Strength of casing and tubing: Difference between revisions

The most important mechanical properties of [[Casing_and_tubing|casing and tubing]] are burst strength, collapse resistance and tensile strength. These properties are necessary to determine the strength of the pipe and to design a casing string.

If casing is subjected to internal pressure higher than external, it is said that casing is exposed to burst pressure loading. Burst pressure loading conditions occur during [http://petrowiki.org/Glossary:Well_control well control] operations, casing pressure integrity tests, pumping operations, and production operations. The MIYP of the pipe body is determined by the internal yield pressure formula found in API Bull. 5C3, Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties''.<ref name="r1">API Bull. 5C3, Bulletin for Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties, fourth edition. 1985. Dallas: API.</ref>''

where

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1. Most casing used in the oilfield has a ''D''/''t'' ratio between 10 and 35. The factor of 0.875 appearing in the equation represents the allowable manufacturing tolerance of –12.5% on wall thickness specified in API ''Bull. 5C2, Performance Properties of Casing, Tubing, and Drillpipe''.<ref name="r2">API Bull. 5C2, Bulletin for Performance Properties of Casing, Tubing, and Drillpipe, eighteenth edition. 1982. Dallas: API.</ref> A pressure at MIYP does not mean the pipe will have a burst or rupture failure which only occurs when the tangential stress exceeds the ultimate tensile strength (UTS). So using a yield strength criterion as a measure of pipe internal pressure resistance is inherently conservative. This is particularly true for lower-grade materials such H-40, K-55, and N-80 whose UTS/YS ratio is significantly greater than that of higher-grade materials such as P-110 and Q-125. The effect of axial loading on the internal pressure resistance is discussed later.

If external pressure exceeds internal pressure, the casing is subjected to collapse. Such conditions may exist during cementing operations, trapped fluid expansion, or well evacuation. Collapse strength is primarily a function of the material's [[Glossary:Yield_strength|yield strength]] and its slenderness ratio, ''D''/''t''. The collapse strength criteria, given in API ''Bull. 5C3, Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties'',<ref name="r1">API Bull. 5C3, Bulletin for Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties, fourth edition. 1985. Dallas: API.</ref> consist of four collapse regimes determined by yield strength and ''D''/''t'' . Each criterion is discussed next in order of increasing ''D''/''t''.

Yield strength collapse is based on yield at the inner wall using the Lamé thick wall elastic solution. This criterion does not represent a "collapse" pressure at all. For thick wall pipes (''D''/''t''

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Plastic collapse is based on empirical data from 2,488 tests of K-55, N-80, and P-110 seamless casing. No analytic expression has been derived that accurately models collapse behavior in this regime. Regression analysis results in a 95% confidence level that 99.5% of all pipes manufactured to American Petroleum Institute (API) specifications will fail at a collapse pressure higher than the plastic collapse pressure. The minimum collapse pressure for the plastic range of collapse is calculated by '''Eq. 3'''.

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Transition collapse is obtained by a numerical curve fit between the plastic and elastic regimes. The minimum collapse pressure for the plastic-to-elastic transition zone, ''P''_''T'', is calculated with '''Eq. 4'''.

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Elastic Collapse is based on theoretical elastic instability failure; this criterion is independent of yield strength and applicable to thin-wall pipe (''D''/''t''

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25±). The minimum collapse pressure for the elastic range of collapse is calculated with '''Eq. 5'''. [[File:Vol2 page 0292 eq 003.png|RTENOTITLE]]....................(5) The applicable ''D''/''t'' range for elastic collapse is shown in '''Table 4'''. <gallery widths="300px" heights="200px">

File:Devol2 1102final Page 294 Image 0001.png|'''Table 4- D/t Range for Elastic Collapse'''

s qualification test data such as lengths to diameter ratio, testing conditions (end constraints), and the number of tests performed.

