Fundamental Principles of Drill-String Mechanics and Their Qualitative Simulation

Abstract

In general mechanics, systems must follow the mechanical equilibrium principle, the minimum potential energy principle, and the minimum dissipation power principle. This paper confirms that a rotating drill string in a wellbore follows these three principles. The study presents three main findings. (1) As the rotary speed of a 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.