Supercritical Thermodynamics of the Rock / Fluid Geothermal System

Abstract

The study of supercritical water is important in geothermal science and in many industrial applications, such as supercritical steam turbines, high pressure devices and supercritical cycles. The temperature gradient between the core and the Earth’s surface results from a continuous flow of natural heat, embracing all kind of thermal resources that can be classified in terms of their depth, from shallow depths (102 m), to medium depths (103 m), and to even deeper depths (104 m), where the immense temperatures of molten rocks are reached. The rock and fluids in very deep reservoirs are at supercritical thermodynamic conditions, at more than 374°C and pressures larger than 221 bars, having higher fluid density, larger volumetric enthalpy and more heat available. Any geothermal system reaching enough pressure and temperature at some depth can attain supercritical conditions. These systems could provide at least, twenty times as much power, per unit fluid volume, as the normal geothermal steam used today. This paper provides a computational description of water thermodynamics at supercritical conditions and the power it represents. Supercritical water properties are defined in terms of the Helmholtz potential or free energy, and calculated as functions of density or of pressure, and temperature. The shown supercritical properties are internal energy, enthalpy, entropy, specific isochoric heat, specific isobaric heat, compressibility, bulk modulus, Joule coefficient, speed of sound, thermal expansivity and thermal diffusivity. All of them are presented in graphical form. Another aim of this paper is to introduce some rock poroelastic coefficients measured at temperatures between 25°C and 700°C. The rock parameters were measured experimentally in a rock’s laboratory.