(Nighswander et al., 1989; Carroll et al., 1991; King et al., 1992; Duan & Sun, 2003; Portier &
Rochelle, 2005). Over the past decades many EOS have been developed to model the thermodynamic
properties of carbon dioxide, water and carbon dioxide-water ± NaCl mixtures over a wide range of
temperature and pressure (Lee & Kesler, 1975; Peng & Robinson, 1976; Kerrick & Jacobs, 1981;
Bowers & Helgeson, 1983; Duan et al., 1992a, b, 1995; Span & Wagner, 1996; Wagner et al., 2000).
However, some Equations of State are not applicable to the range of temperature and pressure of
interest, i.e. reservoir conditions. Below follows a short description of the EOS for CO
2
, H
2
O and CO
2
-
H
2
O mixtures, which are suitably accurate for conditions ranging from 50 to 200°C and 100 to 500
bars.
2.1 Equation of State for carbon dioxide
Well known Equations of State for pure carbon dioxide, water and methane have been developed by
Duan et al. (1992a). Their EOS for CO
2
forms the basis of the solubility model proposed by Duan and
Sun (2003; 2005). The EOS developed by Duan et al. (1992a) is used to describe the chemical potential
of CO
2
in the vapour phase and is based on the EOS developed by Lee and Kesler (1975). The
temperature and pressure range for which this EOS applies is 0 to 1000°C and 0 to 8000 bars.
Of equal quality is the Equation of State developed by Span and Wagner (1996), which covers the
fluid region from the triple point temperature up to 826.85°C and pressures up to 8000 bars. Span and
Wagner (1996) developed a new EOS for the representation of the thermodynamic properties of carbon
dioxide, which is an empirical representation of the fundamental equation explicit in the Helmholtz
energy. The stated fundamental equation is expressed in the form of the Helmholtz energy f with the
two independent variables density ρ and temperature T. The dimensionless Helmholtz energy φ = f/RT
is usually split into an ideal gas part φ° and a residual part φ
r
:
φ(δ,τ) = φ°(δ,τ) + φ
r
(δ,τ) (4)
where δ = ρ/ρ
c
is the reduced density, i.e. the density normalised to the critical density, and τ = T
c
/T is
the inversed reduced temperature, i.e. the inverse of temperature normalised to critical temperature.
The subscript c denotes the critical values of both density and temperature. Here the Helmholtz energy
is described as a function of density and temperature; however, this is just one form of a fundamental
equation and, in fact, all thermodynamic properties of pure carbon dioxide can be calculated by
combing derivatives of this equation (see Table 3 in Span and Wagner (1996)).
Though there is little difference in the quality of the various EOS mentioned above, that developed
by Duan et al. (1992a) is recommended and used here to represent the thermodynamic properties of
carbon dioxide, as it covers the largest PT-range and is also used in the description of the CO
2
-H
2
O
system. Therefore a description of this EOS is given in Appendix 1a.
2.2 Equation of State for water
Though Duan et al. (1992a) also developed an EOS for water, we choose to recommend to use the
Equation of State released by The International Association for the properties of Water and Steam
(IAPWS), for the thermodynamic properties of water (the IAWPS Industrial Formulation 1997, see
Wagner et al. (2000)). This is chosen due to the diminished accuracy at low temperatures of the EOS
developed by Duan et al. (1992a).
The IAWPS-97 covers temperatures from 0 to 800°C up to 1000 bars and temperatures from 800 to
2000°C up to 100 bars. The range of validity of IAWPS-97 is divided into 5 regions, as can be seen in
Fig. 2, each covered by a so-called basic equation. In addition to the basic equations for regions 1, 2,
and 4, so-called backward equations have been developed. These backward equations are used to speed
up the calculation of properties as functions of pressure p, enthalpy h, and entropy s. The equations are
numerically consistent with the basic equations and, alone or together with these basic equations, make
the calculation of properties such as T(P,h), h(P,s), and h’(P) much simpler. In Appendix 1b the basic
equations for all regions are stated, as well as the equation that describes the boundary between region
2 and 3.
8
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