Productivity of Perforated Completions in Formations With or Without Damage
Authors: Hong K.C. 
Published: December 2007

The productivity of perforated completions situated in either homogeneous reservoirs or zones of permeability damage is described. Calculations for both types of reservoirs require use of a perforation skin factor; calculations for a damaged reservoir additionally require a damage skin factor. Nomograms are presented for calculating these factors.

Introduction
In perforated completions, fluids enter the wellbore through tunnels made by bullets or jets that penetrate the casing, cement sheath, and part of the producing formation. The productivity of such completions has been studied by various investigators, with either computer models or electrolytic analog models. Harris recently published a series of curves for calculating skin factors published a series of curves for calculating skin factors in terms of predetermined dimensionless well and perforation parameters. These skin factors are used in computing parameters. These skin factors are used in computing the productivity ratio (the productivity of a cased and perforated completion vs that of an equivalent open-hole perforated completion vs that of an equivalent open-hole completion). Harris' graphs, however, are difficult to use because they are based on dimensionless parameters that must be predetermined, and they require extensive extrapolation predetermined, and they require extensive extrapolation for well diameters larger than 6 in. In addition, Harris' model covers only the simple, regular patterns, and requires that the perforations in a horizontal plane be directly above or below those in adjacent planes. Application of Harris' model is also restricted by the assumption that the formation permeability has not been damaged by the normal drilling and perforating processes. processes. The study reported here describes the productivity of perforated completions situated in either homogeneous perforated completions situated in either homogeneous reservoirs or zones of permeability damage. Calculations for both types of reservoirs require use of a perforation skin factor; calculations for a damaged reservoir additionally require a damage skin factor. Nomograms are presented for calculating these factors. presented for calculating these factors. Separate nomograms are provided for the two basically different types of perforation patterns: simple and staggered. In the latter, perforations in a horizontal plane can be 90 degrees or 180 degrees out of phase with those in adjacent horizontal planes (Table 1). Three samples illustrate the use of these nomograms for calculating skin factors and productivity ratios. The effects on productivity of perforation parameters such as size, patterns, penetration, and density are shown by graphs relating them to the productivity ratio.

Development of Nomograms

Well in a Homogeneous Reservoir
The usual relationship of flow rate and pressure drop for quasi steady-state flow is(1)7.08 krh (p-pw) qr = ln (0.47 re/rw)
which is for one-dimensional radial flow into an open hole. When flow is into perforations that penetrate the formation, the flow geometry takes on three-dimensional aspects. The difference in pressure drop between convergent flow to perforations and radial now to an open hole is the basis for the perforation skin factor, Sp. This factor is used in a similar radial flow equation,(2)7.08 krh(p-pw) qr = [sp+ ln (0.47 re/rw)]
JPT
P. 1027