Effect Of Reservoir Discontinuities Upon Buildup Behavior Following Short Flow Times
Authors: Tippie Douglas B. , van Poollen H.K. 
Published: December 2007

Abstract
Most of the theory developed to date concerning pressure buildup in wells located near reservoir pressure buildup in wells located near reservoir discontinuities assumes that production times prior to buildup were long enough for the discontinuity to influence the pressure drawdown behavior of the well. When this is true, the shape of the pressure buildup curve is indicative of the type of discontinuity present in the reservoir. present in the reservoir. This paper presents the results of a study conducted to determine the influence of production time and reservoir discontinuities on the shapes of pressure buildup curves. It is shown that pressure buildup curves. It is shown that insufficient flow time can lead to anomalous behavior in the buildup curve. For example, the buildup curve from a well located near a sealing fault shows the customary two-to-one slope change when the production time prior to buildup is long enough for the flowing bottom-hole pressure to be affected by the fault. A buildup taken pressure to be affected by the fault. A buildup taken on the same well following a shorter flow period shows a reduction in slope when the fault begins to influence the test. This latter behavior could be incorrectly interpreted as showing an improvement in transmissibility some distance from the well. Similar behavior can be seen in buildup tests on wells producing from reservoirs containing various types of producing from reservoirs containing various types of radial and linear discontinuities. Examples are given for various types of reservoirs.

Introduction
Conventional buildup theory for evaluation of linear discontinuities demonstrates the presence of a single slope change in the Horner buildup plot. The nature of the slope change is dependent upon the type of linear discontinuity. It can range from a two-to-one change associated with no-flow barriers to a final slope approaching zero for a constant pressure barrier. A similar approach has been published for radial-type discontinuities. In cases published in the literature, the flow times prior to the shut-in have been sufficient to insure that the drawdown already has felt the presence of the discontinuity.
The purpose of this paper is to examine buildup behavior when flow time prior to the shut-in has been insufficient to be affected by linear and radial discontinuities. Data presented show the existence of several slope changes in the pressure buildup plots, which are contrary to conventional belief. In addition, the slope measured from the buildup data is affected also by the duration status of drawdown prior to shut-in.
The techniques presented make use of image wells, the radial flow equations, and the superposition principle. For radial discontinuities, published principle. For radial discontinuities, published type-curves are used.

BASIC THEORY
The fundamental theory is based on the point-source solution to the radial diffusivity equation. point-source solution to the radial diffusivity equation. The solution is
(1)
(2)
Then the above equations read
(1a)
(2a)

Infinite Reservoir
A schematic diagram is shown as Fig. 1. For the infinite reservoir, no discontinuity exists.