Million node fracture: size matters?

Abstract

Transmissivity of self-affine fractures was computed numerically as a function of the grid size. One-million-node fractures (1024 × 1024 nodes) with fractal dimensions of 2.2–2.6 were cut into successively smaller fractures (“generations”), and transmissivities computed. The number of fractures in each generation was increased by a factor of 4. Considerable scatter in transmissivity was observed for smaller grid sizes. Average transmissivity of the fractures in the generation decreased with the grid size, without approaching any asymptotic value, which indicates no representative elementary volume (REV). This happened despite the average mean aperture being the same in each generation. The results indicate that it is not possible to estimate the transmissivity of a large fracture by cutting it into smaller fractures, running flow simulations on those and averaging the results. The decrease in transmissivity with the grid size was found to be due to an increase in the flow tortuosity.