as well as along the centerline of the BHA. The different responses of the sensors due to their placement are reported and analyzed. The quality of 1000 Hz continuous-sampled gyro data are discussed, comparing against low-frequency-sampled gyro data. Additionally, this paper shows the downhole HFTO-damping mechanism and lesser known drilling dynamics, such as HFAO with a PDC bit in detail. CORRECTION NOTICE: This paper has been updated from its original version to correct the provenance statement. In addition, the equation numbering on pages 567 and 568 has been corrected from Eqs. 9, 10, and 11 to Eqs. 5, 6, and 7.