The Effect on Well Productivity of Formation Penetration Beyond Perforated Casing

Abstract

Abstract A report is given of electrical analog experiments on the effect of casingperforation completions on well productivity for ideal uniform reservoirs understeady state homogeneous fluid flow conditions. Graphical results are presentedfor the effect of perforations of different densities and various degrees ofpenetration into the formation surrounding the casing or cement sheath. Thelatter range from perforations which terminate flush with the casing to thosewhich extend into the formation a distance equal to the casing diameter. Forthe special case where the perforations terminate immediately beyond the casingwith semi-spherical protrusions the electrical analog results correct andsupersede previously reported theoretical calculations. It is found that thepenetration of the perforations into the surrounding productive section may soincrease the resultant productivity as to approach or even exceed that for openhole completions. Introduction A theoretical analysis of the effect of casing perforation on well completion, without additional penetration of the formation, was reported several yearsago. In this treatment the perforations were represented by mathematical sinksand no explicit account was taken of the imperviousness to flow of the casingin which the perforations were made. This procedure was justified byconsideration of the mutual interference between the sinks, which seemed toindicate that the analytical method automatically eliminated flow across thecasing radius between the perforations. However, both further theoreticalinvestigation and the electrical analog measurements described below showedthat this assumption in the previously developed theory was not valid and thatthe calculated well capacities would considerably exceed the correctvalues. Even if this simplifying assumption were retained the generalization of thetheory to situations where the perforations extend into the producing formationwould be extremely difficult. On the other hand, the electrolytic model analogof this type of steady-state homogenous fluid system is, in principle, sosimple that it has not been worthwhile to attempt to develop the exact analysiseven for the more limited case of strict casing perforation. The whole problemhas therefore been studied anew by electrical models to cover the range fromholes in the casing which terminate flush with the casing surface to such asextend into the surrounding rock to a depth equal to the casing diameter. T.P. 2891