A model for buckling within curved boreholes is important in the drilling of extended reach and horizontal wells. It has been noted in drilling operations that a curved borehole increases the buckling resistance of the drillstring compared to a straight borehole. The effects of the curvature, however, cannot be correctly determined from the current buckling models developed for straight boreholes, from where the current models for curved boreholes in the literature borrow their fundamentals.

A mathematical model for analyzing buckling of drillstring within curved boreholes has been developed. This model predicts the unloading buckling force of a drillstring. The results show that one can apply higher axial forces at the bit and obtain longer extended reach or horizontal sections without putting the drillstring under risk of helical buckling and the consequent lock-up of the column. The model presented here, called the Hypergeometric Model, uses an analytical method employing an inclined beam-column theory with moving boundary conditions. The boundaries are numerically adjusted until a fit between the buckled section and the curved borehole is obtained. The buckling force varies with the inclination along the curved section of a borehole. Thus buckling force curves as functions of inclination can be derived and used in simulations and drillstring design. Excellent experimental results compared to the predictions support the model. This model also includes friction effects between the drillstring and the borehole wall. In this paper we present the mathematics of the Hypergeometric Model with an illustrative result, deferring experimental results, simulations and field applications to a following presentation.