Application of extended reach and horizontal wells for offshore and onshore exploration and production purposes has been continuously increasing over the last decade. To reach the desired targets many of these wells are planed to have there dimensional complex well trajectories. Field experience indicate that running casing into wells with high horizontal departure and complex trajectories is frequently associated with many problems resulting in high cost of operations. In some instances the high pushing force resulted in casing buckling and the casing has not reach the planned depth. To reduce the pushing force one can rotate casing but that requires application of a sufficiently high torque. In any case accurate calculations of drag forces and torque are needed to evaluate casing mechanical integrity and technical feasibility of the casing running operation during planning and drilling stage of well development. In this paper we show the development of an improved characterization of wellbore trajectory by including the wellbore torsion in addition to the traditional wellbore curvature (dogleg severity). We also show the development of 3D drag and torque model that makes allowance for wellbore curvature, torsion, pipe bending stiffness and its weight in fluid. Finally, the paper is furnished with practical examples that show the application of the developed mathematical model. The proposed model is useful for practical design applications such as optimization of a well trajectory, calculating loads on casing and better understanding of field records and observations.
