This paper proposes a method for estimating the surface area of a deformable fracture induced artificially in a hot dry rock. The method is based on a concept of a model consisting of some parallel plannar plates and uses an empirical permeability form including the fracture surface roughness. The fracture surface area is given in a simplified form by A=n·A0, where A is the fracture surface area, A0 the surface area of the planar plate, and n the number of the plate. n is determined by rounding off the value of t2/12K to a whole number, where t is the average fracture aperture and K the fracture permeability. Fluid flow, energy and mass equations which involve the effect of A are solved numerically by the finite difference method. The results show that as A increases the dissolution and precipitation rates of quartz increase and that the computational error for accumulative silica production rate due to round off the value of t2/12K is about 12% for 800 days after water injection.
Laboratory experiments reacting granite with pure water by fluidized tube reactor with temperature gradient have been carried out, in order to simulate water/rock interactions during heat extraction from a Hot Dry Rock (HDR) geothermal system. The tube reactor (1000mm long) was packed with cylindrical granite samples. The inlet temperature was 220°C and the maximum temperature set to be 350°C at the 65 cm downstream from the inlet. The experiments lasted for 20 days in maximum at about 20 MPa and a constant flow rate (0.29 cm/min). Chemical composition of the output solutions was monitored during the experiments. Si concentration was almost unchanged through the experiments (315 ppm on the average). Na, K and Al concentrations became stable after 168 hours at about 6.5, 2.9 and 4.3 ppm respectively. No considerable change of pH was observed (ca. 7.4).The reacted rock samples were divided into four zones from their weight loss/gain behavior. Zone I was located 2 to 18 cm downstream from the inlet and the reaction temperature ranges from 220°C to 275°C, zone II 18-58cm (275-345°C), and zone III 58-72 cm (345-350°C) and zone IV 72-96 cm (350-345°C). The changes of the weight loss/gain of each zone with time were approximated with straight lines. The dissolution of granite was dominant in zones I, II, IV and the weight gain was observed in zone III as a result of the precipitation of new secondary minerals. The apparent dissolution rate was maximum in zone II that was 1.7 times as large as that in zone I and 2.9 times of that in zone IV. The results of the laboratory experiments about water/granite interation processes with a temperature gradient from 220°C to 350°C could be summarized as follows: The rock is dissolved in the injection fluid with increasing temperature, the dissolution rate of rock reaches the maximum in 275°C-345°C, and the precipitation takes place suddenly at 350°C.
A general understanding of groundwater flow due to potential in a pseudo-steady state is described by applying an analytical approach and a numerical method (FEM). The analytical approach assumes the horizontal top surface for the analysis-domain and gives the potential of topography on the surface. In the numerical approach, the top surface of the analysis-domain coincides with the topography. Using these approaches, this paper investigates effects of topography and dip on the motion of ground-water, and the formation of a drainage boundary in the domain. The results are as follows: (1) The general analytical solution of the stream line is derived for the analytical approach. (2) Formations of the drainage boundary depend not only on the topography, but also on the dip. (3) When the topography is approximated by the sine curve with the slope, whose angel is θ, the analytical approach is applicable to understanding whether the regional flow exists or not, in the tangent of θ smaller than 0.1 (or the dimensionless amplitude smaller than around 0.2).
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