A new concept "local down-hole tubular model", which provides a more sophisticated description of tubular string deflection from local perspective, is proposed to overcome the shortcomings of the conventional integral model. The coupling effects of three factors including wellbore configuration, buckling mode and connector are studied in the local model. Firstly, an equivalent beam-column model is proposed to reduce arbitrary wellbores except vertical wellbores into horizontal wellbores. Thus, the tubular behaviors in arbitrary wellbores can be simplified into that in vertical and horizontal wellbores. Secondly, the two-dimensional (2D) lateral deflection, three-dimensional (3D) inter-helical buckling and intra-helical buckling of tubular strings with and without connectors under four contact cases, namely no contact, point contact, wrap contact and full contact, constrained in horizontal and vertical wellbores are studied. Meanwhile, the fitting formulae which depict the effects of connectors on critical buckling loads, contact forces and bending moments are calculated. At last, the integral model is further amended based on the results from the local model. The results show that the effect of wellbore configuration can be equivalent to additional tubular string weight. Connector parameters are closely related to buckling modes, critical buckling loads, post-buckling deflection curves, bending moments, contact forces, etc. The combination of integral and local models, namely the amended integral model, establishes a more sophisticated description of axial force, torque, bending moment, contact force and buckling mode distributions along the entire tubular string.

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