EOS3#
This module is an adaptation of the EOS module of the TOUGH simulator, and implements the same thermophysical properties model (Pruess, 1987). All water properties are represented by the steam table equations as given by the IFC, 1967. Air is approximated as an ideal gas, and additivity is assumed for air and vapor partial pressures in the gas phase, \(P_g = P_a + P_v\). The viscosity of air-vapor mixtures is computed from a formulation given by Hirschfelder et al., 1964. The solubility of air in liquid water is represented by Henry’s law, as follows.
where \(K_h\) is Henry’s constant and \(x_{aq}^a\) is air mole fraction in the aqueous phase. Henry’s constant for air dissolution in water is a slowly varying function of temperature, varying from 6.7 x 10:9 Pa at 20˚C to 1.0 x 1010 Pa at 60˚C and 1.1 x 1010 Pa at 100˚C (Loomis, 1928). Because air solubility is small, this kind of variation is not expected to cause significant effects, and a constant \(P_a\) = 1010 Pa was adopted.
Specifications#
A summary of EOS3 specifications and parameters is given in Table 69.
The default parameter settings are (NK, NEQ, NPH, NB) = (2, 3, 2, 6).
The option NEQ = 2 is available for constant temperature conditions.
The choice of primary thermodynamic variables is (\(P\), \(X\), \(T\)) for single-phase, (\(P_g\), \(S_g\) + 10, \(T\)) for two-phase conditions.
The rationale for the seemingly bizarre choice of \(S_g\) + 10 as a primary variable is as follows.
As an option, we wish to be able to run isothermal two-phase flow problems with the specification NEQ = NK, so that the then superfluous heat balance equation needs not be engaged.
This requires that temperature \(T\) be the third primary variable.
The logical choice of primary variables would then appear to be (\(P\), \(X\), \(T\)) for single-phase and (\(P_g\), \(S_g\), \(T\)) for two-phase conditions.
However, both \(X\) and \(S_g\) vary over the range (0, 1), so that this would not allow a distinction of single-phase from two-phase conditions solely from the numerical range of primary variables.
By taking the second primary variable for two-phase conditions to be \(X2\) = 10 + \(S_g\), the range of that variable is shifted to the interval (10, 11), and a distinction between single and two-phase conditions can be easily made.
As a convenience to users, we retain the capability to optionally initialize flow problems with TOUGH-style primary variables by setting MOP(19) = 1.
In TOUGH we have (\(P\), \(T\), \(X\)) for single-phase conditions, (\(P_g\), \(S_g\), \(T\)) for two-phase conditions.
Components |
#1: water
#2: air
|
Parameter choices |
(
NK, NEQ, NPH, NB) =(2, 3, 2, 6) water and air, nonisothermal (default)
(2, 2, 2, 6) water and air, isothermal
Molecular diffusion can be modeled by setting
NB = 8 |
Primary variables* |
Single-phase conditions:
(\(P\), \(X\), \(T\)): (pressure, air mass fraction, temperature)
Two-phase conditions:
(\(P_g\), \(S_g\) + 10, \(T\)): (gas phase pressure, gas saturation plus 10, temperature)
|
Note
* By setting MOP(19) = 1, initialization can be made with TOUGH-style variables (\(P\), \(T\), \(X\)) for single-phase, (\(P_g\), \(S_g\), \(T\)) for two-phase.