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Casing design · worked example · onshore Kuwait

Casing design load cases: burst, collapse and triaxial

DrillIQ drilling engineeringUpdated 1 October 202612 min read

A casing string is designed against the worst things that can credibly happen to it: a gas kick, a pressure test, losses, cementing, an overpull. Each of those is a load case, a pressure inside and outside the pipe at every depth plus an axial force, and the string has to hold every one of them with margin. This article works the load cases through for the intermediate string of a deep well onshore Kuwait, where a pressure test, the temperature and the sour gas decide the grade between them.

What a load case is

A load case describes one event over the whole length of the string. At each depth it gives the pressure inside (Pi), the pressure outside (Po) and the true axial force. From those come the four checks.

  • Burst: inside pressure exceeds outside. The net load is Pi − Po, and it is compared with the pipe's burst rating.
  • Collapse: outside exceeds inside. ISO 10400 uses an equivalent load, Po − (1 − 2t/D)·Pi, a little above the simple difference.
  • Axial: tension or compression against the pipe body and the connection.
  • Triaxial: all three stresses together at the pipe wall, through the von Mises stress, compared with the yield strength.

Each rating is derated for temperature and wear, and divided by a design factor: 1.10 for burst, 1.00 for collapse (1.10 for liners and production strings), 1.30 for axial and 1.25 for triaxial in the industry set used here. The result is the design line. A string passes when every load, at every depth, sits inside its design line. The safety factor, rating over load, is reported for each case at its worst depth, and the governing case is the lowest anywhere.

The outside pressure matters as much as the inside. For burst, the conservative choice is a light backup, fresh water at 1.00 SG, since behind cement the mud can settle out and the column outside can be lighter than anyone planned. For collapse, the backup is the heavy mud the string was run in.

The standard cases for an intermediate string

An intermediate string protects the hole above it while the next section is drilled, so its loads come from that next section.

  • Gas kick to surface (burst): a kick at the next section's TD, with gas filling the string above it, limited by what the shoe can hold. Gas is light, so the full kick pressure reaches surface: this case is worst at the top.
  • Displacement to gas (burst): the same with the next section's pore pressure and no kick margin. It sets the maximum anticipated surface pressure.
  • Pressure test (burst): the casing tested to that surface pressure, on the mud in the hole. The mud column adds to it all the way down, so it is worst at the shoe.
  • Lost returns (collapse): the next section loses mud to a weak zone, and the level inside falls until the column balances it.
  • Cementing (collapse): heavy slurry outside, displacement mud inside, before the cement sets.
  • Running, shock and plug bump (axial): the hanging weight with drag and a 100 klbf overpull, the shock of stopping the string, and the test pressure on the landed plug.

The method

Pburst = 0.875 · 2 Y t / D

Y(T) = Y · [1 − 0.0003 · (T − 68)],  T in °F

ΔPcollapse = Po − (1 − 2t/D) · Pi,    SF = rating / load ≥ DF

Y
minimum yield strength of the grade (T95: 95,000 psi; C110: 110,000 psi)
t, D
nominal wall thickness and outside diameter; 0.875 allows for the 12.5 % wall tolerance
T
temperature at the depth checked; the yield falls 0.03 % per °F above 68 °F (20 °C)
SF, DF
safety factor and design factor

Burst and collapse ratings follow API TR 5C3 (ISO 10400), collapse in its four regimes with the yield reduced by axial stress. The triaxial check computes the von Mises stress at the inner wall from the radial, hoop and axial stresses (Lamé), with the true axial force, which includes the pressure end loads and the ballooning of the uncemented length.

The example well

The example is a vertical deep well set in conditions typical of onshore Kuwait. Normal pressure, about 1.06 SG, runs to 3,250 m. Below it, an Upper Jurassic section of shale and anhydrite is pressured to 1.36 SG, and the carbonate reservoir under it, from 4,100 m to TD at 4,700 m, holds sour gas at 1.22 SG: 2 mol % H2S and 3 mol % CO2. Temperature is 30 °C at surface plus 2.8 °C per 100 m, 162 °C at TD.

