Buckling of Concentric String Pipe-in-Pipe

Abstract During the design stage of concentric tubular strings, the outer string is always considered to be rigid. However, in reality, the outer string can become displaced through contact with an inner buckled string. An analytical mathematical model was developed that includes this interaction effect and predicts the post-buckling behavior of a dual-string system in vertical wells. Case studies were conducted to compare the prediction results with previous models. The post-buckling configurations are divided into two pre-assumed scenarios: sinusoidal buckling and helical buckling. An analytical mathematical model was developed to describe the post-buckling behavior of dual-string systems based on the minimum energy theory. The effect of contact interaction is considered in this model and evaluated during analysis. Variations of pitch, bending moment, bending stress, and total length change caused by buckling along the tubular can be evaluated using the new model. The model was verified with existing literature before application. A case study was performed to evaluate the improved prediction accuracy of the model during certain scenarios. Two models exist for dual-string buckling—namely, the Christman (1976) and Mitchell (2012) models. The case study in this research determined that the Christman model tends to overestimate the stiffness of a dual-string system, thus leading to an unsafe design. The Mitchell model assumes an unrealistic space configuration for helical buckling, where the buckling is self-balanced and a dual-string system is independent of the wellbore. As a result, the Mitchell model cannot properly explain the influence of wellbore clearance on the buckling configuration. The new model properly solves these issues and provides a reliable prediction as a design reference. It is also observed that the outer string in a dual-string system tends to withstand more moments because of greater stiffness. Proper application of this new dual-string buckling model design can help reduce costs.