Well-Test Analysis for Wells Producing Commingled Zones
Authors: Cobb William M. , Ramey H.J. , Miller Frank G. 
Published: December 2007

Pressure buildup for two-layer no-crossflow systems has been carefully Pressure buildup for two-layer no-crossflow systems has been carefully studied to determine the proper application of conventional analysis methods. Results of using single-layer buildup plotting forms suggested by Muskat, Miller-Dyes-Hutchinson, and Horner indicate that---under well defined conditions-all three methods can also be applied to two-layer systems.

Introduction
The three most common graphical techniques used to interpret buildup behavior are the methods of Muskat, Miller-Dyes-Hutchinson, and Homer. Initially, all three methods were developed for a well producing from a reservoir consisting of a single homogeneous layer. (They were lately reviewed by Ramey and Cobb.) In recent years, however, investigators have conducted studies on wells with commingled fluid production from two or more noncommunicating zones. In those cases, fluid is produced into the wellbore from two or more separate layers and is carried to the surface through a common wellbore. The layers are hydraulically connected only at the wellbore. Lefkovits et al., and Duvaut have presented identical rigorous solutions that describe the pressure behavior of a constant-terminal-rate well producing from a bounded, noncommunicating, multilayer reservoir with contrasting properties. Both Lefkovits et al. and Papadopulos have properties. Both Lefkovits et al. and Papadopulos have presented pressure behavior for the infinitely large presented pressure behavior for the infinitely large mulitlayer case. Although much has been published on the behavior of noncommunicating layered systems, the knowledge of well-test applications must be considered elementary. Consequently, pressure buildup for two-layer, no-crossflow systems has been carefully analyzed to determine the proper application of conventional analysis methods to this class of reservoir system. It is remarkable that the duration of transients is often orders of magnitude longer for multilayer systems than for a single layer. The only existing method for determining fully-static pressure for layered systems requires that pseudosteady state be assumed, so one principal objective of this study was to arrive at improved methods of estimating fully static pressure. As a practical step, we decided to limit our attention to systems of only two commingled zones. Finally, it should be emphasized that certain of the following results were first presented by Lefkovits et al. in a pioneering study of pressure buildup in such systems. For example, Ref. 6 clearly describes the extended duration of transients in multilayered systems and thoroughly presents the pressure behavior during drawdown. But only scanty pressure behavior during drawdown. But only scanty information was presented for analysis of pressure buildup by means of the Horner plot, and the method recommended for determining static pressure was the Muskat trial-and-error plot. The Muskat method requires the assumption that the well had been produced long enough to reach pseudosteady state - a very long time as shown by Lefkovits et al. Determination of static pressure for such systems can be exceedingly important. We wish to emphasize that we believe our contribution through this study is a clear definition of the applicability of conventional pressure buildup analysis methods to this important class of problems.
JPT
P. 27