Stability and Vibrations of a Rotating Drill String in a Horizontal Wellbore

In view of the development of new technologies for the production of hydrocarbon fuels from shale rocks, increasing attention in the oil and gas industry is given to the problems of drilling slant and horizontal wells. The specific character of the processes of drilling such wells is that they are strongly acted upon by the forces of contact and frictional interaction between the drill string surface and the borehole wall, which arise in such cases. This paper formulates a problem of the bifurcation buckling and small bending vibrations of a rotating drill string lying in a horizontal wellbore. With allowance for friction forces and additional constraints, differential equations have been derived, for which solutions of eigenvalue problems of free vibrations of drill strings of finite and unlimited length have been constructed.