On the Effect of the Hard-sphere Term on the Statistical Associating Fluid Theory Equation of State

The hard-sphere system is the reference fluid for most versions of the statistical associating fluid theory (SAFT) equation of state (EoS). In the SAFT-type equations of state, the hard-sphere equation directly affects the reference term and through the radial distribution function, indirectly affects the chain and association terms. Although there are various EoSs for describing the thermodynamic behavior of the hard-sphere fluid, the Carnahan-Starling EoS has traditionally been used to express the hard-sphere contribution in SAFT-type models. In this work, we integrated eight hard-sphere EoS in the simplified SAFT EoS and parameterized the resulting EoS with pressure-density-temperature data. Then, using modified versions of the simplified SAFT (SSAFT), we calculated the thermodynamic properties including pressure, density, temperature, saturated vapor-pressure, isochoric heat capacity, isobaric heat capacity, and speed of sound, for ethane, butane, hexane, and hexatriacontane, and compared the results. In general, the results of calculations show that although the modified Carnahan-Starling, Kolafa, and Carnahan-Starling EoSs have had the best results, considering the simplicity and straightforwardness of the Carnahan-Starling EoS, this EoS is a reasonable choice for developing SAFT-type equations of state.