Casing Strength and Load Analysis: Burst Criterion

Casing Burst Pressure - API Formula Calculation, Failure Mechanics, and Design Safety Engineering

Burst failure is the rupture of a casing string when internal pressure exceeds the pipe's tensile resistance in the hoop (circumferential) direction. It is simultaneously a structural failure mode and an operational catastrophe: a burst casing at 8,500 ft in a gas producer vents wellbore pressure into the annulus, potentially bypassing the BOP and creating a well control situation with no controllable surface path. The 1995 Karachaganak gas field incident, multiple North Sea HPHT completions, and documented Gulf of Mexico production casing failures share a common failure path: burst pressure calculations performed using only the API minimum yield strength table without accounting for the gas column effect, the actual load case during shut-in, or the biaxial correction for axial tension. A 9-5/8" P-110 casing string rated at 10,780 psi API burst can fail at 8,900 psi when high axial tension is present - 17% below its rated value. Understanding the burst calculation, its underlying assumptions, and the corrections required for real field conditions is the foundation of safe casing design against internal pressure.

1. Burst Pressure Fundamentals - The API Formula and Its Basis

1.1 The Barlow/API Burst Pressure Formula

API 5C3 Burst Pressure Formula (Barlow's equation, 87.5% wall thickness factor):
P_b (psi) = 0.875 x (2 x S x t) / OD

Where:
S = minimum yield strength of casing material (psi)
t = nominal wall thickness (in) = (OD - ID) / 2
OD = outer diameter (in)
0.875 = API manufacturing tolerance factor (allows for -12.5% wall thickness variation)

Equivalent form using wall thickness directly:
P_b = 0.875 x 2 x S x t / OD = 1.75 x S x t / OD

Worked example - 9-5/8" P-110, 53.5 ppf:
OD = 9.625", ID = 8.535", t = (9.625 - 8.535) / 2 = 0.545"
S = 110,000 psi (P-110 minimum yield)

P_b = 0.875 x (2 x 110,000 x 0.545) / 9.625
= 0.875 x 119,900 / 9.625
= 0.875 x 12,456
= 10,899 psi API burst rating

(API tables list 10,780 psi - slight difference from rounding in published values)

Worked example - same OD, heavier weight: 9-5/8" P-110, 58.4 ppf:
OD = 9.625", ID = 8.435", t = (9.625 - 8.435) / 2 = 0.595"
P_b = 0.875 x (2 x 110,000 x 0.595) / 9.625 = 0.875 x 13,584 = 11,886 psi

Weight increase from 53.5 to 58.4 ppf (+ 9.2%) → burst rating increase from 10,780 to 11,886 psi (+10.3%)

1.2 API Burst Ratings by Common Casing Grades

Grade	Yield (psi)	9-5/8" 47.0 ppf Burst	9-5/8" 53.5 ppf Burst	9-5/8" 58.4 ppf Burst
J-55	55,000	4,760 psi	5,390 psi	5,940 psi
N-80	80,000	6,930 psi	7,830 psi	8,600 psi
L-80	80,000	6,930 psi	7,830 psi	8,600 psi
P-110	110,000	9,530 psi	10,780 psi	11,850 psi
Q-125	125,000	10,830 psi	12,250 psi	13,470 psi
V-150	150,000	12,990 psi	14,700 psi	16,160 psi

2. Net Burst Load - What API Ratings Do Not Include

2.1 Net Internal Pressure - The Design Load vs Pipe Rating

The API burst rating is a pipe property - a material and geometry number. The design burst load is an operational quantity that must be calculated for each load case. The two are compared through the safety factor. The key principle: burst is driven by the net differential pressure across the pipe wall, not the absolute internal pressure.

Net burst pressure (design load):
P_net_burst = P_internal - P_external

Burst safety factor:
SF_burst = P_b (API rating) / P_net_burst ≥ 1.10 (minimum industry standard)

Critical load case 1 - Full gas column shut-in (governing burst for production casing):
P_internal at surface = P_reservoir - G_gas x TVD
P_external at surface = 0 psi (assume worst case: no fluid in annulus above mud line)

Worked example - gas producer:
Reservoir pressure = 8,800 psi at 14,000 ft TVD
Gas gradient = 0.085 psi/ft
P_internal at surface = 8,800 - 0.085 x 14,000 = 8,800 - 1,190 = 7,610 psi SIWHP
P_external at surface (cement top at 5,000 ft, gas in annulus above) = 0 psi
P_net_burst at surface = 7,610 psi

Using 9-5/8" P-110 53.5 ppf (burst = 10,780 psi):
SF_burst = 10,780 / 7,610 = 1.42 → acceptable

Critical load case 2 - Burst at shoe during kick (governing for intermediate casing):
Kick pressure at shoe = P_reservoir + fluid column weight above
External at shoe = formation pressure (cement + formation)
Net burst at shoe = P_internal_shoe - P_external_shoe

This calculation often governs the intermediate casing grade and must be performed for each depth in the open hole section.

