Effect of ternary four-phase equilibria on computed ternary isopleths

Abstract

Ternary systems may present equilibrium (eq.) among 4 fluid phases, which, from the Phase Rule, has 1 degree of freedom. Hence, the ternary 4-phase eq. (T-4PE) is a line in the pressure vs temperature plane. On the other hand, isopleths are phase diagrams at constant global composition z, which include, e.g., bubble point lines (BPLs, LV), dew point lines (DPLs, VL), cloud point lines (CPLs, LL), and other lines that characterize the isopleth heterogeneous region (HR), such us ternary 3-phase envelopes (T-3PEs). A T-3PE is a boundary between a 2-phase region and a 3-phase region. First in this work, a simple mathematical criterion is proposed toestablish for ternary systems which portions of already computed (ternary) 4-phase lines (T-4PLs) must be included within the HR of a yet to be computed (ternary) isopleth (T-IP) of composition z. Such criterion also makes it possible to identify (ternary) double or triple saturation points (T-DSPs or T-TSPs) at z and ternary) double incipiency 4-phase points (TDI-4PPs) at z, where 2 out of the 4 phases at eq. are incipient. Next, it is shown that at a T-DI-4PP a couple of T-3PEs meet, and hence their computation can be started off at such T-DI-4PP. Computed T-IPs are presented which include T-3PEs and segments of T-4PLs. The graphical abstract (GA) shows a T-IP for system CO2+H2O+2-propanol, computed with the SRK EoS (interaction parameters k12=0.19, k13=0.1215; k23=-0.1727, global mole fractions: z1= 0.025, z2=0.865, z3=0.11). The inset presents the same information than the main chart but for pressure in logarithmic scale. Large numbers in the GA indicate the number of phases. The T-2PE in the GA is made of a T-DPL at low pressure, a T-BPL, and a T-CPL, and it has a T-DSP. The HR presents 3 T-3PEs which define two 3-phase regions (T-3PRs). The boundary between both T-3PRs is a segment of the T-4PL. We conclude that the T-4PE can make the T-IPs quite complex. The GA shows only an example of many possible topologies.