The buckling of elongated rotating drill strings

There is a growing need for the development and implementation of new numerical methods for computer simulation of static and dynamic critical states of drill strings in connection with mastering deeper oil and gas resources. Current methods for analysis of extraordinary behavior of the drill strings, as a rule, concern their post-critical states related to essential change of their shape and contact interaction with borehole wall. In parallel with the post-critical regimes there also are critical modes of operation attended with incipiency of unstable equilibrium states and the DS buckling. Inasmuch as the critical states precede the post-critical ones, sometimes their prognosis can be more important. This paper considers the problem of quasi-static stability of elongated drill string tubes studied with allowance made for destabilizing effects of the longitudinal non-uniform preloading, action of torque, inertia forces of rotation and internal flows of mud. The constitutive equations are deduced, and the methods for their computer solving are proposed. As a result of the completed analysis the critical values of the characteristic parameters are found, and it is shown that the modes of incipient buckling possess complicated shapes associated with the tube spiral curving prevailing in the zone of bottom-hole-assembly.