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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.

A new reduction method for mixture phase stability testing is proposed, consisting in Newton iterations with a particular set of independent variables and residual functions. The dimension of the problem does not depend on the number of components but on the number of components with nonzero binary interaction parameters in the equation of state. Numerical experiments show an improved convergence behavior, mainly for the domain located outside the stability test limit locus in the pressure–temperature plane, recommending the proposed method for any applications in which the problematic domain is crossed a very large number of times during simulations.

We examine the asymptotic behavior of the equilibrium ratios (Ki) near the convergence locus in the pressure-temperature plane. When the Equation of State (EoS) is analytical, which is the case of most EoS of engineering purpose, Ki tends towards unity or, equivalently, its logarithm lnKi tends to zero, according to a power ½ of the distance to this locus. As a consequence, if lnKi is expressed as a linear combination of pure component parameters with coefficients only depending on mixture phase properties (i.e., reduction parameters), these coefficients obey a similar power law. Deviations from the ½ power law are thus fairly limited for lnKi and for the reduction parameters (at least in the negative flash window between the convergence locus and the phase boundaries), which can be exploited to speed up flash calculations and for quickly determining approximate saturation points and convergence pressures and temperatures. The chosen examples are representative synthetic and natural hydrocarbon mixtures, as well as various injection gas-hydrocarbon systems.