Evaulation And Design Optimization Of Perforated Casing
Authors: Hair C.C. , Schwind B.E. 
Published: October 2008

ABSTRACT
Evaluation of the structural capacity of perforated casing was performed for Mobil North Sea Ltd. applications. Initially a closed form solution for crush strength was developed. Empirical data were used to qualify the theoretical development. Since field requirements for perforation geometry exceed the empirical basis, additional crush testing was performed. A perforation geometry was defined which maximized perforation area while having minimal adverse effect on crush strength. Crush tests were performed on both perforated and un-perforated 5-1/2 inch, 17 ppf, L-80 casing in order to obtain an exact definition of perforation effect Calculated values of crush strength were shown to be conservative, with the perforation effect on crush strength predicted within approximately 5 percent.
Following the evaluation of crush resistance, the combined bending and compression capacity was considered both perforated and un-perforated casing was evaluated analytically and experimentally in order to determine ultimate capacity under combined bending (150/1OO') and compassion. Calculated results predicted an ultimate compressive load for perforated casing to be 76.2% of un-perforated casing test results indicated 77.3%.
As a result of these findings it is concluded that general equations have been developed to predict both the transverse crush strength and the combined compression and bending capacity of casing with and without perforations. These equations have been verified empirically and provide sufficient accuracy for engineering calculations such as design optimization.

FIELD APPLICATION
The following development work was performed for Mobil North Sea Limited in support of the Lancelot Development well 48/17a. 5-1/2 inch, 17 ppf L-80 pre-drilled perforated casing will be used in the 3000 foot (914 meter) lateral section of the well. This casing was required to be run through a 15 degree/100 foot deviation, and subsequently sustain transverse crush loads due to formation overburden.
As a result of these requirements it was necessary to design a perforated section which would both maximize total perforation area, while having minimal adverse effect on structural capacity. In order to design an optimum perforation geometry general relationships were developed for ultimate capacities. These relationships gave clear indications on perforation geometry optimization, which were incorporated into the design of the cost effective perforation pattern. Finally, having both the recommended perforation configuration and calculation methods for failure loads, the calculations were verified using full scale physical testing.

CRUSH STRENGTH EQUATION DEVELOPMENT
Mobil used a plastic hinge analogy to determine ultimate capacity of casing because transverse loading induces a bending mode of failure, which is best described with the plastic hinge. The moment at each plastic hinge is given by:(Mathematical equation) (available in full paper)
The approach taken for the perforated casing was to simply derate the load capacity of the plastic hinge by an amount equal to the material removed in drilling the perforations. This derating amount is given by:(Mathematical equation) (available in full paper)
Theoretical results were then compared to empirical data presented in several papers by George King1,2, and additional testing performed by Mobil in order to demonstrate equation accuracy. The successful comparison to empirical data marked the end of equation development.