Three principles of drill-string mechanics: Mechanical equilibrium, minimum potential energy and minimum dissipation power and their qualitative simulation

Abstract

Painstaking efforts have been made to study drill-string dynamics; however, the phenomena involved are still not clearly understood. In general mechanics, systems must follow the mechanical equilibrium principle, the minimum potential energy principle and the minimum dissipation power principle. The research question addressed in this study is whether the rotating drill string in the wellbore also follows these three principles, and how these principles should be expressed. This study confirms that drill-string mechanics follows these three principles. Any point in the drill string at any time must meet the mechanical equilibrium equation. If this results in multiple solutions, the minimum potential energy principle is first applied to determine the true solution. If multiple solutions still remain, the minimum dissipation power principle is applied to determine the true solution. Because of drill-string instability, the minimum dissipation power principle does not include the minimum potential energy principle. Therefore, it is incorrect to replace the minimum potential energy principle with the minimum dissipation power principle. The experiments led to the following findings: (1) As the rotary speed of the rod string increases, its deflection decreases nearer to the borehole center. (2) There exists a whirl-state transition critical rotary speed. If the rotary speed is below this critical rotary speed, the dissipation power increases as the rotary speed increases. If the rotary speed is higher than this critical rotary speed, the dissipation power first decreases rapidly as the rotary speed increases and the deflection of the rod string abruptly decreases, and then the dissipation power increases as the rotary speed increases. (3) As the viscosity of the liquid increases, the whirl-state transition critical rotary speed decreases. As the axial load increases, the whirl-state transition critical rotary speed decreases.