2.2 Burst Load Cases by Operation Phase

Load Case	Internal Pressure	External Pressure	Critical Depth
Drilling - kick from below shoe	Gas/fluid influx pressure at shoe	Formation pressure above shoe	Casing shoe (max net burst)
Cementing - plug bump	Pump pressure + cement column	Formation + mud column	Surface (pump pressure spike)
Production - full gas shut-in	Reservoir P - gas gradient x TVD	Completion fluid or packer fluid	Surface (SIWHP)
Gas lift injection	Injection pressure at valve depth	Formation / tubing annulus	Injection valve depth
Well test / pressure test	Test pressure (typically 80% of rated burst)	Completion fluid column	Surface (test pressure)
EOR - injection well	Injection pressure at wellhead	Formation fracture gradient	Surface (injection WHP)

3. Burst Failure Mechanics - Elastic vs Plastic

3.1 Failure Mode Progression

Three-stage burst failure progression:

Stage 1 - Elastic deformation (P < 0.8 x P_b API):
Pipe wall deforms elastically; hoop stress below yield. Pipe returns to original shape when pressure is released. No permanent damage - this is the normal operating regime below design limits.

Stage 2 - Partial yielding (0.8 x P_b < P < P_b API):
Outer fibers of the pipe wall yield first (highest hoop stress). Inner fibers still elastic. At P = P_b API, the average stress across the wall = yield. Permanent deformation at the outer surface begins. This stage can pass temporarily during a well control event without catastrophic failure.

Stage 3 - Plastic collapse / rupture (P > P_b API):
Full wall yield through the wall thickness. Pipe expands radially and ruptures longitudinally (split), creating a pathway from inside the casing to the annulus. Irreversible - requires fishing or sidetrack to remediate.

Pressure at which full plastic failure occurs (Pb_plastic):
P_b_plastic = (2 x sigma_yield / sqrt(3)) x ln(OD / ID)
= (2/sqrt(3)) x 110,000 x ln(9.625/8.535)
= 1.1547 x 110,000 x ln(1.1277)
= 1.1547 x 110,000 x 0.1202
= 15,272 psi for 9-5/8" P-110 53.5 ppf

API Barlow rating: 10,780 psi
Plastic failure: 15,272 psi
The 0.875 API factor, plus the use of minimum yield rather than average yield, builds in a margin of ~41% between API rating and actual rupture. The safety factor specified in design (1.10-1.25) adds an additional layer on top of this inherent conservatism.

3.2 Biaxial Correction - Burst Rating Reduction Under Axial Tension

Biaxially corrected burst rating (API 5C3 Appendix):
P_b_biaxial = P_b_API x [sqrt(1 - 0.75 x (sigma_a/S)²) - 0.5 x (sigma_a/S)]

Where:
sigma_a = axial tensile stress (psi) = F_axial / A_steel
S = minimum yield strength (psi)
P_b_API = uniaxial burst rating (psi)

Worked example - same 9-5/8" P-110 53.5 ppf under tension:
Axial tensile load = 600,000 lbs
A_steel = pi/4 x (9.625² - 8.535²) = 15.55 in²
sigma_a = 600,000 / 15.55 = 38,585 psi
sigma_a/S = 38,585 / 110,000 = 0.351

P_b_biaxial = 10,780 x [sqrt(1 - 0.75 x 0.351²) - 0.5 x 0.351]
= 10,780 x [sqrt(1 - 0.0924) - 0.1755]
= 10,780 x [sqrt(0.9076) - 0.1755]
= 10,780 x [0.9527 - 0.1755]
= 10,780 x 0.7772
= 8,378 psi biaxially corrected burst rating

Reduction: 10,780 → 8,378 psi = 22.3% loss of burst capacity from axial tension alone

This is why an API burst check that shows SF = 1.42 can become SF = 1.10 when the biaxial correction is applied - still acceptable but with no remaining margin for operational uncertainty.

4. Complete Burst Design Example - Gas Producer

4.1 Full Design Calculation Sequence

Well parameters:
9-5/8" production casing, TVD = 14,000 ft, Reservoir P = 8,800 psi
Gas gradient = 0.085 psi/ft, completion fluid = 8.5 ppg brine
Cement top = 8,000 ft, 11.5 ppg cement slurry from 8,000 to 14,000 ft
Axial tension at surface = 550,000 lbs (buoyed weight of string)

Step 1 - Calculate SIWHP (max internal pressure at surface):
P_SIWHP = 8,800 - 0.085 x 14,000 = 8,800 - 1,190 = 7,610 psi

Step 2 - Calculate external pressure at surface (worst case: gas in annulus above cement top):
Cement top at 8,000 ft; above cement, annulus fluid = 8.5 ppg brine
P_external at surface = 0 psi (brine open to atmosphere at wellhead)
Net burst at surface = 7,610 - 0 = 7,610 psi

