On the formulation and solution of the boundary value problem of drilling well by differently mounted drilling bits

The tensity of the drilled rock under the influence of two circular and annular drilling bits rotating in opposite directions is of profound interest. The aforecited method solves the problem of spin moment removal from the drill string. Assessment of the tensity determines the formation stimulation during drilling. Inasmuch as the drill bits are circular in the axial plane of the aperture, the elastic strain range is not simply-connected. To solve this problem, it is proposed to consider the equations of the elasticity theory in a toroidal coordinate. This statement corresponds to the axisymmetric torsion problem articulated by A.I. Lurie [1]. The task is formulated and solved in the displacements indicating the subsequent transition to tensions. An outstanding feature in comparison with the Laplace equation is the presence of an additional summand. The boundary conditions are displacements' equality to zero on the axis and on the walls of the aperture. Then an additional solution of the problem is carried out in a cylindrical coordinate, shifted to the bottom of the slaughter. Two solutions are compared.