Modeling of drill string dynamics in directional wells for real-time simulation

Simple and computationally efficient drill string models running real-time describing motion in all axes in directional wells are important for the implementation of closed-loop control and assisted monitoring during drilling operations. This paper proposes a new simplified three-dimensional model based on a parametric curve and lumped-parameter modeling, where Kane's method is used to establish the equations of motion. Validation of the steady-state motion and convergence for the lumped model in vertical and horizontal alignment was compared with a finite-element model. The configuration and restoring forces show good results compared with finite-element analysis. Hence, the model demonstrate the axial contraction as a function of the body restoring forces being oriented to the inertial frame, inherently producing nonlinear coupled axial tension forces. The qualitative response of the model is confirmed in simulation case studies, being showcased by a deviated J-well configuration. Traveling block velocity and top drive torque are included as actuated inputs to analyze off-bottom friction and contact along the wellbore. The model is proposed to act as a virtual sensor for drilling directional wells.