Width of mineral filling vein was precisely measured for veins in granitic rocks, that were observed on draft wall of the Kamaishi Mine (250 m Level) and in boring cores from geothermal wells at Hijiori HDR test site (HDR-3 well). An exponential relationship between rescale range and bandwidth was demonstrated, using position-aperture data, where the rescale range was defined as Rt (variation in vein width, for a given bandwidth, T) divided by St (standard deviation within the bandwidth). For fractal analysis, Rt/St can be described as a power function, such as Rt/St∝(T/L)H, where H is the Hurst index and L is trace length of the vein. The Rt/St ratio for hydrothermal veins in granitic rock typically indicates strong fractal properties, with H values for veins at Kamaishi being 0.29, while hydrothermal veins in cores at Hijiori have H values of 0.20. Based on those characteristics, a fractal fracture model has been proposed. The Hurst index was used as the fractal dimension to infer the numerical aperture. Permeability, flow rate and effective surface area of a fractal single fracture were examined at conditions given by the Hurst indexes. Calculated results show that entire flow rate and permeability were evaluated by using the flat parallel fracture model, however, effective surface area of fracture was larger than for the flat parallel fracture, depending on the minimum grid size. The fractal fracture model, based on the power function described by the Hurst index, is a useful method to evaluate flow direction, surface condition, chemical and hydraulic properties of open fractures in rock and formation.
An analytical modeling approach based on the cylindrical source function for vertical U-tube ground heat exchangers was applied for the evaluation of operation histories of a geothermal heat pump system constructed in Hirosaki City. The calculation result of the analytical modeling well reproduced the heat exchange behavior in the ground heat exchanger. The vertical effective thermal conductivity profiles of formation also showed a good correlation with the general trend of geological and groundwater settings in Hirosaki City. Consequently, the analytical modeling based on the cylindrical source function is considered to be an effective choice for the interpretation of long-term performances of geothermal heat pump systems located in regions with ground-water flows.