When pipe is subjected to increasing compressive loads, it will undergo several stages or changes in configuration. The first stage is referred to as sinusoidal buckling. In this stage the pipe assumes a 2dimensional waveform shape resembling a sine wave, winding back and forth along the bottom of the wellbore.
When the compressive forces are increased further, the second stage (helical buckling) occurs. This causes the pipe to ride up the sides of the wellbore in the shape of a helix (coil). The increase in the wall contact area increases drag thereby requiring more axial load to maintain the same bit weight. The additional axial load causes higher well contact force, which further increases drag. Therefore, helical buckling should be avoided.
When the compressive forces are increased further, the increased wall contact force will eventually generate so much drag that no amount of slacking off will move the pipe. In the sliding mode, this third and final stage is commonly referred to as lockup. At this point, a change is required for drilling to continue, and the configuration of the drill string is usually altered.
When the drill string is rotated, most of the axial drag present while sliding is converted to rotational drag. This increases torque and decreases axial drag. The decrease in drag allows the pipe to move down the wellbore more freely. Therefore, rotary drilling is usually possible beyond the point where a BHA would lockup in the sliding mode. The critical force required to helically buckle the pipe remains unchanged, but a greater bit weight is necessary in the rotary mode to reach this critical force.
The main difference between rotating and sliding from a buckling standpoint is that substantial fatigue damage occurs when the string is rotated while buckled. This greatly increases the risk of fatigue failure. In the sliding mode, the pipe will experience very little or no damage, even if buckling occurs, as long as the pipe is not rotated. Therefore, from an operational perspective, it is important to always pick up off bottom before starting to rotate if the drill string is buckled.
Sinusoidal buckling (2D). This is the first phase in which the drill string is deflected (buckles) in the form of a two dimensional sine wave. The theoretical compression at which sinusoidal buckling will start to occur is calculated with the DawsonPaslay equation:


Sinusoidal buckling 
DawsonPaslay 

Helical buckling (3D). As compressional forces increase, the drill string will be deflected in a three dimensional helical shape (coil). Helical buckling will lead to additional normal force (contact force) which is taken into account in the Torque & Drag calculation model (postbuckling analysis). For the calculation of the helical buckling force, two equations are available: Chen & Cheatham and Wu & JuvkamWold. The equation may be selected in Settings & Parameters.
Helical buckling 
Chen & Cheatham 
Wu & JuvkamWold 
Lockup. If helical buckling is occurring and compressional forces increase even further, the additional normal forces may become so high that it is no longer possible to lower the string. The resulting drag forces have become higher that the the weight (axial force) of the string below. In some cases these forces may actually go towards infinity (mathematically). If this happens, the program will display an error message and the calculation will be aborted.
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