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

Beatriz Giner1, Timothy Sheldon1, Michaela Pollock1, Claire S. Adjiman1, Amparo Galindo1, George Jackson1, Denis Jacquemin2, Valerie Wathelet2, and Eric A. Perpete2. (1) Department of Chemical Engineering, Imperial College London, Centre for Process Systems Engineering, London, SW7 2AZ, United Kingdom, (2) Chemistry, Facultes Universitaires Notre Dame de la Paix, Rue de Bruxelles, 61, Namur, 5000, Belgium

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.   

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