Investigation of the Relationship Between Drillstring Whirl State and Rate of Penetration in Vertical Wells: Influencing Mechanisms and Insights

Summary Harmful vibrations significantly impact drilling efficiency by reducing the rate of penetration (ROP) and shortening the service life of the drillstring and associated drilling tools. However, how vibrations influence drilling speed in the absence of tool damage remains unclear. Severe lateral vibrations, commonly known as a whirl, are considered the most detrimental type of vibration. Current research on drillstring whirl predominantly focuses on its dynamics and implications for drillstring safety. Although field practices suggest a strong relationship between ROP and the whirl types exhibited by the drillstring, publicly available studies addressing this connection remain limited due to a lack of research methods. Therefore, the relationship between the whirl state and ROP is investigated in this paper based on an integrated dynamic model, and its influencing mechanism is also revealed. One intriguing phenomenon is that, beyond the three commonly recognized whirl types, the drillstring can also exhibit a nonrevolution motion, consistent with the earlier hypothesis of rotation devoid of orbital movement. Under the model parameters used in this study, when the friction coefficient between the drillstring and the borehole wall is 0.05 and the mass eccentricity is 0.5 cm, the drillstring remains in this nonrevolution motion. Increasing the mass eccentricity to 2.50 cm transitions the drillstring to a forward whirl state. And, raising the friction coefficient to 0.20 induces a backward whirl state. When both parameters are adjusted simultaneously to 0.15 and 1.50 cm, respectively, the drillstring enters an irregular motion state. The most significant contribution of this study lies in the first-time observation in numerical simulation results that ROP decreases from 26.90 to 20.90 m/hr when the drillstring transitions into a state of backward whirl, along with an explanation of the underlying causes for this phenomenon. This is due to the increase in friction between the drillstring and the wellbore, resulting in a decrease in real weight-on-bit (RWOB) which is the axial interaction force between the drill bit and the rock. Because the normal contact force between the drillstring and the wellbore is caused by centrifugal force, the higher the rotational speed, the greater the normal contact forces become. This is verified by the ratio of ROP corresponding to nonbackward and backward whirl at three different rotation speeds, 60, 86, and 120 rev/min.