The casing programme of the example well
StringShoe (m)Hole and mudShoe test
18⅝″ 87.5 ppf K55, BTC65024″, 1.10 SGLOT 1.62 SG
13⅜″ 72 ppf Q125, BTC2,60017½″, 1.18 SGLOT 1.82 SG
9⅝″ 53.5 ppf, T95 to 1,300 m, C110 below, premium gas-tight4,05012¼″, 1.42 SG, through the pressured sectionLOT 2.00 SG
7″ 35 ppf C110 liner, premium, from 3,900 m4,7008½″, 1.30 SG, the reservoirnone

The 9⅝″ is cemented with 1.70 SG lead from 2,300 m and 1.95 SG tail over the bottom 450 m. The module generated 37 load cases from this design basis. Seven are switched off with their reason: full evacuation of the three upper strings, which partial evacuation by lost returns covers on a normally pressured well, and four annular-pressure-build-up cases, because a land wellhead can bleed the annuli.

A hand check at the shoe

The governing load on the 9⅝″ is the pressure test, at the shoe.

  1. Test pressure. Displacement to gas from the 8½″ TD: 1.22 × 0.0981 × 4,700 = 562.3 bar, less 4,700 m of gas at 0.0226 bar/m = 456 bar at surface. Rounded up, the test is 460 bar, 6,670 psi.
  2. Inside at the shoe. 460 bar plus 1.42 SG of mud over 4,050 m: 460 + 564.0 = 1,024.0 bar.
  3. Outside. Fresh-water backup, 1.00 × 0.0981 × 4,050 = 397.2 bar. The net burst load is 626.8 bar, 9,091 psi.
  4. Rating. T95 53.5 ppf: 0.875 × 2 × 95,000 × 0.545 / 9.625 = 9,414 psi.
  5. Temperature. 143.4 °C at the shoe is 222 °F above 68 °F: the yield falls 6.66 %, and the rating to 8,786 psi.
  6. Safety factor. 8,786 / 9,091 = 0.97, against a design factor of 1.10. C110 gives 10,900 psi, 10,174 psi derated, and 1.12.

DrillIQ's engine gives the same 626.8 bar load and the same safety factors, 0.966 and 1.119. Two things stand out. The 1.42 SG mud inside adds 2,420 psi more than the water outside by the time it reaches the shoe, so a test set by surface pressure becomes the biggest burst load at the bottom of the string. And at 143 °C the steel has lost a fifteenth of its strength.

Burst along the string

Figure 1 Burst loads on the 9⅝″ intermediate casing
  • Gas kick 0.06 SG, gas to surface
  • Pressure test 460 bar on 1.42 SG mud
  • Design line: derated burst rating ÷ 1.10, T95 to 1,300 m, C110 below
  • Design line if the string were T95 throughout
  • Below 65 °C: C110 not allowed in sour service
below 65 °C5001,0001,5002,0002,5003,0003,5004,00002,0004,0006,0008,00010,000Burst load, inside less outside (psi)Depth (m)T95 above, C110 belowGas kickPressure testT95 onlyShoe: 9,091 psiC110 limit 9,249T95 limit 7,988

DrillIQ's Casing & Tubing Design engine (load_builder.generate_load_cases, results.design_plots). Fresh-water backup outside; ratings derated 0.03 %/°F above 20 °C on 30 °C + 2.8 °C/100 m.

