Ronald J. Bakker
CREGU, BP 23, 54501 Vandoeuvre-lès-Nancy, France
where T, P, V, and R are temperature, pressure, molar volume, and the gas constant, respectively. am and bm are measures of intermolecular attractive forces and molecular size, respectively, which are defined by the mixing rules (eq.2a and 2b) as originally proposed by Waals (1873) :
where aij correspond to the molecular interaction between gas species i and j. For non-polar gases, aij was set equal to . Santis et al. (1974) introduced a temperature function for ai terms (eq.3) for pure gas species:
The above mixing rule is not valid for polar mixtures and Santis et al. (1974) proposed that the aij term for mixtures of polar and non-polar gases is given by :
where i stands for polar gases (like H2O or CO2), and j stands for non-polar gases (like CH4 and N2) as defined by eq.3. The aij term for mixtures of H2O-CO2 contains an additional term for complex forming in the gas phase:
where K stands for the temperature dependent equilibrium constant. Holloway (1977) estimated the temperature dependence of and . These functions were partly adopted by Bowers & Helgeson (1983), who introduced a temperature and salinity dependence for the , , and terms. Originally, Bowers & Helgeson (1983) developed an EOS to predict the region of immiscibility, and not to predict the position of isochores at conditions that exceeds this miscibility gap. However, they offer a relative simple method to calculate isochores in salt-bearing systems that contains H2O and CO2. As mentioned before, only the a and b values for H2O were regarded as functions of salinity, and those for CO2 remained unaffected. Using a similar approach for other gas species, this EOS can be easily extended to CH4-N2 bearing fluid system, assuming that their a and b values are not affected by the presence of salts. These values are defined by critical properties of the individual gas species (Redlich & Kwong, 1949), and they are assumed to be temperature independent. In addition, other gas species like CO, H2, H2S can also be included.
The gases CH4 and N2 are introduced in the EOS as proposed by Bowers & Helgeson (1983) according to the above mentioned mixing rules. These modifications do not affect the accuracy of the original model, and they should be regarded as a first approach to calculate isochores in complex fluid mixtures containing NaCl and several gas species (H2O-CO2-CH4-N2).