Hydraulic fracturing is an important well stimulation technique that has been widely used in the oil and gas industry. Most of the pressure transient analysis techniques to analyze pressure responses of fractured wells are based on the assumption that the fracture is either vertical or horizontal. However, a hydraulic fracture could be inclined with a non-zero angle with respect to the vertical direction. Field studies have shown that most hydraulic fractures are never perfectly vertical. Thus, for an inclined hydraulic fracture, the vertical orientation assumption may lead to erroneous results in well test analysis especially when the inclination angle is significant. However, there are very few studies concerning pressure transient analysis of inclined hydraulic fracture and there is no applicable well test analysis procedure available for inclined fractures. For this reason, it is important to develop well test analysis procedures for this type of fracture.

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 type curve matching technique was developed in this study using both pressure and pressure derivative curves. This type curve matching procedures can be used to obtain the following parameters: half fracture length, inclination angle, formation permeability and the pseudo-skin factor. The results should be verified with other pressure plots such as semi-log plot of ?P vs. t and ?P vs. t1/2 plot. A set of type curves with associated data was also provided for uniform flux and infinite conductivity inclined fracture models. Detailed explanations, tables, figures and numerical examples are included in this paper.

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