Effect Of Coning On Clean Production Rate Of Well In Heterogeneous Reservoir
Authors: Outmans H.D. 
Published: December 2007

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This paper is to be presented at the 39th Annual Fall Meeting to be held in Houston, Tex., on Oct. 11–14, 1964, and is considered property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Engineers or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper.
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Abstract
Formulas are derived for the production rate of an oil or gas well in a heterogeneous reservoir with the top and/or bottom cone intersecting the wellbore at the upper and/or lower end of the completion interval.
For a given completion, terminated above the water table or below the gas-oil contact, these formulas give the maximum rate at which gas or oil, uncontaminated by the fluid in the cone, can be produced. For completions close to the original oil-water or oil-gas contacts they represent lower bounds of this maximum rate.
The types of reservoir heterogeneity for which the formulas are developed include discontinuous variations of permeability with radial distance from the well or with depth and continuous variations of permeability with depth.

Introduction
Two basically different methods have been developed for calculating the maximum rate of' clean production from a well with coning water and/or gas.
In the earlier study it is shown, by means of a stability analysis, that the maximum rate of production obtains when the corresponding steady-state cone, which intersects the wellbore at some finite distance below or above the completion interval, becomes unstable and breaks in the well. Calculation of the maximum rate by this method is cumbersome and inexact.
In the second study 2 the tacit assumption is made that all cones outside the completion interval are stable. Maximum clean production obtains when the cone intersects the wellbore just where the completion interval begins. The assumption is attractive because it simplifies calculation of the maximum rate but is not compatible with the earlier stability anal sis and, for this reason has been criticized.
Assuming, however, that the second study is valid, and there is some evidence supporting this viewpoint, we can without great difficulty extend the maximum rate calculations of that study to heterogeneous reservoirs. As in Ref. 2, we will analyze water coning in an oil or gas reservoir, gas coning in an oil reservoir and for the latter case also the combination of gas and water coning.
We consider heterogeneities similar to those in Ref. 6; that is, continuous or discontinuous variation of the permeability with depth or discontinuous variation with radial distances. The well is assumed to produce through a perforated section of the casing.
Below we give a summary of the formulas derived in this paper.