On the Analysis of Well Test Data Influenced by Wellbore Storage, Skin, and Bottomwater Drive
Authors: Chu W.C. , Chen J.C. , Reynolds A.C. , Raghavan R. 
Published: December 2007

Summary
The combined influence of wellbore storage, wellbore damage, and partial penetration on the analysis of pressure data is discussed. The effect of a gas cap or bottomwater aquifer (constant pressure boundary) also is documented. We demonstrate that the magnitude of the wellbore storage constant dictates the type and amount of information that can be gleaned from a pressure test during the storage dominated period. For small values of the dimensionless storage constant and large values of dimensionless well length, the flow capacity of the perforated (open) interval and the skin factor, which reflects impediments to flow around the sand face, can be determined from data affected by wellbore storage. This information can be obtained from the wellbore storage type curves (the complete penetration solutions) available in the literature. Values of the dimensionless well length and storage constant for which this information can be obtained are specified in the paper.
For other cases, the flow capacity of the entire interval and the total skin factor can be estimated. Again, storage type curves for the complete penetration solutions can be used to obtain this information if both boundaries are sealed. If one of the boundaries is at a constant pressure (water drive or gas cap), then the new solution presented in this paper should be used. If the storage type curves presented in the literature are used, then we recommend the procedure of Earlougher and Kersch, which incorporates the effective wellbore radius concept to combine the influence of storage and skin.

Introduction
Bilhartz and Ramey were the first to examine the combined influence of wellbore storage, wellbore damage, and partial penetration on the pressure response at a well. They concluded that the wellbore storage effect usually will obscure the fact that partial penetration exists -- information on anisotropy and on partial penetration cannot be obtained if storage effects are dominant. Their work assumed that the top and bottom boundaries are sealed. Often, wells are completed as partially penetrating wells to prevent or delay the intrusion of unwanted fluids from either a gas cap or a bottomwater aquifer. A gas cap or a bottomwater aquifer usually provides pressure support; that is. the influence of a gas cap or an aquifer is similar to that of a constant pressure boundary. Recently, Buhidma and Raghavan showed that if a constant pressure boundary exists at the top (or bottom) of the reservoir, then the semilog straight line reflecting the pseudoradial flow period does not exist. This observation implies that, for this situation, the formation flow capacity and skin factor cannot be determined by conventional means. Thus, if early-time data are dominated by storage, then the only recourse is to analyze data in the transitional period. Streltsova-Adams has discussed a procedure to examine the pressure response in this case.
Our goal is to examine the combined effects of partial penetration, wellbore storage, and wellbore damage on the well response and to draw conclusions about pressure transients in these cases. More specifically, the objectives of this study are:to discuss analysis procedures when the pressure response is influenced by the previously mentioned effects,to determine the parameters that can be determined from a well test under the circumstances mentioned previously,to compare well responses when both boundaries are closed with the responses obtained when one of the boundaries is at constant pressure (bottomwater or gas cap drive), andto combine the parameters of interest and correlate the well response in terms of dimensionless groups commonly used in well test analysis.
Our work is different from Ref. 5 in the following respects. First. we demonstrate quantitatively the effect of the wellbore storage coefficient on well test data. Second, we conclusively demonstrate that in some cases the permeability estimate obtained by type-curve matching will reflect the flow capacity of the open interval; in other cases the estimate will reflect the permeability of the entire interval. Third, we suggest a simple way to incorporate the effect of penetration ratio (length of open interval/formation thickness), whenever the penetration ratio is important, and, thus. for these circumstances separate type-curves are not needed. Fourth, we discuss the determination of wellbore damage from test data.
From this discussion, it should be clear that if the lower boundary is at a constant pressure then conventional semilogarithmic methods cannot be used to analyze data. For such cases, type-curve matching is the only recourse.
JPT
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