Show the data
DepthGas kick 0.06 SGPressure test 460 barDesign line, final stringDesign line, T95 throughout
0.07,5496,6728,5128,512
67.57,4756,7128,5038,503
1357,4016,7528,4948,494
2007,3306,7918,4868,486
2707,2536,8338,4778,477
3387,1806,8738,4688,468
4007,1116,9118,4608,460
4727,0326,9548,4518,451
5406,9586,9948,4428,442
6006,8927,0308,4348,434
6756,8107,0758,4248,424
7426,7367,1158,4168,416
8006,6737,1508,4088,408
8786,5897,1968,3988,398
9456,5157,2368,3898,389
1,0006,4557,2698,3828,382
1,0806,3677,3178,3728,372
1,1486,2937,3578,3638,363
1,2006,2367,3898,3568,356
1,2826,1467,4388,3468,346
1,3506,0727,4789,6538,337
1,4185,9987,5189,6438,328
1,4855,9247,5599,6338,320
1,5525,8507,5999,6238,311
1,6205,7767,6399,6138,302
1,6885,7027,6809,6038,293
1,7555,6287,7209,5938,285
1,8225,5557,7619,5828,276
1,8905,4817,8019,5728,267
1,9585,4077,8419,5628,258
2,0255,3337,8819,5528,250
2,0925,2597,9229,5428,241
2,1605,1857,9629,5328,232
2,2285,1118,0029,5228,223
2,2955,0388,0439,5128,215
2,3624,9648,0839,5028,206
2,4304,8908,1239,4928,197
2,4984,8168,1649,4818,188
2,5654,7428,2049,4718,180
2,6324,6688,2449,4618,171
2,7004,5958,2859,4518,162
2,7684,5218,3259,4418,153
2,8504,4308,3749,4298,143
2,9024,3738,4069,4218,136
2,9704,2998,4469,4118,127
3,0504,2118,4949,3998,117
3,1054,1518,5279,3908,110
3,1724,0778,5679,3808,101
3,2503,9938,6139,3698,091
3,3083,9308,6489,3608,084
3,3753,8568,6889,3508,075
3,4503,7748,7339,3398,065
3,5103,7088,7699,3308,058
3,5783,6348,8099,3208,049
3,6503,5558,8529,3098,039
3,7123,4878,8909,2998,031
3,7803,4138,9309,2898,023
3,8503,3368,9729,2798,013
3,9153,2659,0109,2698,005
3,9823,1919,0519,2597,996
4,0503,1179,0919,2497,988

The two burst cases cross. The gas kick, a 0.06 SG kick over the 8½″ section's 1.30 SG mud with gas to surface, puts 7,550 psi on the top of the string and falls with depth as the fresh-water backup outside grows. Against the T95 at the top, derated to 9,362 psi at 30 °C, that is a safety factor of 1.24. The pressure test starts at 6,670 psi and grows to 9,091 psi at the shoe.

A T95 string throughout would fail from about 2,550 m down, where the test line crosses its dashed design line, and by the shoe it is 1,100 psi short. The module also offers a pore-pressure backup and a mud-and-mix-water backup for burst. Neither saves T95 here: with pore pressure outside, the worst point moves up to 3,240 m, still in normally pressured rock, at 1.07; with mud and mix water it stays at the shoe at 0.99. The bottom of the string needs a stronger grade.

Sour service decides the taper

A C110 string throughout passes every load case. It fails the sour-service check. At the reservoir's 562 bar, 2 mol % H2S is a partial pressure of 11.25 bar, 163 psia, more than three thousand times the 0.05 psia threshold of ISO 15156. The 9⅝″ is exposed: a kick while drilling the reservoir brings sour gas into it. Table A.3 of ISO 15156-2 allows T95 at any temperature, but C110 only at 65 °C and above, because its sulphide stress cracking resistance relies on the warmth. On this geothermal gradient that is below 1,250 m.

So the final string is T95 from surface to 1,300 m and C110 below, with a 50 m margin on the temperature limit. The upper section carries the gas kick, where T95 is strong enough; the lower section carries the pressure test, where only C110 is. Both are premium gas-tight connections rated at the pipe body. The CO2, 16.9 bar of partial pressure, is flagged as corrosive for the liner and the completion, which is a materials decision beyond the 9⅝″.

