A naturally fractured reservoir is characterized as a system of matrix blocks with each matrix block surrounded by fractures. The fluid drains from the matrix block into the fracture system which is interconnected and leads to the well. Warren and Root(1) introduced a mathematical model for this dual porosity matrix-fracture behaviour.
Their model has been widely used for many types of reservoirs, including tight gas and coalbed methane reservoirs. A key part of their model is a geometrical parameter (shape factor) which controls the drainage rate from the matrix to the fractures. Although Warren and Root gave formulas for calculating shape factors, many other authors have presented alternate formulas, leading to considerable confusion.
In addition to the size and shape of a matrix element, two cases are considered by the authors: constant drainage rate from a matrix block and constant pressure in the adjacent fractures.
The current work confirmed the correct formulas for shape factors by using numerical simulation for the various cases. It was found that some of the most popular formulas do not seem to be correct. A summary of the correct shape factor formulas is presented.