American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.
Methods of analyzing pressure buildup data from stabilized wells have been presented by several authors. All of the methods attempt to use some type of straight-line Horner plot. This paper must be considered controversial in that it shows that there is no theoretical basis for expecting a straight-line Horner plot from a stabilized well's pressure buildup data regardless of the "producing time" used.
A simplified method is presented which analyzes buildup data by working with only the pressure change caused by the negative rate induced when the well is shut in. The pressure change that would have occurred had the well not been shut in is taken into account before the pressure plot is constructed. This approach permits the calculation of the undamaged transmissibility of the reservoir, the skin factor or damage ratio, and the average pressure in the well's drainage radius. These calculations can be completed with less data than required for the analysis of a pressure buildup from an infinite acting reservoir, provided the pressure change with time during stabilized production is known from past surface pressure observations, past BHP surveys, or a pressure survey just before shut-in.
Except for pressure surveys run in connection with drillstem tests, most pressure buildup data are obtained from wells that are stabilized at the time of shut-in. The well known Horner type of pressure buildup analysis is based on infinite acting reservoir equations and thus is not directly applicable to most of the available pressure buildup data. Several methods have been proposed for analyzing pressure buildup data from stabilized wells, but all of the methods present some difficulties in application. The published methods attempt to adapt the Horner plot to stabilized wells. They also require trial-and-error solutions and/or reservoir data which are not normally available. The method developed in this paper does not require a trial-and-error solution nor does it require any more reservoir data than does the Horner type of analysis of an infinite acting reservoir.
The Horner pressure buildup equation can be written in two terms in practical units as,
The first term represents the pressure change that would occur in (tp + delta t) days, if the well had not been shut in. The second term represents the pressure increase which occurs due to introducing a -q rate at the well when the well is shut in for delta t days. van Everdingen and Hurst showed that these pressure changes are a function of the log of the time only as long as the reservoir is infinite acting. This paper presents a method of analysis that concerns itself with the second term of this equation and for a delta t small enough for the effect to be infinite acting.