Constraining fracture permeability by characterizing fracture surface roughness
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Open and connected fractures, where present, control fluid flow and dominate solute transport. Flow through fractures has major implications for water resource management, underground waste repositories, contaminant remediation, and hydrocarbon exploitation. Complex fracture morphology makes it difficult to quantify and predict flow and transport accurately. The difficulty in usefully describing the complex morphology of a real fracture from a small 3-D volume or 2-D profile sample remains unresolved. Furthermore, even when complex fracture morphology is measured across three-dimensions, accurate prediction of discharge remains difficult. High resolution x-ray computed tomography (HXRCT) data collected for over 20 rock surfaces and fractures provide a useful dataset to study fracture morphology across scales of several orders of magnitude. Samples include fractured rock of varying lithology, including sandstone, volcanic tuffs and crystalline igneous and metamorphic rocks. Results suggest that the influence of grain size on surface roughness is not readily apparent due to other competing variables such as mechanics, skins and coatings, and weathering and erosion. Flow tests of HXRCT-scanned fractures provide real discharge data allowing the hydraulic aperture to be directly measured. Scale-invariant descriptions of surface roughness can produce constrained estimates of aperture variability and possibly yield better predictions of fluid flow through fractures. Often, a distinction is not made between the apparent and true fracture apertures for rough fractures measured on a 2-D topographic grid. I compare a variety of local aperture measurements, including the apparent aperture, two-dimensional circular tangential aperture, and three-dimensional spherical tangential aperture. The mechanical aperture, the arithmetic mean of the apparent local aperture, is always the largest aperture. The other aperture metrics vary in their ranking, but remain similar. Results suggest that it may not be necessary to differentiate between the apparent and true apertures. Rock fracture aperture is the predominant control on permeability, and surface roughness controls fracture aperture. A variety of surface roughness characterizations using statistical and fractal methods are compared. A combination of the root-mean-square roughness and the surface-to-footprint ratio are found to be the most useful descriptors of rock fracture roughness. Mated fracture surfaces are observed to have nearly identical characterizations of fracture surface roughness, suggesting that rock fractures can be sampled by using only one surface, resulting in a significantly easier sampling requirement. For mated fractures that have at least one point in contact, a maximum potential aperture can be constrained by reflecting and translating a single surface. The maximized aperture has a nearly perfect correlation with the RMS roughness of the surface. These results may allow better predictions of fracture permeability thereby providing a better understanding of subsurface fracture flow for applications to contaminant remediation and water and hydrocarbon management. Further research must address upscaling fracture morphology from hand samples to outcrops and characterizing entire fracture networks from samples of single fractures.