Step 3 - Calculate net burst at cement top (8,000 ft):
P_internal at 8,000 ft = 7,610 + 0.085 x 8,000 = 7,610 + 680 = 8,290 psi
P_external at 8,000 ft = 0.052 x 8.5 x 8,000 = 3,536 psi
Net burst at 8,000 ft = 8,290 - 3,536 = 4,754 psi

Governing burst load = 7,610 psi at surface

Step 4 - Biaxial correction at surface:
sigma_a/S = (550,000 / 15.55) / 110,000 = 35,370 / 110,000 = 0.321
P_b_biaxial = 10,780 x [sqrt(1 - 0.75 x 0.103) - 0.5 x 0.321]
= 10,780 x [0.9618 - 0.1605] = 10,780 x 0.8013 = 8,638 psi

Step 5 - Safety factor check:
SF_burst = 8,638 / 7,610 = 1.135 → acceptable (minimum 1.10), but tight

If reservoir pressure were 9,200 psi (400 psi higher than predicted):
SIWHP = 9,200 - 1,190 = 8,010 psi
SF_burst = 8,638 / 8,010 = 1.079 → BELOW MINIMUM → upgrade to Q-125

4.2 Grade Selection to Meet Burst Safety Factor

Scenario	Net Burst Load	Required API Rating (SF=1.10)	Minimum Grade (9-5/8" 53.5 ppf)
Moderate pressure gas well	5,500 psi	6,050 psi	N-80 (7,830 psi) ✓
High-pressure gas well (biaxial-corrected)	7,610 psi	8,371 psi	P-110 biaxial 8,638 psi ✓ (tight)
HPHT gas well (uncertainty margin)	8,010 psi	8,811 psi	P-110 fails → Q-125 (12,250 psi) ✓
Ultra-HPHT (>10,000 psi SIWHP)	10,200 psi	11,220 psi	Q-125 marginal → V-150 (14,700 psi) ✓

5. Burst Design Safeguards and Operational Considerations

5.1 API Burst Standard Limitations

1. Minimum yield assumption: API uses minimum specified yield (PSL-1). Actual pipe frequently has yield 10-15% above minimum, but design must use minimum for conservatism.
2. No biaxial correction in basic formula: API 5C3 Barlow is uniaxial. Biaxial correction must be applied manually per API 5C3 Appendix when axial stress exceeds 20% of yield.
3. No temperature derating: API ratings are at ambient temperature (~77°F). HPHT wells above 300°F require yield derating of 0.03-0.05% per °F above baseline.
4. No wear allowance: Running drill string inside casing during the next section wears the casing wall. A 20% wall wear (common in ERD wells) reduces burst rating by approximately 20%.

5.2 Operational Safeguards Against Burst

Safeguard	Mechanism	Burst Risk Reduction
Wellhead safety valve (SCSSV / DHSV)	Closes on loss of control line pressure; limits shut-in column below valve	Prevents full gas column from pressurizing wellhead
Packer fluid design	Weighted completion fluid in annulus increases external backup pressure	Reduces net burst load by 500-2,000 psi
Burst disc in wellhead	Ruptures at set pressure to vent to controlled relief	Last-resort pressure relief; prevents uncontrolled rupture
Real-time pressure monitoring	Permanent downhole gauges alert to pressure build-up before reaching design limit	Early warning allows controlled bleed-off before burst
Pressure test at installation	Confirms pipe and connections intact before production loading	Detects manufacturing defects before they become failures

Conclusion

The burst calculations in this article - API rating of 10,780 psi for 9-5/8" P-110 53.5 ppf, biaxially corrected to 8,638 psi at 550,000 lbs axial tension (22.3% reduction), and safety factor collapsing from 1.135 to 1.079 when reservoir pressure increases 400 psi beyond prediction - show exactly how the gap between an API table lookup and a complete burst design can represent the difference between a well that survives its full production life and one that fails during first shut-in. The plastic failure pressure of 15,272 psi versus the API Barlow rating of 10,780 psi confirms that the Barlow formula carries substantial inherent conservatism - but the biaxial correction can consume most of that margin in wells with high axial tension, and the remaining safety factor exists only if the reservoir pressure prediction is accurate to within ±5%.

Burst design is a forward-looking engineering activity. The maximum internal pressure a casing string will ever see may not occur during drilling or completion - it may occur 15 years later during an EOR water injection program that exceeds the original reservoir pressure, or during a workover squeeze cement job that pumps above fracture pressure, or during an annular pressure test prior to a tubing string replacement. The burst safety factor designed for the initial production phase must accommodate all future well interventions within the planned operational envelope. The cost of upgrading a 9-5/8" production string from P-110 to Q-125 is $80,000-150,000 in additional tubular material. The cost of a burst failure at 8,500 ft discovered during production is $3M-15M in well kill, fishing, sidetrack or abandonment, and lost production revenue during the remediation period.

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