Potential Distribution About A Perforation
Authors: Hilchie D.W. , Hogan R. , Kohlhaas C. , Bass D. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 49th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Texas, Oct. 6–9, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The potential distribution around perforations, as a function of perforation penetration, in cased and perforated wells has been determined for several perforation patterns using an electrolytic model. Ideal perforations were simulated. Additionally, the distance from the well bore at which radial flow exists was determined so that the potential (pressure) distributions around an ideal perforation would not be influenced by assumed boundary conditions. Flow lines are perpendicular to the measured equipotential surfaces.

Introduction
The performance of well perforations has been of concern since the initial advent of gun perforating, in 1932. The importance of be perforation/formation flow relationship has increased as the usage of perforations to complete wells has increased and the use of such techniques as pressure build-up, pressure draw-down, pulse testing and sand control play a pressure draw-down, pulse testing and sand control play a more important role in well completions.
The potential distribution as determined in this study define the flow lines (perpendicular to the equipotential surfaces) in the formation. Flow in a reservoir at a great distance from the well bore is radial. That is it converges upon the wellbore as if it were a sink. If the well is completed openhole -all the way through the formation and the formation is isotropic and homogenous, radial flow will occur everywhere in the reservoir. When a perforation exists in a thin zone or many perforations have been made in a thick zone, the flow becomes perforations have been made in a thick zone, the flow becomes nonradial at some distance from the wellbore. Our experiments show that the flow patterns change significantly near the perforated casing. Figure 1 shows the type of flow patterns that perforated casing. Figure 1 shows the type of flow patterns that develop from the plot of equipotential lines which are perpendicular to the flow lines. A long distance from the wellbore, perpendicular to the flow lines. A long distance from the wellbore, the flow is radial as viewed from above (plan view) and from the side view (parallel to the top and bottom of the bed). At some point nearer the wellbore flow starts to converge and become nonradial. This nonradial flow, when the flow is still parallel to the top and bottom of the bed, but is no longer parallel to the top and bottom of the bed, but is no longer radial from a plan view, is designated nonradial flow phase 1. At some position, the flow starts converging towards the perforation instead of the wellbore and the casing/cemented borehole perforation instead of the wellbore and the casing/cemented borehole becomes an obstacle. Nonradial flow phase 2 takes place when the fluid (from a side view) stops being parallel to the top and bottom of the bed. The flow from both a plan and side view is converging towards the perforation.