## Resistance to buckling

The buckling theory showed that for buckling to occur, the reduced axial force, Fa*, must be negative. However, it is not necessarily the case that buckling will occur if the reduced axial force is less than zero.

The capacity of the pipe to resist buckling will depend upon its dimensions, material properties, the well profile and the supports. Below the different sections of the well trajectory and their influence on the buckling capacity are addressed.

## Vertical wellbore sections

A distinction is made between the conductor casing buckling capacity and the other casing strings buckling capacity, because of the relatively short unsupported length and larger cross-sectional area of the conductor casing.

A conductor casing may fail in an elastic or plasting buckling mode when subjected to compressional loads. The applicable failure mode is determined by the geometry of the free standing portion of the conductor casing. This geometry is expressed in the slenderness ratio.

## Inclined straight wellbore sections

In an inclined wellbore, where the casing lies against the low side of the borehole, a restraint is effectively provided against lateral displacement. As a result, the capacity of the casing to resist buckling is higher than that given by the Euler buckling force.

It is assumed that the unsupported, i.e. uncemented sections of conductor casing are always near vertical, and therefore are not included in this paragraph.

## Curved wellbore sections

The topic of casing buckling in curved well bore sections is complex and subject of recent studies. The analysis requires computerised solution techniques and specialist knowledge.

## Use of top cement to prevent buckling

The required top of cement, Zc, to prevent buckling can be obtained by setting z = Zc in the general reduced axial force equation. The condition that the reduced axial force must be greater than or equal to the critical reduced buckling force at that depth must then be fulfilled. Since the top of cement is not known, the loads which are a function of Zc, i.e. buoyancy and temperature loads, must be written in full. Solving this equation will lead to the required top of cement.

## Use of centraliser spacing to prevent buckling

The positioning of centralisers in the casing annuli will prevent the helix, which would occur without centralisers, from establishing. Obviously, onset of buckling must have occurred as discussed in the previous paragraphs. The positioning of centralisers to suppress (Euler) buckling of the conductor casing and the other casing strings can be addressed.

### Centraliser spacing for conductor casing

The compressive load on conductor casing can be very large due to the suspended weight of the subsequent strings. Especially in offshore platform developments placement of centralisers is therefore required to prevent buckling of this string. Since in general the acting compressive stresses are larger than half the yield strength the spacing of the centralisers is based on the theories for plastic buckling mode. These advanced theories are rather complex and expert advice should be sought from a Structural Engineering company to establish a centraliser spacing.

### Centraliser spacing for Surface, intermediate, production casing

For these slender strings mostly the elastic buckling mode (Euler mode) does apply since the acting compressive stresses are smaller than half the yield strength. The spacing of the downhole centralisers to prevent buckling is therefore based on the elastic buckling theory and is applied below.

## Use of surface force to prevent buckling

From the expression for reduced axial force Fa*, it can be seen that this force is directly influenced by DFs, the change in surface force. By determining the critical reduced buckling force Fc* for the casing in question, the casing hanger can be landed (after the cement has set) with an additional surface force such that the reduced axial force is greater than the critical reduced buckling force at all points in the uncemented portion of the string.

### Example:

If the reduced axial force in a string at the top of cement is -100,000 lb and the critical reduced buckling force at that point is -50,000 lb, then the buckling potential can be eliminated by introducing at least 50,000 lb of tension into the string at surface. Note that the effects of drag should be taken into account to ensure that sufficient additional axial force is transmitted to the casing at the top of cement.

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