(596c) An Approach for Developing Intermolecular Models for Use within Saft-Vr from Quantum Mechanical Calculations and Experimental Data

Molecular equations of state such as SAFT
(statistical associating fluid theory) and its variants [1] are particularly
well suited to describing the fluid phase behavior of complex systems such as
polymers and hydrogen-bonding compounds. However, such approaches require a
minimum of three parameters for each pure compound to be modeled, and
additional parameters for mixtures. Their use is thus dependent upon the
availability of reliable parameter values for the compounds of interest.

SAFT parameters for pure components are usually
obtained using fluid phase equilibrium data. In order to obtain statistically
significant values of the parameters, a large number of experimental data
points are required. Furthermore, it is desirable to include different types of
data, such as saturated vapor pressures and saturated liquid densities to allow
the resolution of different parameters: the density is known to be most
sensitive to size parameters, while the vapor pressure depends most strongly on
energy parameters. Even when a large and varied data set is available, some of
the parameter values remain difficult to determine with precision. In SAFT-like
methods, this is the case of the chain-length (aspect ratio) parameter, m,
which is often fixed a priori based on physical arguments, rather than fitted
to experimental data [e.g., 2]. When using SAFT with variable range (SAFT-VR),
the identification of the range parameter can be made more reliable by
including additional data such as the speed of sound [3]. Finally, when association
is present, it can be difficult to partition the attractive interactions
between the dispersive and associating terms and data such as the fraction of
bonded molecules can be useful [4].

In practice, there are few compounds for which
extensive experimental data are available. It is therefore desirable to look
for alternative approaches which provide reliable parameter values while
reducing the dependence on experimental data. Several efforts have been made in
this direction, since the pioneering work of Wolbach and Sandler [5].
Approaches based on quantum mechanics and/or molecular simulations have been
developed and applied to small sets of compounds [e.g., 6].

In this work, we focus on deriving the size
parameters of the SAFT-VR equation of state ab initio, making sure that
the approach is applicable to different types of compounds. We present two
approaches. In the first approach, only the chain-length parameter, m,
is obtained from quantum mechanics calculations at the Hartree-Fock level of
theory, and the remaining parameters are fitted to vapor pressure and saturated
density data. In the second approach, both m and s are obtained from quantum mechanics,
and the remaining parameters are estimated from data. We apply these two
procedures to a wide range of compounds, including long-chain and associating
compounds, for which the SAFT-VR equation is well-suited. The test set of
compounds comprises n-alkanes, cyclic and aromatic compounds, small
gases, refrigerants and refrigerant intermediates. We show that high quality
results can be obtained by following this approach in terms of the average
error on vapor pressure and saturated density. The models derived are
consistent with physical trends, for instance in terms of carbon number. This
provides confidence that the models can be successfully used in modeling
mixture behavior. This is demonstrated on a few sample mixtures.

The applicability of the approach when no density
data are available is also investigated. In this case, the values of m
and s derived from quantum
mechanics prove particularly useful: it is shown that the SAFT-VR models thus
developed can be used to predict saturated densities in the absence of such
data. If s is instead obtained
by fitting to vapor pressure data only, physically unrealistic values of s  are derived and the density
predictions are very poor.   

1.     
W.G. Chapman, K.E. Gubbins, G.
Jackson and M. Radosz, Fluid Phase Eq. 52 (1989) 31; W.G. Chapman, K.E.
Gubbins, G. Jackson and M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709; E.A. Müller and K.E.
Gubbins, Ind. Eng. Chem. Res. 40 (2001) 2193.

2.      C. McCabe and G. Jackson, Phys. Chem. Chem. Phys. 1
(1999) 2057;
P. Paricaud, A. Galindo and G. Jackson, Ind. Eng. Chem. Res. 43 (2004) 6871.

3.     
T. Lafitte, D. Bessieres,
M.M. Piñeiro, J.-L. Daridon, J. Chem. Phys.
124 (2006) 024509.

4.     
G. Clark, A. J. Haslam, A.
Galindo, and G. Jackson, Mol. Phys., 104 (2006) 3561.

5.     
J.P. Wolbach and S.I.
Sandler, Ind. Eng. Chem. Res. 36
(1997) 4041.

6.     
J.P. Wolbach and S.I. Sandler,
Int. J. Thermophysics 18 (1997) 1001; M. Yarrison and W.G. Chapman, Fluid Phase Eq. 226
(2004) 195;
M. Fermeglia and S. Pricl, Fluid Phase Eq. 166 (1999) 21; M. Fermeglia, A.
Bertucco, D. Patrizio, Chem. Eng. Sci. 52 (1997) 1517.