Joule-Thomson inversion curves of mixtures by molecular simulation in comparison to advanced equations of state: natural gas as an example

or, using basic thermodynamics relations,

where c p is the isobaric heat capacity. The JT inversion curve, connecting all state points with µ=0, divides the pressure-temperature plane into two regions. In the lower region, µ is positive so that an adiabatic expansion leads to a decrease in temperature. In the upper region, µ is negative. It can be shown that the cooling effect is maximized if an expansion starts from the inversion pressure.

The experimental determination of a fluid’s JT inversion coefficient demands precise measurements of volumetric and caloric properties, while the JT inversion curve extends over a broad range of temperature and pressure. Temperature and pressure reach up to a five-fold and twelve-fold of their critical values, respectively. Experimental JT inversion curve data are therefore scarce, sometimes unreliable [1], and mostly available only for pure fluids [2]. An example for mixture data is the work of Charnley et al. [3] on e.g. carbon dioxide + nitrous oxide, carbon dioxide + ethylene. A good overview over experimental data is given in [2].

For industrial applications there is a need for a proper representation and also for the prediction of JT data, as it is not feasible to measure it for all relevant and often very different blends. Some authors, e.g., Miller [4] or Gunn et al. [5], have proposed direct representations of the JT inversion curve, which are correlations in terms of reduced temperature and pressure. They provide rule-of-thumb data for simple fluids, but have little predictive power. Significantly more valuable are proper equations of state (EOS) that contain much more thermodynamic information and are valid for a broad range of state points. Thus, extensive efforts are made to use EOS for predictions of the JT inversion curve. Examples for the use of cubic EOS are modified versions of Peng-Robinson [6,7], Redlich-Kwong [6,8], Soave-Redlich-Kwong [7], Patel-Teja [6] or other cubic EOS [9] with varying parameter functions. Both type of cubic EOS and type of parameter function strongly influence the JT inversion curve, particularly in the high temperature region. A given combination might yield good results for a specific fluid, but fails for others [6,7,8,9]. Hence, it can be concluded that cubic EOS are not generally reliable for JT inversion curve predictions.

Among mixtures, natural gases are the ones that were investigated most extensively both experimentally and theoretically so that very reliable thermodynamic data and models are available. Therefore, natural gases are excellent test systems to validate thermodynamic models for mixtures.

Natural gas from the rig is a mixture of typically seventeen components (containing methane, nitrogen, carbon dioxide, ethane, propane) [10], but usually its main component is methane [11,12]. As a natural product, it has a great variability in composition and, depending on conditions in the formation process, considerable quantities of nitrogen (up to 60 mole %), carbon dioxide (up to mole 50 %) or ethane (up to mole 20 %) are encountered [11].

For a number of pure natural gas components, reference EOS have been developed based on a vast experimental data set considering different thermodynamic properties, e.g., methane [13], nitrogen [14], carbon dioxide [15] and ethane [16].

Reference EOS have an empirical background, but they are parameterized extremely carefully, taking also available experimental JT coefficients into account.

Hence, they are regarded in this work as the best available information.

For mixtures, the National Institute of Standards and Technology (NIST) [17] provided two classical phenomenological EOS, i.e. DDMIX [18,19] and SUPER-TRAPP [20]. DDMIX is an implementation of the NIST extended corresponding states model for mixtures, whereas SUPERTRAPP is based on both a modified Peng-Robinson EOS and the NIST extended corresponding states model for mixtures. Both were parameterized to experimental pure substance and mixture data. Particularly SUPERTRAPP is often used in the literature as a property model for designing cooling cycles with mixed coolants, e.g. [21,22].

There are also physically based EOS that take the different molecular interactions, like dispersion or polarity, explicitly into account; an example is the BACKONE-EOS [23]. Such EOS can be parameterized for real substances with a very small experimental data set, e.g. a few vapour-liquid equilibrium data points, as they have a good predictive power. Furthermore, the GERG-2004

Wide-Range Reference EOS [24] has become available recently

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