Flow channeling in a single fracture as a two‐dimensional strongly heterogeneous permeable medium

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Abstract
The void space of a rock fracture is conceptualized as a two‐dimensional heterogeneous system with variable apertures as a function of position in the fracture plane. The apertures are generated using geostatistical methods. Fluid flow is simulated with constant head boundary conditions on two opposite sides of the two‐dimensional flow region, with closed boundaries on the remaining two sides. The results show that the majority of flow tends to coalesce into certain preferred flow paths (channels) which offer the least resistance. Tracer transport is then simulated using a particle tracking method. The apertures along the paths taken by the tracer particles are found to obey a distribution different from that of all the apertures in the fracture. They obey a distribution with a larger mean and a smaller standard deviation. The shift in the distribution parameters increases with increasing values of variance for the apertures in the two‐dimensional fracture. Provided that the correlation length is no greater than one fifth of the scale of measurement, the aperture density distributions of tracer particle paths remain similar for flow in two orthogonal directions, even with anisotropy ratio of spatial correlation up to 5. These results may be applicable in general to flow and transport through a two‐dimensional strongly heterogeneous porous medium with a broad permeability distribution, where the dispersion of the system may be related to the parameters of the permeability distribution along preferred flow channels.