This paper describes a statistical methodology to estimate dominant fracture orientation and dispersion from seismically-calculated 3D structural attributes. The dispersion parameter, the circular variance, can be easily associated with the Fisher coefficient, a key parameter in the probability density function used in discrete fracture network modeling to stochastically generate fracture orientations. We show examples of applications to seismic constrained DFN modeling and perform flow simulations on fractured models built using different dispersion parameter models to discuss possible implications for drainage of naturally fractured, unconventional reservoirs.
The design of horizontal wells and hydraulic fracture stimulation requires a detailed understanding of the variations in relative orientations of natural fractures and local stress field across the reservoir. Structural attributes extracted from poststack 3D seismic data such as curvature, semblance or dip, have been used in the estimation of preferential orientation in the subsurface, in particular orientation of natural fractures. Attributes derived from the analysis of prestack amplitude variations vs. offset and azimuth (AVOZ) have also been used for this purpose (Rüger, 2002). After careful calibration with log derived fracture orientations, orientations derived from seismic data may be used as a proxy for orientations of the natural fractures. However, these orientations may be misleading or difficult to interpret when multiple fracture orientations are present.
The model-based nature of AVOZ analyses (which assume either a single set of vertical fractures, two sets of orthogonal vertical fractures or any of the above with a tilted axis of symmetry) may yield uncertain results when the assumptions of the fracture model are not met. In many geological settings, several non-orthogonal fracture sets occur with different dips and azimuths that overlap in the same volume of rock. Approaches that use poststack data and overcome the model-based limitations of using prestack data typically yield a single orientation per sample with no indication of how to interpret it when multiple orientations are present. Chopra et al. (2009), however, do go beyond single-orientation answers. The authors generate what they refer to as " 3D rose diagrams" volumes after analyzing orientations of the azimuth of minimum curvature for each horizontal time slice. Even though their rose diagrams provide a visual idea of the dispersion in fracture orientation, no quantitative estimates of this dispersion are generated. Furthermore, rose diagrams based on 2D time slices fall short in capturing the real 3D nature of the fracture orientation that requires two parameters (dip and dip-azimuth) instead of only one used to generate rose diagrams (dip-azimuth).