Collapse

Figure 2 Collapse loads on the 9⅝″ intermediate casing
  • Lost returns: level falls to 289 m
  • Cementing: 1.70 and 1.95 SG slurry outside
  • Design line: derated collapse rating ÷ 1.0, lowest over the cases
5001,0001,5002,0002,5003,0003,5004,00001,0002,0003,0004,0005,0006,0007,0008,000Collapse load, ISO 10400 equivalent (psi)Depth (m)Design lineLost returnsCementingShoe: 2,014 psiSF 3.81, lost returns

Same engine run. Collapse load as the ISO 10400 equivalent, Po − (1 − 2t/D)·Pi. The rating near surface is lower because tension reduces collapse strength (biaxial); the step at 1,300 m is the grade change. The line is the lowest rating over the cases; each case's safety factor uses its own.

Show the data
DepthLost returnsCementingDesign line
0.0003,989
67.5136154,036
135273314,083
200404464,128
270529624,176
338602774,221
400626924,262
4726541084,309
5406801244,353
6007021374,391
6757311544,438
7427571704,480
8007781834,515
8788082014,562
9458332164,602
1,0008542294,634
1,0808852474,681
1,1489102634,719
1,2009302744,749
1,2829622934,795
1,3509873095,908
1,4181,0133245,936
1,4851,0393405,963
1,5521,0643555,990
1,6201,0903716,016
1,6881,1163866,042
1,7551,1414016,068
1,8221,1674176,094
1,8901,1934326,119
1,9581,2184486,144
2,0251,2444636,169
2,0921,2704796,193
2,1601,2954946,217
2,2281,3215106,241
2,2951,3475336,265
2,3621,3725656,288
2,4301,3986086,312
2,4981,4246506,334
2,5651,4496926,357
2,6321,4757346,379
2,7001,5007776,402
2,7681,5268196,423
2,8501,5578716,450
2,9021,5779046,466
2,9701,6039466,487
3,0501,6339966,512
3,1051,6541,0316,529
3,1721,6801,0736,549
3,2501,7091,1226,572
3,3081,7311,1586,589
3,3751,7571,2006,609
3,4501,7861,2476,631
3,5101,8081,2856,648
3,5781,8341,3326,667
3,6501,8621,3906,687
3,7121,8851,4526,704
3,7801,9111,5186,723
3,8501,9381,5876,741
3,9151,9621,6516,759
3,9821,9881,7176,776
4,0502,0141,7836,794

Collapse is not the problem for this string. In the lost-returns case the 8½″ mud falls to 289 m, where the 1.30 SG column balances the 1.22 SG reservoir at TD, with the 1.42 SG mud the casing was run in outside. At the shoe that is an equivalent load of 2,014 psi, a safety factor of 3.81. Cementing is lighter still. The design line is lowest near surface, because tension there takes some of the collapse strength away. Collapse matters more on the 7″ liner, which is checked for full evacuation in production: 1.30 SG outside and nothing inside at 4,700 m, a safety factor of 1.41 against its 1.10 production factor.

The triaxial check

Figure 3 Triaxial check of the C110 section
  • Pressure test 460 bar
  • Gas kick 0.06 SG
  • Lost returns
  • Cementing
  • Von Mises at yield ÷ 1.25
  • API design limits
  • Von Mises at yield
-12,000-8,000-4,00004,0008,00012,000-2,000-1,500-1,000-50005001,0001,5002,000True axial force (klbf, tension positive)Inside less outside pressure (psi)von Mises ÷ 1.25burst ÷ 1.10tension ÷ 1.30collapseShoe, pressure testSF 1.25 on von Mises-127 klbf, 9,091 psi

Same engine run (results.triaxial), 9⅝″ 53.5 ppf C110 from 1,300 to 4,050 m, yield derated to 102,670 psi at the shoe. Ellipse at the inner wall, burst side with Po = 0 and collapse side with Pi = 0; every third load point along the section.

