Design of oil wells using analytical friction models

Abstract Recent wells have been drilled to more than 10 km from the platform, and companies are planning to extend these beyond 12 km. Well friction is one of the most important limiting factors in this process. Torque and drag prognoses are developed today on in-house simulators. Although this is a good tool for planning, improvements are made on a trial and error basis, and these simulators have limited availability. To provide more insight into the frictional aspect, a larger study was undertaken. Explicit analytical equations are derived to model drill string tension for hoisting or lowering of the drill string. The equations are developed for straight sections, build-up sections, drop-off sections and side bends. Both constant curvature models and a new modified catenary model are derived. The new catenary model is developed for arbitrary entry and exit inclinations. Equations to determine well friction in three-dimensional well profiles are also given. In addition, expressions for torque and drag are developed based on the tension equations. Equations for combined motion and drilling with a motor are also given. Using these equations, the total friction in a well is derived from the sum of the contributions from each hole section. Examples are provided to demonstrate the application for ordinary production wells, catenary wells, long-reach wells and horizontal wells. Optimization criteria are developed to design the well for minimum friction.

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