Casing Design - Tension, Collapse, and Burst Criteria with Safety Factor Calculations

Casing design is a triaxial stress problem. The casing must simultaneously resist three independent load cases: burst (internal pressure exceeding external), collapse (external pressure exceeding internal), and tension (axial tensile force from casing weight and operational loads). A casing string that passes the burst check but fails the collapse check is not a valid design. A string that passes both pressure checks but has insufficient tensile capacity at the top joint is not a valid design either. Each load case requires its own calculation, its own safety factor, and its own verification against the selected grade and weight. The engineer who designs casing by checking only the most obvious load case and accepting a grade that "seems strong enough" is working without the calculations that would reveal which load case actually governs the design.

1. The Tri-Axial Design Framework

1.1 The Three Load Cases and Their Governing Scenarios

Load Case Definition Governing Scenario Minimum Safety Factor
Burst Internal pressure exceeds external pressure - net outward force on pipe wall Shut-in on a full gas kick (maximum surface pressure). Lost returns scenario (mud evacuated from annulus). Production casing with full reservoir pressure against empty annulus. SF ≥ 1.10 (API), 1.25 (operator typical)
Collapse External pressure exceeds internal pressure - net inward force on pipe wall Lost circulation during cementing (casing partially empty). Production casing with depleted internal pressure after production. Subsalt casing under high external stress. SF ≥ 1.00 (API), 1.10 (operator typical)
Tension Axial tensile force - pulling the casing string apart along its length Maximum hook load during running (casing string hanging in air before landing). Overpull during stuck pipe. Thermal contraction in cold deepwater. SF ≥ 1.60 (API), 1.80 (operator typical)

2. Burst Design - Maximum Internal Pressure Calculation

2.1 The Worst-Case Burst Scenario - Full Gas to Surface

Maximum surface casing pressure (full gas kick, no mud in annulus):
P_burst_surface = P_formation - rho_gas x 0.052 x TVD

Where rho_gas = gas gradient (typically 0.1 ppg effective for natural gas)

Example: Production casing, TVD = 12,000 ft, Formation pressure gradient = 14.2 ppg:
P_formation = 14.2 x 0.052 x 12,000 = 8,861 psi
rho_gas contribution = 0.1 x 0.052 x 12,000 = 62 psi
P_burst_surface = 8,861 - 62 = 8,799 psi surface burst pressure

Burst pressure at any depth D (psi):
P_burst_D = P_burst_surface + rho_gas x 0.052 x D - rho_external x 0.052 x D

External fluid assumed: mud weight 14.0 ppg on outside of casing (cement displaced with mud during lost circulation)
At depth 6,000 ft:
P_burst_6000 = 8,799 + (0.1 x 0.052 x 6,000) - (14.0 x 0.052 x 6,000)
= 8,799 + 31 - 4,368 = 4,462 psi burst at 6,000 ft depth

Maximum burst is at surface (8,799 psi) for full gas column. Check API burst rating of selected casing must exceed this value by the required safety factor.

2.2 API Minimum Internal Yield Pressure (Burst Rating)

API Barlow equation for minimum burst pressure (psi):
P_burst = 0.875 x (2 x Yp x t) / OD

Where:
0.875 = API manufacturing tolerance factor (87.5% of nominal wall thickness guaranteed)
Yp = minimum yield strength (psi) - from grade designation
t = nominal wall thickness (inches)
OD = outside diameter (inches)

Common grade yield strengths:
J-55: 55,000 psi | N-80: 80,000 psi | L-80: 80,000 psi | P-110: 110,000 psi | Q-125: 125,000 psi

Example: 9-5/8" P-110 casing, 47 lbs/ft (wall thickness t = 0.545"), OD = 9.625":
P_burst = 0.875 x (2 x 110,000 x 0.545) / 9.625
= 0.875 x 119,900 / 9.625 = 0.875 x 12,457 = 10,900 psi burst rating

Safety factor check: SF = 10,900 / 8,799 = 1.24 → Meets 1.10 minimum, borderline on 1.25 target
Consider upgrading to Q-125 or checking the operator's specific requirement.