The design-limit plot puts every load point of the C110 section on one picture: true axial force across, pressure difference up. The ellipse is the von Mises stress at yield, the bold one at yield divided by 1.25, and the dashed box the uniaxial API limits. Points inside the bold ellipse pass.

The test points sit at the top of the picture, and the worst is at the shoe: 9,091 psi of burst with 127 klbf of compression. At the bottom of a hanging string the mud pushes up on the pipe's end, and the cement locks that force in. In that corner the ellipse cuts inside the box, so the triaxial check is tighter than the burst check: 1.253 against its design factor of 1.25, a utilisation of 99.8 %, where burst alone gave 1.12 against 1.10. Burst with compression is the quadrant to watch on any deep intermediate string tested on heavy mud.

The whole programme

Lowest safety factor in each check, final design (design factors 1.10 / 1.00 / 1.30 / 1.25; liner collapse 1.10)
StringBurstCollapseAxialTriaxial
18⅝″ K551.58 test1.18 cementing2.81 plug bump1.80
13⅜″ Q1251.21 test1.80 cementing2.09 plug bump1.38
9⅝″ T95 / C1101.12 test3.81 lost returns1.52 plug bump1.25
7″ C110 liner3.58 test1.41 evacuation9.37 cementing1.64

All 30 active cases pass. The 13⅜″ went through the same step as the 9⅝″: in P110 it failed its own pressure test at the shoe at 1.08, so it is Q125. It is not sour-exposed, because the 9⅝″ covers it before the reservoir is drilled. On the three upper strings the tightest check is a pressure test or a cementing load, and on the liner it is full evacuation. On none of them is it the kick.

A checklist for the design review

  • Check every case along the whole string; burst from a gas kick is worst at the top, from a pressure test at the shoe.
  • State the burst backup and the collapse fluid for every case, and test the design against the alternatives.
  • Derate the yield for the temperature at each depth, and for predicted wear where the string will be rotated in.
  • Set the casing test pressure from the maximum anticipated surface pressure, and check what it does at the shoe on the mud in the hole.
  • In sour service, check each section's grade against the temperature it will see, and taper where the stronger grade is not allowed.
  • Run the triaxial check: burst with compression at the shoe can govern when uniaxial checks pass.
  • Recheck connections against the same loads; premium envelopes for gas-tight strings.

How DrillIQ handles it

DrillIQ's Casing & Tubing Design module builds the design basis from the pressure window published by the Pore Pressure & Geomechanics module, the shoe tests and the temperature, and generates the standard load cases for every string from it, each with the reason it is on or off. It checks every case along every string with API TR 5C3 ratings, temperature derating, ISO equivalent collapse, the true axial force and von Mises, and draws the design lines and the triaxial plot shown above. Tapered strings, API and premium connection checks, casing wear, the ISO 15156 sour-grade check, annular pressure build-up, tubing movement and an optimiser that proposes the lightest passing taper are part of the same engine, and a design that fails any check cannot be published.

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References

  1. API TR 5C3 / ISO 10400. Calculating Performance Properties of Pipe Used as Casing or Tubing. American Petroleum Institute, 2008.
  2. API Specification 5CT / ISO 11960. Casing and Tubing. American Petroleum Institute.
  3. ISO 15156-2:2020. Petroleum and natural gas industries: Materials for use in H2S-containing environments in oil and gas production, Part 2.
  4. Rahman, S.S. and Chilingarian, G.V. Casing Design: Theory and Practice. Elsevier, 1995.
  5. Mitchell, R.F. and Miska, S.Z. (eds.) Fundamentals of Drilling Engineering. SPE Textbook Series Vol. 12, 2011.

About this example. The well in this article is a representative scenario set in typical onshore Kuwait conditions and worked through with DrillIQ's engines. It is not a client's well, and its figures are not field results.