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**Collapse resistance of a tubular, release 10a, issued 11 May 2008. JIT version.**

This worksheet exists in two versions. They are identical apart from the way they are formatted. The Work version hides intermediate calculations and allows the user to see the results just below the inputs. This is useful for quick “what-if” games, changing various inputs to see what works best. The JIT version displays all intermediate calculations, plus adds tutorial text to explain the methodology.

ALL the figures published in API 5C2 for burst, tension, collapse and biaxial have been checked against this worksheet. Only three are different by more than rounding errors. These are noted at the bottom of the worksheet.

This “**Just In Time Learning**” tutorial version of the worksheet explains the theories behind the calculations, it shows the formulae and intermediate results. It is assumed that you are familiar with the concepts of Stress, the relationship between Stress and Strength, Temperature derating of yield stress and strength and the Biaxial effect. Each of these topics is or will be covered in other DDC worksheet tutorials. Use the Work version of the worksheet if you just want to run the numbers.

Tutorial text is shown in blue. It should take 20-25 minutes to work through this tutorial. Leave the user input as it is for the tutorial.

At the end of this tutorial, YOU will be able to;

1. Describe the theoretical basis for calculating the collapse resistance of tubulars.

2. Name the four collapse formula models and state how they were derived.

3. Explain how the formulae are used to calculate for the Biaxial effect.

4. Correctly account for internal pressure when calculating collapse resistance.

5. Use this worksheet (both Working and Tutorial versions) to evaluate casing collapse including the effects of axial stress, temperature, internal pressure and Design Factor.

If a full audit trail of the calculations is needed, or if you wish to audit the formulae and methodology, this version can be used instead of the work version and saved in a format which can be pasted into a document.

*Description*

This worksheet takes inputs of tubular OD, wall thickness, grade, axial force, internal pressure and temperature. It uses the formulae defined in the referenced documents to calculate the collapse resistance and will account for the effects of temperature, internal pressure and tension.

Tension or compression at the depth of interest can be entered to allow the biaxial effect to be calculated. It is normal to account for the reduction in collapse resistance due to axial tension but not usual to take advantage of the increase in burst due to tension. This may be defined by your own company’s policy.

You can also enter a Design Factor to include in the calculation, or set the DF to 1 if this is not required.

*User input*

4.5″ 9.5 ppf4.5″ 10.5 ppf4.5″ 11.6 ppf4.5″ 13.5 ppf4.5″ 15.1 ppf5″ 11.5 ppf5″ 13 ppf5″ 15 ppf5″ 18 ppf5″ 21.4 ppf5″ 23.2 ppf5″ 24.1 ppf5.5″ 14 ppf5.5″ 15.5 ppf5.5″ 17 ppf5.5″ 20 ppf5.5″ 23 ppf5.5″ 26.8 ppf5.5″ 29.7 ppf5.5″ 32.6 ppf5.5″ 35.3 ppf5.5″ 38 ppf5.5″ 40.5 ppf5.5″ 43.1 ppf6.625″ 20 ppf6.625″ 24 ppf6.625″ 28 ppf6.625″ 32 ppf7″ 17 ppf7″ 20 ppf7″ 23 ppf7″ 26 ppf7″ 29 ppf7″ 32 ppf7″ 35 ppf7″ 38 ppf7″ 42.7 ppf7″ 46.4 ppf7″ 50.1 ppf7″ 53.6 ppf7″ 57.1 ppf7.625″ 24 ppf7.625″ 26.4 ppf7.625″ 29.7 ppf7.625″ 33.7 ppf7.625″ 39 ppf7.625″ 42.8 ppf7.625″ 45.3 ppf7.625″ 47.1 ppf7.625″ 51.2 ppf7.625″ 55.3 ppf7.75″ 46.1 ppf8.625″ 24 ppf8.625″ 28 ppf8.625″ 32 ppf8.625″ 36 ppf8.625″ 40 ppf8.625″ 49 ppf9.625″ 32 ppf9.625″ 36 ppf9.625″ 40 ppf9.625″ 43.5 ppf9.625″ 47 ppf9.625″ 53.5 ppf9.625″ 58.4 ppf9.625″ 59.4 ppf9.625″ 64.9 ppf9.625″ 70.3 ppf9.625″ 75.6 ppf10.75″ 32.75 ppf10.75″ 40.5 ppf10.75″ 45.5 ppf10.75″ 51 ppf10.75″ 55.5 ppf10.75″ 60.7 ppf10.75″ 65.7 ppf10.75″ 73.2 ppf10.75″ 79.2 ppf10.75″ 85.3 ppf11.75″ 42 ppf11.75″ 47 ppf11.75″ 54 ppf11.75″ 60 ppf11.75″ 65 ppf11.75″ 71 ppf13.375″ 48 ppf13.375″ 54.5 ppf13.375″ 61 ppf13.375″ 68 ppf13.375″ 72 ppf16″ 65 ppf16″ 75 ppf16″ 84 ppf16″ 109 ppf18.625″ 87.5 ppf20″ 94 ppf20″ 106.5 ppf20″ 133 ppf8.625″ 44 ppf |

