Pressure-Transient Analysis of a Well With an Inclined Hydraulic Fracture

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 nonzero angle with respect to the vertical direction. Field studies have shown that most hydraulic fractures are not 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 fractures, and there is no applicable well-test-analysis procedure available for inclined fractures. The purpose of this study is to develop a technique, on the basis of the pressure-derivative concept, for interpreting pressure-transient tests in wells with an inclined hydraulic fracture. Detailed analysis of unsteady-state pressure behavior of a 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 flow regimes similar to those for vertical fractures. Those flow regimes are linear and pseudoradial flow for both uniform-flux and infinite-conductivity models. However, for the infinite-conductivity model, a biradial- (or elliptical) flow regime is also observed. In the case of a high formation-thickness/fracture-half-length ratio and high angle of inclination, both uniform-flux and infinite-conductivity inclined-fracture models exhibit an additional flow regime, called early radial (ER) flow in this paper. This ER-flow regime for an inclined hydraulic fracture has 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 procedure can be used to obtain the following parameters: fracture half-length, inclination angle, formation permeability, and the pseudoskin factor. The results should be verified with other pressure plots such as the semilog plot of Delta p vs. t and the Delta p-vs.-t(1/2) 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 a numerical example are included in this paper.