A priori determination of the region of the three physical volume root loci in the Perturbed-Chain SAFT EOS

In this work, the physical region exhibiting the common three volume roots is located a priori for the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) equation of state without the need to determine the other non-physical volume roots. The loci of all multiple volume roots are first determined and investigated for the PC-SAFT equation of state over a broad range of temperatures and pressures using bifurcation diagrams. The study then illustrates how the number of multiple volume roots varies with temperature and pressure. The influence of each SAFT term is studied for several kinds of fluids ranging from spherical molecules to polymers. The technique presented in this study provides a simple method to identify artificial two-phase separation regions. Our study demonstrates that the problem of multiple volume roots found in non-cubic equations of state can be easily managed once the variation of volume loci with temperature and pressure are analyzed and understood using bifurcation diagrams.