Select a casing

100000 |

kgflbfNkN |

Enter axial force at the depth of interest (tensile is +ve). F_{a} =

80 |

FCK |

Enter the temperature at the depth of interest. Temp =

3000 |

psiPakPaMPa |

Enter the internal pressure at the depth of interest. p_{i} =

80 |

Enter the number part of the steel grade eg for L80, enter 80 (units are kpsi). Gr =

1 |

Enter design factor for collapse or use 1 if design factor is not to be considered. DF_{c} =

**Click here when any values are modified to update the result.**

Calculate the pipe cross sectional area.

Calculate the API Minimum Yield Strength

When calculating burst or tensile strength, engineering principles are used to make accurate calculations. The minimum tensile yield strength of a pipe is simply the cross sectional area times the minimum yield stress. Collapse is much more complex. The formulae and methods used below arise from a mixture of theoretical, numerical and statistical tools that were developed by the industry many years ago and have since been borne out in practice.

There are four recognised collapse failure modes and a set of calculations for each are defined by API 5C3 and ISO 10400. The factor governing which collapse mode to calculate for (which formula to use) is the ratio of outside diameter, D, to wall thickness, t. This is the D/t ratio. Except for Elastic Collapse, the collapse resistance also is a function of the Minimum Yield Stress, σ_{ymn}. These formulae are used to calculate the collapse resistance values in Tables 1 and 4 of API Bulletin 5C2. Every figure in API 5C2 has been compared to results from this worksheet, most come within a few psi and the difference looks like rounding in the API tables. Only 3 are different by more than a few psi, these are documented at the bottom of this sheet.

**Yield Collapse** – occurs when the external pressure causes the steel on the inside surface of the tube to exceed the Minimum Yield Stress of the material. The formula was derived theoretically.

**Plastic Collapse** – predominates with small D/t ratios, <15. The formula was derived using the results of 2488 collapse tests using K55, N80 and P110 grade pipes.

**Elastic Collapse** – occurs when the tube collapses due to instability before the minimum yield stress of the steel is exceeded. This is a likely failure mode for large D/t ratios, >25. The formula was derived theoretically.

A large slice of uncertainty exists in the model between Plastic and Elastic collapse. Therefore there is a fourth formula called **Transition Collapse** to cover this area. API interpolated values between Plastic and Elastic collapse to derive the equation.

First, three empirical constants A_{c}, B_{c} and C_{c} are calculated, then constants F_{c} and G_{c} are calculated from A_{c} and B_{c} for the transition case.

Note that Mathcad enforces units consistency while the API / ISO calculations do not. In order to get around this, the Minimum Yield Stress σ_{ymn} figures are divided by 1 psi to get around Mathcad’s unit enforcement. The result is the same as would be achieved with a calculator, ignoring units.

The ratio of D/t determines which of the four formulae to use. The relevant D/t ratio is calculated using a set of formulae given in API 5C3 and ISO 10400. So the next step is to calculate the D/t ratio and the ratio ranges for each formula, so that the correct formula can be selected.

The formula for Yield Collapse should be used when the D/t ratio is less than Dt_{yp};

NOTE – formula 36 in ISO/TR10400 is incorrect and uses Minimum Yield Strength f_{ymn} when it should use Minimum Yield Stress σ_{ymn}. The equation here is from API 5C3.

The formula for Plastic Collapse should be used when Dt is above Dt_{Yp} but less than;

The formula for Transition Collapse should be used when Dt is above Dt_{PT} but less than;

Now the worksheet has calculated the ratio , the correct formula can be found by using an IF function which compares the Dt ratio to the required range for each formula. Where the Dt ratio is out of range for the formula, a zero is returned.

