Analysis of PDC bit wobbling and drilling string buckling
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Earlier study of failure of Polycrystalline-diamond-compact (PDC) bits was attributed to "bit-whirling" theory which caused cutter chipping due to down-hole bit vibrations. Based on the bit-whirl theory, the PDC bit design was modified by changing the cutters orientation, introduction of low-friction pads around the bit so that the net imbalance forces from the cutters are minimized. The "bit-whirl" theory by itself was not sufficient to address the failure mechanism as it considered only the kinematics of the bit and the geometric aspect of the bit dynamics was neglected. The study in the paper focuses on another theory known as PDC "bit-wobbling" which takes into account the bit down-hole dynamics. Based on this theory, a kinetic model of the bit and the bottom-hole assembly (BHA) is developed. The various forces acting on the model are presented and analyzed. Sensitivity analysis is carried out on the model to study the effects of stabilizer position, phase angle, bit velocity, bit weight, drill-collar stiffness etc. on the backward cutter velocity. This study identifies possible solutions for reducing the bit-wobbling. The theory of buckling is applied to derive the analytical solutions to drill-string buckling. Based on the analytical solutions, the different buckling orders are modeled and analyzed. The buckled drill-string and bending moment profiles of first and higher-order buckling are generated through computer programs given in the Appendix. The effect of various parameters on drill-string buckling is studied and presented..