Axial Buckling Stability Of Cemented Pipe
Authors: Wilson William N. , Perkins Thomas K. , Striegler John H. 
Published: December 2007

Abstract
This paper reviews criteria for axial buckling stability of laterally supported pipes. If lateral support is obtained with a surrounding elastic medium, the axial buckling force will approach an asymptotic limit as the length of pipe approaches an infinite length. The minimum buckling force for a very long pipe is a function of pipe properties and the elastic modulus of the surrounding medium. For field conditions, the modulus of surrounding cement or soil needed to avoid buckling is generally small.
In addition to mathematical analysis, this study has included the development of experimental equipment and techniques to measure the elastic modulus and failure criteria of cement samples when cylindrical pipes are forced laterally into the cement under pipes are forced laterally into the cement under triaodal stress conditions.
As an example of the application of this technology, new cement blends have been formulated for cementing of casing through permafrost wells. Studies have indicated that surface casing cemented through permafrost might be stressed beyond the yield point permafrost might be stressed beyond the yield point by permafrost thawing and compaction. A laboratory experiment was devised and used to evaluate the effect of various supporting cements outside a thin-walled tube. The tube was subjected to compressive casing strains well beyond its elastic limit while appropriate stress conditions were maintained inside the tube and in the cement and sail around it. Through the elastic loading region and into the plastic region (maximum axial pipe strain of 0.7%), plastic region (maximum axial pipe strain of 0.7%), the pipe did not buckle when supported by the cement even though irreversible shortening was experienced.

Introduction
A recent study has shown that in 1977, cement and cementing services to the U.S. oil industry cost about $370 million. The annual cost increase for these services from the year 1977 to 1978 was estimated to be 11.2%. Assuming a similar cost increase from 1978 to 1979, the 1979 cost of these services is expected to approach one-half billion dollars. In addition to these direct costs, an appreciable amount of rig time is expended when circulating before cementing, waiting on cement, and drilling cement. These direct and indirect costs become of increasing concern as drilling operations are carried out in very remote locations where rig costs are exceptionally high. Also, the transportation cost of cementing materials can become a substantial part of the overall cementing cost. A continued part of the overall cementing cost. A continued improvement in the understanding of cementing mechanics, formulations, and processes will help to minimize the cost of this vital part of well completions.
Cement generally is used to anchor or stabilize pipe, or to serve as a seal or barrier to fluid pipe, or to serve as a seal or barrier to fluid flow. This paper considers in some detail only one of those functions: to stabilize the pipe in order to avoid axial buckling. Such problems are of particular interest when large axial stresses can particular interest when large axial stresses can be induced in the cemented pipe by compaction and subsidence resulting from fluid withdrawal or permafrost thaw, or by large changes in pipe permafrost thaw, or by large changes in pipe temperature such as in geothermal or steamflood wells.

BUCKLING MECHANICS
Although buckling criteria are known 2 for a number of pipe loading configurations, the two cases shown on Fig. 1 illustrate the most important concepts from the point of view of axial buckling of laterally unsupported pipe. If pipe ends are hinged (i.e., free to rotate, but not move laterally), then the critical load, F., which will cause the pipe to buckle, is given by Eq. 1. pipe to buckle, is given by Eq. 1.
(1)
When the ends are fixed (not free to rotate or move laterally), then the critical load for a laterally unsupported pipe will be increased, as is shown by Eq. 2.