If the pipe is subjected to both external and internal pressures, the equivalent external pressure is calculated as

In '''Eq. 7''', we can see the internal pressure applied to the internal diameter and the external pressure applied to the external diameter. The "equivalent" pressure applied to the external diameter is the difference of these two terms.

The axial strength of the pipe body is determined by the pipe body yield strength formula found in API ''Bull. 5C3, Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties''.<ref name="r1">API Bull. 5C3, Bulletin for Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties, fourth edition. 1985. Dallas: API.</ref>

Axial strength is the product of the cross-sectional area (based on nominal dimensions) and the yield strength.

All the pipe-strength equations previously given are based on a uniaxial stress state (i.e., a state in which only one of the three principal stresses is nonzero). This idealized situation never occurs in oilfield applications because pipe in a wellbore is always subjected to combined loading conditions. The fundamental basis of casing design is that if stresses in the pipe wall exceed the [[Glossary:Yield_strength|yield strength]] of the material, a failure condition exists. Hence, the yield strength is a measure of the maximum allowable stress. To evaluate the pipe strength under combined loading conditions, the uniaxial yield strength is compared to the yielding condition. Perhaps the most widely accepted yielding criterion is based on the maximum distortion energy theory, which is known as the Huber-Hencky-Mises yield condition or simply the von Mises stress, triaxal stress, or equivalent stress.<ref name="r3">Crandall, S.H. and Dahl, N.C. 1959. An Introduction to the Mechanics of Solids. New York City: McGraw-Hill Book Company.</ref> Triaxial stress (equivalent stress) is not a true stress. It is a theoretical value that allows a generalized three-dimensional (3D) stress state to be compared with a uniaxial failure criterion (the yield strength). In other words, if the triaxial stress exceeds the yield strength, a yield failure is indicated. The triaxial safety factor is the ratio of the material<nowiki>’</nowiki>s yield strength to the triaxial stress. The yielding criterion is stated as [[File:Vol2 page 0295 eq 001.png|RTENOTITLE]]....................(9) where

'''Eq. 12''' calculates the equivalent stress at any point of the pipe body for any given pipe geometry and loading conditions. To illustrate these concepts, let us consider a few particular cases.

Assuming that σ_''z''

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Combined burst and compression loading corresponds to the upper left-hand quadrant of the design envelope. This is the region where triaxial analysis is most critical because reliance on the uniaxial criterion alone would not predict several possible failures. For high burst loads (i.e., high tangential stress and moderate compression), a burst failure can occur at a differential pressure less than the API burst pressure. For high compression and moderate burst loads, the failure mode is permanent corkscrewing (i.e., plastic deformation because of helical buckling). This combined loading typically occurs when a high internal pressure is experienced (because of a tubing leak or a buildup of annular pressure) after the casing temperature has been increased because of production. The temperature increase, in the uncemented portion of the casing, causes thermal growth, which can result in significant increases in compression and buckling. The increase in internal pressure also results in increased buckling.

Combined burst and tension loading corresponds to the upper right-hand quadrant of the design envelope. This is the region where reliance on the uniaxial criterion alone can result in a design that is more conservative than necessary. For high burst loads and moderate tension, a burst yield failure will not occur until after the API burst pressure has been exceeded. As the tension approaches the axial limit, a burst failure can occur at a differential pressure less than the API value. For high tension and moderate burst loads, pipe body yield will not occur until a tension greater than the uniaxial rating is reached.

Taking advantage of the increase in burst resistance in the presence of tension represents a good opportunity for the design engineer to save money while maintaining wellbore integrity. Similarly, the designer might wish to allow loads between the uniaxial and triaxial tension ratings. However, great care should be taken in the latter case because of the uncertainty of what burst pressure might be seen in conjunction with a high tensile load (an exception to this is the green cement pressure test load case). Also, connection ratings may limit your ability to design in this region.

