Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction

Horizontal oilwell drillstring failures are very costly. Vibration causes excessive wear and tear on the bottom hole assembly and reduces the life of the drill bit, and has motivated extensive research on these types of drillstring vibrations. Two key factors in simulation of motions of horizontal drillstrings are to have a model capturing coupling among various types of vibration, and an accurate but efficient treatment of the wellbore friction. In this paper, a bond graph dynamic model of a horizontal oilwell drillstring has been developed that predicts longitudinal motion, torsional motion, and coupling between longitudinal and torsional motion excited by bit-rock interaction. A lumped segment modeling approach of vertical drillstring dynamics has been extended to include dynamic wellbore friction in the 'build' and 'horizontal' sections of the drillstring. The model incorporates torsional viscous damping, longitudinal hydrodynamic damping, and buoyancy effect due to drilling fluid; an extended bit-rock interaction model that allows the drillstring to advance at the rate of penetration, a downhole mud motor, and top drive ac motor dynamics. The friction coefficient between drillstring and wellbore has been tuned with the aid of field data from a horizontal oilfield in Canada. The model predicts the expected coupling between weight on bit, bit speed, and bit-rock interaction conditions; and their effect on longitudinal and torsional motions. Finally, an experiment was conducted with a downhole axial vibration tool (“Agitator®”). A force excitation source, which simulates the Agitator® tool, in the longitudinal direction has been implemented in the horizontal section of the virtual drillstring. Simulations show a better weight transfer to the bit, with a low frequency and high amplitude force excitation giving best performance.