On the Numerical Modeling of Water Flows in Porous Media under Near-Critical Conditions

Abstract

The problem of the numerical modeling of nonisothermal water and vapor flows in a porous medium under near-critical thermodynamic conditions is considered. It is shown that the equations of single-phase and two-phase flows in porous media become degenerate at the critical point of water. Some disadvantages of flow modeling methods that are able to exclude degeneracy by selecting the pressure and enthalpy as independent model variables are discussed. A new method of modeling under near-critical thermodynamic conditions in the standard pressure–temperature variables is proposed. This method is based on an approxinate description of the fluid phase diagram with linear splines that eliminates the degeneracy of conservation laws at the critical point and enables the application of equations of state for predicting the fluid properties in pressure and temperature variables.