Estimating Skin Effect in a Partially Completed Damaged Well
Authors: Jones L.G. , Watts J.W. 
Published: December 2007

Presented here are equations for estimating true and total skin erect for Presented here are equations for estimating true and total skin erect for partially completed wells when the amount and depth of permeability partially completed wells when the amount and depth of permeability reduction are known. It is shown that the magnitude of true skin due to formation damage is essentially inversely proportional to the length of the perforated interval. perforated interval. Introduction
Broadly speaking, pressure drop represented by the difference between the average pressure in the bulk of a reservoir and the flowing well pressure consists of two factors. One of these is pressure drop normally associated with more or less radial fluid flow. The second is abnormal pressure drop associated with non-radial flow patterns near the well or with changes in permeability near the well. permeability near the well. The skin effect concept was created to allow mathematical treatment of abnormal pressure drop. The magnitude of skin effect is directly proportional to the difference between actual pressure drop and that predicted by unsteady-state radial flow theory. Skin predicted by unsteady-state radial flow theory. Skin effect is used quantitatively in predicting well performance under various operating conditions, and is performance under various operating conditions, and is particularly valuable for predicting the probable results particularly valuable for predicting the probable results of well stimulation. As originally conceived by van Everdingen, and Hurst, skin effect was thought to be due to an infinitesimally thin zone of formation damage around a producing well. Hawkins extended the concept to a producing well. Hawkins extended the concept to a zone of finite thickness by developing an algebraic equation relating reservoir permeability, skin permeability, well radius, and skin radius to skin magnitude. permeability, well radius, and skin radius to skin magnitude. For radial flow those early concepts of skin effect are adequateOn the other hand, if the well is partially completed in other words, if only part of the producing interval is perforatedthere is an apparent skin due to the constriction in flow. This apparent skin can be calculated using the work of Brons and Marting, or Odeh. However, neither Brons and Marting nor Odeh considered the possible occurrence of actual well damage in a partially completed well. If formation damage is present around such a well, Hawkins' equation for calculating the skin due to this damage does not apply, since flow into the well is no longer radial. This paper presents an adaptation of Hawkins' equation paper presents an adaptation of Hawkins' equation that applies when a well is partially completed. The results should be of value to all who are concerned with well testing and estimating well productivity.

Analysis
The approach used here is to assume radial flow into the partially completed portion of a well in order to derive an approximate formula for calculating the skin due to actual formation damage. Then two sets of skin are calculated, one using this formula and one using a finite difference model described in Appendix A. By comparing these skins, an empirical correction to the approximate formula is developed. Using Hawkins' approach, for an undamaged well completed over the entire length of producing interval the pressure drop from an arbitrary radius, rs, to rw is
(1)
P. 249