The SAFT equation of state

Technology overview

SAFT representations of water and nonionic surfactant molecules highlighting the incorporation of association sites

SAFT is an equation of state that embodies significant advances over the traditional van der Waals equation or cubic engineering equations such as Peng-Robinson, which are better suited to near-spherical molecules.

Significant advantages over existing methods

The main advantage of SAFT is that it is underpinned by a physically realistic representation of the molecule that includes its shape, size and specific interactions – for example, hydrogen bonding – with other molecules of the same or different type within a mixture.

This means that, unlike many other equations of state, SAFT is able to account for non-spherical molecules, attraction and repulsion between molecules and strong directional interactions. As a consequence, SAFT’s predictive capability can extend well beyond the conditions covered by the available experimental data.

Because the associating fluid approach can account for the electrostatic, polar and other association forces that are the basis of the physical of the molecular interactions, SAFT provides an unprecedented capability for modelling the behaviour of systems involving complex materials such as polar solvents, hydrogen bonded fluids, and polymers.

How SAFT works

There are various implementations of the basic SAFT formulation, which differ principally in terms of the mathematical representation of the molecule and the specific forms of the various contributions. The current gSAFT implementation is based on SAFT-VR, where VR stands for 'variable range'.

The molecules are built from spherical square-well segments

Segment definition and interaction

Square-well segment-segment interaction

Molecular size

A molecule is represented by a number of segments, m, and a segment diameter, σ.These two parameters capture the size and non-sphericity of the molecule.

Attraction & repulsion

In SAFT-VR the attraction-repulsion between segments or molecules separated by a distance r is modelled using u(r), a potential energy function characterised by three parameters:

σ, the diameter of the segment,
λ, a parameter describing the range of dispersion interactions, and
ε, the strength of dispersion interactions.

In the current gSAFT implementation, the 'square-well' potential function shown on the right is used.

The width or range of the zone of attraction is different for different types of segment or component, hence the 'variable range' description.

Association sites

Key to the behaviour of molecules that form hydrogen bonds, such as water or the amine solvent MEA is the definition and characterisation of association sites which are used to mediate the formation of hydrogen bonds formation between molecules.

These are characterised as electron donors or electron acceptors of a defined strength. It is these association sites that provide SAFT's unique capability in dealing with aqueous solutions, surfactants and other strongly-associating components.

SAFT applies Wertheim's theory to associating segments with multiple association sites. An association site might represent a lone pair of electrons on an oxygen atom or a hydrogen bonded to a very electronegative atom.

SAFT parameters

The SAFT parameters have a physical basis.

For example, a chain molecule is characterised by the number of segments in the chain, in addition to the three potential parameters σ, λ and ε describing the diameter of each segment, and the range and magnitude of attractive interactions, respectively.

For an associating or hydrogen bonding molecule, additional physical parameters are necessary:

the number of types of association sites
the number of sites of each type
the association energy (related to the change in enthalpy of association)
the bond volume (related to the change in entropy on association) for association between two site types.

One advantage of the physical basis of these parameters is that values of parameters for one molecule may be used systematically to describe similar molecules (e.g. other compounds within the same homologous series, or those sharing some functional groups with the original molecule). A second advantage is that some of the SAFT parameters can be determined from spectroscopy or from quantum mechanics.

Parameters defining the relevant quantities for a given molecule are estimated for each molecule from experimental data – mostly pure component and, where available, mixture data. A key activity of the Imperial MSE team is to build the growing databank of pure component and mixture parameters.