Analytical solutions that include real gas pseudo pressures are presented for pressure drawdown and buildup analysis of horizontal wells in anisotropic reservoirs with tectonic, regional or contractional natural fractures. The reservoir might be limited by parallel sealed boundaries. The solutions have been obtained with the use of Fourier and Laplace transforms. Wellbore storage has been handled using a finite difference scheme of the convolution integral.
These solutions have led to the identification of the following flow periods:
Wellbore storage which might mask many of the subsequent flow periods.
A first radial flow period at early times from the natural fractures into the horizontal well. This occurs in a vertical plane.
A transition period due to flow from the matrix into the natural fractures.
A second radial flow period, still in a vertical plane, which starts when pressures in matrix and fractures reach an equilibrium. This pressure equilibrium can also be attained at a later flow period in which case the second radial period would not be present.
A linear flow period when the pressure transient reaches the upper and lower boundaries of the reservoir.
A pseudo radial flow period towards the wellbore in a horizontal plane.
A linear flow period when the pressure transient reaches the outer parallel boundaries.
It is concluded that recognition of these flow periods can lead to calculation of pi or p*, permeabilities in the x, y and z directions, storativity ratio omega, average distance between natural fractures, fracture porosity, fracture aperture, skin, and pseudo skin due to vertical and horizontal partial penetration. Calculations are illustrated with an example.