drilling · torque drag
Sinusoidal & Helical Buckling Onset (Dual Mode)
Fcr = C·√(E·I·w·sinα / r) — C=2 sinusoidal onset (Dawson-Paslay) | C=2√2 helical onset (Chen-Lin-Cheatham)
click formula to derive ↑
Inputs
GPa
in
in
lb/ft
°
in
Description
Computes two sequential buckling thresholds for a pipe in an inclined wellbore: the onset of sinusoidal buckling (Dawson-Paslay, 1984) and the onset of the more severe helical mode that follows it at higher axial load (Chen-Lin-Cheatham, 1990). These are two different physical states of the same pipe, not two competing estimates of the same threshold. Sinusoidal onset is the universally agreed criterion in the literature; the helical-onset constant itself is genuinely unsettled, with published values ranging roughly 2.83-5.65 depending on assumed boundary conditions — Chen-Lin-Cheatham's energy-method result (2√2 ≈ 2.83) is one specific, commonly cited estimate, not the definitive value.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Fcr_DP | lbf | Sinusoidal Onset Load (Dawson-Paslay) |
| Fcr_CLC | lbf | Helical Onset Load (Chen-Lin-Cheatham) |
| E | GPa | Elastic modulus of the pipe steel. 200 GPa is standard for API steel grades. |
| D | in | Specified outside diameter of the pipe (114.3 mm = 4-1/2 in). |
| t | in | Nominal wall thickness, used with D to compute the section's moment of inertia. |
| w | lb/ft | Buoyed weight per unit length — see casing_buoyed_weight to compute this from air weight and mud weight. |
| α | ° | Inclination from vertical in the tangent section being evaluated. 0° (vertical) gives zero lateral load and no sinusoidal buckling by this model. |
| r | in | Radial gap between pipe OD and hole/casing ID. Use the tightest clearance along the section (e.g. at tool joints) for a conservative result. |
Assumptions
- Pipe behaves as a linear-elastic beam (no plastic deformation)
- Evaluated in a single tangent section of constant inclination — not valid through a curved/dogleg interval (curvature introduces an additional contact-force term neither model includes)
- Radial clearance r is constant along the buckling wavelength
- No torque or internal/external pressure ballooning effects included
Limitations
- The helical-onset value (Fcr_CLC) is one of several non-equivalent helical buckling constants published in the literature (≈2.83-5.65) — unlike sinusoidal onset, there is no industry consensus on the correct helical constant; treat it as indicative, not definitive
- Does not include torque-buckling interaction — applied torque reduces the critical buckling load (see Mitchell 1986/2002 for combined loading)
- Does not account for tool joints or connections that locally reduce annular clearance below the nominal value used here
- Fcr_DP and Fcr_CLC describe two different buckling modes, not competing answers to the same question — there is nothing to "choose" between for design purposes; both onset loads are physically meaningful checkpoints as axial compression increases
Use Cases
- → Slimhole/liner buckling risk screening: Screen liners or slimhole completions in deviated wells for sinusoidal buckling risk before running, and check how much additional compression margin exists before the more severe helical mode would set in.
- → Coiled tubing / workstring buckling assessment: Check whether a coiled tubing or workstring will buckle while running in hole under its own buoyed weight in a high-angle well.
- → Sinusoidal-to-helical margin assessment: Use the gap between Fcr_DP and Fcr_CLC to gauge how much load above the sinusoidal onset a string can tolerate before reaching the (less certain, but clearly higher) helical-onset region.
Related Calculations
Region Notes
Permian Basin
High-angle laterals (85-91° inclination) in the Wolfcamp/Bone Spring put long workstring sections near horizontal, where sinα approaches 1 and buckling risk is maximized for a given weight and clearance.
North Sea
Extended-reach and horizontal North Sea wells were a primary proving ground for both the Dawson-Paslay sinusoidal criterion and Chen-Lin-Cheatham's helical-mode work during the 1980s-90s ERD boom; which helical constant to design against remains an actively discussed question in ERD design literature for this region.
Global
Mitchell & Miska (2011) recommend checking both the sinusoidal and helical onset loads in practice; absent project-specific guidance, the sinusoidal onset (Dawson-Paslay) is the appropriate conservative design limit since it is reached first.
References
Primary source
Primary source
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