Algorithmic Simulation of Flow in Rock Fractures

Abstract

The two sides of a rock fracture are geometrically often very different. The difference or heterogeneity can be captured using aperture. This is also practically very significant because locally low or zero aperture in a rock fracture impedes flow. The aperture measurements of each of five paired rock blocks are discretely digitized (0–9). Each resulting weakly continuous two-dimensional matrix is then traversed by the nflow (new-flow) flow algorithm, once from each entry at one end to the other end. The paths are either incomplete and end surrounded by zeros or are completed at the other (exit) end. The numerical digit distribution is held constant from block to block. Fracture through-flow is defined as the average percentage of complete paths from one end to the other for that block. Fracture roughness is negatively correlated with fracture through-flow (r ~ −0.893). A rough fracture will only allow little flow compared with a smooth fracture with a smoother aperture distribution. Channeling of complete paths toward exit points is discussed for all blocks. Channeling is not related to roughness. A long complete sample path in a very rough fracture is shown. The distribution of numbers of complete paths is also investigated.