Improving the SAFT-γ Mie equation of state to account for functional group interactions in a structural (s-SAFT-γ Mie) framework: Linear and branched alkanes

Abstract

The group contribution SAFT-γ Mie EoS is based on the statistical associating fluid theory for fused heteronuclear molecules. While the chain term of the model has been modified to account for the new functional group-specific parameters, it does not impose a bonding order to these functional groups, only considering intergroup interactions in the monomer reference fluid. This leaves the model unable to account for the different physical properties of structural isomers and implicitly introducing modeling bias to species where the molecular structure mimics those used in the parameter regression. In this work, a simple but physically meaningful modification to the chain term in SAFT-γ Mie is proposed that accounts for the number of intergroup bonds, thereby encoding structural information in the model, without introducing an additional regressed parameter. The resulting structural SAFT-γ Mie (s-SAFT-γ Mie) requires reparameterization of the group parameters, which we present for linear and branched alkanes (CH3, CH2, CH, and C groups) here. Following an identical parameterization procedure to the original model, validation showed that the modification actually improves prediction accuracy for linear alkanes while addressing the original inability of the framework to distinguish between structural isomers. The good predictive performance seen in this work, for both pure component and mixture properties, lays a good foundation for expansion to other functional groups in future work.

Extending the Structural (s)-SAFT-γ Mie Equation of State to Primary Alcohols

“…The fixed value of the segment number is discussed further below. To be consistent with SAFT-γ Mie and previous work, 54 the combining rules for the unlike segment diameter (σ kl ) and the unlike interaction potential (λ kl r ) defined by Papaioannou et al 41 are also used in s-SAFT-γ Mie. These are shown in eqs 6 and 7.…”

“…However, SAFT-γ Mie is not fully heteronuclear: The contribution of each functional group to the Helmholtz free energy arising from chain bonding is determined from molecular average parameters. 54 Moreover, the monomer (hard sphere and dispersion) term describes a molecule as consisting of free-floating spheres. These spheres are disordered rather than arranged in a well-defined sequence.…”

“…However, the value of GC modeling approaches lies in their ability to model systems containing a wide variety of molecular species. Shaahmadi et al 54 proposed a modification to the model that yields a fully heteronuclear chain term. This altered EoS is termed the "structural" (s)-SAFT-γ Mie.…”

“…The empirical variables b k,i * and b kl,i * are given in eqs 4 and 5. 54 The former is the fraction of intragroup bonds on group k relative to the total number of bonds on molecule i. The latter is the fraction of bonds on molecule i that occur between groups.…”

“…Arguably, b k,i * is physically meaningful, as intragroup contributions would rightly be zero for molecules in which the segment number is v k *=1. 54 v k,i is the number of times group k appears on molecule i, while v kl,i is the number of times segments from k and l bond with each other. v kl,i is the only s-SAFT-γ Mie parameter that is not present in SAFT-γ Mie.…”