Geothermal Reservoir Simulation Using Nonequilibrium Thermodynamics

A phenomenological interpretation of the evolution of a steam/water system is proposed from a nonequilibrium mixture perspective. This type of thermodynamic behavior is structurally stable on the basis of catastrophe theory and therefore offers an unorthodox alternative approach to the simulation of geothermal reservoirs. Use of this approach in a one-dimensional (ID) finite-difference simulator yields results that can be compared with a traditional numerical scheme. Introduction All numerical simulators of geothermal reservoirs depend on an accurate representation of the thermodynamics of the steam/water system. This information is required to render tractable the system of balance equations derived from the physics of flow through porous media. While it is generally recognized that the porous media. While it is generally recognized that the two-phase system is not in thermodynamic equilibrium, equilibrium thermodynamics is universally employed in its description for numerical simulators (see Ref. 1 for a state-of-the-art review of these models). In this paper, we present an alternative view on nonequilibrium thermodynamics. A phenomenological investigation of the proposed approach has been reported by Nguyen at From this new perspective, we constrict a computational scheme that eliminates the difficulties often encountered in the two-phase region. Preliminary results of this work were reported by Preliminary results of this work were reported by Nguyen and Pinder. This study provides a description of a ID mathematical model of two-phase hydrothermal flow, an outline of the finite-difference procedure employed to approximate its solution. and a concise summary of the proposed nonequilibrium thermodynamics theory for the proposed nonequilibrium thermodynamics theory for the steam/water system. Also included are the computation scheme for the phase-transition problem and a numerical simulation that uses the experimental conditions given by Arihara et al. Governing Equations The equations describing unsteady I D flow in a horizontal two-phase hydrothermal system have been developed by several authors, and the derivation methods are not repeated here. These equations have the following forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) where p is fluid pressure and h is enthalpy of the fluid mixture., and are nonlinear coefficients defined as follows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3) SPEJ p. 613