Vibration and Dynamic Analysis of Oil Well Drillstring Considering Coupled Axial and Torsional Effects Using Cylindrical Superelement

In this paper axial and torsional vibrations of a drillstring are studied using cylindrical superelement. Drillstring vibration equation is derived by calculating kinetic and potential energy and work done by external forces on drillstring, and utilizing Hamilton’s principle. The model is analyzed by implementing finite element technique with consideration drillstring weight, centrifugal force due to rotation of drillstring, axial force resulting from bit with the formation contact and torsional torque caused by the stick-slip phenomenon. To calculate the vibrational response of drillstring, a computational finite element scheme was developed. For a typical case of oil well drillstring, the time response of axial and torsional vibrations of bit are presented. Also, time history of rotational speed of bit and frictional torque caused by the stick-slip phenomenon on bit, are calculated. Very good agreement is found between findings with implementing superelement and those were reported in the literature. The time consumption by conventional finite element method is very larger than implementing cylindrical superelement for the same problem. This indicates by implementing a few cylindrical superelements, the same results in much smaller computer time than the conventional finite element method, can be extracted.