Calculation of Joule–Thomson inversion curves for two-phase mixtures

The Joule–Thomson inversion curve (JTIC), defined as the locus in the p–T plane where the adiabatic Joule–Thomson (JT) coefficient is zero, separates regions for which heating and cooling occur upon an isenthalpic expansion. JTIC calculation for mixtures is a clear matter for single-phase conditions. For two-phase mixtures, an apparent JT coefficient can be defined, which incorporates: (i) JT effects and (ii) phase distribution changes effects. Three different ways for calculating the apparent JTIC are presented: a volumetric approach, an approach based on enthalpy departure variation, and an approach based on isenthalpic flashes. Cubic equations of state are used in this work, but any thermodynamic model can be used. Several examples show that for mixtures, the locus separating heating/cooling regions may have two or three distinct branches, and that at phase boundaries there are discontinuities in the JT coefficient corresponding to angular points of enthalpy variations.