A dynamic method for post buckling analysis of drill string in vertical wells

In this paper, a dynamic method, which includes a coupled dynamic model of full-hole drill string and its numerical implementation approach, is developed to analyze the post buckling of drill string in vertical wells. The coupled dynamic model is established based on Lagrange's equations and finite difference method. Its numerical implementation approach is achieved by using the direct integration method and Rayleigh damping formula. Especially the developed dynamic method is able to consider the coupling of axial vibration, lateral vibration, torsional vibration and the effects of rotating speed, damping from the drilling fluid, the discontinuous contact and friction between drill string and borehole, which enable it to predict the post bucking behaviors of drill string in vertical wells more efficiently and accurately. The developed dynamic method is validated by the comparison with the static theoretical solution of drill string, and then it is used to calculate the dynamic post buckling of drill string in vertical wells. The calculation results show that the contact length increases with the increase of the friction coefficient when the weight on bit is stable. There are critical speeds to make the contact length take the extreme value, and the critical speeds vary with the change of weight on bit and drill string length. The increase of drill string length does not change the quasi-static contact length, but will make the dynamic contact length fluctuate greatly. The fluctuation of weight on bit and torque on bit make the contact length fluctuate near the quasi-static contact length under most weight on bit. This work provides important theoretical and technical support for the comprehensive analysis of the dynamic buckling characteristics of drill string in vertical wells. • A coupled dynamic model of full-hole drill string in vertical well is established. • The model includes effects of friction, rotary speed, string length and weight on bit. • Wellbore friction aggravates the dynamic post buckling under stable weight on bit. • Dynamic post buckling deteriorates at some critical speeds and drill string lengths.