The behavior of naturally fractured reservoirs including fluid flow in matrix blocks

An alternative analytical solution to the system of equations for fluid flow through a double-porosity medium with a boundary condition of an equipotential surface is given in this paper. The problem is reduced to solving an integral equation. The solution is straight-forward, and involves only ordinary Bessel functions. Numerical results show that D, the ratio of matrix system permeability to fracture system permeability, has a strong effect on the two semilog straight lines characteristic of the pressure response in a double-porosity medium. As D increases from zero (the Warren-Root model) to one, the first semilog straight line moves closer to the second. This is similar to the effect of increasing ω, the ratio of storage capacity of the fracture system to total storage capacity, in the Warren-Root model which neglects the flow within matrix blocks.