Casing Burst & Collapse Formula

Casing design requires evaluating burst (internal pressure exceeding external) and collapse (external pressure exceeding internal) loads throughout the well. Burst resistance prevents casing rupture during kick situations, pressure testing, or stimulation. Collapse resistance prevents casing deforma...

Overview

Theory

Casing is rated for three primary loads:

Burst: Internal pressure > external pressure (e.g., during a kick)
Collapse: External pressure > internal pressure (e.g., during cementing or lost circulation)
Tension: Axial load from casing weight and operational loads

The API ratings for burst and collapse are published for standard casing sizes, weights, and grades.

Formulas

Burst Pressure (Barlow's Formula)

P_burst = 0.875 * 2 * σy * t / OD

where σy = minimum yield strength (psi), t = wall thickness (in), OD = outer diameter (in), 0.875 = 87.5% wall thickness factor (API manufacturing tolerance).

Collapse Pressure (API Bulletin 5C3)

API defines four collapse regimes based on D/t ratio:

Yield Strength Collapse (low D/t):

Pc = 2 * σy * ((D/t - 1) / (D/t)^2)

Plastic Collapse:

Pc = σy * (A / (D/t) - B) - C

Transition Collapse:

Pc = σy * (F / (D/t) - G)

Elastic Collapse (high D/t):

Pc = 46.95e6 / ((D/t) * ((D/t) - 1)^2)

where A, B, C, F, G are functions of yield strength (tabulated in API 5C3).

Design Factors

Burst Design Factor = P_burst_rating / P_burst_load ≥ 1.1 (typical)
Collapse Design Factor = P_collapse_rating / P_collapse_load ≥ 1.0 to 1.125
Tension Design Factor = σy * A_pipe / F_tension ≥ 1.6 to 1.8

Burst Load (Kick Scenario)

P_burst_load = P_formation - P_mud_outside + P_kick

At surface (worst case):

P_surface = SICP (shut-in casing pressure during kick)

Collapse Load

P_collapse_load = P_mud_outside - P_inside

Worst case: full mud column outside, empty inside (lost circulation or evacuation).

Worked Example

Given: 9-5/8" 47 lb/ft N-80 casing. OD = 9.625", ID = 8.681", t = 0.472".

Burst (Barlow):

P_burst = 0.875 * 2 * 80,000 * 0.472 / 9.625
        = 0.875 * 75,520 / 9.625
        = 6,866 psi

(API rated: 6,870 psi — matches)

Collapse check (D/t = 9.625/0.472 = 20.39):

For N-80, D/t = 20.39 falls in plastic collapse regime:

A = 3.071, B = 0.0667, C = 1955
Pc = 80,000 * (3.071/20.39 - 0.0667) - 1955
   = 80,000 * (0.1506 - 0.0667) - 1955
   = 80,000 * 0.0839 - 1955
   = 6,712 - 1955
   = 4,757 psi

(API rated: 4,750 psi — matches)

Design check at 10,000 ft, 12.0 ppg mud outside, empty inside:

Collapse load = 0.052 * 12.0 * 10,000 = 6,240 psi
DF_collapse = 4,757 / 6,240 = 0.76 → FAILS (need heavier wall or higher grade)

Valid Ranges

Parameter	Common Values
Casing grades	H-40, J-55, K-55, N-80, L-80, C-95, P-110, Q-125
OD (surface)	13-3/8", 16", 20"
OD (intermediate)	9-5/8", 10-3/4", 11-3/4"
OD (production)	5-1/2", 7", 7-5/8"
Burst DF	1.1 – 1.25
Collapse DF	1.0 – 1.125
Tension DF	1.6 – 2.0

References

API TR 5C3 — Technical Report on Equations and Calculations for Casing, Tubing, and Line Pipe.
API 5CT — Specification for Casing and Tubing.
Rabia, H. (2002). Well Engineering & Construction. Entrac Consulting.
PetroWiki — Casing design: https://petrowiki.spe.org/Casing_design

Casing Burst & Collapse