Application of the Line Source Solution To Flow in Porous Media--A Review
Authors: Ramey H. J. 
Published: December 2007

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Abstract
Ideal flow of slightly compressible single phase fluids from horizontal, isotropic reservoirs of linear and radial shapes has been thoroughly discussed in the literature, although specific information for closed radial reservoirs at large re/rw ratios is not readily accessible. Superposition of the continuous line source solution can be used to generate solutions for large drainage area-well radius ratio cases for a variety of reservoir shapes. Application of this method to pressure build-up testing of wells in a variety of reservoir shapes was made by Matthews, Brons and Hazebroek. Application of their results to the general problem of fluid flow from odd reservoir shapes is demonstrated in this paper. Results can also be used to generate Miller-Dyes-Hutchinson type pressure build-up curve for a variety of reservoir shapes, or to produce dimensionless pressure-drop data from Miller-Dyes-Hutchinson type data. Other applications include generation of flow equations for steady-state injection in developed well patterns, and heat conduction shape factors for circular sources and sinks in bounded shapes.

Introduction
Transient flow of a slightly compressible fluid from horizontal isotropic reservoirs of constant thickness has been thoroughly studied for radial and linear systems. Flow in other reservoir geometries [e.g., square, rectangular, triangular, etc.] has been considered thoroughly in connection with pressure build-up but only sporadically for depletion type of, flow. Although it is not often necessary to consider production from oddly shaped reservoirs, there are cases where such information is useful. It is the purpose of this paper to organize available information in the literature on flow from oddly shaped reservoirs, to develop pertinent relationships and to demonstrate the utility of the information.

THEORY
The laminar flow of a slightly compressible fluid in a radial, horizontal, isotropic reservoir under the, condition of small pressure gradients in the reservoir may be described by the diffusivity equation in radial coordinates:
.....(1)