Modeling the dynamics of a geothermal reservoir fed by gravity driven flow through overstanding saturated rocks

We formulate a mathematical model for a geothermal basin with an idealized geometry characterized by: (1) radial symmetry around an extracting well (or a cluster of wells), (2) a relatively thin horizontal fractured layer lying underneath a low permeability, low porosity rock layer, saturated with water. Vaporization is allowed only at the boundary of the extracting well (or well cluster). The model is based on the assumption that the flow from the reservoir to the well is fed by a gravity driven flow through the overstanding rocks. Despite the various simplifying assumptions, the resulting mathematical problem is considerably difficult also because we consider the effect of thermal expansion and thermal variation of viscosity. Though there is no evidence that the assumed configuration of the basin approaches the structure of a known geothermal field, the results obtained match with surprising accuracy the data of a specific field in the Mt. Amiata area (data kindly provided by ENEL Green Power through Tuscany Region).