Post-buckling loads of a horizontal pipe string with variable length

Horizontal well is one of the main measures to improve oil and gas production capacity. However, with the extension of horizontal section, the risk of pipe string buckling will be increased. In the quasi-static finite element calculation, it is difficult to identify the contact with the cylindrical wellbore due to the jumping changes of the sinusoidal and helical buckling configurations of the pipe string. Therefore, this method is difficult to solve the calculation convergence problem, especially with the increase of horizontal pipe string length and greater flexibility, this problem becomes particularly prominent. We propose a finite element calculation strategy, namely, using the dynamic relaxation method, to transform the static buckling of the horizontal pipe string into a virtual dynamic problem. We put forward the identification methods of sinusoidal and helical post buckling modes, as well as their critical load determination methods. The research results show that the use of large damping in the dynamic relaxation method can significantly restrain the vibration phenomenon of alternating contact and separation between the horizontal pipe string and the cylinder wall, reduce the response time to reach the stable buckling mode, and also can significantly improve the calculation efficiency. The change trend of critical load is the same when the length of horizontal pipe string is extended for a certain length. Within the extended length range, the horizontal pipe string has the same half sine wave or helix number, and the critical loads of sine and helix buckling will gradually decrease with the extension of the string length, and eventually tend to be constant. This trend is more obvious when the number of half sine waves or helixes of horizontal pipe string is more. The dimensionless critical loads of sinusoidal and helical buckling tend to 1.00 and root 2 respectively, and the corresponding dimensionless string lengths are 3.73 pi and 6.21 pi, respectively. However, other researchers underestimated the effect of length on the critical load of helical buckling. We have verified the critical loads for sinusoidal and helical buckling of short and long pipe strings. The results of this paper are practical for post-buckling analysis of horizontal wells with various lengths of pipe string.