A Nonlinear Dynamic Model for Characterizing the Downhole Motions of the Sidetracking Tool in a Multilateral Well

It is of practical interest to investigate the mechanical behaviors a sidetracking tool system and describe tool’s vibration response, as this can provide an important basis for evaluating optimizing structure effectively controlling profile window. In article, three nonlinear dynamic models with ten, six, two degrees freedom, respectively, are established using Lagrange method characterize behavior tool. should be noted that in these models, axial, lateral, torsional fully coupled. The process mills casing-pipe wall divide into typical stages, i.e., window mill, pilot watermelon mill grinding casing, respectively. response stages studied more analyze influence deformation on width. Runge–Kutta method, which easy implement, applied solve supposed model, some useful findings follows. effects vibrations at different widening size illustrated quantitatively. trajectory pattern from conventional drilling due whipstock, changes general whirling motion X reciprocating pattern, amplitude decreases. Due lateral amplitude, widened. widened 3.30 mm 2.74 mm, extended 0.07 while maximum width formed by 374.34 mm. This work proposes, first time, coupled model system, helpful better understand tool, laying foundation optimization parameters.