Investigation of Drillstring Transverse Vibrations at Rotary Drilling of Inclined Wells

Abstract

Significant part of axial compression load transferred to the bit while drilling of wells with high zenith angles is resisted by service drill pipes. By the action of static critical load, buckling of drillstring occurs initially in the shape of a sinusoid and subsequently, as the load increases, in the shape of a helix. Drillstring rotation promotes the occurrence of critical modes. As a result the drillstring can start snaking motion at the low side of the hole. When the rotary speed grows, whirling of the drillstring can occur with axial load much lower than the buckling load. In this paper, a nonlinear mathematical model of lateral vibrations of a rotating drillstring in straitened space of a straight inclined hole is proposed. A numerical method to solve drillstring motion equations has been developed that allowed to reduce time of computation. This made it possible to conduct a detailed study of how the main drilling parameters (compression load, drillstring rotary speed, hole angle, friction factor, etc.) effect drillstring motion in the well. Results of the study may be used to choose drillstring operation modes for rotary drilling of inclined and horizontal wells.

Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well

“…(21), (22) into Eq. (20) and rearranging the equation based on the order of ε, while O(ε 2 ) and higher order terms are neglected, the following set of equations will be obtained:…”

“…(43) into Eqs. (21), (25). Therefore the response and the nonlinear frequency of response can be expressed as:…”