Does Anisotropy in Fracture Clustering Translate into Anisotropy in Intrinsic Permeability?

Lacunarity is a parameter that can quantify the clustering of spatial patterns. Two of the authors have previously used it to differentiate between a set of 7 nested natural fracture maps with the same fractal dimension, but different visual appearances. In the present study, we investigate the use of lacunarity for determining if differences in clustering of fractures along the NS and EW directions of the same maps control the differences in steady-state 2-dimensional Darcy flow along those directions. Directional lacunarity was found by computing the average lacunarity values of scanlines laid every 10 pixels in these respective directions. PFLOTRAN, an open-source, massively parallel simulator for reactive flows in geologic porous media, was used to compute steady-state Darcy flows. Structured computational grids were constructed from rasterized fracture maps. Each pixel of a map was considered a cell which was assigned porosity and permeability values based on whether it represented a fracture or matrix such that a 1042 x 1042 pixel map was modeled as a domain comprising 1042 x 1042 x 1 cells. In order to determine the effective intrinsic permeability in the EW direction, a pressure gradient was set up in that direction, while the NS edges were considered no-flow boundaries. The flow system was then rotated to give the NS values. The simulations were run using 120 processor cores on Jaguar, a Cray XT5 system housed at the Oak Ridge National Laboratory. The results from these flow simulations and lacunarity analyses indicate a relationship between anisotropy in clustering of fractures in a network and anisotropy in the intrinsic permeability values.

AAPG Search and Discovery Article #90142 © 2012 AAPG Annual Convention and Exhibition, April 22-25, 2012, Long Beach, California