An Analytical Study of Transient Flow in Stratified Systems with Fluid Banks

Abstract

ABSTRACTA study was made of the behavior of reservoirs composed of horizontal layers with fluid banks, unconnected except at the well and filled with a slightly compressible fluid. The new solution described in this paper is an analytical solution for a circular well with a skin effect and wellbore storage. Each layer has a composite system with a circular inner region whose diffusivity is different from the one in the outer region. There may be either a constant pressure, closed, or infinitely-distant outer boundary. The solution method is Laplace transformation followed by a numerical inversion scheme.A recent study of transient flow in one layer systems with radial discontinuities, paper SPE No, 93997, indicated that it was possible to measure the volume of the gas filled displaced region with accuracy and the method did not depend upon regular geometry for the displaced region. There appeared to be very important potential application for enhanced oil recovery and geothermal reservoirs with phase boundaries. This paper is an extension of that study to the reservoirs composed of horizontal layers and investigates the effects of various reservoir and fluid parameters including the shape of the fluid front.Theoretical injectivity and falloff curves from such reservoirs are presented, and the influence of a skin effect and wellbore storage are also evaluated. The results of injectivity and falloff tests are given.The study of injectivity tests indicate a short duration wellbore storage effect, followed by a semilog straight line whose slope is related to the average permeability-thickness of the swept volume. The semilog straight line is then followed by a pseudosteady Cartesian straight line characteristic of the swept volume. Finally, a second semilog straight line appears, characteristic of the average permeability-thickness of the unswept region. It is possible to find the nearest distance to the front and also the average distance to the front by evaluating the first a few hours of the injectivity test data.The analysis of the falloff tests also shows a short duration wellbore storage effect, followed by a semilog straight line. It is then followed by a transition region. To detect the nearest distance to the front may be possible but the falloff tests do not show any pseudosteady state behavior. Detecting the nearest distance to the front is not always possible due to the fact that the producing time makes the analysis of a falloff test for such a system more complex as indicated in the literature. When the producing time is not long enough a flattening region following the first semilog straight line masks the portion of the data whose characteristic is used to detect the nearest distance.