Knowledge of the orientation and spatial distribution of fractures in rocks is important for predicting the flow of fluids. Masihi et al. (2007) developed a new method of modeling these distributions beginning with theoretical results from the physics of fracturing. We implemented and extended this modeling technique to generate models that better incorporate field observations. The method starts with an energy function based on the pair-wise spatial correlation of fractures that also serves as an objective function for a simulated annealing algorithm (SA) that generates realizations of correlated fracture networks. We improved this technique by incorporating periodic boundary conditions, including criteria to limit maximum range of the pair-wise calculations, and by suggesting methods to constrain models to match field data. For most subsurface rocks (with Poisson ratio ? = 0.25), this method generates orthogonal sets of fractures, a pattern that is commonly observed during basin formation or subsidence. This new method is compared with conventional discrete fracture network (DFN) modeling by computing the fractal dimension of the networks. We also examine the implications for seismic reservoir characterization by computing effective seismic velocities and the resulting synthetic seismograms. The new approach can be considered better than DFN as DFN generates realizations based on only statistical distributions, without any knowledge of physics of fracturing.
The quantification of the spatial concentrations and orientations of fractures in low permeability rocks is essential since they control the nature of fluid flow in those rocks. Generally, these spatially distributed fractures form complex networks that can either act as fluid carriers or barriers depending upon fracture connectivity. Therefore, understanding the connectivity pattern, and areas of high and low fracture density zones, is essential to characterize flow inside the earth. To date much research has considered the effect of geometrical properties of fractures such as length (Berkowitz, 1995; Bour and Davy, 1997) and orientation (Balberg et al., 1984; Masihi et al., 2005) on the scaling laws of the connectivity of fractures. However, fewer studies have examined the spatial correlation of quantities such as length, orientation and position of fractures, though some of the studies examined the long-range density correlations using fractal geometry (Berkowitz et al., 2000; Darcel et al., 2003). These spatial correlation parameters are important as they affect the connectivity of fractures.
A common approach used to model fractures is the discrete fracture network (DFN) method. Generally DFN modeling specifies the statistical distributions of several parameters such as fracture density, orientation, location, size, etc. to generate several realizations for production estimation and reservoir planning (Al-Harbi et al., 2004). Here, we implement and extend a new model of the spatial distribution of fractures based on the physics of the fracturing process (Masihi et al., 2007; see also Shekhar, 2008) which is not explicitly considered in DFN modeling. The idea for modeling is based on the assumption that the elastic free energy associated with the fracture density follows the Boltzmann distribution.