Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment

Literature data on the thermophysical properties of the Lennard-Jones fluid, which were sampled with molecular dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data were complemented by simulation data from the present work that were taken in regions in which previously only sparse data were available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility β, thermal pressure coefficient γ, internal energy u, isochoric heat capacity cv, isobaric heat capacity cp, Grüneisen parameter Γ, Joule–Thomson coefficient μJT, speed of sound w, Helmholtz energy a, and chemical potential) were considered, as well as data on the vapor–liquid equilibrium (for given T: vapor pressure ps, saturated liquid and vapor densities ρ′ and ρ″, respectively, enthalpy of vaporization Δhv, and as well as surface tension γ). The entire set of available data, which contains about 35 000 data points, was digitalized and included in a database, which is made available in the Supporting Information of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated pointwise using data from their respective vicinity and equations of state. Approximately 10% of all homogeneous bulk data were discarded as outliers. The vapor–liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius–Clapeyron equation, and by an outlier test. Seven particularly reliable vapor–liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporization—excluding the region close to the critical point.

Multi-criteria Optimization for Parameterization of SAFT-type Equations of State for Water

Finding appropriate parameter sets for a given equation of state (EoS) to describe different properties of a certain substance is an optimization problem with conflicting objectives. Such problem is commonly addressed by single-criteria optimization in which the different objectives are lumped into a single goal function. We show how multi-criteria optimization (MCO) can be beneficially used for parameterizing equations of state. The Pareto set, which comprises a set of optimal solutions of the MCO problem, is determined. As an example, the perturbed-chain statistical associating fluid theory (PC-SAFT) EoS is used and applied to the description of the thermodynamic properties of water, focusing on saturated liquid density and vapor pressure. Different options to describe the molecular nature of water by the PC-SAFT EoS are studied and for all variants, the Pareto sets are determined, enabling a comprehensive assessment. When compared to literature models, Pareto optimization yields improved models.

Density Measurements of Two Liquefied Biomethane-Like Mixtures over the Temperature Range from (100 to 180) K at Pressures up to 9.0 MPa

Densities of two synthetic biomethane-like mixtures were measured in the homogeneous liquid phase and the supercritical region using a low-temperature single-sinker magnetic-suspension densimeter. Both mixtures consist of methane, nitrogen, hydrogen and oxygen, whereas the second mixture additionally contains carbon dioxide. For the first mixture, four isotherms from (100 to 160) K were studied over the pressure range from (1.5 to 6.6) MPa. The second mixture was investigated along three isotherms from (140 to 180) K at pressures of (2.6 to 9.0) MPa, where only the densities at 180 K are usable due to solidification of the carbon dioxide at the lower temperatures. The relative expanded combined uncertainty (k = 2) of the experimental densities was estimated to be in the range of (0.022 to 0.027) % for the first mixture and (0.046 to 0.054) % for the second mixture, respectively. Due to a supercritical liquefaction procedure and the integration of a special VLE-cell, densities in the homogeneous liquid phase could be measured without changing the composition of the liquefied mixture. Moreover, saturated-liquid densities were determined by extrapolation of the experimental single-phase liquid densities to the vapor pressure, which was determined experimentally for the mixture without carbon dioxide and calculated with an equation of state (EOS) for the mixture containing carbon dioxide. The relative expanded combined uncertainty (k = 2) of the saturated-liquid densities is less than 0.08 % in most cases. The new experimental results were compared with the GERG-2008 equation of state; the deviations are less than 0.17 %.