Wellbore tortuosity, defined as the degree of wellbore deviation from the smooth trajectory, and wellbore rugosity, defined as the degree of wellbore diameter irregularity, are critical elements in determining torque and drag (T&D) magnitudes in the drilling of long-reach horizontal wells and deep verticals. Current three-dimensional well trajectory models represented by the minimum curvature method (MCM) tends to mathematically smoothen the wellpath between survey-stations creating an artificially low tortuosity expressed as dogleg severity (DLS). This can lead to the miscalculation of the actual true vertical depth (TVD), leading to the underestimation of T&D magnitude. A robust three-dimensional trajectory model, the Advanced Spline-Curve (ASC) model, has been developed by the Colorado School of Mines to overcome these limitations. The ASC model provides realistic results and accurately calculate the spatial course of the wellpath.

The principal method proposed using the ASC model is a step toward more accurate representation of wellbore trajectories, as compared to other methods using constant curvature, minimum curvature or tangential calculations. This curve has continuous derivatives up to the third order (C3) along the entire wellpath. It is fairly straight-forward and has the robustness and flexibility to calculate complex, three-dimensional wellbore trajectories.

In this paper, various applications of the ASC model are presented and its results have been validated using two approaches: (a) an academic wellbore example of a known trajectory path, and (b) the use of high resolution continuous gyroscopic (HRCG) survey data recorded at one survey per foot. The calculated trajectory utilizing ASC model guarantees continuity along the entire wellpath with significant better accuracy as compared to MCM. These findings allow better wellbore positioning, more realistic tortuosity and the introduction of a rugosity measurement. This helps to evaluate drilling equipment and procedures while drilling highly deviated wells and extended verticals.

A HRCG survey recorded at one survey per foot provides a high level of wellbore positioning, tortuosity and rugosity accuracy; however, this is usually after the wellbore had been drilled and thus an improved calculation method such as the ASC model brings operational value.

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