FLOW IN ROCK FRACTURES - THE LOCAL CUBIC LAW ASSUMPTION REEXAMINED

We investigate the validity of applying the ''local cubic law'' (LCL) to flow in a fracture bounded by impermeable rock surfaces. A two-dime nsional order-of-magnitude analysis of the Navier-Stokes equations yie lds three conditions for the applicability of LCL flow, as a leading-o rder approximation in a local fracture segment with parallel or nonpar allel walls. These conditions demonstrate that the ''cubic law'' apert ure should not be measured on a point-by-point basis but rather as an average over a certain length. Extending to the third dimension, in ad dition to defining apertures over segment lengths, we find that the ge ometry of the contact regions influences flow paths more significantly than might be expected from consideration of only the nominal area fr action of these contacts. Moreover, this latter effect is enhanced by the presence of non-LCL regions around these contacts. While contact r atios of 0.1-0.2 are usually assumed to have a negligible effect, our calculations suggest that contact ratios as low as 0.03-0.05 can be si gnificant. Analysis of computer-generated fractures with self-affine w alls demonstrates a nonlinear increase in contact area and a faster-th an-cubic decrease in the overall hydraulic conductivity, with decreasi ng fracture aperture; these results are in accordance with existing ex perimental data on flow in fractures. Finally, our analysis of fractur es with self-affine walls indicates that the aperture distribution is not lognormal or gamma as is frequently assumed but rather truncated-n ormal initially and increasingly skewed with fracture closure.