Nonlinear dynamics of a drillstring system with PDC bit in curved wells based on the finite element method

Abstract

In this paper, a nonlinear mathematics model for axial-torsional-lateral dynamics of drillstring system equipped with a PDC bit in curved wells is established and analyzed. In the proposed model, using the finite element method, the drillstring structure is spatially discretized by Euler-Bernoulli beam elements with twelve degrees of freedom. Based on rock surface morphology of bit-rock interaction, a more realistic cutting and friction model with state-dependent delay effects is introduced to represent the bit-rock interaction. Meanwhile, a new top boundary condition is proposed to simulate the desired weight on bit (WOB). The nonlinear dynamic model is discretized in time-domain employing the generalize-α method, and the modified Newton iteration method is employed to calculate displacement response at the while-time step. Finally, the parametric analysis is carried out for discussing the influences of weight on bit and rotating speed on the nonlinear vibration of the drillstring system, respectively.