In a presentation to the First Stanford Geothermal Workshop last year, we outlined the basic philosophy, assumptions and general approach to finding an optimal rate of energy extraction from a hot water geothermal field. In this paper, we present the explicit relationships governing the physical processes and economic factors of our model, as well as the modifications to the model that have been necessary to accommodate the more specific articulation of these relationships. The conceptual modifi-cations of the earlier model are subtle, but of great importance in making our work more useful for geothermal resource management.

This study is concerned with the optimal management, and in particular the optimal timing of energy extraction from a geothermal reservoir. For the conclusions of this optimization problem to be meaningful, the analysis must be carried out in the context of a particular hydro-thermal model. Furthermore, some assumption regarding the future value of geothermal energy must be made. Accordingly, we adopt the hydro-thermal model developed by Gringarten and Sauty ( l ), and assume that the value of geothermal energy is known as a function of time and the quantity of the extracted energy. We note however that our optimization model can be modified to accommodate other hydrothermal models such as that of Kasameyer and Schroeder, which combines fractured and porous media flow ( 2 ). In view of the increase in the attractive ness of geothermal energy for space heating ( 3, 6 ), we also assume that the extracted energy is used, for generation of steam to be used forth is purpose. However, we are well aware that the hot brine, depending on the parameters of a particular field, may be more economically utilized for some other purpose (e.g., electric power generation, direct utilization of hot water for domestic and industrial use, mineral extraction and desalination). In this paper, we restrict our attention to the case where the decision has already been made to use the geothermal energy for space heating.

The quantity of the extracted energy is a function of both the rate at which hot brine is extracted and the degree to which it is cooled before reinjection in the reservoir. Hence, we seek an extraction rate, a reinjection temperature and an economic life that maximize the net discounted value of the extracted energy.

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