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.

高扭矩，低速钻井泥浆马达通常用于驱动旋转导向系统（RSS），以提高RSS井底钻具（BHA）的穿透率（ROP）。当将动力RSS BHA推至最大钻探性能极限时，通常会发生井下钻探功能障碍。钻头，RSS的钻头盒，RSS的慢速旋转外壳（SRH），泥浆马达的钻头盒和钻头的顶部子组件（sub）嵌入了高频（HF）连续记录的紧凑型钻井动力学传感器。泥浆马达，以更好地了解整个北美不同页岩气层的钻井条件。与安装在中心线上的传感器相比，放置在BHA外径上的嵌入式传感器提供了不同的测量响应和对BHA中所经历的实际动力学的不同见解。

HF传感器已部署在内部开发的按位RSS和泥浆电动机中，使我们能够使用分析模型和有限元分析模型对电动机辅助RSS BHA进行建模，以预测HF扭转振动（TO）和轴向振荡（AO）频率。本文详细推导了高频轴向振动（HFAO）和TO分析方程。在一项示例性的电动辅助RSS BHA分析中，仿真结果显示，基本高频扭转振动（HFTO）频率为11.1 Hz，而基本HFAO基本频率为32.9 Hz，约为基本频率的三倍。模式HFTO频率。

发现并报告了两种新型的带有多晶金刚石复合片（PDC）的HF轴向钻削动力学-（1）三阶模式HFAO和（2）HFTO与纵轴耦合的谐波。本文的一个示例表明，主要的HFTO频移发生在钻台的中间，没有涉及连接且表面参数没有变化。对时域信号的检查显示，（1）HFTO引起的切向加速度的“基线”是由于泥浆电机每分钟的输出转速（RPM）（2）HFTO引起的峰值切向加速度的变化来自（3）76和114 Hz HFTO引起的加速度都近似呈正弦波形，除了在3秒的过渡期中，观察到两种频率的混合。在钻头盒处测得的114 Hz-HFTO引起的切向加速度与0.16 Hz的钻柱粘/滑振动相结合。提供了分析方程式，以将HFTO与粘滞/滑差相结合来描述，类似于通信理论。此外，对HFTO和HFAO进行了广泛的建模和现场测量，从而减轻了对电动辅助RSS BHA中有害的HF钻孔动力学的测量。本文对所提出的HFTO缓解机制进行了建模，仿真和演示。提供了分析方程式，以将HFTO与粘滞/滑差相结合来描述，类似于通信理论。此外，对HFTO和HFAO进行了广泛的建模和现场测量，从而减轻了对电动辅助RSS BHA中有害的HF钻孔动力学的测量。本文对所提出的HFTO缓解机制进行了建模，仿真和演示。提供了分析方程式，以将HFTO与粘滞/滑差相结合来描述，类似于通信理论。此外，对HFTO和HFAO进行了广泛的建模和现场测量，从而减轻了对电动辅助RSS BHA中有害的HF钻孔动力学的测量。本文对所提出的HFTO缓解机制进行了建模，仿真和演示。

最新一代的嵌入式HF钻孔动态传感器位于BHA的外径上以及BHA的中心线上。报告并分析了传感器由于其位置的不同响应。讨论了1000 Hz连续采样陀螺仪数据的质量，并与低频采样陀螺仪数据进行了比较。此外，本文还详细介绍了井下HFTO阻尼机制和鲜为人知的钻井动力学，例如带有PDC钻头的HFAO。

更正通知：本文已从其原始版本进行了更新，以更正来源声明。此外，第567和568页上的方程式编号已根据公式进行了校正。9、10和11至等式 5、6和7。