We use two- and three-dimensional, fractal and non-fractal networks of interconnected fractures as models of a fractured geothermal field, and study two-phase flow and heat-transfer in such a system. We show that a fractal fracture network is much more efficient than a non-fractal network in heat recovery from a hot matrix. Moreover, the efficiency of a geothermal reservoir is very sensitive to its structure and the location of the producing well, and there may be an optimum configuration of the producing and injection wells for extracting hat and vapor from the reservoir.
Simultaneous flow of a liquid and its vapor in porous media occurs in many processes of practical interest which are driven by temperature gradients. Some practical applications include the problem of extraction of heat from geothermal reservoirs, thermal oil recover and nuclear waste disposal. Laboratory investigations have concentrated on mainly porous heat pipes, boiling and drying. A comprehensive description of Bow with vapor-liquid equilibria in porous media is not presently available, and the conventional approach has been based on the assumption that the vapor and liquid phases both obey Darcy's law with saturation-dependent relative permeabilities. Steady-state vapor-liquid Bows in porous media have been modelled with such methodology for decades. Recent applications to steam-water counterflow include studies by Martin et al, Schubert and Straus, Barn and Torrance and Udell. The first two papers focused on geothermal applications, in which the authors neglected capillarity but included heat conduction through the solid matrix of the reservoir. By contrast Udell considered heat pipes in which capillarity predominates, but conduction is neglected. In the same context Bau and Torrance presented a simplified analysis, where both conduction and capillarity were neglected. More recently, Satik, Palar and Yortsos presented a unified approach to the same problem where they considered capillarity, heat conduction and Kelvin effects. More interesting, and also more complex, is the problem of two-phase Sow of a vapor and its liquid in a fractured rock. Such rocks are often in the form of a network of interconnected fractures with varying degrees of connectivity. Single- and two-phase flows in fractured rocks have not been studied as extensively as they should be, mainly because of he complex structure of fractured rocks. However, a consistent modelling approach for transient two-phase flow in such media is needed, especially when one considers the importance of such phenomena and modelling approaches to realistic prediction of the production capability, pressure decline and total life-time of geothermal reservoirs, such as The Geysers Field in northern California, or two-phase flow and thermal oil recovery processes in highly fractured reservoirs. While the above studies have been instrumental in the understanding of some aspects of vapor-liquid flow in porous media, important aspects such as the effects of the connectivity and heterogeneity of the fractured media have not been investigated yet. This investigation is the modest goal of this paper. We present here a simple model for simultaneous flow of a liquid and its vapor through a number of different homogeneous ad heterogeneous fractured media with various structures and connectivities. We restrict our attention mainly to applications to geothermal reservoirs, but our methodology is more general and we are currently extending it to other phenomena and processes in fractured media.
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