Tubing Stress

Basic Calculations for Packer and Completion Analysis

Introduction
The design and installation of a well bore completion typically involves running tubing with a packer into the well to facilitate production or injection of fluids from or into the well. Once the packer is set, its position is fixed whereas the tubing may be allowed free, limited, or no movement. Over the service life of thecompletion, the well experiences changes in temperature, pressure, flow rate, etc. which cause tubing stress and strain. If the tubing is free to move at the packer, this strain translates into movement relative to the packer. Obviously, this movement should not exceed the seal bore length at the packer. If tubing movement is limited at the packer, stresses translate into force on the packer whichmust not exceed operating limits. Likewise, the total combined effect of all stresses may result in tubing failure due to burst, collapse, or material yield. A major aspect of down-hole tubular movement is buckling. Indeed, the analysis of tubing movement and packer forces is often taken to be synonymous with buckling analysis. Unlike the analysis of other influences on tube movement which isgenerally straight-forward, the analysis of tubular buckling is much less obvious. It is essential to understand that there are two types of buckling: • Mechanical Buckling: buckling may result from applied mechanical compression on the tubing . For example, this may occur in response to weight slacked-off at surface onto the packer during or after installation. Or, changes in the down-holeconditions such as temperature may cause an increase in tubing length which cannot be accommodated by movement at the packer. And so buckling occurs. • Hydraulic Buckling: it is often not understood that tubing installed in a packer can buckle simply due to difference in hydrostatic pressure inside the tubing versus the annulus. In this regard, buckling of production tubing in a packer differs from freehanging tubing such as drillstring or coiled tubing. For free hanging tubing, pressure changes inside the tubing and/or in the wellbore annulus have no net effect on buckling. Why does tubing in a packer behave differently? Because the packer functions as a down-hole pressure barrier and, in particular, it isolates the end of the tubing from the annular pressure effects above the packer.Surprisingly, this hydraulically related buckling often may exist even in the presence of tubing to packer tension. The following sections show how tubing strain and stress are calculated and how to model the resulting tubing movements and/or forces on the packer. It is important to understand how each different physical condition affects tubing stress and strain. In real life many different simultaneousphysical factors affect the tubing. The net result of all the factors combined is not always obvious. The theory discussed is the basis for the numerical simulations in PACA, a part of the Cerberus modeling suite. Some analytical equations are provided as a means of double-checking simulation results in the simple case of a vertical well.

1. Basic Components of Tube Movement – No Packer
It ishelpful first to analyze forces and stresses on tubing with no packer. A tubing string run into a vertical well without a packer will undergo change in length, i.e. stretch, simply due to elastic effects of hanging weight. Variation in temperature or fluid pressure with depth will cause additional stretch. We choose to define stretch as a length change relative to the nominal length of the tubing atthe original surface conditions. Thus, a tubing string with nominal length at surface L will undergo some initial length change or stretch, δL (Figure 1a). As different processes and operations are carried out during the life of the well, the tubing experiences more changes in temperature, pressure, fluid density etc. which result in a different amount of stretch δL* with respect to the nominal...