This paper presents analytic solutions of the pressure transient behavior of a well intersected by a finite-conductivity fracture in an infinite-acting, or in cylindrically or rectangularly bounded finite reservoirs. These solutions include the practical effects of reservoir permeability anisotropy and dual porosity behavior. Those solutions are analytic, and thus do not require discretization in space.
The analytical solutions of the finite-conductivity fracture transient behavior presented in this paper eliminate the numerical difficulties associated with other mathematically rigorous finite-conductivity fracture solutions that have been reported in the literature. Both the pressure and rats transient responses can be accurately evaluated using the finite conductivity fracture solutions presented in this paper. This is especially important for low-conductivity fractures, for which the pressure and rate transient behavior is often difficult to evaluate accurately using the solutions available in the literature.