Excessive frictions in directional wells lead to various downhole problems such as pipe stuck that requires frequent workover operations, during which it is very challenging to accurately determine the effective drag (axial) forces and torques for releasing a jam at a stuck position due to the complex downhole situations. In this study, mathematical models have been formulated, validated, and applied to accurately determine such forces and torques in directional wells by taking the frictions caused by string-stiffness into account. The stiffness-based contact (normal) force is correlated with the deflection of a string segment by treating the bending segment as a simple beam that has both continuous and point contacts with the wellbore wall. Subsequently, the conventional soft-string model proposed by Johancsik et al. in 1984 is modified through coupling such a contact-force term into the original equations. Both the original soft-string model and the modified model are employed to perform the force and torque calculations for two field wells, based on which the effect of string-stiffness and the associated sensitivities are analyzed. Comparing the modified model with the conventional model, it has been found from their field applications that effective drag forces and torques for releasing a jam at a stuck point can be determined with an averaged relative deviation of 23.35% and 37.59%, respectively, indicating a considerable effect of string-stiffness that cannot be neglected for an accurate and efficient operation of jam release.

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