A Theoretical and Numerical Investigation of the Pseudoskin Factor
Authors: Zeidani K. , Zhang C. , Cunha L.B. 
Published: March 2010

Abstract
Partial completion of wells to inhibit gas and/or water coning in producing wells has been a common practice in the petroleum. industry for many years. This procedure, however, causes an additional pressure drop or pseudoskin that reduces the well productivity. In formations that are producing with partial completion, the precise quantification of this additional pressure drop is of paramount importance for completely identifying the existence. of formation damage. Many authors have proposed mathematical solutions that can be used to estimate the pseudoskin factor caused by restricted entry. In this work, a comprehensive investigation of the available models listed in the literature used for the estimation of pseudoskin due to restricted entry was performed. Selected models were implemented in a methodology and computer program. Then, a sensitivity analysis focusing on producing wells was carried out. The effect of the height of the producing interval, height rom the. middle portion of the producing interval to the bottom of the reservoir, reservoir thickness, horizontal and vertical permeabilities and wellbore radius were investigated. Furthermore, the extension of the methodology for the determination of mechanical skin in injectivity and fall-off tests executed in injector wells is described. At the end of this paper, an example highlights the range of applicability and potential benefits of the proposed methodology.

Introduction
It is very frequent that wells are completed over only a fraction of their productive zone in order to delay water and/or gas coning. A well completed in this manner is referred to as a partially penetrated or restricted-entry well. Two questions of practical importance in this scenario are:what is the productivity loss caused by the partial penetration; and,should the well be stimulated?
The answer to these questions requires an estimation of the pseudoskin factor caused by the partial penetration and an estimation of the mechanical (real) skin caused by formation damage or stimulation.
In this work, a comprehensive investigation of the available models listed in the literature used for the estimation of pseudoskin due to restricted entry was performed. A methodology and computer code was established that, if given the relative position of the perforated interval with respect to the producing zone and the values of vertical and horizontal permeability, the pseudoskin (dimensionless pressure drop) due to the restricted entry can be computed. Five selected formulas were studied, including Streltsova-Adams(1), Kuchuk and Kirwan(2), Papatzacos(3), Yeh and Reynolds(4) and Odeh(5). The assumptions, simplifications and range of validity associated with each formula are presented. All the pseudoskin formulas used in this work assume the single phase of a fluid with small compressibility and constant viscosity. The reservoir is considered homogeneous and isotropic, with constant thickness and infinite extension. The reservoir top and base are considered impermeable. The gravitational effects are considered negligible. Considering all these assumptions, the total skin obtained from a well test interpretation is given by:
Equation 1 Available in Full Paper