Construction method for three-dimensional dynamic configuration of reciprocating sucker rod string in actual wellbore

The sucker rod string-serving as the core component of rod-pumped oil production systems-exhibits an ultra-slender geometric configuration. Under downhole reciprocating motion, it is prone to complex three-dimensional spatial deformation and may come into contact with the tubing wall, thereby inducing eccentric wear or, in severe cases, mechanical failure such as fracture. Since the dynamic spatial configuration of sucker rod strings is essential for understanding and mitigating tubing-rod eccentric wear, this study proposes a method to construct its three-dimensional spatial configuration under reciprocating movement. The method is grounded in a three-dimensional coupled dynamic model of the sucker rod string within tubing, incorporates buckling stability theory, and introduces smooth transition conditions that ensure deformation continuity of sucker rod string across distinct buckling modes. Finally, engineering case studies are employed to analyze the evolution of the sucker rod string's three-dimensional spatial configuration within the tubing across distinct phases of reciprocating motion; moreover, the pivotal role of dynamic bottomhole pressure in triggering buckling mode transitions is elucidated.