It should be noted that the strengths require down rating to account for the effects of wear, corrosion and fatigue and for the effect of temperature on yield strength.
The appearance of commercial casing analysis software has made triaxial stress analysis possible. The allowable value of the Von Mises equivalent stress is usually the yield strength of the material adjusted for temperature effects. However, it should be noted that for collapse loading, corrections are required to allow for the elastic behaviour of thin-walled pipe.
1 Collapse strength
A casing experiences a collapse loading when the external pressure exceeds the internal pressure. The magnitude of the collapse load is generally taken as the difference in pressure, i.e. Pe-Pi. In the uniaxial design this load is compared to the uniaxial collapse capacity.
API Bull. 5C3 contains four formulae to calculate the external pressure, the collapse capacity at which a casing will collapse in ribbon-type mode.
The background to these four formulae will be expanded upon by addressing the behaviour of the extreme geometries first, i.e. do/t > 25 and do/t < 15. This will be followed by a discussion on the transition zone.
Loaded by external pressure only, a thin-walled tube (do/t > 25) will collapse as a result of elastic instability of the wall, before yield occurs. The theoretical pressure at which this elastic collapse occurs is given by Clinedinst.
The elastic collapse pressure is independent of the material yield strength, but highly dependent on the casing dimensions: i.e. the geometry.
However, for thick-walled tubes (do/t < 15) yield of the casing wall occurs before instability. As shown in Section 3.10, the highest tangential stress st always occurs at the inside wall even for collapse loading. Thus, by assuming sa to be zero, and sr negligible, the collapse capacity can be assumed to be reached when the inner wall tangential stress reaches the material yield strength, sy.
No satisfactory analytical model has been found to describe the collapse pressure in the transition between the two basic modes of collapse. Accordingly, the API have adopted two empirically derived equations spanning the transition based on laboratory collapse tests reported by Clinedinst. The API refer to these equations as describing the transition collapse pressure and the plastic collapse pressure. In deriving the empirical equations, statistical regression analysis was used to determine minimum performance properties from the collapse test data. In order to provide a smooth progression from the minimum properties in the transition zone to the properties in the zone of elastic instability, the theoretical elastic collapse values have been reduced to obtain minimum values.
By using this approach, the API collapse performance properties in the "Plastic collapse", "Transition collapse", and "Elastic collapse" ranges are, in effect, corrected for the spread in the dimensional and metallurgical properties that may effect the tubular strength in collapse. This does not apply for "Yield strength collapse" range.
For the common casing sizes, it can be seen that collapse mode will generally be Plastic or Transition.
It should be noted that if the material yield strength is downrated due to high temperatures, the downrated yield strength must be inserted into the relevant collapse pressure formulae.
Many casing manufacturers market what they claim to be "high collapse" resistance casing. The basis of the claims, usually tight manufacturing tolerances, should always be thoroughly checked before the claimed performance ratings are accepted and used in design calculations.
In the event that the collapse load consists of an external pressure and a smaller internal pressure, the Lamé equation for the resulting tangential stress can be set against that same tangential stress derived for external pressure only, using an effective external pressure, Peff.
It should be noted that a small negative axial load, i.e. a small amount of compression, increases the allowable collapse pressure. However, the formula is not frequently used in such circumstances since its omission gives additional conservatism.
It is important to note that since this API correction procedure is based on the bi-axial Von Mises yield criterion, it relates only to the yield strength type of collapse. The API suggests, however, that their axial load correction factor be applied for all casing regardless of do/t ratio. In reality, the correction is only truly applicable for do/t ratios less than about 15, i.e. thick-walled tubulars which fail by yield at the inner wall. For increasing do/t ratios, the effects of elastic instability progressively reduce the amount of correction required, until for complete elastic collapse, there is no correction for axial load at all
In general, ribbon-type mode of collapse is chosen to quantify the collapse capacity since it requires less energy than trough-type collapse. API collapse tests are performed in a pressure vessel such that there is sufficient clearance for the pipe to collapse in ribbon-type mode. However, for most casing/hole size combinations, ribbon-type collapse is impossible, because of the restraining hole wall.
Consider a 133/8 in diameter casing in a 171/2 in diameter hole. For ribbon collapse, the width of the collapsed casing is given by pdo/2, which in this case is 21 in. As a result, trough-type collapse is a more realistic assumption in a gauge hole and the figures published in API Bull. 5C2 can be regarded as conservatve in this respect.
The effect of a cement sheath around the casing on collapse capacity has been the subject of research, however no clear conclusions can yet be drawn.
Research shows that a do/t ratio of about 4 or less is necessary to support a non-uniform salt load. Since this would lead to impractical casing schemes, it is attempted to avoid non-uniform loads by implementing suitable operational practices introducing uniform loads like minimising wash-outs and placing cement over salt intervals. All relevant casing design is therefore based on uniform loads.
2 Burst strength
A casing experiences a burst loading when the internal pressure exceeds the external pressure. The magnitude of the burst load is generally taken as the difference in pressure, i.e. Pi- Pe. In the uniaxial design this load is compared to the uniaxial burst capacity.
The highest st always occurs at the inner wall. Thus, by assuming sa is zero and sr is negligible, the burst capacity can be assumed to be reached when the inner wall tangential stress, st, reaches the yield strength sy. From the Lamé equation for tangential stress
The basic API burst formula is lacking in three respects:
- any external pressure is not accounted for
- the effect of axial load is not accounted for
- the effect of the cement sheath is disregarded.
The maximum burst loading usually occurs at surface, as does the maximum tensile loading. There would therefore appear to be a case for applying a bi-axial correction to the burst rating at the top of the string.
The ellipse representing the Von Mises yield criterion, indicate an increase in burst resistance occurs at moderate levels of tension, while a decrease occurs in compression and at high levels of tension.
The conservative approach of using the burst rating for zero axial load is most often adopted, although this approach is only conservative if compression or high tension is avoided.
Compressive loads can arise in production strings, for example, in high pressure/high temperature wells, where thermal expansion of the steel is significant. Under these circumstances the burst rating should be reduced by determining a maximum allowable value of st in the presence of sa in analogy with the correction discussed in the paragraph on collapse capacity.
The effect of the cement sheath around the casing on the burst capacity has been the subject of research, however, no clear conclusions can yet be drawn.
The triaxial capacity, for comparison with the Von Mises Equivalent stress, sVME, is taken as the minimum yield strength of the casing material, sy.
Manufacturers or API Spec. 5CT can provide detailed information on the value of the minimum yield strength. It should be noted that the yield strength is temperature dependent. For most steels the yield strength decreases as temperature increases. For some low strength casing grades (J55) yield strength will initially decrease as temperature increases, but as temperature further increases, the yield strength could rise to a level above that evident at room temperature.