Tubing stress analysis

What is a tubing stress analysis

The completion string will be exposed to stresses during the installation and during other well scenarios that may occur natural or accidental during the operational lifetime of the well. The tubing stress analysis will analyse all relevant scenarios and related stresses in the entire completion string. These stresses must be known to make a safe and reliable completion string and will provide input to material yield and dimensions for e.g. the tubing, the downhole safety valve and the production packer. The following loads have the potential for making stresses in the completion string:

  Pressure  -  Ballooning due to inside pressure makes tension stresses 
  Pressure -  Reverse ballooning due to outside pressure makes compression stresses 
  Pressure  -  Piston effects due to end pressure makes compression stresses and buckling
  Temperature  -  Increasing temperature makes compression stresses 
  Temperature  -  Reducing temperature makes tension stresses 
  Weight  -  Makes tension stresses and depends on buoyancy and inclination 
  Pick-up  -  Makes tension stresses 
  Set down  -  Makes compression stresses 
  Torque  -  Makes shear stresses 
  Bending  -  Make axial stresses and depends on dogleg and buckling 
  Fluid flow  -  Friction makes compression stresses 

The stress level is highly dependent on the strings ability to move. Most stresses are made only if the string is anchored and temperature changes will normally give the highest effect. Stresses made by torque and bending are independent of free moving string or not. Tubing stresses are calculated by experts using software programs like WellCat. The basic formulas are described in papers and completion manuals. This page aims to describe the basics of the tubing stress analysis.


The following calculation process is suggested:

Step 1: Clarify worst case scenarios

Typical completion string scenarios that may occur during the entire lifetime of the well must be evaluated. That could be cold shut-in, cold pump-in etc. Examples follow:

Loads related to each scenario must be clarified. Typical plots to be worked out for different scenarios are:

  • Temperature plots vs. well depth (initial- and final condition)
  • Pressure plots vs. well depth (initial- and final condition)
  • How fast the tubing temperature is dropping when temperature is changed

Step 2: Make stress calculation

Service loads lines are plotted in the von Mises equivalent (VEM) yield stress envelope to illustrate combined stresses over the entire length of the tubing.

Figure 1: Presentation of combined loads in VME envelope with limitations

Step 3: Make limitations

There are several limitations that must be clarified before making any decisions:

Safety factor

The tubing string has separate safety factors to the yield stress. These factors are company and well dependent, but have normally the highest factor for axial tension due to the potential for e.g. overpull during string manipulation. Components in the completion string normally have other (and less) safety factors than the tubing.


Most corrosion resistant alloys have different mechanical properties in different directions. This is especially true for cold worked alloys, but also for alloys being hardened by e.g. quenching and tempering due to different cooling times for e.g. heavy wall tubulars. The axial yield stress is available for most metals, also as a function of the diameter for heavy wall tubulars, but not always the tangential and radial yield stresses for e.g. cold worked alloys. Cold worked alloys may also have diffrent yield strength and compressive strength. The opposed to anisotropy is isotropy, which means homogeneity in all directions. The material is then said to be isotropic.

Reduced yield stress

The yield stress will be reduced at increasing temperature. This effect may be especially high for cold worked alloys that have been given high yield strength by increasing the number of dislocations in the material. The process is called annealing and is the same process as is used during tubular manufacturing.


The third and forth quadrant of the von Mises envelope (external pressure) may have a reduced pressure limit compared to the von Mises stresses due to instability factors in the tubing.

Step 4: Make decisions

The above process will result in the following decisions:

  • Tubing size (outside diameter)
  • Tubing material
  • Tubing weight (wall thickness)
  • Tubing threads
  • PBR or not

The above process will also provide input to the vendors of completion string components like the downhole safety valve and the production packer. Make sure all components in the completion string are available for the stresses before the tubing design is fixed. Use of a polished bore receptacle (PBR) will allow completion string movement and thus reduced stresses, but this is not a preferred solution due to limited PBR reliability.  

Updated: 07.01.2013

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