Drill String Buckling Calculator: Sinusoidal and Helical Critical Loads

Drilling Engineering
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Sinusoidal onset (kip)
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Helical onset (kip)
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Moment of inertia (in4)
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Buoyed weight (lb/ft)

Drill String Buckling Result

Generated by calculatgeek.com Drill String Buckling Calculator

Three drill pipe states inside a wellbore showing straight pipe below critical load, sinusoidal snaking buckling, and helical corkscrew buckling with the Dawson-Paslay critical load formula
Compress a drill string past its critical load and it snakes sinusoidally against the borehole wall; push about 40 percent harder and it corkscrews helically, where drag climbs toward lockup.

Every foot of weight on bit has to travel down the drill string as compression, and slender steel tubes have opinions about being compressed. Below a critical load the pipe stays straight and delivers weight cleanly. Cross that load and it buckles into a sinusoidal snake lying against the low side of the hole; drag rises, but drilling continues. Push roughly 40 percent further and the string flips into a helix that presses against the borehole wall all the way around, and now the friction from those contact forces can grow faster than the axial load you add, the condition drillers call lockup: pushing harder at surface delivers nothing at the bit.

The equations behind the calculator

For inclined hole, the Dawson and Paslay result recognizes that gravity holds the pipe against the low side, and lifting it into a buckle costs energy. The sinusoidal critical load is:

Fsin = 2 x sqrt(E x I x w x sin(inclination) / r)

with E the steel modulus, I the pipe moment of inertia, w the buoyed weight per unit length, and r the radial clearance between pipe and hole. Helical onset follows at about 1.41 times that. In near-vertical hole the sine term vanishes and the calculator switches to the Lubinski form, which produces the famously tiny critical loads that explain why vertical wells put their weight on bit through stiff drill collars instead of compressed drill pipe.

Worked example

  • 5 in, 19.5 lb/ft drill pipe (ID 4.276 in) in 8.5 in hole, 10 ppg mud, 30 degree inclination
  • I = 14.3 in4, buoyed weight 16.5 lb/ft, radial clearance 1.75 in
  • Sinusoidal onset: about 26 kip of compression; helical onset: about 37 kip
  • The same pipe in vertical hole buckles at under 2 kip, a factor of thirteen difference

Reading the physics like a directional driller

The counterintuitive gift of the sine term is that high-angle hole is the easiest place to run pipe in compression: the wall does most of the supporting. That is the quiet enabler of horizontal drilling, where sliding intervals routinely put drill pipe in compression that would be unthinkable in vertical hole. The clearance term cuts the other way: buckling resistance improves in snug hole, which is why heavyweight pipe inside casing behaves so much better than the same pipe in an enlarged washout. When the numbers say you are flirting with helical onset while sliding, the standard menu applies: add heavyweight or collars above the motor to shift compression into stiffer pipe, rotate instead of slide where the well plan allows (rotation dramatically relieves the drag part of the problem even though the buckle geometry remains), or accept less weight on bit. And treat these onset loads as onset, not failure: sinusoidal buckling is a working condition with a drag penalty, while sustained helical buckling with rotation adds fatigue on top of drag, which is the combination that shears pins and washes out connections.

Related Calculators and Reference

The buoyancy factor in this calculation comes from the buoyancy factor calculator, the drag that buckling amplifies is modeled in the torque and drag calculator, and the weight on bit this limits feeds the MSE optimization calculator. The PetroWiki page on tubular buckling covers the Dawson-Paslay and Lubinski derivations.