An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment

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. Abstract Due to the cost of extended pressure-drawdownor buildup well tests and the possibility of acquisitionof additional information from well tests, the moderntrend has been toward development of well-testanalysis methods pertinent for short-time data."Short-time" data may be defined as pressureinformation obtained prior to the usual straight-lineportion 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-timedata are too complex for meaningful interpretations. Among these factors are wellbore storage, variousskin effects such as perforations, partial penetration, fractures of various types, the effect of a finiteformation thickness, and non-Darcy flow. A numberof recent publications have dealt with short-timewell-test analysis. The purpose of this paper isto present a fundamental study of the importance ofwellbore storage with a skin effect to short-timetransient flow. Results indicate that properinterpretations of short-time well-test data can bemade under favorable circumstances. Upon starting a test, well pressures appearcontrolled by wellbore storage entirely, and datacannot be interpreted to yield formation flowcapacity or skin effect. Data can be interpreted toyield the wellbore storage constant, however. Afteran initial period, a transition from wellbore storagecontrol to the usual straight line takes place. Dataobtained during this period can be interpreted toobtain formation flow capacity and skin effect incertain cases. One important result is that thesteady-state skin effect concept is invalid at veryshort times. Another important result is that thetime required to reach the usual straight line isnormally not affected significantly by a finite skineffect. Introduction Many practical factors favor short-duration welltesting. These include loss of revenue during shut-in, costs involved in measuring drawdown or buildupdata for extended periods, and limited availabilityof bottomhole-pressure bombs where it is necessaryto survey large numbers of wells. on the other hand, reservoir engineers are well aware of the desirabilityof running long-duration tests. The result is usuallya compromise, and not necessarily a satisfactoryone. This situation is a common dilemma for thefield engineers who must specify the details of specialwell tests and annual surveys, and interpret theresults. For this reason, much effort has been givento the analysis of short-time tests. The term"short-time" is used herein to indicate eitherdrawdown or buildup tests run for a period of timeinsufficient to reach the usual straight-line portions. Drawdown data taken before the traditional straight-lineportion 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-testdata that were abandoned when it was realized thatthe straight line had not been reached. This situationis particularly odd when it is realized that earlydata are used commonly in other technologies whichemploy similar, or analogous, transient test. It is the objective of this study to investigatetechniques which may be used to interpret informationobtained form well tests at times prior to the normalstraight-line period. THEORY The problem to be considered is the classic oneof flow of a slightly compressible (small pressuregradients) fluid in an ideal radial flow system. Thatis, flow is perfectly radial to a well of radius rwin an isotropic medium, and gravitational forces areneglected. We will consider that the medium isinfinite in extent, since interest is focused on timesshort enough for outer boundary effects not to befelt at the well. SPEJ p. 279