Shlyun N. Stability loss of drill strings in the channels of curvilinear bore-holes

In the dissertation new mathematic models and analysis methods are elaborated for investigation of the processes of drill strings buckling in channels of curvilinear bore-holes. They are based on the choice of the theory of curvilinear flexible rods for their simulation. The use of this theory jointly with the methods of differential geometry, theory of channel surfaces and special reference systems (moving trihedron) permitted to divide the unknown variables and to determine them separately in the certain sequence. As this takes place, the differential equations system is reduced to four. Through the application of methods of structural mechanics for analysis of elastic system stability, the linearized homogeneous equations (frictionless and frictional models) are constructed for computer simulation of the drill string buckling in the bore-hole channels with rectilinear, circumferential, and general curvilinear axis lines. The numerical analysis of the drill string buckling in the bore-holes with variable angles of the trajectories inclinations and curvatures values are performed for different values of the bore-hole depths and their extensions from the rigs, as well as values of the friction coefficient. The critical values of the external influences are found, the modes of stability loss are constructed. It is shown that they have the modes of boundary effects or shortpitched wavelets localized in the internal zones of the bore-holes.