Torque and drag [T&D] are critical elements in drilling deep vertical wells with unnoted tortuosity along the borehole and in extended-reach and deviated wells with high and repeated tortuosity. Current T&D models generate unreliable predictions due to the assumption that borehole trajectories are composed of constant curvature arcs between survey stations [the minimum curvature calculation method]. This assumption causes the bending parameter in the T&D equilibrium balance equations to be nil. Today's T&D models are either based on a continuous drillstring to wellbore contact [the soft-string model] or intermittent contact due to drillstring stiffness [the stiff-string model]. In both cases, the wellbore trajectory is based on the minimum curvature method.

The T&D model proposed is a phase II initiative of the non-constant curvature trajectory model: the advanced spline curves [ASC] borehole trajectory model published at the 2016 IADC/SPE Drilling Conference and Exhibition (Abughaban el al. 2016). This modified three-dimensional [3D] T&D model [the ASC 3D T&D model] is a stiff-string model that includes geometric torsion, wellbore curvature, change in the rate of wellbore curvature and drillstring bending stiffness in the T&D equilibrium balance equations. The model has been validated using field cases with real-time forces that define T&D measured at the surface. The calculated outputs from these wells provide more accurate view of the drilling conditions downhole, including the downhole weight on bit and torque on bottom.

The novelty of the proposed model is the ability to estimate a more realistic bending effects, accurately predict the contact forces between the drillstring and the wellbore, and solve T&D parameters from surface to total depth in reasonable time using standard engineering computer. Accurately estimating these parameters will allow drilling engineers to update the driller with surface weight on bit and torque parameters to improve the drilling performance without taking undue risks with the drilling system such as stuck pipe, casing and drillpipe wear and drillstring fatigue. Thus, the ASC 3D T&D model is not only an alternative approach to accurately model downhole T&D parameters to be used in real-time operation centers [RTOC]; it can also serve as a step toward drilling automation.

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