3. Collapse Design - External Pressure Dominance

3.1 The Worst-Case Collapse Scenario

Worst-case collapse: Empty casing (gas kick evacuated all mud from inside), full mud column outside

P_collapse_D = rho_external x 0.052 x D - P_internal

For empty casing (P_internal = 0 gauge):
P_collapse_D = rho_external x 0.052 x D

Maximum collapse load is at the shoe (maximum depth):
P_collapse_shoe = 14.0 x 0.052 x 12,000 = 8,736 psi collapse pressure at shoe

API collapse pressure rating (empirical, depends on D/t ratio):
For 9-5/8" 47 lb/ft P-110 (D/t = 9.625/0.545 = 17.66):

D/t = 17.66 falls in the elastic-plastic transition range.
From API tables: Collapse resistance = approximately 8,530 psi for this combination

SF = 8,530 / 8,736 = 0.98 → FAILS minimum SF of 1.00

This casing is inadequate for collapse at the shoe depth with this loading scenario.
Options: (1) Upgrade to 53.5 lb/ft (t=0.625", D/t=15.4 → higher collapse rating ~10,780 psi, SF=1.23), or (2) Accept reduced collapse scenario (partial fluid inside casing), or (3) Use biaxial correction to account for tension reducing effective collapse resistance.

3.2 The Biaxial Effect - How Tension Reduces Collapse Resistance

When a casing string is simultaneously under axial tension and external collapse pressure, the combined stress state reduces the effective collapse resistance below the uniaxial API value. This is the biaxial correction that is essential for correctly sizing casing in deep wells where high axial tension coexists with high collapse pressure:

Ellipse of biaxial yield (API Bulletin 5C3):
Ypa = Yp x [sqrt(1 - 0.75 x (Sa/Yp)^2) - 0.5 x (Sa/Yp)]

Where:
Ypa = apparent yield strength under combined loading (psi)
Yp = minimum yield strength (psi)
Sa = axial stress = Axial_force / As (psi) - positive for tension

Example: 9-5/8" 47 lb/ft P-110, axial tension = 500,000 lbs at the shoe:
As = pi/4 x (9.625^2 - 8.535^2) = pi/4 x (92.64 - 72.85) = pi/4 x 19.79 = 15.54 in2
Sa = 500,000 / 15.54 = 32,174 psi tension
Sa/Yp = 32,174 / 110,000 = 0.2925
Ypa = 110,000 x [sqrt(1 - 0.75 x 0.2925^2) - 0.5 x 0.2925]
= 110,000 x [sqrt(1 - 0.0642) - 0.1463]
= 110,000 x [sqrt(0.9358) - 0.1463]
= 110,000 x [0.9674 - 0.1463]
= 110,000 x 0.8211 = 90,321 psi apparent yield (vs 110,000 psi uniaxial)

The collapse resistance at this point must be recalculated using Ypa = 90,321 psi instead of 110,000 psi.
This typically reduces collapse resistance by 15-25% in the upper section of deep casing strings where tension is highest.

4. Tension Design - The Complete Axial Load Calculation

4.1 Axial Load Profile Through the Casing String

The axial load at any depth in the casing string is the sum of all loads acting on the string above that depth, minus the buoyancy effect of the mud:

Axial tension at depth D from surface (lbs):
F_tension_D = Sum of buoyed weights above D + Overpull load + Bending load at doglegs

Buoyed weight of vertical casing from surface to depth D (lbs):
W_buoyed = w_air (lbs/ft) x D x (1 - rho_mud/65.5)

Bending load at dogleg (lbs):
F_bending = 63 x w_air x OD x DLS

Where w_air in lbs/ft, OD in inches, DLS in °/100 ft

Example: 9-5/8" 47 lb/ft casing, total depth 12,000 ft, 14 ppg mud, maximum DLS = 3°/100 ft at 4,500 ft:

Buoyed weight (entire string): W = 47 x 12,000 x (1 - 14/65.5) = 47 x 12,000 x 0.786 = 443,016 lbs

Bending load at 3°/100 ft dogleg: F_bend = 63 x 47 x 9.625 x 3.0 = 63 x 47 x 28.875 = 85,507 lbs

