An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment
- Ram G. Agarwal (Pan American Petroleum Corp.) | Rafi Al-Hussainy (Mobil Research and Development Corp.) | H.J. Ramey Jr. (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- September 1970
- Document Type
- Journal Paper
- 279 - 290
- 1970. Society of Petroleum Engineers
- 5.2.2 Fluid Modeling, Equations of State, 4.1.2 Separation and Treating, 2.4.3 Sand/Solids Control, 2.2.2 Perforating, 4.3.4 Scale, 5.6.4 Drillstem/Well Testing
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Agarwal, Ram G., Pan American Petroleum Corp. Tulsa, Okla., Pan American Petroleum Corp. Tulsa, Okla., Al-Hussainy, Rafi, Junior Members AIME, Mobil Research and Development Corp., Dallas, Tex., Ramey Jr., H.J., Member AIME, Stanford U. Stanford, Calif.
Due to the cost of extended pressure-drawdown or buildup well tests and the possibility of acquisition of additional information from well tests, the modern trend has been toward development of well-test analysis methods pertinent for short-time data. "Short-time" data may be defined as pressure information obtained prior to the usual straight-line portion of a well test. For some time there has been portion of a well test. For some time there has been a general belief that the factors affecting short-time data are too complex for meaningful interpretations. Among these factors are wellbore storage, various skin effects such as perforations, partial penetration, fractures of various types, the effect of a finite formation thickness, and non-Darcy flow. A number of recent publications have dealt with short-time well-test analysis. The purpose of this paper is to present a fundamental study of the importance of wellbore storage with a skin effect to short-time transient flow. Results indicate that proper interpretations of short-time well-test data can be made under favorable circumstances. Upon starting a test, well pressures appear controlled by wellbore storage entirely, and data cannot be interpreted to yield formation flow capacity or skin effect. Data can be interpreted to yield the wellbore storage constant, however. After an initial period, a transition from wellbore storage control to the usual straight line takes place. Data obtained during this period can be interpreted to obtain formation flow capacity and skin effect in certain cases. One important result is that the steady-state skin effect concept is invalid at very short times. Another important result is that the time required to reach the usual straight line is normally not affected significantly by a finite skin effect.
Many practical factors favor short-duration well testing. These include loss of revenue during shut-in, costs involved in measuring drawdown or buildup data for extended periods, and limited availability of bottomhole-pressure bombs where it is necessary to survey large numbers of wells. on the other hand, reservoir engineers are well aware of the desirability of running long-duration tests. The result is usually a compromise, and not necessarily a satisfactory one. This situation is a common dilemma for the field engineers who must specify the details of special well tests and annual surveys, and interpret the results. For this reason, much effort has been given to the analysis of short-time tests. The term "short-time" is used herein to indicate either drawdown or buildup tests run for a period of time insufficient to reach the usual straight-line portions. Drawdown data taken before the traditional straight-line portion are ever used in analysis of oil or gas portion are ever used in analysis of oil or gas well performance. Well files often contain well-test data that were abandoned when it was realized that the straight line had not been reached. This situation is particularly odd when it is realized that early data are used commonly in other technologies which employ similar, or analogous, transient test. It is the objective of this study to investigate techniques which may be used to interpret information obtained form well tests at times prior to the normal straight-line period.
The problem to be considered is the classic one of flow of a slightly compressible (small pressure gradients) fluid in an ideal radial flow system. That is, flow is perfectly radial to a well of radius rw in an isotropic medium, and gravitational forces are neglected. We will consider that the medium is infinite in extent, since interest is focused on times short enough for outer boundary effects not to be felt at the well.
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