The formula for Yield Collapse should be used when Dt is less than Dt_{yp}.

The formula for Plastic Collapse should be used when Dt is above Dt_{Yp} but equal to or less than Dt_{p}.

The formula for Transition Collapse should be used when Dt is above Dt_{p} but equal or less than Dt_{T}.

The formula for Elastic Collapse should be used when Dt is above Dt_{T}.

Only one of the four formulae above should have returned a result. Now the worksheet adds all four results together – three of which are zero – to determine the Collapse Resistance of the pipe, whichever formula returned the result.

For the JIT Tutorial, to compare the result to Table 1 or 4 of API 5C2, 7″ 26 ppf P110 casing at ambient temperature (20C or 68F) has a collapse resistance of 6230 psi vs the worksheet result of 6232 psi.

When a pipe is under axial stress (tension or compression is applied), the collapse and burst resistances both change. This is called the Biaxial Effect. Within limits, if the pipe is under positive axial stress (tension) then the burst resistance is increased and the collapse resistance is reduced.

API 5C3 / ISO 10400 account for this by calculating a modified yield stress, then re-apply the calculations for the empirical constants and the collapse resistance formulae to determine the new collapse resistance.

Calculate the axial stress σ_{a} arising in the pipe as a result of the tensile or compressive load.

To calculate the reduced collapse resistance for a pipe under axial tension, the yield stress is modified by the following formula;

The revised empirical constants and collapse resistances are now recalculated as before;

The ranges for Dt to use to select the correct formula are also revised with the modified yield stress.

The formula for Yield Collapse should be used when the D/t ratio is less than Dt_{yp};

The formula for Plastic Collapse should be used when Dt is above Dt_{Yp} but less than;

The formula for Transition Collapse should be used when Dt is above Dt_{PT} but less than;

Calculate for each of the four formula; only one should return a result.

For the JIT Tutorial, to compare the result to Table 4 of API 5C2. 7″ 26 ppf P110 casing at ambient temperature (20C or 68F) under an axial stress of +10,000 psi has a collapse resistance of 6120 psi vs the worksheet result of 6124 psi.

Apply the Temperature Correction Factor and Design Factor;

You might think that if the pipe has 1000 psi or 6895 kPa inside, that the collapse resistance would also increase by the same amount. While that is approximately correct, in fact API 5C3 / ISO 10400 have a formula to calculate for it which shows that the collapse resistance increases by slightly less than the internal pressure.

Adjust the final figure with Biaxial, TCF and DF for internal pressure of or .

Percentage of axial stress related to Minimum Yield Stress

*Results*

Pipe cross sectional area

Ratio of OD to wall thickness, D/t ratio

Temperature Correction Factor

Pipe body axial stress at depth of interest

(Axial stress as a % of Minimum Yield Stress)

API collapse resistance, ambient, no axial force or DF

API collapse resistance with TCF, DF and Biaxial

API collapse resistance with TCF, DF, Biaxial & internal pressure

*Worksheet references*

API Specification 5CT, 5th Edition, April 1 1995 “Specification for Casing and Tubing (U.S. Customary Units)”.

API Bulletin 5C3, 6th Edition, October 1 1994 “Bulletin on Formulas and Calculations for Casing, Tubing, Drill Pipe, and Line Pipe Properties”, also ISO/TR10400:2007 which is expected to replace API 5C3 during 2008.

API Bulletin 5C2, 21st Edition, October 1999 “Bulletin on Performance Properties of Casing, Tubing and Drill Pipe”.

Formulae for Temperature Correction Factor taken from the Exxon Casing Design Manual.

SG of steel from http://www.simetric.co.uk/si_metals.htm taken as 7.85.

Version 1 of this worksheet released on 1 January 2008.

Version 10 released after testing against API 5C2 21st Edition for burst, tension, collapse and biaxial. The only significant differences were found in Table 4 (biaxial) as follows, with all other results the same within normal rounding;

9.625″ 40ppf Grade 80 at -10,000 psi axial load, this worksheet showed 3167 psi vs API 3107

7.625″ 45.3ppf Grade 95 at -10,000 psi axial load, this worksheet showed 14,241 psi vs API 14,330

9.625″ 43.5ppf Grade 110 at 25000 psi axial load, this worksheet showed 4205 psi vs API 4130