Saturated flow in a single fracture: Evaluation of the Reynolds equation in measured aperture fields

Fracture transmissivity and detailed aperture fields are measured in analog fractures specifically designed to evaluate the utility of the Reynolds equation. We employ a light transmission technique with well-defined accuracy (similar to 1% error) to measure aperture fields at high spatial resolution (similar to 0.015 cm). A Hele-Shaw cell is used to confirm our approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two rough-walled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large (similar to 22-47%) to exclude numerical and experimental errors (<2%) as a source. We conclude that the three-dimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. We also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stakes flow. Various formulations for link transmissivity are shown to converge at high resolution (similar to 1/5 the spatial correlation length) in our smoothly varying fracture. At coarser resolutions the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.