Overpull for stuck pipe design: typically 100,000 lbs standard

Maximum tensile load (at surface, with overpull + bending):
F_max = 443,016 + 85,507 + 100,000 = 628,523 lbs maximum tensile design load

4.2 Casing Body and Connection Tensile Ratings

Casing body tensile strength (lbs):
F_yield = Yp x As

Example: 9-5/8" 47 lb/ft P-110 (As = 15.54 in2, Yp = 110,000 psi):
F_yield = 110,000 x 15.54 = 1,709,400 lbs pipe body yield strength

Body safety factor: SF_body = 1,709,400 / 628,523 = 2.72 → Excellent margin on pipe body

However, connection tensile strength is typically lower than pipe body:
API LTC (Long Thread Coupling) connection efficiency ≈ 60-75% of pipe body
API BTC (Buttress Thread) connection efficiency ≈ 85-95% of pipe body
Premium connections (VAM, TenarisHydril) ≈ 95-100% of pipe body

For API BTC on 9-5/8" P-110 47 lb/ft:
Connection tensile strength = 0.90 x 1,709,400 = 1,538,460 lbs
Connection SF = 1,538,460 / 628,523 = 2.45 → Acceptable

Critical check: Connection rating must be verified separately from pipe body.
Many casing failures occur at connections, not in the pipe body, because connection efficiency is assumed rather than verified.

4.3 ERD-Specific Tension Considerations

In extended-reach drilling, the horizontal section adds drag force to the tensile load that must be overcome during casing running. Unlike a vertical well where the casing weight acts purely in tension, in a horizontal section the casing weight acts as a normal force against the wellbore wall, creating friction drag that must be added to the tensile load at the bend:

Well Section Tensile Load Contribution Calculation
Vertical section Full buoyed weight in tension w_buoyed x TVD_vertical
Build section Component of buoyed weight along wellbore + friction from contact force w_buoyed x L_build x sin(avg inclination) + mu x w_buoyed x L_build x cos(avg inclination)
Horizontal section Zero weight in tension direction + full weight as normal force generating friction drag F_drag = mu x w_buoyed x L_horizontal (pure friction, zero gravity component in tension direction)
Total running load at surface (ERD) Sum of all three sections + overpull + bending loads at DLS concentrations

5. The Combined Design Check - Worked Summary

Casing selection verification for 9-5/8" production casing, 12,000 ft TVD, 14 ppg mud:

Load Case Design Load P-110 47 lb/ft Rating Safety Factor Result
Burst (at surface, full gas kick) 8,799 psi 10,900 psi 1.24 PASS (min 1.10)
Collapse (at shoe, empty casing) 8,736 psi 8,530 psi 0.98 FAIL (min 1.00)
Tension (at surface, with overpull + bending) 628,523 lbs 1,538,460 lbs (connection) 2.45 PASS (min 1.60)

Conclusion from combined check: The P-110 47 lb/ft casing fails the collapse check at the shoe by a small margin (SF = 0.98 vs 1.00 minimum). The burst and tension checks pass comfortably. The correct response is to upgrade to the 53.5 lb/ft version of the same grade - the tension and burst ratings improve, and the collapse rating increases significantly due to the thicker wall. Running the 47 lb/ft because it passes burst and tension while ignoring the collapse failure would leave the well with a casing shoe that is rated below the maximum external pressure it will experience during the empty-casing scenario.

Conclusion

The combined design check table at the end of this article demonstrates why casing design must evaluate all three load cases simultaneously. The P-110 47 lb/ft casing that comfortably passes burst (SF 1.24) and tension (SF 2.45) fails collapse at the shoe by 2%. The engineer who designs for burst and tension alone selects this casing with confidence. The engineer who completes all three checks selects the 53.5 lb/ft version. Both engineers are working from the same grade and the same OD - the difference is one additional calculation that takes 10 minutes and prevents a casing collapse failure at 12,000 ft that would require a complete remediation workover.

The biaxial correction shows that the upper section of a deep casing string, where axial tension is highest, simultaneously has its collapse resistance reduced by 18% from the API uniaxial value. This combination - highest collapse load at the shoe, highest tension at the top, and biaxial interaction reducing collapse resistance throughout - is why deep production casing design requires a depth-by-depth load analysis rather than a check at a single critical point.

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