Effects of Friction on Post-Buckling Behavior and Axial Load Transfer in a Horizontal Well

Abstract

In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5. Velocity analysis shows that lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can increase the critical load of helical buckling significantly. However, once buckling is initiated, axial velocity becomes dominant again and lateral friction becomes negligible for post-buckling behavior and axial-load-transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. Analytical solutions for both sinusoidal and helical post-buckling configurations are derived, and a practical procedure for modeling of axial load transfer is proposed. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions. IntroductionIt is well known that, when a pipe is subjected to an axial compressive load, the pipe will shorten because of axial compression. As the axial load increases, the pipe will change its configuration from straight to a sinusoidal-wave-like shape and eventually a helical shape. These three different configurations are all static equilibrium states of a pipe subjected to axial compressive load. However, for a given axial load, only one configuration is stable. The critical load beyond which a pipe will change its configuration from a straight line to a sinusoidal-wave-like shape is called the critical load for sinusoidal buckling. The critical load beyond which a pipe will change its configuration from a sinusoidal-wave-like shape to a helical shape is called the critical load for helical buckling.We need to address the difference between stability or buckling analysis and post-buckling analysis of a pipe constrained in a wellbore. Buckling analysis is focused on determination of the critical condition (or critical load) under which a pipe will change its configuration from one type into another; for example, the critical load beyond which a pipe will change from a straight line to a sinusoidal shape or from a sinusoidal shape to a helix. On the other hand, post-buckling analysis is focused on analyzing the relationship between parameters that define the post-buckling configuration and axial load; for example, the relationship between amplitude of the sinusoidal wave and axial load for sinusoidal postbuckling analysis or the relationship between pitch of the helix and axial load for helical post-buckling analysis. The principle of virtual work and the energy-conservation law apply for both buckling and post-buckling analysis.

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

“…Mitchell (2000) and Mitchell and Stefan (2006) further studied the helical buckling of a tubular string in a vertical wellbore for the no contact case. The results show that the tubular string approximately buckles helically when the axial compression is low while the effect of connectors on bending stress (Gao and Miska 2010a) becomes significant when the axial compression is high. Mitchell's results are verified by Duman's experiments (Duman et al 2001(Duman et al , 2003 which show that connectors have no effect on the critical sinusoidal buckling load but increase the critical helical buckling load by 20 %.…”

“…(4) for a weightless tubular string without torque (Mitchell 1988;Gao 2006). The parameter A is approximately solved with the perturbation method by assuming A to be a small term (Liu 1999;Gao and Miska 2010a). The critical load F crh which converts the sinusoidal buckling to helical buckling is obtained when the contact force N between the tubular string and the high side of the inclined wellbore is equal to zero (Liu 1999).…”

“…Gao and Miska (2010a) deduced the critical axial forces for sinusoidal buckling and helical buckling in a horizontal wellbore considering the sliding friction force with the energy method:…”

Research on Buckling Behavior and Analysis of Sensitive Factors in Horizontal Well Drilling

“…However, none of them considered the effect of friction between drill string and borehole wall, while the frictional resistance is just one of the key factors deciding the drilling length of the horizontal section. More recently, Gao et al [19,20] took account of the friction between drill string and borehole wall, and the modified model of buckling critical load had been proposed as follows: …”

Sinusoidal buckling of a thin rod with connectors constrained in a torus

“…Mitchell (Mitchell, 1999) deduced the critical condition for helical buckling in curved wellbore with buckling differential equation. Gao (Gao and Miska, 2010) studied the effect of friction on the critical condition for buckling. Gao (Gao, 2006) and Liu (Liu, 1999) systematically analyzed the critical conditions for sinusoidal buckling and helical buckling in vertical, straight inclined and curved wellbores.…”