Calculation of Joule-Thomson and isentropic expansion coefficients for two-phase mixtures

Joule-Thomson (JT) and isentropic expansion coefficients describe the temperature change induced by a pressure variation under isenthalpic and isentropic conditions, respectively. They are commonly used to model a variety of processes in which either fluid compression or expansion is involved. While a lot of work has been devoted to inferring the JT coefficient from an equation of state when the fluid is a single phase, little attention has been paid to multiphase fluids, where phase equilibrium has to be taken into account; previous work has only addressed the construction on the JT inversion curve. In the present paper, we describe and implement an approach to calculate these two coefficients for multi-component fluid systems, including when they form two different phases, liquid, and vapor, in thermodynamic equilibrium. The only ingredients are an equation of state and expressions for the ideal part of the specific heats of the fluid components. We make use of cubic equations of state, but any thermodynamic model can be used in the proposed framework. Calculations conducted with typical geofluids, some of them containing CO2, show that these coefficients are discontinuous at phase boundaries (where enthalpy and entropy variations exhibit angular points), as expected with any thermodynamic quantity built from first-order derivatives of state functions, and cannot be simply inferred from the coefficients of the liquid and vapor phases.