The purpose of this study is to develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture. Detailed analysis of unsteady-state pressure behavior of fully penetrating inclined fracture in an infinite slab reservoir was provided. Both uniform flux and infinite conductivity models were considered. The study has shown that inclined fracture pressure data exhibit similar flow regimes as for vertical fracture counterpart. Those flow regimes are linear and pseudo-radial flow for both uniform flux and infinite conductivity models. However, for infinite conductivity model, a bi-radial flow regime is also observed. In the case of high formation thickness to fracture half length ratio and high angle of inclination, both uniform flux and infinite conductivity inclined fracture model exhibit an additional flow regime called early radial flow. Both bi-radial flow and early radial flow regimes for inclined hydraulic fracture have not been mentioned in the literature before.
A step by step procedure based on Tiab's Direct Synthesis (TDS) was developed in this study. Fracture properties such as half fracture length, inclination angle, formation permeability and pseudo-skin factor can be obtained from the direct interpretation of the log-log plot of pressure and pressure derivative without the need of any type curve matching. Several unique features of the pressure and pressure derivative plots of both uniform flux and infinite conductivity inclined fracture models were identified including the points of intersection of straight lines for different flow regimes. These points can be used to verify the results or to calculate unknown parameters. Equations associated with these features were derived and their usefulness was demonstrated. Numerical examples with both pressure build-up and drawdown data were also demonstrated for this procedure.