Pseudoskin Factor Caused by Partial Penetration
Authors: Reynolds A.C. , Chen J.C. , Raghavan R. 
Published: December 2007

Summary
In this study we examine the pseudoskin factor caused by partial penetration in a two-layer reservoir when only partial penetration in a two-layer reservoir when only one layer is open to flow. We show that the pseudoskin factor can be correlated as a unique function of three reservoir parameters and in many cases can be correlated accurately as a function of two reservoir parameters. We present graphs and procedures for estimating the pseudoskin factor. pseudoskin factor. Introduction
Frequently, wells are perforated over only a portion of the productive zone to delay or to prevent water and/or gas coning. This situation is called "partial penetration" or "restricted entry."This type of well completion has received considerable attention in both the petroleum and groundwater hydrology literature. The problem was studied as early as 1949 by Muskat and has subsequently been studied in a plethora of papers including Refs. 2 through 10. Desirable information papers including Refs. 2 through 10. Desirable information on this problem includes procedures for the analysis of well-test data and the evaluation of the productivity loss from partial penetration or restricted entry. This work provides information on the second topic; specifically, it provides information on the second topic; specifically, it provides methods for evaluating the pseudo skin factor caused provides methods for evaluating the pseudo skin factor caused by partial penetration. As shown in Refs. 1 through 6, the pseudo skin factor determines the productivity decrease pseudo skin factor determines the productivity decrease resulting from partial penetration. The results of Refs. 1 through 10 consider only single-phase flow, whereas in reality partial penetration or restricted entry exists to prevent the partial penetration or restricted entry exists to prevent the production of an undesirable fluid under multiphase flow production of an undesirable fluid under multiphase flow conditions i.e., to prevent or delay water and/or gas coming. Ref. 11, clearly indicates that the single-phase correlations for the pseudo skin factor do not accurately predict the pseudo skin factor caused by partial penetration under multiphase flow conditions. The results of Ref. 11, which are for an oil/ water system, indicate that if horizontal saturation gradients are negligible, then the two-phase flow situation should be analogous to single-phase flow in a layered reservoir with the oil, transition, and water zones each representing a separate layer. If the transition zone is small, the two-phase flow partial penetration situation should resemble single-phase flow partial penetration situation should resemble single-phase flow in a two-layer reservoir. This provides the motivation for the single-phase flow two-layer reservoir problem considered here. Our main objective is to present methods for estimating the pseudo skin factor in a two-layer reservoir with only one layer pseudo skin factor in a two-layer reservoir with only one layer open to flow. If this can be done, the true skin factor can be estimated by subtracting the pseudo skin factor from the total skin factor computed by semilog analysis techniques. The results of Refs. 1 through 6 are restricted to single-layer, single-phase flow problems. It is relevant to point out that a partially penetrating well in a layered reservoir has been studied previously; see Refs. 7 and 9. However, to our knowledge, no one has identified the key parametric groups that uniquely determine the pseudo skin factor caused by partial penetration in a two-layer reservoir or provided methods for computing this pseudo skin factor. The intended contribution of this paper is pseudo skin factor. The intended contribution of this paper is to provide this knowledge.
Pseudo skin Computation Pseudo skin Computation Hereafter we refer to the pseudo skin factor caused by partial penetration as simply the pseudo skin factor. In this major penetration as simply the pseudo skin factor. In this major section, the mathematical model and the procedure used to compute this factor are discussed.

Mathematical Model.
To compute the pseudo skin factor, we consider a single well in the center of a two-layer cylindrical reservoir with impermeable top, bottom, and outer boundaries. The layers are assumed homogeneous and contain a slightly compressible fluid of constant viscosity. The initial pressure is assumed uniform throughout the reservoir. Gravitational and wellbore storage effects are neglected. Each layer can be either isotropic or anisotropic, but the vertical permeabilities of the two layers are nonzero so that cross flow can occur between the two layers. The well is produced at a constant rate. Since the reservoir pressure exhibits radial symmetry, the mathematical model is two-dimensional i.e., an r-z model (Fig. 1). The pseudo skin factor results presented in this work were obtained by generating the pressure response for the model shown in Fig. 1 under the assumption that only Layer 1 is perforated; that is, all production is from Layer 1 and all perforated; that is, all production is from Layer 1 and all of Layer 1 is open to flow.
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