Roughness efects on fluid flow and transport: Implications for predictive modeling

Fractures dominate fluid flow and transport of solutes when they are open and connected. The prediction of flow through fractured media has implications for development of water resources, petroleum reservoir exploitation, contamination and remediation assessment, and site evaluation for waste repositories. Assessing the impact of surface roughness on fluid flow and solute transport through fractured media from samples on the order of 100 cm² assumes the existence of a relationship between fracture morphology and discharge that is scale invariant or at least smoothly transformable. Although some studies assume that the length scale at which surface roughness significantly contributes to the discharge through a fracture falls within the size of a typical hand sample, there is a dearth of empirical data supporting an extension of the relationships found at small scales to larger samples. Furthermore, an appropriate metric to describe a fracture volume accurately must be chosen. We compile data from physical flow tests and numerical modeling of two discrete natural fractures of different scales in rhyolitc tuff. The University of Texas HRXCT facility provided computed tomography representations of the fractures that allow analysis of surface roughness and aperture statistics at 0.25mm grid resolution, which form the basis for transmissivity field inputs to numerical models. We illustrate small scale roughness effects on flow and transport with a 2D solution of Navier-Stokes equations on one profile of aperture data. Recognizing the existence of channeling at the hand sample scale (10s of cm), we show a generally smoother surface within channels defined by particle tracking and volumetric budget versus the surface as a whole. We show that although a small (10cm²) representative surface can describe roughness, aperture fields are not so well behaved. We compare physical flow test results, modeled flow, and analytical solutions of the cubic law using various methods of assigning a meaningful aperture to illustrate the challenges of accurate modeling of fracture flow without a priori flow information. While a geometric mean aperture of the entire aperture field closely approximates the hydraulic aperture, an arbitrary profile mean aperture has little utility for predictive purposes.