Buckling Analysis of Tubular Strings in Horizontal Wells

Abstract

A new buckling equation in horizontal wells is derived on the basis of the general bending and twisting theory of rods. The boundary conditions of a long tubular string are divided into two categories: the sum of the virtual work of bending moment and shear force at the ends of tubular strings is equal to zero, and the sum of the virtual work of bending moment and shear force at the ends is not equal to zero. Buckling solutions under different boundary conditions are obtained by solving the new buckling model. For the boundary conditions of the first category, the buckling solutions are identical with previous results. For the boundary conditions of the second category, the buckling solutions are different from the results under the boundary conditions of the first category. The results indicate that buckling behaviors depend on both the axial force and the boundary conditions. Compared with previous results, buckling solutions of the new model provide a more comprehensive description of tubular-buckling behaviors.

A review of down-hole tubular string buckling in well engineering

“…However, in the unloading process, the tubular string tends to lose contact with the wellbore but the pitch of the helix remains constant. Huang et al (2015a) verified Cheatham's results from the view of the buckling differential equation and further pointed out that the contact force reaches its maximum value when Eq. (10) is satisfied and its minimum value when Eq.…”

“…Huang et al (2015a) further proved that sinusoidal buckling and helical buckling are just two special periodical solutions of the buckling differential equation.…”

Boundary Conditions: A Key Factor in Tubular-String Buckling

“…The length of the total transition section (g 1 þ g 2 þ g 3 ) in the fixed-end case is larger than that in the pinned-end case. If it is assumed that the transition section includes only one no-contact section and a perturbed-helix section (Liu 1999), the values of g 1 are slightly larger than that in our model, but the length of the total transition section is smaller than that in our model. If it is assumed that the transition section only includes one no-contact section (Mitchell 1982), the values of g 1 are larger than those in the previous two models, but the length of the total transition section is smaller than that in the previous two models.…”

“…The shear-contact force on the contact point is not zero in the Mitchell (1982) model, and the contact force on the perturbed-helix section is negative in the Liu (1999) model. The new model in this paper overcomes these shortcomings.…”

“…The critical condition for sinusoidal-buckling and helicalbuckling and post-buckling behaviors of the tubular string (Lubinski and Althouse 1962;Paslay and Bogy 1964;Chen et al 1990;Wu 1992;Mitchell 1997Mitchell , 1999Mitchell , 2008Liu 1999;Gao 2006;Gao and Miska 2009;Huang et al 2014c). 2.…”