A General Pressure Buildup Theory for a Well in a Closed Drainage Area (includes associated paper 6563 )

Abstract

Pressure buildup analysis, when properly done, yields the same results nomatter which of the conventional methods is used. As illustrated here with aclosed square, general interpretation equations may be derived that are correctfor closed drainage regions of any shape. Introduction In 1935, Theis1 showed that buildup pressures in a shut-in waterwell should be a linear function of the logarithm of the time ratio(t+?t)/?t, and that the slope of the line is inverselyproportional to the mean formation effective permeability. Muskat discussedpressure buildup in oil wells in 1937, and proposed determination of staticpressure by a semilog trial-and-error plot that has been found to be applicableto a variety of buildup cases. In the late 1940's, van Everdingen presented aseries of lectures on well test analysis in the U.S. that related to aclassical study of unsteady flow by van Everdingen and Hurst.3 In1951, Horner4 presented a study of pressure buildup that appears tohave summarized fundamental efforts of a number of pioneering researchers inthe Shell companies. Horner also recommended a semilog buildup curve identicalwith the Theis curve, and presented a method for extrapolation to fully builtup static pressure for a closed circular reservoir. This sort of semilogpressure buildup plot is often referred to in the oil industry as a Hornerplot. About the same time, Miller-Dyes-Hutchinson5 presented ananalysis for buildup when the well had been produced long enough to reachpseudosteady, or true steady state prior to shut-in. Their work indicated thatbuildup pressures should plot as a linear function of the logarithm of shut-intime. As in the Horner plot, the slope of the straight line was shown to beinversely proportional to the permeability to the flowing fluid. It isinteresting that about the same time Jacob6 presented a similarapproach to determine aquifer transmissibility for a water well productiontest. Miller-Dyes-Hutchinson presented several important extensions of builduptheory. One was an initial attempt to apply buildup theory to multiphase flow. This problem was later resolved by Perrine.7 More important to thisstudy, an approach to extrapolation to fully built-up static pressure waspresented for outer boundary conditions of either no flow (closed), or constantpressure (water drive). Thus, by the early 1950's, both Horner and Miller-Dyes-Hutchinson hadpresented methods for determining permeability and static pressure from buildupdata. Although there were similaries - both involved semilog plotting - therewere confusing differences between the methods. Perrine7 presented an excellentreview of this theory in 1956 that clearly indicates the state of understandingat that time. He stated that Horner-type plot (which he referred to as the vanEverdingen-Hurst method) was valid for a new well in a large reservoir, butthat the Miller-Dyes-Hutchinson approach was best for older wells in fullydeveloped fields. The latter is a widely held misconception.