In many situations, a completion string may consist of several size of strings and components so total axial force must be carefully considered by applying a free body diagram concept. When the tubing string is free to move, forces will affect the tubing above where the force is applied.
Tapered string is a string which consists of more than one size of tubing. Hence, forces acting at tapers must be accounted for. Force depends on configurations of pipe and pressure and it will either decrease or increase surface load.
Figure 1 illustrates diagram of a tapered completion string. Wherever in the string there is a difference in outside diameter or inside diameter, there will be downwards or upwards force acting against the tapered edge. It is imperative to analyze each ledge and combine all the results in order to see the total effect. From Figure 1, F1 and F2 cause compression, but F3 creates tension force.
Expandable devices such as polished bore receptacles (PBR) and expansion joints are used in a well to accommodate tubing movement. Causes of tubing movements are piston effect, thermal, buckling, ballooning and production.
Figure 3 illustrates the cross section view of both PBR and expansion joint. Each type has a different configuration in the cross section area. Therefore, force reaction will be different for each one. The change in cross sectional areas directly affects how long the tubing movement is. This can lead to pipe elongation or pipe contraction. The pipe movement will be discussed in a later topic.
Ap = cross section area of packer
Ai = cross section area based on inside diameter
Ao = cross section area based on outside diameter
Pi = internal pressure
Po = outside pressure
Jonathan Bellarby, 2009. Well Completion Design, Volume 56 (Developments in Petroleum Science). 1 Edition. Elsevier Science.
Wan Renpu, 2011. Advanced Well Completion Engineering, Third Edition. 3 Edition. Gulf Professional Publishing.
Ted G. Byrom, 2014. Casing and Liners for Drilling and Completion, Second Edition: Design and Application (Gulf Drilling Guides). 2 Edition. Gulf Professional Publishing.
Lubinski, A., & Althouse, W. S. (1962, June 1). Helical Buckling of Tubing Sealed in Packers. Society of Petroleum Engineers. doi:10.2118/178-PA