Dynamic Similarity Experiments on Drill String Whirl in 10,000 m Ultra-Deep Wells

This study investigates the influence of rotary speed on drill string whirl and vibration in 10,000 m ultra-deep wells through dynamic similarity experiments. A 1:4 geometrically scaled drill string–wellbore model was tested at 50–400 rpm under a weight on bit of 0.7 t and a torque of 100 N·m. Three laser rangefinders were used to reconstruct the drill string center trajectory and determine its translational and orbital responses. Forward whirl occurred at 50 and 100 rpm, a transition in whirl direction emerged at 350 rpm, and sustained backward whirl developed at 400 rpm, identifying 350–400 rpm as the critical transition interval. After zero-phase Butterworth filtering, the maximum center velocity increased from 0.241 to 0.579 m/s, while the maximum center acceleration rose from 3.014 to 15.813 m/s2 and approached a plateau. The signed orbital angular velocity reversed from approximately +2975 rpm at low speeds to −2857 rpm at 400 rpm, whereas orbital angular acceleration exhibited a non-monotonic response. The measured vibration acceleration at 100 rpm was comparable in magnitude to field data from well SHY001-X3, supporting the physical plausibility of the observed trends. These results demonstrate that drill string vibration risk should be evaluated using multiple dynamic indicators. The experiments support qualitative identification of whirl transition and vibration risk intervals, although quantitative field prediction requires coupled models that account for fluid effects, structural dynamics, and contact interactions, together with calibration against full-scale measurements.