In calculating negative skin, treating the skin as a zone of infinitesimal thickness leads to mathematical difficulties. These can be overcome by assuming an enlarged wellbore radius and using the same equations that apply for positive skin.

Introduction

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkins has shown that the radius and the permeability of this zone are related to the skin by:

(1)

If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin.

Van Everdingen and Hurst, have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure, which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins.

Theoretical Development

Van Everdingen and Hurst, through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore:

(2)

where tD, dimensionless time, is given by:

(3)

By use of the superposition technique, Eq. 2 can be expressed as

(4)

The values for QtD, reported extensively by van Everdingen and Hurst, are obtained from the following integral:(5)

JPT

P. 1483ˆ

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