An Analysis on Thermodynamic Properties of Steam in Subsurface Porous-Permeable Horizons of Hydrothermal Systems

Abstract

The present model analyses thermodynamic properties of steam which separates from a water body in the proximity of the top of reservoir in the subsurface of a hydrothermal system. Starting with the continuity equation, DarcyÅfs law and the fluid-rock energy equation in the one-dimensional case, we define two coupled non-linear parabolic equations expressed in terms of fluid-rock temperature T(z) and fluid density Éœ f (z). The steady state case is examined and it is reduced to a third order non-linear ordinary differential equation in y(z)= Éœ f (z)T(z). This equation is then solved numerically using an implicit scheme. The mathematical solutions exhibit stable or unstable behaviour of the thermo-dynamic properties of steam depending on the initial conditions which may occur at depth in the vicinity of the top of the reservoir and in particular on the value of the parameter Éø = Éœ f Å› z (Éœ f T )Å? Éœ f Å› z P R, where R is the gas constant and P the added pore fluid pressure over the hydrostatic value. A theoretical tool is thus supplied, for instance for the management of dry steam producing geothermal systems.