The Analysis Of Spherical Flow With Wellbore Storage

Abstract

Introduction The subject of well test analysis is one of great interest in Petroleum Engineering and the large number of publications bear witness to the considerable effort directed at obtaining a better understanding of the subject. The majority of the reported research assumes a radial flow profile which is valid for most test situations. There are certain well test situations which can be more adequately modelled by assuming a spherical flow profile, e.g. vertical interference testing and wireline formation testing. However few papers have been published on spherical flow. In single-well pressure transient tests, the presence of wellbore storage has long been recognised presence of wellbore storage has long been recognised to have adverse effects on the analysis of the test results which can lead to erroneous interpretations if the period dominated by wellbore storage is not properly identified. The purpose of this paper is to properly identified. The purpose of this paper is to present a theoretical analysis of how wellbore storage present a theoretical analysis of how wellbore storage can influence transient pressure analysis in systems characterised by spherical flow geometry. Type curve methods have been used to apply this theory. The problem to be considered is the flow of slightly compressible (small pressure gradient) single phase fluid in an ideal spherical system, i.e. the phase fluid in an ideal spherical system, i.e. the flow is assumed to be perfectly spherical to a well of radius r in an isotropic medium with the effects of gravitational forces being negligible. Since the prime concern is the consideration of pressure transients at short times when outer boundary effects are not seen, the reservoir is assumed to be infinite in extent. The initial condition for an infinite medium can then be taken as a constant pressure, p, at a radius greater or equal to the wellbore radius, r. The inner boundary condition will be taken as production at constant surface rate from a wellbore production at constant surface rate from a wellbore of finite volume with significant wellbore storage. Since the reservoir is assumed to be infinite, the outer boundary condition implies that the pressure drop equal zero at all time. THEORY The basic, partial differential equation describing the flow of a slightly compressible fluid in a homogeneous porous medium, governed by spherical geometry, can be stated as: (1) where the porosity, compressibility and mobility are assumed to be constant and where gravitational effects can be neglected. The various dimensionless variables are defined in field units as follows: dimensionless radius, (2) dimensionless time, (3) dimensionless pressure (4) where rsw is defined as the pseudo spherical wellbore radius and depends upon many factors such as wellbore condition, type of well completions, i.e. either partially or fully completed, etc. partially or fully completed, etc.