Fractal model and hydraulic properties of hydrothermal veins in granite

摘要

Veins of laumontite, stilbite and quartz +/- calcite occur in granite, in the draft wall of Kamaishi Mine (Japan). Vein widths were precisely measured, and structural characteristics assessed, on the basis of a 5x5 m~2 fracture map. Surface images of bored core from geothermal wells at Hijiori (Japan) were visualized as a plane digital dot image, using a newly developed core scanning apparatus. An exponential relationship between rescale range and bandwidth is demonstrated, using position-aperture data, where the rescale range is defined as R, (variation in vein width, for a given bandwidth, T) / S_t (standard deviation within the bandwidth). For fractal analysis, R_t/S_t can be described as a power function, such as R_t/S_t ∝ T~H, where H is the Hurst index. The R_t/S_t ratio for hydrothermal veins in granite typically indicates strong fractal properties, with H values for veins at Kamaishi being 0.29, whilst hydrothermal veins in cores at Hijiori have H values of 0.20. Based on these characteristics, a fractal fracture model has been proposed. The Hurst index was used as the fractal dimension to infer the numerical aperture. Permeability, and effective surface area for heat exchange of a fractal single fracture were examined at conditions appropriate to the Hurst indexes. Channeling and isotropic fluid flow was obtained through the fractal fracture model. Calculated results show that permeability depends on flow direction, and effective area of a natural fracture is 10%-50% larger than for a flat parallel fracture. The fractal fracture model, based on the power function described by the Hurst index, is a useful method to evaluate fluid flow through natural fractures, and is applicable to understanding flow direction, surface condition of natural fractures, and hydraulic properties in geothermal and/or oil reservoirs.