A double porosity model for heat and mass transfer analysis in fractured media was implemented in order to assess the heat recovery rate from a hot fractured formation by injecting cold water. Two different types of fractured media were considered; one is a rock formation with a single major fracture, the other a fracture network consisting of several major fractures. Proper nondimensionalization of the governing equations reveals 6 dimensionless parameters, K, φ, λ, σ, h and Pe which are respectively the permeability, porosity, thermal conductivity ratio, thermal capacity ratio, heat transfer coefficient in space and the injected flow rate. Amongst these it is the dimensionless heat transfer coefficient h that is the most characteristic in this particular model and the most important for determining the heat recovery rate. Due to the large number of parameters in the system, φ, λ and σ were fixed in the present study, whilst K, h and Pe were varied in order to examine the effects on the thermal output and the spatial temperature distribution in the hot formation. In the present parametrrc range of investigation it is found that the heat transfer coefficient per unit volume h and the permeability distribution K are the most influential in determining the heat flow in the fractured formation.
In rock masses, discontinuities of faults, joints, etc. exist and exert large influences on the mechanical property of rock masses. In the coupled problems of heat transfer, seepage flow and stress in discontinuous rock masses, analysis was made on the stress balance using the modified virtual displacement method and on the mass conservation and energy conservation laws using the integrated finite difference method. The analytic method makes possible the analysis using arbitrary polygonal elements via the Voronoi division and also the coupled analysis considering the openings and slides of rock mass joints. In this paper we describes the formulation with the stress balance, shear failure, tensile fracture, and the change of stiffness, and reports the simulation results of the elastic failure analysis and 3D analysis with a triaxial stress test.
This paper describes characteristics of subsurface fracture extension examining acoustic emission (AE) event sequences detected during hydraulic fracturing at Ogachi Hot Dry Rock geothermal fields in Akita Prefecture, Japan. We detected two types of AE signals: i.e., P-wave-dominant high frequency signals (Type I) and low frequency signals with both P-and S-waves (Type II). Impulse series which represented the AE onsets were analyzed to characterize the time intervals of their occurrences. Power spectra of the impulse series for the high frequency AE sequences were flat, which signifies that the high frequency AE events occurred independently of each other. On the other hand, the power spectra of the low frequency AE sequences could be represented in the low frequency range below 0.007 Hz by S(f) ∝f-n. This power law index n varied during the hydraulic fracturing experiment. Moreover, periodic intervals, about 0.02 Hz, whose intensity varied in relation to the water injection, were found. The subsurface fracture extension process during the hydraulic fracturing was studied relating the results of the AE sequences analysis to the other AE properties: AE activity and AE source location. This analysis indicates that the subsurface fracture extended in three stages during the hydraulic fracturing experiment.
The authors have investigated effects of distribution of saturation in a geothermal reservoir on relative permeabilities. Because the grid cells in a numerical calculation of reservoir simulation are not so small that the distributions of saturation in the cells are not assumed to be uniform. This paper proposes a model of saturation distribution, using a probability density function. The model, based on the Bernoulli trials, gives the following relation between the average value of the relative permeability for water phase, krwa and the arithmetical mean of the normalized water saturation, Sw*a : krwa= Sw*a, m (1≤m≤4). Also, the relative permeability of the steam phase, krga is as follows: krga=1-2Sw*a+2Sw*a(2m+1)/3-Sw*am(1≤m≤4), where m is an index representing the non-uniformity of saturation. When m equals 4, krwa and krga each agree with the, so-called, Corey's equations. Then, the saturation is assumed to be distributed uniformly in the grid cell. On the other hand, when m=1, the flow of each phase is isolated one another . The proposed correlation equations are investigated through some experimental data already reported by the authors. The equations agree quite well with the experimental results of mass transfer in water-steam flow with boiling in a porous medium.