Theoretical simulation of geometrical imperfections influence on drilling operations at drivage of curvilinear bore-holes

The stress–strain states of a drill string constrained by the walls of a curvilinear bore-hole are studied with the aim to identify the resistance forces impeding its motion. It is considered that the axis line of the bore-hole has geometrical imperfections in the shape of localized smoothed breaks. A “stiff–string” differential model for simulation of the drag/torque phenomena in the bore-hole is proposed. The system of ordinary differential equations is first derived based on the theory of curvilinear flexible elastic rods. The method for numerical solution of the constructed equations is described. With the proposed method, the phenomena of the drill string movement, its contact interaction with the bore-hole surface, and the frictional lock up are simulated for different values of geometrical combinations of velocities, directions of rotation and axial motion of the string. Some numerical examples are presented to illustrate the applicability of the method proposed for the regimes of drilling and the drill string lowering and raising.