For many pipes used in the oil field, collapse is an inelastic stability failure or an elastic stability failure independent of [[Glossary:Yield_strength|yield strength]]. The triaxial criterion is based on elastic behavior and the yield strength of the material and, hence, should not be used with collapse loads. The one exception is for thick-wall pipes with a low ''D''/''t'' ratio, which have an API rating in the yield strength collapse region. This collapse criterion along with the effects of tension and internal pressure (which are triaxial effects) result in the API criterion being essentially identical to the triaxial method in the lower right-hand quadrant of the triaxial ellipse for thick-wall pipes.

Triaxial analysis is perhaps most valuable when evaluating burst loads. Hence, it makes sense to calibrate the triaxial analysis to be compatible with the uniaxial burst analysis. This can be done by the appropriate selection of a design factor. Because the triaxial result nominally reduces to the uniaxial burst result when no axial load is applied, the results of both of these analyses should be equivalent. Because the burst rating is based on 87.5% of the nominal wall thickness, a triaxial analysis based on nominal dimensions should use a design factor that is equal to the burst design factor multiplied by 8/7. This reflects the philosophy that a less conservative assumption should be used with a higher design factor. Hence, for a burst design factor of 1.1, a triaxial design factor of 1.25 should be used.

'''Fig. 2''' graphically summarizes the triaxial, uniaxial, and biaxial limits that should be used in casing design along with a set of consistent design factors.

*Saving money in burst design by taking advantage of the increased burst resistance in tension

*Accounting for large temperature effects on the axial load profile in high-pressure, high-temperature wells (this is particularly important in combined burst and compression loading)

*Evaluating buckling severity (permanent corkscrewing occurs when the triaxial stress exceeds the yield strength of the material)

Second, the accuracy of triaxial analysis is dependent upon the accurate representation of the conditions that exist both for the pipe as installed in the well and for the subsequent loads of interest. Often, it is the change in load conditions that is most important in stress analysis. Hence, an accurate knowledge of all temperatures and pressures that occur over the life of the well can be critical to accurate triaxial analysis.

In the examples that are discussed next, burst and collapse criteria are examined. Triaxial stresses are calculated for a variety of load situations to demonstrate how the casing strength formulas and the load formulas are actually used.

Assume that we have a 13 ³/₈-in., 72-lbm/ft N-80 intermediate casing set at 9,000 ft and cemented to surface. The burst differential pressure for this casing is given by '''Eq. 1'''.

The maximum von Mises stress is at the inside of the 13 ³/₈-in. casing with a value that is 66% of the yield stress. In the burst calculation, the applied pressure was 89% of the calculated burst pressure. Thus, the burst calculation is conservative compared to the von Mises calculation for this case.

For the sample collapse calculation, we will test the collapse resistance of a 7-in., 23-lbm/ft P-110 liner cemented from 8,000 to 12,000 ft. Comparing the 7-in. liner properties against the various collapse regimes, it was found that transition collapse was predicted for this liner. The collapse pressure for this liner is calculated from '''Eq. 4''' with the following values for ''F'' and ''G'', as taken from '''Table 3'''.

Because ''p''_''e'' exceeds ''p''_''c'' (4,440 psi), the liner is predicted to collapse. It is not appropriate to calculate a von Mises stress for collapse in this case because collapse in the transitional region is not strictly a plastic yield condition.

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<references />

[[Casing_design|Casing design]]

[[PEH:Casing_Design]]

''Manual for Steel Construction, Load and Resistance Factor Design''. 1986. Chicago: American Institute of Steel Construction.

Mitchell, R.F.: “Casing Design,” in Drilling Engineering, ed. R. F. Mitchell, vol. 2 of Petroleum Engineering Handbook, ed. L. W. Lake. (USA: Society of Petroleum Engineers, 2006). 287-342.

Rackvitz, R. and Fiessler, B. 1978. Structural Reliability Under Combined Random Load Processes. ''Computers and Structures'' '''9:''' 489.

Timoshenko, S.P. and Goodier, J.N. 1961. ''Theory of Elasticity'', third edition. New York City: McGraw-Hill Book Co.