Summary
This paper examines the effects of fluid pressures and flowing fluid momentum on curved tubing, casing, or drillpipe in a wellbore. Special cases, such as the "fictitious force" used in tubing buckling analysis, are developed and explained in terms of actual physical behavior. New problems, such as the effect of tubing eccentricity on fluid forces, are identified. Lateral forces developed in curved tubulars due to fluid pressure can be much higher than expected, with significant impact on friction drag loads.
Introduction
The effect of fluid pressure on buckling has long been known. The current understanding of the role of fluid forces can be traced to a paper by Klinkenberg. This paper resolved many of the questions about the effect of fluid pressures on the neutral point by examining a column immersed in liquid. In a written discussion of this paper, H.B. Woods expanded Klinkenberg's results by considering different internal and external pressures. In this analysis, he introduced many of the ideas later used by Lubinski in the analysis of tubing buckling. Lubinski presented tubing buckling equations based on a "fictitious" buckling force that included the effects of internal and external pressure, but was developed for fluids of constant density. Hammerlindl expanded Lubinski's formulas to tapered strings and multiple fluid interfaces. Other authors (e.g. Chesney and Garcia) recognized that the "fictitious" force could be expressed as:
(1)
where F, is the "fictitious" force (compression positive), Fa is the compressive axial force in the pipe, pi is the internal pressure, ri is the inside radius of the pipe, po is the external pressure, and ro is the outside radius of the pipe.
However, the way in which fluid forces load the tubing has always been somewhat unclear. In particular, the "fictitious force" used as the buckling force in the tubing analysis has caused considerable confusion. In this analysis, the fluid forces are shown to generate lateral forces proportional to the curvature of the tubing. When this result is used in the buckling equations, the "fictitious force" is determined clearly. Furthermore, the extension of buckling analysis to deviated wells is developed. For example, fluid forces are developed in the build section of a deviated well that are not usually considered.