Except for coiled tubing, most tubular goods used for down-hole operations such as drilling pipe and sucker rod have connectors. Since a connector and the pipe-body have different outer radius, the deformation and buckling behavior of a pipe with connectors constrained in a wellbore are much more complicated. However, most buckling models were established by neglecting the existence and effects of connectors.

In this paper, buckling equations of a pipe with connectors in horizontal wells were derived with application of elastic beam theory. The axis of an unbuckled pipe is a 2-D curve in the vertical plane, and has three configurations: no contact, point contact and wrap contact. We derived the two critical distances between connectors, Lc1 and Lc2, beyond which a pipe changes its configuration from one to another. The authors proposed an algorithm to determine the critical force (Fcrs) of buckling by numerically solving the buckling equations using the 4th order Ronge-Kuta method.

Both the distance between two adjacent connectors (Lc) and the radius difference between a connector and the pipe-body (Δrc) have significant impact on the critical force, in addition to net clearance between a pipe and wellbore (r0), bending stiffness (EI) and weight per unit length (w) of pipe. When Lc is small, radial deflection is negligible. Fcrs increases as Δrc increases. However, when Lc is close to Lc1, effects of radial displacement become significant, and Fc decreases dramatically as Δrc increases. Fcrs decreases as Lc increases when Lc< Lc1, and it reaches its minimum at Lc=Lc1. When Lc> Lc1, Fcrs fluctuates as Lc increases. Some curves of Lc1, Lc2 and Fcrs, all in dimensionless forms, were calculated and presented in this paper for practical applications.

Our numerical results show that the critical force may reduce 20-60% for commonly used drill pipes and sucker rods with centralizers, which indicates that a pipe string designed without considering the effects of connectors may be risky. The results presented in this paper may provide some practical guidance for optimal design of centralizers for sucker rod strings, or may avoid some risks due to improper design of drilling pipe strings.