Developing intermolecular‐potential models for use with the SAFT‐VRMie equation of state

Abstract

A major advance in the statistical associating fluid theory (SAFT) for potentials of variable range (SAFT-VR) has recently been made with the incorporation of the Mie (generalized Lennard-Jones [LJ]) interaction between the segments comprising the molecules in the fluid (Lafitte et al. J. Chem. Phys. 2013;139:154504). The Mie potential offers greater versatility in allowing one to describe the softness/hardness of the repulsive interactions and the range of the attractions, which govern fine details of the fluid-phase equilibria and thermodynamic derivative properties of the system. In our current work, the SAFT-VR Mie equation of state is employed to develop models for a number of prototypical fluids, including some of direct relevance to the oil and gas industry: methane, carbon dioxide and other light gases, alkanes, alkyl benzenes, and perfluorinated compounds. A complication with the use of more-generic force fields such as the Mie potential is the additional number of parameters that have to be considered to specify the interactions between the model molecules, leading to a degree of degeneracy in the parameter space. A formal methodology to isolate intermolecular-potential models and assess the adequacy of the description of the thermodynamic properties in terms of the complex parameter space is developed. Fluid-phase equilibrium properties (the vapor pressure and saturated-liquid density) are chosen as the target properties in the refinement of the force fields; the predictive capability for other properties such as the enthalpy of vaporization, single-phase density, speed of sound, isobaric heat capacity, and Joule-Thomson coefficient, is appraised. It is found that an overall improvement of the representations of the thermophysical properties of the fluids is obtained using the more-generic Mie form of interaction; in all but the simplest of fluids, one finds that the LJ interaction is not the most appropriate.

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

“…The association kernel I has been parameterised as a polynomial in the dimensionless temperature T * = k B T/ε, dimensionless density ρ * = Nσ 3 /V, and the repulsive exponent λ r , as reported in [37,38]; note that in our current work, we employ the Lennard-Jones (12-6) form of the association kernel.…”

“…The chemical potential of ion i at the reference state of unit molality corresponds to the molar Gibbs free energy of formation G f i (aq) of 1 mol kg −1 of the solvated ion. Using Equation (38) and the expressions for the chemical potential of the solid salt and solvated ions, the solidliquid equilibrium condition for fully dissociated salts given by Equation (37) can be rewritten to obtain a solubility equation for the salt as…”

“…The SAFT-VR EOS has now been reformulated for the more versatile and realistic Mie [35] potential form together with an improvement in the underlying statistical-mechanical theory, now taken to third order in the high-temperature perturbation expansion [36]. The novel SAFT-VR Mie EOS has brought a new level of reliability in the development of an accurate platform for the thermodynamic properties of complex fluids and fluid mixtures [36][37][38]. The approach has also been cast as a group-contribution methodology (SAFT-γ ) [39,40], where the molecules are represented in terms of the underlying chemical functional groups, providing an enhanced predictive capability.…”

Interfacial tensions of systems comprising water, carbon dioxide and diluent gases at high pressures: Experimental measurements and modelling with SAFT-VR Mie and square-gradient theory

“…A model of the fluid-fluid interface is obtained in this work by applying the square-gradient theory [9,11,13,100,101] together with the SAFT-VR Mie [48,102] equation of state to evaluate the Helmholtz free energy of the systems of interest. In SGT, a description of the free energy of the interface is provided as an expansion in free energy and density [103].…”

“…For example, the SAFT-VR Mie model parameters for CO 2 , N 2 and Ar are taken from reference [102], whereas parameters for H 2 O (with the generic Mie association kernal) are taken from reference [49].…”