In down-hole interventions, the thin elastic coiled tubing (CT) extended for thousands of meters underground would typically undergo helical buckling as a result of axial compressive force. This paper builds an analytical model to describe the unbuckling behavior of a helically buckled CT with a new view to the stretching process in the plug milling operations. The new dynamic unbuckling equation is built on the basis of the general bending and twisting theory of rods. Under the continuous contact assumption, the helical angle is only subject to time; thus, the dynamic equations can be simplified and the analytical solutions can be obtained. By using the new governing equations, the angular velocity, axial force, and contact force relative to CT are analyzed in the unbuckling process. The calculation results indicate that the parameters including CT diameters and wellbore diameters have a strong influence on the variation of axial force and wellbore contact force. Moreover, the wellbore contact force is greater than zero during the whole unbuckling process which confirms the continuous contact assumption. These new results provide important guidance for accurate job design for the plug milling operations during the well completion stage.

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