Burst Resistance of Pipe Cemented Into the Earth
Authors: Zinkham R.E. , Goodwin R.J. 
Published: December 2007

Abstract
A mathematical study has been made of the amount of support a cement sheath could provide to casing cemented into the earth. Several assumptions were required to make the analysis, but only two of them are limiting:the pipe must be completely surrounded with cement, andany mud filter cake between the cement and formation has the same physical properties as either the cement or formation.
The calculations showed that little support would be provided to the pipe before an unsupported cement sheath failed in tension; however, when the cement is confined between the pipe and wellbore and is loaded in compression, the pipe could receive a considerable amount of support. In fact, the theoretical results indicate the lower grades and larger sizes of pipe could have their working pressures doubled when reasonable compressive loads were applied to a surrounding cement sheath. These data are shown in six charts. Other down-hole conditions such as setting the cement under pressure, increased temperature and cement confinement all tend to increase the potential usefulness of the sheath. Because of size limitations, a laboratory program to verify the most important results of this mathematical study would be very difficult. However, small-scale field tests would be practicable. This paper shows that, if a solid cement sheath can be obtained in the field by either primary cementing or by repair after detection of flaws by surveys such as the new cement-bond logs, the use of this approach to reducing pipe costs merits further consideration.

Introduction
A modification in casing design practices is proposed which may either reduce the amount and grade of steel required to contain a specified internal pressure or permit the working pressure to be increased for a specified weight and grade of pipe. One of the more important considerations in casing design is its resistance to collapse; however, Bowers' and, more recently, O'Brien and Goins have shown many casing programs are unnecessarily conservative in this respect, and they have indicated how savings can be made by designing for more realistic down-hole conditions. Earlier, Saye and Richardson showed that pipe costs could be reduced by considering the cement sheath as a part of the casing string when collapse resistance was being calculated. More recently, Rogers has raised the question as to whether a cement sheath might be considered in the design for burst resistance of the cemented casing. Calculations have been made for the increased burst resistance a cement sheath would provide for casing in a wellbore, and the results show that a sizable amount of support could be obtained in some instances. These data are presented in addition to a discussion of several other factors that are considered to affect the burst strength of pipe supported by cement. Two types of support are treated: Case I for tensile loading of the unconfined cement sheath, and Case II for compressive loading of the confined cement sheath.

ANALYTICAL TREATMENT AND RESULTS

CASE I-TENSILE STRESSES IN AN UNCONFINED CEMENT SHEATH
Conditions like this would most likely occur in a greatly enlarged portion of the hole where the cement was not in immediate contact with either the formation or a thin and hard mud cake. The mathematical analysis for this condition, as shown in the Appendix, rests on the following concepts. Pressure inside a unit length of pipe causes:a tensile or tangential stress to be exerted over the longitudinal cross-sectional areas of the pipe and cement; andan equal amount of strain in both the pipe and cement that is uniformly distributed over the wall thickness of each.
This analysis was then used to make several calculations for a cement sheath around 5 1/2-in. OD pipe. The results are illustrated in Fig. 1, which shows that a tensile stress of 500 psi is imposed on a 5-in. thick sheath when the casing contains a pressure of only 1,450 psi. It also shows that a 10-in. thick sheath would be stressed to 500 psi in tension when the pipe contained a pressure of only 2,350 psi. Alternatively, if the stress analysis is made by means of the Lame thick-wall cylinder theory, the inner fibers of the 10-in. thick sheath will be stressed to 500 psi in tension when the pressure in the pipe is only 990 psi. This, of course, reveals that an unconfined sheath is of little support to the pipe in burst; however, an entirely different result is obtained when the cement is confined between the pipe and formation.
JPT
P. 1033^