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International Heat Transfer Conference 12

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

Mathematical Modeling of Convection Heat Transfer in a Geothermal Reservoir of Fractal Geometry

Sergei Fomin
Fracture Research Institute, Tohoku University, Aoba 01, Aramaki, Aoba-ku, Sendai 980-8579, Japan

Ayumu Shimizu
Fracture Research Institute, Tohoku University, Aoba 01, Aramaki, Aoba-ku, Sendai 980-8579, Japan

Toshiyuki Hashida
Fracture Research Institute, Tohoku University, Aoba 01, Aramaki, Aoba-ku, Sendai 980-8579, Japan

DOI: 10.1615/IHTC12.4700
6 pages

Abstract

Many numerical models have been proposed for simulating the geothermal systems. The numerical model FRACSIM developed by the research group in Tohoku University (Watanabe et al., 1995; Willis-Richards et al., 1996; Shimizu et al., 2000) is proved to be an appropriate approximate model capable to address simultaneously the problems associated with hydraulic stimulation, fluid circulation and heat extraction. The structure of the fractured rock is approximated with the network models of "fractal geometry". The models of fracture networks are generated by distributing fractures randomly in space and adopting the fractal correlation N=Cr-D that incorporates the number of fractures N, fracture characteristic length r, fractal dimension D, and fracture density within the rock mass C. This procedure makes possible to characterize the geothermal reservoirs by parameters measured from the field data. In the present study an improved mathematical model, which accounts for the influence of thermal dispersion on heat flow during the geothermal energy extraction process, is proposed. In the previous studies it was proved both theoretically and experimentally that for the fluid flow in the fractured and porous media with relatively high fluid velocities the values of the effective thermal conductivities in the longitudinal and transverse to the flow directions are directly proportional to the fluid velocity. The comparative numerical analysis based on the 3D model of the fluid flow within the fractured media proves the importance of the thermal dispersion factor for the assessment of the total amount of heat extracted from the reservoir. The results show that ignoring the effect of thermal dispersion, especially at the high flow rates, which are typical for the fractured reservoirs, leads to the underestimation of the computed output temperature up to 20 percent. The latter constitutes a significant fraction of total heat obtained during the reservoir exploitation.

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