Productivity of Perforated Completions in Formations With or Without Damage

Abstract

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

Assessment of Total Skin Factor in Perforated Wells

“…A great number of experimental, numerical, empirical, and semianalytical models have been constructed to predict the perforation pseudoskin and perforation total skin (Jones and Slusser 1974;Harris 1966;Klotz et al 1974;Hong 1975;Locke 1981;Tariq 1987;McLeod 1983;Karakas 1991;Bell et al 1995;SPAN 1999;SPAN 2002;Thomas et al 1992;Yildiz 2002;Pan and Tang 1989). Some of these models will be described briefly below.…”

Flow around a rock perforation surrounded by crushed zone: Experiments vs. theory

“…In his analysis perforations were represented by mathematical sinks distributed spirally around the wellbore and did not extend into the formation. Other early investigators used finite difference modelling approaches to examine the flow in perforated completions (e.g., Harris, 1966;Hong, 1975;Bell et al, 1972). Klotz et al (1974), Locke (1981) and Tariq (1987) were the first to apply the finite element method, which models the geometry of the perforation with greater precision.…”

“…He also conducted a grid-or mesh-sensitivity analysis to ascertain the effect of grid or mesh size on their results without the non-Darcy effect. Based on this exercise, Tariq concluded that Harris (1966) and Hong (1975) used insufficient grid cells and unrealistic wedge-shaped perforations in their study, and although Locke's geometrical representation (1987) was precise, the grid size 0920-4105/$ -see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2005.10.004 was too large for accurate modelling of high pressure gradients near the perforation tip.…”

Measurement and Modelling of Gas Condensate Flow Around Rock Perforation

“…Muskat (1943) presented the first analytical treatment of the problem in 1943 representing perforation tunnels as point sinks in his analysis. Other early investigators used finite difference modelling approaches to examine the flow in perforated completions (e.g., Harris, 1966;Hong, 1975;Bell et al, 1972). Later investigators applied finite element methods, which model the geometry of the perforation with greater precision (e.g., Koltz et al, 1974;Locke 1981;Tariq, 1987).…”