Thermodynamic consistency of the multi-scale Gibbs–Helmholtz constrained equation of state

The multi-scale Gibbs-Helmholtz constrained (GHC) equation is a new predictive cubic equation of state that constrains the energy parameter in the SRK equation to satisfy the Gibbs-Helmholtz equation. It makes use of internal energies of departure calculated from NTP Monte Carlo simulations at the molecular length scale and a novel up-scaling expression to determine the energy parameter at the bulk phase length scale.In this article it is shown that mathematical representation of isothermal molecular internal energies of departure as a staircase function in pressure leads directly to thermodynamic consistency of the multi-scale GHC equation. Experimentally validated numerical results for density for pure components and mixtures, two- and three-phase equilibrium, comparisons with other cubic EOS, and geometric illustrations are presented to illustrate key ideas and to show that the GHC equation provides both accurate and thermodynamically consistent numerical results. © 2013 The Institution of Chemical Engineers